JP5673920B2 - Cascaded boost type switching power supply circuit - Google Patents

Description

  The present invention relates to a switching power supply circuit, and more particularly to a cascaded boosting switching power supply circuit in which boosting switching power supply circuits that boost a voltage are connected in cascade.

Conventionally, a step-up switching power supply circuit is known (see Patent Document 1 and Patent Document 2). The basic circuit of these step-up switching power supply circuits is shown in FIG. The step-up switching power supply circuit shown in FIG. 35 includes a switch element S ₁ , an inductor L ₁ , a diode D ₁ , and a capacitor C ₁ . The boosting switching power supply circuit shown in FIG. 35 is an ideal circuit (ideal boosting switching power supply circuit) in which each of the switching element S ₁ , the inductor L ₁ , the diode D ₁ , and the capacitor C ₁ has no loss. In an ideal step-up switching power supply circuit, the input voltage E _d (the value (voltage value) of the input voltage E _d is E _d . The same applies hereinafter) and the output voltage E _o (the value (voltage value) of the output voltage E _o is E It is known that the ratio of “ _o” (the same shall apply hereinafter) is expressed by Expression (51). Here, T _s is a period of one cycle in which the switch element S ₁ is turned on and off, and T _off is a time when the switch element S ₁ is off.

E _o / E _d = T _s / T _off (51)

JP 2009-261040 A JP 2009-118552 A

  Although it is conceivable to obtain a desired output voltage by cascading two or more stages of such boosting switching power supply circuits instead of one stage, which are cascaded boosting switching power supply circuits cascaded in this way? It is not yet known whether an advantageous effect is produced in such a case.

  The problem to be solved by the present invention is a cascaded boosting switching power supply circuit configured by cascading two or more boosting switching power supply circuits, which is appropriate according to the voltage ratio between the input voltage and the output voltage. A cascade-connected step-up switching power supply circuit having a number of cascade-connected stages is provided.

The present invention connects one end of an inductor, one end of a switch element, and one end of a diode, the other end of the inductor and the other end of the switch element are input sides, and the other end of the diode and the other of the switch element A plurality of step-up switching power supply circuits formed by connecting a capacitor between the two ends of the capacitor and having both ends of the capacitor as output sides, and obtained by cascading the plurality of step-up switching power supply circuits. A connection boost type switching power supply circuit,
The ratio of the output power output to the output side of the last stage of the cascaded boost type switching power supply circuit and the input power input to the input side of the cascaded boost type switching power supply circuit is defined as power efficiency η _n
The resistance value corresponding to the loss of the last step-up switching power supply circuit of the cascaded step-up switching power supply circuit is represented by r _nn .
The value of the equivalent load resistance connected to the output side of the cascaded boost type switching power supply circuit is R,
The value of the output voltage output to the output side of the cascaded boost type switching power supply circuit is E _o, and the value of the input voltage input to the input side of the cascaded boost type switching power supply circuit is E _d ,
The cycle of turning on and off the switch element is T _s , the switch element off time is T _offn ,
The number of boosting switching power supply circuits satisfying the following formula 1 and given by an integer n that maximizes the value of the power efficiency η _n represented by the following formula 2 is cascaded.
_{E o = (T s / T} offn) n × E d × [1 / {1+ (T s / T offn) 2 × (r nn / R)}] n ······· Formula 1
η _n = 1 / {1+ (T _s / T _offn ) ² × (r _nn / R)} ^n.

_Further , the length of the time T _offn that is the time when the switch element is turned off may be a predetermined fixed value, and is set to the value E _o of the output voltage detected from the output side of the cascaded step-up switching power supply circuit. Depending on the length, it may be a suitable length.

Further, (n−j) switch elements, which are the switch elements of the step-up switching power supply circuit in the number given by (integer n−integer j; n> j) It is turned off for a time T _{offn calculated} from
The j switch elements, which are the switch elements of the step-up switching power supply circuit in the number given by the integer j, are turned off for a variable time,
The variable time as a length corresponding to the value E _o of the output voltage detected from the output side of the cascaded step-up switching power supply circuit, but may be controlled the output voltage.

The output voltage value E _o output to the output side of the cascaded boost type switching power supply circuit is a constant value, and the input voltage value E _d input to the input side of the cascaded boost type switching power supply circuit. Is a variable value,
In the minimum value of the input voltage value E _d input to the input side, the number of boosts that is given by an integer n that satisfies Equation 1 and maximizes the value of power efficiency η _n expressed by Equation 2 A cascaded boost type switching power supply circuit obtained by cascading n-stage switching power supply circuits
In accordance with the value E _{d of the} input voltage input to the input side, the number given by the integer k that satisfies the following formula 3 and maximizes the value of the power efficiency η _k represented by the following formula 4 is obtained. The switch elements may be controlled to be turned on / off, and (nk) (where n> k) switch elements are always turned off.
E _o = (T _s / T _offk ) ^k × E _d × [1 / {1+ (T _s / T _offk ) ² × (r _nn / R)}] ^k.
η _k = 1 / {1+ (T _s / T _offk ) ² × (r _nn / R)} ^k.

Further, an integer smaller than the integer n is an integer i, an integer larger than the integer n is an integer p, and an i-stage cascaded step-up switching power supply is given in advance, where a predetermined decrease in efficiency allowed is an allowable decrease ε. power efficiency eta _p of the power efficiency eta _i or p cascaded step-up switching power supply circuit of the circuit, power efficiency eta _n - power efficiency eta _{i <allowable} decrease epsilon, or power efficiency eta _n - power efficiency eta _p < The number of cascade connections may be set so that the allowable decrease amount ε.

  The on / off control timing of the odd-numbered switch elements and the on / off control timing of the even-numbered switch elements of the cascaded boost switching power supply circuit may have a phase difference of 180 degrees. Is.

  In addition, m boosting switching power supply circuits are formed by connecting in parallel the capacitors of each stage of the cascaded boosting switching power supply circuit, and the switches of the m boosting switching power supply circuits connected in parallel are connected. The on / off control timing of the element may have a phase difference of (360 / m) degrees.

In another aspect of the present invention, one end of the inductor, one end of the switch element, and one end of the diode are connected, the other end of the inductor and the other end of the switch element are input, and the other end of the diode and the switch A capacitor is connected between the other end of the element, and a plurality of boosting switching power supply circuits formed with both ends of the capacitor as output sides are connected in cascade. A cascaded boost type switching power supply circuit obtained,
The ratio of the output power output to the output side of the last stage of the cascaded boost type switching power supply circuit and the input power input to the input side of the cascaded boost type switching power supply circuit is defined as power efficiency η _n
The resistance value corresponding to the loss of the last step-up switching power supply circuit of the cascaded step-up switching power supply circuit is represented by r _nn .
The value of the equivalent load resistance connected to the output side of the cascaded boost type switching power supply circuit is R,
The value of the output voltage output to the output side of the cascaded boost type switching power supply circuit is E _o, and the value of the input voltage input to the input side of the cascaded boost type switching power supply circuit is E _d ,
A real number n is obtained as a power efficiency η _n satisfying the following formula 5, and the number n of the step-up switching power supply circuits equal to an integer obtained by rounding down or rounding up or rounding up the real number n is cascaded.
∂η _n / ∂n = ∂ [1 / << 1 + <[1- {1−4 × (r _nn / R) × (E _o / E _d ) ^{2 / n} } ^1/2 ] / {2 × (r _nn / R) × (E _o / E _d ) ^{1 / n} }> ² × (r _nn / R) >> ⁿ ] / ∂n = 0.

  According to the step-up switching power supply circuit of the present invention, it is possible to provide a cascade connection step-up switching power supply circuit having an appropriate number of cascade connection stages according to the voltage ratio between the input voltage and the output voltage of the cascade connection step-up switching power supply circuit. .

It is a figure which shows the equivalent circuit of a 1 step | paragraph boosting type | mold switching power supply circuit when there exists a circuit loss. It is a figure showing the equivalent circuit shown in FIG. 1 with two equivalent circuits according to the ON state and the OFF state of a switch element. FIG. 3 is a diagram showing an equivalent circuit introduced in the process of representing the equivalent circuit of turning on the switching element shown in FIG. 2A and the equivalent circuit of turning off of the switching element shown in FIG. It is a figure which shows the equivalent circuit which put together the circuit shown to Fig.3 (a), and the circuit shown in FIG.3 (b) into one circuit. FIG. 5 is a diagram illustrating an equivalent circuit viewed from the equivalent load resistance R side by further modifying the equivalent circuit shown in FIG. 4. It is a figure which shows the equivalent circuit in the steady state obtained from the equivalent circuit shown in FIG. It is a figure which shows the cascade connection switching power supply circuit which connected the circuit of the same topology as the circuit shown in FIG. 1 in two stages. It is a figure which shows the cascade connection switching power supply circuit which connected the circuit which has the same topology as the circuit shown in FIG. 1 in three stages. It is a figure which shows the cascade connection switching power supply circuit which connected the circuit which has the same topology as the circuit shown in FIG. 1 in n stages. The figure which shows typically what kind of relationship the off time of 1 stage | paragraph, the off time of 2 stage cascade connection, and the off time of 3 stage cascade connection when obtaining the same output voltage from the same input voltage It is. It is a figure which shows the efficiency in the range whose resistance ratio of loss resistance / equivalent load resistance is 0.01, and the step-up ratio of output voltage / input voltage is 1.5-5. It is a figure which shows the efficiency in the range whose resistance ratio of loss resistance / equivalent load resistance is 0.01, and the step-up ratio of output voltage / input voltage is 6-10. It is a figure which shows the efficiency in the range whose resistance ratio of loss resistance / equivalent load resistance is 0.01, and the step-up ratio of output voltage / input voltage is 11-15. It is a figure which shows the efficiency in the range whose resistance ratio of loss resistance / equivalent load resistance is 0.01, and the step-up ratio of output voltage / input voltage is 16-20. It is a figure which shows the efficiency in the range whose resistance ratio of loss resistance / equivalent load resistance is 0.01, and the step-up ratio of output voltage / input voltage is 21-25. It is a figure which shows the efficiency in the range whose resistance ratio of loss resistance / equivalent load resistance is 0.01, and the step-up ratio of output voltage / input voltage is 26-30. It is a figure which shows the efficiency in the range whose resistance ratio of loss resistance / equivalent load resistance is 0.01, and the step-up ratio of output voltage / input voltage is 31-35. It is a figure which shows the efficiency in the range whose resistance ratio of loss resistance and equivalent load resistance is 0.005, and the step-up ratio of output voltage and input voltage is 1.5-5. It is a figure which shows the efficiency in the range whose resistance ratio of loss resistance / equivalent load resistance is 0.005, and the step-up ratio of output voltage / input voltage is 6-10. It is a figure which shows the efficiency in the range whose resistance ratio of loss resistance / equivalent load resistance is 0.005, and the step-up ratio of output voltage / input voltage is 11-15. It is a figure which shows the efficiency in the range whose resistance ratio of loss resistance / equivalent load resistance is 0.005, and the step-up ratio of output voltage / input voltage is 16-20. It is a figure which shows the efficiency in the range whose resistance ratio of loss resistance / equivalent load resistance is 0.005, and the step-up ratio of output voltage / input voltage is 21-25. It is a figure which shows the efficiency in the range whose resistance ratio of loss resistance and equivalent load resistance is 0.005, and the step-up ratio of output voltage and input voltage is 26-30. It is a figure which shows the efficiency in the range whose resistance ratio of loss resistance / equivalent load resistance is 0.005, and the step-up ratio of output voltage / input voltage is 31-35. It is a block diagram of the electric power system of an Example. FIG. 26 is a circuit diagram of a cascaded boost type switching power supply circuit that boosts a voltage obtained from the solar cell shown in FIG. 25. It illustrates an embodiment of another timing as shown in FIG. 10 the timing of driving the switching elements S _{1 ~} switching element S ₃ in the circuit shown in FIG. 10 the timing for driving the switching elements S _{1 ~} switching element S ₃ in the circuit shown in FIG. 8 is a diagram showing an embodiment in which another timing as shown in FIG. 27. It is a figure which shows not only cascade connection but the cascade connection step-up type | mold switching power supply circuit which connects each stage of the same structure in parallel. It is a figure which shows in the timing chart the example which makes different the phase of the ON / OFF timing of the switch element in each stage connected in parallel. FIG. 29 is a diagram showing an embodiment in which the timing for driving the switch element in the circuit shown in FIG. 26 is different from that shown in FIGS. 10, 27, and 28. FIG. 29 is a diagram illustrating an embodiment in which the timing for driving the switch element in the circuit illustrated in FIG. 8 is different from that illustrated in FIGS. 10, 27, and 28. It is a figure which shows the cascade connection step-up type | mold switching power supply circuit which has the load corresponding to several different voltage. It is a figure which shows the cascade connection step-up type | mold switching power supply circuit which has the load corresponding to several different voltage. It is a figure which shows the basic circuit of the step-up type switching power supply circuit of background art.

  The cascaded step-up switching power supply circuit according to the embodiment of the present invention is configured by cascading step-up switching power supply circuits in n stages, and is cascaded according to the voltage ratio between the input voltage and the output voltage. The number of steps of the step-up switching power supply circuit is made appropriate.

  In the mode for carrying out the invention, one end of the inductor, one end of the switch element, and one end of the diode are connected, the other end of the inductor and the other end of the switch element are set as the input side, and the other end of the diode and the switch element are connected. A plurality of boosting switching power supply circuits formed by connecting a capacitor between the other end and having both ends of the capacitor as the output side, and cascaded by connecting a plurality of boosting switching power supply circuits in n stages A connection boost type switching power supply circuit is configured. Then, the efficiency (power efficiency) which is the ratio of the output power output to the output side of the cascaded boost type switching power supply circuit and the input power input to the input side of the cascaded boost type switching power supply circuit, and the cascaded boosting Of the resistance corresponding to the loss of the boost switching power supply circuit at the last stage of the step-up switching power supply circuit and the value of the equivalent load resistance connected to the output side, and output to the output side of the cascaded step-up switching power supply circuit Boosting switching power supply circuit of the number given by the integer n that maximizes the value of power efficiency from the relationship between the value of the voltage to be input and the value of the input voltage input to the input side of the cascaded boosting switching power supply circuit Are connected in cascade.

  In another embodiment for carrying out the invention, as described above, the number of boosting switching power supply circuits that are given by an integer n that maximizes the value of power efficiency is connected in cascade, corresponding to each of the n stages. Among the n switch elements, (n−j) switch elements are turned off for a predetermined fixed time, and j switch elements are turned off for a variable time to control the variable time. Thus, the output voltage is controlled. Here, the integer j can be set as an arbitrary integer from 0 to an integer n. When the integer j is 0, control is performed to turn off all the n switch elements of the n-stage step-up switching power supply circuit for a predetermined fixed time. When the integer j is an integer n, control is performed to turn off all the n switch elements of the n-stage step-up switching power supply circuit for a variable time that varies according to the output voltage. When the integer j is in the range of 1 to (n−1), (n−j) switch elements are turned off for a predetermined fixed time, and the j switch elements are turned on according to the output voltage. Control is performed to turn off during the changing variable time.

  In another form for carrying out the invention, when the value of the input voltage of the cascaded step-up switching power supply circuit changes, the boosting is performed so that the efficiency with respect to the lowest input voltage is the highest. The number of cascade connection of the type switching power supply circuit is set in advance, and the number of switch elements that are always off is changed according to the input voltage.

In still another embodiment for carrying out the invention, an integer different from the integer n is set to an integer i (i <n) or an integer p (p> n), and an allowable reduction amount of a predetermined efficiency given in advance is allowed. as reduction epsilon, power efficiency eta _p of the power efficiency eta _i or p cascaded step-up switching power supply circuit of the i cascaded step-up switching power supply circuit, power efficiency eta _n - power efficiency eta _{i <allowable} decrease epsilon Alternatively, the number of cascade connections is set so that power efficiency η _n −power efficiency η _p <allowable decrease amount ε.

  In still another embodiment for carrying out the invention, in determining the number of cascaded switching power supply circuits having the maximum power efficiency value in the cascaded boosting switching power supply circuit, the power efficiency is cascaded. A function represented by the number n of Then, the power efficiency is partially differentiated by a number n to obtain a real number n that maximizes the power efficiency, and the real number n is converted to an integer by performing any of the operations of rounding down, rounding off, and rounding up. The number of cascade connection of the step-up switching power supply circuit that maximizes the value of is obtained.

  Specific embodiments will be described below. When a general n-stage cascaded boosting switching power supply circuit (n-stage cascaded boosting switching power supply circuit) is described, the description will be given in the following order. First, a one-stage boosting switching power supply circuit when there is a circuit loss will be described. Next, a step-up switching power supply circuit (two-stage cascade connection step-up switching power supply circuit) in which there is a circuit loss will be described. Further, a description will be given of a step-up switching power supply circuit (three-stage cascade connection step-up switching power supply circuit) in a case where there is a circuit loss. Finally, an n-stage cascaded step-up switching power supply circuit when there is a circuit loss will be described. In the following, n refers to a positive integer, except that n is a real number.

(Boost type switching power supply circuit when there is circuit loss)
First, a one-stage boosting switching power supply circuit when there is a circuit loss will be described.

Although not represented in the circuit shown in FIG. 35, loss caused by the step-up switching power supply circuit, the forward voltage drop losses of the switching element S _1, the switching loss of the switching element S _1, the inductor L ₁ copper loss, inductor L ₁ of the core loss, the forward voltage drop losses of the diode D _1, switching loss of the diode D _1, a dielectric loss of the capacitor C ₁ is what the Lord. Such an equivalent circuit of a step-up switching power supply circuit when there is a circuit loss has not been studied so far. The reason for this is that in a single-stage boosting switching power supply circuit, no matter how the loss is replaced with an equivalent circuit, the circuit analysis is not greatly affected. However, accurate analysis is difficult for cascaded boost type switching power supply circuits unless circuit loss is taken into consideration. After describing an equivalent circuit of a one-stage boosting switching power supply circuit, a two-stage cascaded boosting switching power supply circuit, and a three-stage cascaded boosting switching power supply circuit suitable for analysis when there is a circuit loss, an n-stage An equivalent circuit that is an extension of the cascaded boost type switching power supply circuit will be described.

FIG. 1 is a diagram showing an equivalent circuit of a one-stage step-up switching power supply circuit when there is a circuit loss. That is, the equivalent circuit shown in FIG. 1 is an equivalent circuit when there is a loss with respect to the equivalent circuit when there is no loss (see FIG. 35). In Figure 1, the forward voltage drop losses of the switching element _{S 1,} the switching loss of the switching element _{S 1,} the copper loss of the inductor _{L 11,} the iron loss of the inductor _{L 11,} the forward voltage drop losses of the diode _{D 1,} a diode _{D 1} switching loss is representative as a loss resistance r ₁₁ losses, including all of the dielectric loss of the capacitor C _11. The load has a resistance value R corresponding to a value obtained by dividing the output voltage applied to the load by the current flowing through the load, not only in the case of a resistance load but also in the case where the electronic circuit is a load. The equivalent load resistance R will be treated below.

FIG. 2 is a diagram showing the equivalent circuit shown in FIG. 1 as two equivalent circuits depending on the state of the switch element. FIG. 2A is an equivalent circuit when the switch element S1 of the circuit shown in FIG. ₁ is on. At this time, switching element S ₁ is conducting is on (on), the circuit shown in FIG. 1 because the diode D ₁ is a an is nonconductive off (off), as shown in FIG. 2 (a) Represented as two separate circuits. Here, the switch element S ₁ and the diode D ₁ are both treated as ideal switch elements.

FIG. 2B is an equivalent circuit when the switch element S1 of the circuit shown in FIG. ₁ is off. At this time, switching element S ₁ is non-conductive OFF (off), the diode D ₁ is the conduction is on (on), as the circuit shown in FIG. 1 are shown in FIG. 2 (b), the one It is expressed as a circuit.

FIG. 3 is a diagram showing an equivalent circuit introduced in the process of representing the equivalent circuit shown in FIG. 2A and the equivalent circuit shown in FIG. 2B as one equivalent circuit. 3 (a) is an equivalent circuit when the switch element _{S 1} is turned on (on), 3 (b) is an equivalent circuit when the switch element _{S 1} is off (off). The difference between FIG. 3A and FIG. 3B is that the winding ratio of the ideal transformer is 1: 0 in FIG. 3A, whereas the winding ratio of the ideal transformer is FIG. ) Is 1: 1.

FIG. 4 is a diagram of an equivalent circuit obtained by modifying the equivalent circuit shown in FIG. 3 and combining the circuit shown in FIG. 3A and the circuit shown in FIG. 3B into one circuit. Here, T _s is a period of time in which the switching element S ₁ has an on period and an off period, and this one period is repeated continuously. T _off1 is the time switching element _{S 1} is off. Taking the state average during one period, the equivalent circuit shown in FIG. 4 is obtained. In the equivalent circuit of the state average during one period shown in FIG. 4, the winding ratio of the ideal transformer is 1: T _off1 / T _s .

FIG. 5 is a diagram showing an equivalent circuit viewed from the equivalent load resistance R side by further modifying the equivalent circuit shown in FIG. That is, when viewed from the equivalent load resistance R side, the value of the input voltage is (T _s / T _off1 ) × E _d , the value of the loss is (T _s / T _off1 ) ² × r ₁₁ , and the inductor L The inductance value of ₁₁ is (T _s / T _off1 ) ² × L ₁₁ . It is an element on the side of the equivalent load resistor R in the equivalent circuit, the value of the capacitance of the capacitor C ₁₁ C _11, the value of resistance of the equivalent parallel resistor R is R, the same value as in Figure 1.

6 is a diagram showing an equivalent circuit in a steady state obtained from the equivalent circuit shown in FIG. In the steady state, the inductor L ₁₁ and the capacitor C ₁₁ are not involved, so the relationship between the output voltage E _o and the input voltage E _d is expressed by Equation (1).

E _o = (T _s / T _off1 ) × E _d × [1 / {1+ (T _s / T _off1 ) ² × (r ₁₁ / R)}]
(1)

From the formula (1), the power consumed by the equivalent load resistance R (resistance value R) (load power) and the power consumed by the loss resistance r ₁₁ (resistance value r ₁₁ ) (loss power) are obtained. The efficiency η ₁ is expressed by Equation (2).

η ₁ = load power / (load power + loss power)
= R × (load current) ² / {R × (load current) ² + (T _s / T _off1 ) ² × r ₁₁ × (load current) ² }
_{= R / {R + (T} s / T off1) 2 × r 11}
_{= 1 / {1+ (T s} / T off1) 2 × (r 11 / R)} (2)

  Moreover, Formula (3) is obtained from Formula (1) and Formula (2).

E _o = (T _s / T _off1 ) × E _d × η ₁ (3)

That is, when the value of the loss resistance r ₁₁ is 0 (when the efficiency η ₁ is 1 (100%)), the value of E _o obtained by Equation (3) is E _o = (T _s / T _off1 ) × E _d , which matches the equation (51).

A cascade-connected boosting switching power supply circuit according to the present embodiment, which will be described later, is obtained by cascading a plurality of one-stage boosting switching power supply circuits having the same topology. Here, the same topology means that the circuit elements are of the same type and have the same connection. Each stage of the cascade step-up switching power supply circuit, as shown in FIG. 1, connects the one end with one end of the switching element S ₁ with one end of the diode D ₁ of the inductor L _11, the other end and the switch of the inductor L ₁₁ the other end of the element S ₁ as input, boosting connect the capacitor C ₁₁ between the other ends and the switching element S ₁ of the diode D _1, is formed at both ends of the capacitor C ₁₁ as an output side The topology is the same as the type switching power supply circuit.

In such a step-up switching power supply circuit, losses replaced with equivalently loss resistance r _11, the load connected to the output side is replaced equivalently equivalent load resistor R. The value of the loss resistance _{r 11} and _{r 11,} equivalent load value of the resistor R and the R, 1 a period of time and _{T s,} the on-off control off time of the switching element _{S 1} is in every cycle _{T off1} Then, (r ₁₁ / R) and (T _s / T _off1 ) are related to the efficiency η ₁ .

If (r ₁₁ / R), E _o which is the value of the output voltage, and E _d which is the value of the input voltage are given, from the relational expression shown in Equation (1), (T _s / T _off1 ) The value is obtained, and the value of efficiency η ₁ can be obtained by substituting the value of (r ₁₁ / R) and the value of (T _s / T _off1 ) into the relational expression shown in Equation (2).

(Two-stage cascaded step-up switching power supply circuit when there is circuit loss)
Next, a two-stage cascaded step-up switching power supply circuit when there is a circuit loss will be described.

FIG. 7 is a diagram showing a two-stage cascaded step-up switching power supply circuit that is a circuit in which two stages of circuits having the same topology as the circuit shown in FIG. 1 are cascade-connected. Switching element S ₁ and switching element S ₂ is controlled so that the time off (off) in one period becomes the same value. Here, the switch element S ₁ and the switch element S ₂ are controlled by setting T _s as one cycle and T _off2 as an off time. An efficiency η ₂ is obtained for a two-stage cascaded step-up switching power supply circuit having an input voltage E _d , an output voltage E _o , and having an equivalent load resistance R (resistance value R). In determining the efficiency η ₂ , first, a relational expression of the output voltage E _o , the voltage E ₁ , and the input voltage E _d is determined as shown below. Here, the voltage E ₁ is the first stage output voltage closest to the input side, is also the second stage input voltage at the same time.

The relationship between the output voltage E _o and the voltage E ₁ in the steady state of the circuit shown in FIG. 7 is expressed by Equation (4). The relationship in a steady state of the input voltage E _d and the voltage E ₁ is expressed by Equation (5). Here, r ₂₁ is obtained by replacing the loss of the first step-up switching power supply circuit (step-up switching power supply circuit connected to the input side) with a resistor, and r ₂₂ is the second step boost switching switching circuit. The loss of the power supply circuit (step-up switching power supply circuit connected to the output side) is replaced with a resistor, and R ₂₁ is the equivalent load resistance in the steady state of the first step-up switching power supply circuit.

E _o = (T _s / T _off2 ) × E ₁ × [1 / {1+ (T _s / T _off2 ) ² × (r ₂₂ / R)}] (4)
_{E 1 = (T s / T} off2) × E d × [1 / {1+ (T s / T off2) 2 × (r 21 / R 21)}] (5)

From equation (4) and Equation (5) erases the voltage _{E 1,} as shown in Equation (6), to obtain a relationship between the output voltage _{E o} and the input voltage _{E d.}

E _o = (T _s / T _off2 ) ² × E _d × [1 / {1+ (T _s / T _off2 ) ² × (r ₂₁ / R ₂₁ )}] × [1 / {1+ (T _s / T _off2 ² × (r ₂₂ / R)}] (6)

From Equation (6), the efficiency η ₂ of the two-stage cascaded step-up switching power supply circuit when there is a circuit loss is given by Equation (7).

η ₂ = [1 / {1+ (T _s / T _off2 ) ² × (r ₂₁ / R ₂₁ )}] × [1 / {1+ (T _s / T _off2 ) ² × (r ₂₂ / R)}] ( 7)

Here, the first term on the right side of Equation (7) is the efficiency η ₂₁ of the first step-up switching power supply circuit, and the second term on the right side of Equation (7) is the second step-up switching power supply circuit. which is the efficiency η _22. Efficiency η ₂ = η ₂₁ × η ₂₂

When the power supplied to the equivalent load resistor R and W _R, loss W ₂₂ in the step-up switching power supply circuit of the second stage is obtained by the equation (8), the loss in the step-up switching power supply circuit of the first stage W ₂₁ Is obtained by Equation (9).

_{W 22 = W R × (1} -η 22) / η 22 (8)
_{W 21 = W R × (1} -η 21) / (η 21 × η 22) (9)

  Expression (10) is obtained from Expression (8) and Expression (9).

_{W 21 / W 22 = {W} R × (1-η 21) / (η 21 × η 22)} / {W R × (1-η 22) / η 22} = (1-η 22) × η 21 / (1-η ₂₁ ) (10)

Here, in Equation (7), when (r ₂₁ / R ₂₁ ) = (r ₂₂ / R), the efficiency η ₂₁ of the first step-up switching power supply circuit and the step-up switching of the second step The efficiency η _{22 of the} power supply circuit is equal.

Strictly speaking, as shown in the equations (8) to (9), the loss of the step-up switching power supply circuit in the previous stage becomes larger, but in the case of η ₂₁ = η ₂₂ ≈1 (that is, r ₂₂ << R, r ₂₁ << R ₂₁ and (r ₂₁ / R ₂₁ ) = (r ₂₂ / R)), the loss W ₂₁ of the first step-up switching power supply circuit and the second stage The loss W ₂₂ of the step-up switching power supply circuit can be made substantially equal. In this way, it is preferable to make the losses in each stage substantially the same in terms of preventing heat concentration by making the heat generation in each stage substantially uniform.

In the case of (r ₂₁ / R ₂₁ ) = (r ₂₂ / R), (r ₂₁ / R ₂₁ ) can be deleted from Equation (6) to obtain Equation (11). Here, it is clear from the equivalent circuit shown in FIG. 7 that R ₂₁ = (T _off2 / T _s ) ² × R and r ₂₁ = (T _off2 / T _s ) ² × r ₂₂ .

E _o = (T _s / T _off2 ) ² × E _d × [1 / {1+ (T _s / T _off2 ) ² × (r ₂₂ / R)}] ² (11)

From Equation (11), the efficiency η ₂ of the two-stage cascaded step-up switching power supply circuit when there is a circuit loss is given by Equation (12).

η ₂ = [1 / {1+ (T _s / T _off2 ) ² × (r ₂₂ / R)}] ²
= 1 / {1+ (T _s / T _off2 ) ² × (r ₂₂ / R)} ² (12)

In short, the two-stage cascaded step-up switching power supply circuit of the present embodiment is obtained by cascading two step-up switching power supply circuits in two stages. The first stage (previous stage) of the two-stage cascaded step-up switching power supply circuit connects one end of the inductor L ₂₁ , one end of the switch element S ₁ , and one end of the diode D ₁ , and the other end of the inductor L ₂₁ and the switch the other end of the element S ₁ to the input side. Then, connect the capacitor C ₂₁ between the other end and the other end of the switch element S ₁ of the diode D _1, is intended to be formed at both ends of the capacitor C ₂₁ as an output side. Further, loss is replaced equivalently loss resistance r _21.

Further, the second stage of this two-stage cascaded step-up switching power supply circuit (latter stage) connects the one end with one end of the switching element S ₂ of the one end and the diode D ₂ of the inductor L _22, the other end of the inductor L ₂₂ to the input side and the other end of the switch element S _2. Then, connect the capacitor C ₂₂ between the other end and the other end of the switch element S ₂ of the diode D _2, are those formed with both ends of the capacitor C ₂₂ as an output side. The loss is replaced with equivalently loss resistance r _22, the load connected to the output side is replaced equivalently equivalent load resistor R.

The value of the loss resistance r ₂₂ and r _22, the value of the equivalent load resistor R and R, one cycle time and T _s, the switch element S ₁ is turned on and off control for each _cycle, the switching element S ₂ If the off time is T _off2 , (r ₂₂ / R) and (T _s / T _off2 ) are related to the efficiency η ₂ . Here, the value of the equivalent load resistance R ₂₁ in the steady state as viewed from the first step-up switching power supply circuit is R _21, and the value of the loss resistance r ₂₁ according to the loss of the first step-up switching power supply circuit. Is r ₂₁ . If the efficiency of each stage is equal, the relationship of (r ₂₂ / R) = (r ₂₁ / R ₂₁ ) is established.

If (r ₂₂ / R), E _o which is the value of the output voltage, and E _d which is the value of the input voltage are given, from the relational expression shown in Equation (11), (T _s / T _off2 ) Motomari value can be obtained the value of efficiency eta ₂ by substituting the value of the relational expression shown in equation (12) and the value of _{(r 22 / R) (T} s / T off2).

(Three-stage cascaded step-up switching power supply circuit when there is circuit loss)
Further, a three-stage cascaded step-up switching power supply circuit when there is a circuit loss will be described.

FIG. 8 is a diagram showing a circuit in which three stages of circuits having the same topology as the circuit shown in FIG. 1 are connected in cascade. The switch element S ₁ , the switch element S _2, and the switch element S ₃ are controlled so that the off times in one cycle have the same value. Here, _assuming that one period is controlled as T _s and an off time is controlled as T _off3 , the efficiency η ₃ is obtained for a circuit having E _{d as} an input voltage value and E _o as an input voltage value. . When obtaining the efficiency η ₃ , _first , the relational expressions of the output voltage E _o , the voltage E ₁ , the voltage E ₂ , and the input voltage E _d are obtained as shown below.

The relationship between the output voltage E _o and the voltage E ₂ in the steady state of the circuit shown in FIG. 8 is expressed by Equation (13). The relationship in a steady state of the voltage _{E 2} and the voltage _{E 1} is expressed by Equation (14). The relationship in a steady state of the input voltage _{E d} and the voltage _{E 1} is expressed by Equation (15). Here, r ₃₁ is obtained by replacing the loss of the first step-up switching power supply circuit (step-up switching power supply circuit connected to the input side) with a resistor, and r ₃₂ is the second stage step-up switching power supply. circuit is intended by replacing the loss of (is connected to an intermediate step-up switching power supply circuit) to the resistance, r ₃₃ is the step-up switching power supply circuit of the third stage (step-up switching power supply circuit connected to the output side) The loss is replaced by a resistor, R ₃₁ is an equivalent load resistance in a steady state as seen from the first step-up switching power supply circuit, and R ₃₂ is a steady state as seen from the second step-up switching power supply circuit. It is equivalent load resistance in the state.

E _o = (T _s / T _off3 ) × E ₂ × [1 / {1+ (T _s / T _off3 ) ² × (r ₃₃ / R)}] (13)

E ₂ = (T _s / T _off3 ) × E ₁ × [1 / {1+ (T _s / T _off3 ) ² × (r ₃₂ / R ₃₂ )}] (14)

_{E 1 = (T s / T} off3) × E d × [1 / {1+ (T s / T off3) 2 × (r 31 / R 31)}] (15)

From equation (13) to Equation (15), the voltage _{E 1,} and erase voltage _{E 2,} shown in equation (16), to obtain a relationship between the output voltage _{E o} and the input voltage _{E d.}

E _o = (T _s / T _off3 ) ³ × E _d × [1 / {1+ (T _s / T _off3 ) ³ × (r ₃₁ / R ₃₁ )}] × [1 / {1+ (T _s / T _{off3 ^{) 3 × (r 32 / R}} 32)}] × [1 / {1+ (T s / T off3) 3 × (r 33 / R)}] (16)

From Equation (16), the efficiency η ₃ of the three-stage cascaded step-up switching power supply circuit when there is a circuit loss is given by Equation (17).

η ₃ = [1 / {1+ (T _s / T _off3 ) ³ × (r ₃₁ / R ₃₁ )}] × [1 / {1+ (T _s / T _off3 ) ² × (r ₃₂ / R ₃₂ )}] × [1 / {1+ (T _s / T _off3 ) ² × (r ₃₃ / R)}] (17)

Here, the first term on the right side of Equation (17) is the efficiency η ₃₁ of the first step-up switching power supply circuit, and the second term on the right side of Equation (17) is the second step-up switching power supply circuit. of an efficiency eta _32, the third term on the right side of equation (17) is the efficiency eta ₃₃ of the step-up switching power supply circuit of the third stage. Efficiency η ₃ = η ₃₁ × η ₃₂ × η ₃₃

When the power supplied to the equivalent load resistor R and W _R, loss W ₃₃ in the step-up switching power supply circuit of the third stage is determined by the equation (18), the loss in the step-up switching power supply circuit of the second stage W ₃₂ Is obtained by Equation (19), and the loss W ₃₁ in the first step-up switching power supply circuit is obtained by Equation (20).

W ₃₃ = W _R × (1-η ₃₃ ) / η ₃₃ (18)
_{W 32 = W R × (1} -η 32) / (η 32 × η 33) (19)
_{W 31 = W R × (1} -η 31) / (η 31 × η 32 × η 33) (20)

Expressions (21) to (23) are obtained from Expressions (18) to (20).

W ₃₃ / W _R = (1−η ₃₃ ) / η ₃₃ (21)

W ₃₂ / W ₃₃ = (1-η ₃₂ ) / {(1-η ₃₃ ) × η ₃₂ } (22)

W ₃₁ / W ₃₂ = (1-η ₃₁ ) / {(1-η ₃₂ ) × η ₃₁ } (23)

When the efficiency η ₃₁ of the first step-up switching power supply circuit and the efficiency η ₃₂ of the second step-up switching power supply circuit are equal to the efficiency η ₃₃ of the third step-up switching power supply circuit, In Expression (17), (r ₃₁ / R ₃₁ ) = (r ₃₂ / R ₃₂ ) = (r ₃₃ / R) can be set.

Strictly speaking, as expressed by the equations (18) to (20), the loss of the previous step-up switching power supply circuit becomes larger, but in the case of η ₃₁ = η ₃₂ = η ₃₃ ≈1 (that is, , R ₃₃ << R, r ₃₂ << R ₃₂ , r ₃₁ << R ₃₁ ), the loss W ₃₁ of the first step-up switching power supply circuit and the second step-up switching power supply circuit The loss W ₃₂ and the loss W ₃₃ of the third step-up switching power supply circuit can be made substantially equal. In this way, it is preferable to make the losses in each stage substantially the same in terms of preventing heat concentration by making the heat generation in each stage substantially uniform.

When (r ₃₁ / R ₃₁ ) = (r ₃₂ / R ₃₂ ) = (r ₃₃ / R), from equation (16), (r ₃₁ / R ₃₁ ) and (r ₃₂ / R ₃₂ ) are changed. By erasing, the equation (24) can be obtained. Here, R ₃₂ = (T _off3 / T _s ) ² × R, R ₃₁ = (T _off3 / T _s ) ² × R ₃₂ , and r ₃₂ = (T _off3 / T _s ) ² × r ₃₃ It is _apparent that r ₃₁ = (T _off3 / T _s ) ² × r _{32 as} in the two-stage cascaded boost type switching power supply circuit.

E _o = (T _s / T _off3 ) ³ × E _d × [1 / {1+ (T _s / T _off3 ) ² × (r ₃₃ / R)}] ³ (24)

From Equation (24), the efficiency η ₃ of the three-stage cascaded step-up switching power supply circuit when there is a circuit loss is given by Equation (25).

η ₃ = [1 / {1+ (T _s / T _off3 ) ² × (r ₃₃ / R)}] ³
= 1 / {1+ (T _s / T _off3 ) ² × (r ₃₃ / R)} ³ (25)

In short, the three-stage cascaded step-up switching power supply circuit of this embodiment is obtained by connecting three boost-type switching power supply circuits in three stages. First stage of this three-stage cascade step-up switching power supply circuit (former stage) connects the one end with one end of the switching element S ₁ one end of the diode D ₁ of the inductor L _31, the other end and the switch of the inductor L ₃₁ the other end of the element S ₁ to the input side. Then, connect the capacitor C ₃₁ between the other end and the other end of the switch element S ₁ of the diode D _1, is intended to be formed at both ends of the capacitor C ₃₁ as the output side. Further, loss is replaced by the loss resistance r ₃₁ equivalently.

Further, the second stage of this three-stage cascade step-up switching power supply circuit (middle) connects the one end with one end of the switching element S ₂ of the one end and the diode D ₂ of the inductor L _32, the other end of the inductor L ₃₂ to the input side and the other end of the switch element S _2. Then, connect the capacitor C ₃₂ between the other end and the other end of the switch element S ₂ of the diode D _2, are those formed with both ends of the capacitor C ₃₂ as an output side. The loss is equivalently replaced with a loss resistance r ₃₂ , and the load connected to the output side is equivalently replaced with an equivalent load resistance R ₃₂ . The input side of the second stage (middle stage) of the boosting switching power supply circuit is connected to the output side of the first stage (previous stage) of the boosting switching power supply circuit, and the second stage (middle stage) of the boosting switching power supply circuit. The output side is connected to the input side of the third stage (middle stage) of the step-up switching power supply circuit.

Also, the third stage of the three-stage cascade step-up switching power supply circuit (latter stage) connects the one ends and the diode D ₃ in one end and the switching element S ₃ of the inductor L _33, the other end of the inductor L ₃₃ to the input side and the other end of the switch element S _3. Then, connect the capacitor C ₃₃ between the other ends and the switching element S ₃ of the diode D _3, are those formed with both ends of the capacitor C ₃₃ as an output side. The loss is equivalently replaced by the loss resistance r ₃₃ , and the load connected to the output side is the equivalent load resistance R. The third stage input side of the step-up switching power supply circuit is connected to the second stage (middle stage) output side of the step-up switching power supply circuit.

The value of the loss resistance _{r 33} and _{r 33,} the value of the equivalent load resistor R and R, one cycle time and _{T s,} the switch element _{S 1} is turned on and off control for each cycle, the switching element _S 2, If the off time of the switch element S ₃ is T _off3 , (r ₃₃ / R) and (T _s / T _off3 ) are related to the efficiency η ₃ . Here, the value of the equivalent load resistance R ₃₁ in the steady state as viewed from the first step-up switching power supply circuit is R ₃₁ , and the value of the equivalent load resistance R ₃₂ in the steady state as viewed from the second step-up switching power supply circuit. The value is R ₃₂ , the value of the loss resistance r ₃₁ according to the loss of the first step-up switching power supply circuit is r ₃₁ , and the value of the loss resistance r ₃₂ according to the loss of the second step-up switching power supply circuit is Let r ₃₂ . In this case, when the efficiency in each stage is equal, (r ₃₃ / R) = (r ₃₁ / R ₃₁ ) = (r ₃₂ / R ₃₂ ) holds.

If (r ₃₃ / R), E _o that is the value of the output voltage, and E _d that is the value of the input voltage are given, from the relational expression shown in Equation (24), (T _s / T _off3 ) The value is obtained, and the value of efficiency η ₃ can be obtained by substituting the value of (r ₃₃ / R) and the value of (T _s / T _off3 ) into the relational expression shown in Equation (25).

(N-stage cascaded step-up switching power supply circuit when there is circuit loss)
The analysis method of the above-described two-stage cascade connection boosting switching power supply circuit and three-stage cascade connection boosting switching power supply circuit is extended to a general n-stage cascade connection boosting switching power supply circuit. FIG. 9 is a diagram showing an n-stage cascaded step-up switching power supply circuit. In FIG. 9, the description of the step-up switching power supply circuit from the second stage to the (n−1) stage is omitted.

  Equation (26) can be obtained when Equation (16) is expanded to n stages, and Equation (27) can be obtained when Equation (17) is expanded to n stages.

E _o = (T _s / T _offn ) ⁿ × E _d × [1 / {1+ (T _s / T _offn ) ² × (r _n1 / R _n1 )}] × [1 / {1+ (T _s / T _offn ) ² × (r _n2 / R _n2 )}]... × [1 / {1+ (T _s / T _offn ) ² × (r _nm / R _nm )}] ... × [1 / { 1+ (T _s / T _offn ) ² × (r _nn−1 / R _nn−1 )}] × [1 / {1+ (T _s / T _offn ) ² × (r _nn / R)}] (26)

η _n = [1 / {1+ (T _s / T _offn ) ² × (r _n1 / R _n1 )}] × [1 / {1+ (T _s / T _offn ) ² × (r _n2 / R _n2 )}] ····· × [1 / {1+ (T _s / T _offn ) ² × (r _nm / R _nm )}]... × [1 / {1+ (T _s / T _offn ) ² × (r _nn−1 / R _nn−1 )}] × [1 / {1+ (T _s / T _offn ) ² × (r _nn / R)}] (27)

By arranging the formulas (26) and (27), the output voltage E _o and the efficiency η _n are given by the formulas (28) and (29), respectively.

_{E o = (T s / T} offn) n × E d × [1 / {1+ (T s / T offn) 2 × (r nn / R)}] n (28)

η _n = [1 / {1+ (T _s / T _offn ) ² × (r _nn / R)}] ⁿ
= 1 / {1+ (T _s / T _offn ) ² × (r _nn / R)} ⁿ (29)

In short, the n-stage cascaded step-up switching power supply circuit of this embodiment is obtained by connecting n boost-type switching power supply circuits in n stages. The first stage (frontmost step-up switching power supply circuit) on the input side of this n-stage cascaded step-up switching power supply circuit connects one end of the inductor L _n1 , one end of the switch element S ₁ , and one end of the diode D _1. and, the other ends of the switching element S ₁ of the inductor L _n1 and the input side. Then, connect the capacitor C _{n1 (foremost} capacitor) between the other end and the other end of the switch element S ₁ of the diode D _1, is intended to be formed at both ends of the capacitor C _n1 as the output side. Further, loss is replaced equivalently loss resistance r _n1.

Further, the second stage of the n cascaded step-up switching power supply circuit includes an inductor L _n2 connects the one end with one end of the switching element S ₂ of the one end and the diode D _{2 (not} shown), the inductor L _n2 the other end of the other end and a switching element S ₂ to the input side. Then, connect the capacitor C _{n2 (not} shown) between the other end and the other end of the switch element S ₂ of the diode D _2, are those formed with both ends of the capacitor C _n2 as the output side. The loss is equivalently replaced with a loss resistance r _n2 (not shown), and the load connected to the output side is equivalently replaced with an equivalent load resistance R _n2 (not shown). The second stage input side of the step-up switching power supply circuit is connected to the first stage output side of the step-up switching power supply circuit, and the second stage output side of the step-up switching power supply circuit is connected to the step-up switching power supply circuit. Connected to the input side of the third stage. Similarly, the input side of each step-up switching power supply circuit is connected to the output side of the step-up switching power supply circuit in the previous stage, and the output side of each step-up switching power supply circuit is connected to the input side in the subsequent stage. Connected in cascade.

Further, n-th stage of the n cascaded step-up switching power supply circuit connects the one ends and the diode D _n of one end and the switching elements S _n of the inductor L _nn, inductor L _nn other end and a switching element _Let the other end of Sn be the input side. Then, connect the capacitor C _nn between the other end of the other end and a switching element S _n diode D _n, it is those formed with both ends of the capacitor C _nn as the output side. The loss is replaced equivalently loss resistance r _nn. The input side of the nth step-up switching power supply circuit is connected to the output side of the (n-1) th step-up switching power supply circuit, and the output side of the nth step-up switching power supply circuit is the equivalent load. Connected to resistor R.

The value of the loss resistance r _nn (resistance corresponding to the loss) of the n-th step-up switching power supply circuit is set to r _nn , the value of the equivalent load resistance R is set to R, and the time of one cycle is set to T _s. switching element _{S 1} is turned on and off control, if the off-time of the switching element _S 2 · · · · switching element _{S n} and _{T OFFN,} and the _(r nn / _R) and _{(T s /} T offn) efficiency is related to η _n . Here, the value of the equivalent load resistance R _n1 in the steady state as viewed from the first step-up switching power supply circuit is represented by R _n1 , and the value of the equivalent load resistance R _n2 in the steady state as viewed from the second step-up switching power supply circuit. The value of R _n2 ,... (N−1) is the equivalent load resistance R _{(n−1) 1} of the step-up switching power supply circuit, and R _{(n−1) 1} . The value of the equivalent load resistance R of the nth step-up switching power supply circuit is R. In addition, the resistance values corresponding to the losses of the respective step-up switching power supply circuits from the first stage to the n-th stage are denoted by r _n1 , r _n2 ,... R _{(n−1) 1} and r _n1 . In this case, assuming that the efficiency of each stage is equal, (r _nn / R) = (r _n1 / R _n1 ) =... = (R _{(n−1) 1} / R _{(n -1) 1} ) is established.

In this case, given (r _nn / R), E _o that is the value of the output voltage, and E _d that is the value of the input voltage, from the relational expression shown in Equation (28), (T _s / T Motomari value of _OFFN), it is possible to determine the value of the efficiency eta _n by substituting the value of the relational expression shown in equation (29) and the value of _{(r nn / R) (T} s / T offn). _{Alternatively} , an expression not including (T _s / T _offn ) is obtained from Expression (28) and Expression (29), and each value of output voltage E _o , input voltage E _d , (r _nn / R) is directly calculated. The value of efficiency η _n can be obtained by substitution.

(Relationship between the number of cascaded stages n of the step-up switching power supply circuit and the off time T _offn )
FIG. 10 shows a case where the same output voltage E _o is obtained from each of the one-stage step-up switching power supply circuit or the three-stage cascaded step-up switching power supply circuit with the same input voltage E _d . What is the relationship between the off time T _{off1 of} the one-stage boosting switching power supply circuit, the off time T _{off2 of} the two-stage cascaded boosting switching power supply circuit, and the off time T _{off3 of} the three-stage cascaded boosting switching power supply circuit? It is a figure which shows typically whether it becomes.

Here, for simplicity of explanation, when each of the efficiency η ₁ , efficiency η ₂ , and efficiency η ₃ is 1 (when there is no loss where r ₁₁ = 0, r ₂₂ = 0, r ₃₃ = 0) ) Will be explained first. In this _{case, T off1} is expressed by Equation _{(30), T off2} the equation _{(31), T off3} the equation (32). In addition, the n-stage cascaded step-up switching power supply circuit is expressed by Expression (33) when the efficiency η _n is 1.

T _off1 = T _s × (E _d / E _o ) (30)

T _off2 = T _s × (E _d / E _o ) ^1/2 (31)

T _off3 = T _s × (E _d / E _o ) ^1/3 (32)

T _offn = T _s × (E _d / E _o ) ^{1 / n} (33)

1, 7, 8, in the step-up switching power supply circuit shown in FIG. _9, since it is _E d _/ E o <1, from Equation (30) - equation _{(33), T off1 <T} off2 <T off3 The relationship is established. Moreover, the general relationship between the time that the switch element in the n cascaded step-up switching power supply circuit is turned off (off) _{is, T off1 <T off2 <T} off3 ····· <T offn ( _{However, T OFFN} is off time corresponding to n equal to or greater than 4). _{Incidentally, r 11 ≠ 0, r 22} ≠ 0, if it is _{r 33} ≠ 0 (if losses are present) also, when the efficiency of each stage are _equal, T _{off1 <T} off2 _{<relation T off3} is satisfied To do. _{Then, r 11 ≠ 0, r 22} ≠ 0, r 33 when ≠ a 0 · · · · · _{r nn} ≠ 0 _{also, T off1} <T _off2 <generally of _T off3 ····· _<T offn A relationship is established.

(Relationship between the number of cascaded stages n of the step-up switching power supply circuit and the efficiency η _n )
The efficiency η _n of the n-stage cascaded step-up switching power supply circuit is _{expressed as} follows: T _s / T _offn (period / off time time ratio) and r _nn / R (step-up switching in the final stage) It is expressed as a function of the power supply circuit loss resistance / equivalent load resistance resistance ratio). Here, as shown in Equation (28), T _s / T _offn is expressed as a function of E _o / E _d (a boost ratio of output voltage / input voltage) and r _nn / R. The efficiency η _n of the n-stage cascaded step-up switching power supply circuit is expressed as a function of E _o / E _d and r _nn / R.

In short, the ratio of the output power output to the output side of the n-stage cascaded step-up switching power supply circuit and the input power input to the input side is (power) efficiency η _n, and the number of cascade connections is n. The integer _n that maximizes η _n is determined as follows.

An equivalent load resistance connected to the output side of the n-stage cascaded step-up switching power supply circuit, where r _nn is the resistance value corresponding to the loss of the last boost-type switching power supply circuit of the n-stage cascaded step-up switching power supply circuit The value of R is R, the value of the output voltage output to the output side of the n-stage cascaded boost type switching power supply circuit is Eo, and the value of the input voltage input to the input side of the n-stage cascaded boost type switching power supply circuit Is E _d . In this case, the number given by the integer n that satisfies the above formula (28) and maximizes the value of the power efficiency η _n represented by the above formula (29) is the number of cascade connections that maximize the efficiency. is there. Therefore, a cascade-connected boosting switching power supply circuit obtained by cascade-connecting boosting switching power supply circuits in n stages is most efficient.

The process of solving the binary simultaneous equations for obtaining the number given by the integer n that satisfies the above formula (28) and maximizes the value of the power efficiency η _n represented by the above formula (29) is shown below. . In order to simplify the notation of each mathematical expression, M = E _o / E _d is set, k _n = T _s / T _offn is set, and b = r _nn / R is set. In this way, Expression (34) is obtained from Expression (28).

^{_{M = k n n {1 /}} (1 + k n 2 × b)} n = {k n / (1 + k n 2 × b)} n (34)

Equation (34), because it is quadratic equation for k _n, from the official roots of the quadratic equation, it is possible to obtain a formula (35).

k _n = {1 ± (1−4 × b × M ^{2 / n} ) ^1/2 } / (2 × b × M ^{1 / n} ) (35)

  Here, the meaning of Equation (35) will be examined. Formula (35) is composed of two formulas, Formula (36) and Formula (37).

k _n = {1- (1−4 × b × M ^{2 / n} ) ^1/2 } / (2 × b × M ^{1 / n} ) (36)

k _n = {1+ (1−4 × b × M ^{2 / n} ) ^1/2 } / (2 × b × M ^{1 / n} ) (37)

First, Formula (36) is examined. The limit value (b-> 0) where b = r _nn / R approaches 0, that is, k _n = T _s / T _offn when there is no loss and the efficiency is 1, is expressed by Expression (38). .

k _n = M ^{1 / n} (b → 0)
_{= T s / T offn = (} E o / E d) 1 / n (38)

  Further, when the relational expression shown in the mathematical formula (33) when there is no loss and the efficiency is 1, the mathematical formula (39) is obtained.

T _s / T _offn = (E _o / E _d ) ^{1 / n} (39)

That is, since the mathematical formula (38) and the mathematical formula (39) match, k _n = {1- (1−4 × b × M ^{2 / n} ) ^1/2 } / (2 shown in the mathematical formula (36). Xb * M1 ^{/ n} ) is confirmed to be a significant solution consistent with the physical phenomenon.

On the other hand, the case of Formula (37) will be examined. The limit value where b = r _nn / R approaches 0 is expressed by Equation (40).

k _n = ∞ (b → 0) (40)

That is, the formula (40) and the formula (39) do not match, and k _n = {1+ (1−4 × b × M ^{2 / n} ) ^1/2 } / (2 × b) shown in the formula (37). It is confirmed that (× M ^{1 / n} ) is not a significant solution consistent with the physical phenomenon.

Obtained in Equation (36), a _{k n} are substituted into Equation _(29), erases the _{T s /} T offn, it is possible to obtain a formula (41). Then, again introduced for simplifying the operation, M can be returned to E _o / E _d and b can be returned to r _nn / R to obtain equations (41) and (42).

η _n = 1 / {1+ (T _s / T _offn ) ² × (r _nn / R)} ⁿ
= 1 / {1+ (k _n ) ² × b} ⁿ
= 1 / <1 + [{1- (1-4 * b * M2 ^{/ n} ) ^1/2 } / (2 * b * M1 ^{/ n} )] ² * b> ⁿ (41)

η _n = 1 / << 1 + <[1- {1-4 × (r _nn / R) × (E _o / E _d ) ^{2 / n} } ^1/2 ] / {2 × (r _nn / R) × ( E _o / E _d ) ^{1 / n} }> ² × (r _nn / R) >> ⁿ (42)

(Calculation example)
FIG. 11 to FIG. 24 are graphs showing the relationship of the efficiency η _n with respect to the number n of cascaded stages of the step-up switching power supply circuit using E _o / E _d and r _nn / R as parameters. That is, the horizontal axis represents the value of the cascade connection stage number n, and the vertical axis represents the overall efficiency of the cascaded step-up switching power supply circuit having n stages. Each of these graphs is obtained by calculation from Expression (28) and Expression (29) or Expression (42).

11 to 17 show the efficiency in the range of r _nn /R=0.01 and E _o / E _d of 1.5 to 35, and the number of cascaded stages of the boost type switching power supply circuit between 1 and 10. It shows the result of calculation by changing. 18 to 24 show the efficiency in the range of r _nn /R=0.005 and E _o / E _d of 1.5 to 35, and the number of cascaded stages of the step-up switching power supply circuit is 1 to 10. It shows the result of calculation by changing between.

FIG. 11 is a graph showing the efficiency in the range of r _nn /R=0.01 and E _o / E _{d of} 1.5-5. FIG. 12 is a graph showing the efficiency in the range of r _nn /R=0.01 and E _o / E _d of 6 to 10. FIG. 13 is a graph showing the efficiency in the range of r _nn /R=0.01 and E _o / E _d of 11-15.

FIG. 14 is a graph showing the efficiency in the range of r _nn /R=0.01 and E _o / E _d of 16-20. FIG. 15 is a diagram showing the efficiency in the range of r _nn /R=0.01 and E _o / E _d of 21 to 25. FIG. 16 is a graph showing the efficiency in the range of r _nn /R=0.01 and E _o / E _d of 26-30. FIG. 17 is a diagram showing the efficiency in the range of r _nn /R=0.01 and E _o / E _d of 31 to 35.

FIG. 18 is a diagram showing the efficiency in the range of r _nn /R=0.005 and E _o / E _d of 1.5 to 5. FIG. 19 is a diagram showing the efficiency in the range where r _nn /R=0.005 and E _o / E _d is 6 to 10. FIG. 20 is a graph showing the efficiency in the range of r _nn /R=0.005 and E _o / E _d of 11-15. FIG. 21 is a diagram showing the efficiency in the range of r _nn /R=0.005 and E _o / E _d of 16-20. FIG. 22 is a diagram showing the efficiency in the range of r _nn /R=0.005 and E _o / E _d of 21 to 25. FIG. 23 is a diagram showing the efficiency in the range of r _nn /R=0.005 and E _o / E _d of 26-30. FIG. 24 is a diagram showing the efficiency in the range of r _nn /R=0.005 and E _o / E _d of 31 to 35.

The numbers n (number of converters n) 1, 2,..., 10 of the number n of cascade connections on each horizontal axis in FIGS. 11 to 24 indicate the number of step-up switching power supply circuits connected in cascade. When E _o / E _d changes in the range of 1.5 to 35, the value of efficiency η (Efficiency) shown on the vertical axis is smaller as the value of the step-up ratio E _o / E _d is smaller at an arbitrary number of stages n. You can see that it grows. In general, in the step-up switching power supply circuit, the input voltage _Ed is a voltage having a voltage value within a predetermined range obtained under constraints, and the output voltage _Eo is a desired voltage. That is, the step-up switching power supply circuit is intended to obtain a desired output voltage by obtaining a desired step-up ratio E _o / E _d .

In the case of the resistance ratio r _nn /R=0.01, the following results can be seen from FIGS. When the value of the step-up ratio E _o / E _d is 1.5 or 2, the efficiency is maximized with the number of stages n = 1 (see FIG. 11). When the value of the step-up ratio E _o / E _d is 3, the efficiency is maximized with the number of stages n = 2 (see FIG. 11). When the value of the step-up ratio E _o / E _d is 4 or 5, the efficiency is maximized with the number of stages n = 3 (see FIG. 11). When the value of the step-up ratio E _o / E _d is 6 to 9, the efficiency is maximized with the number of stages n = 4 (see FIG. 12). When the value of the step-up ratio E _o / E _d is 10 to 15, the efficiency is maximum at the number of stages n = 5 (see FIGS. 12 and 13). When the value of the step-up ratio E _o / E _d is 16 to 22, the number of stages n = 6 maximizes the efficiency (see FIGS. 14 and 15). When the value of the step-up ratio E _o / E _d is 23 to 35, the efficiency is maximum at the number of stages n = 7 (see FIGS. 15, 16, and 17).

In the case of the resistance ratio r _nn /R=0.005, the following results can be seen from FIGS. When the value of the step-up ratio E _o / E _d is 1.5, the efficiency is maximized with the number of stages n = 1 (see FIG. 18). When the value of the step-up ratio E _o / E _d is 2, the efficiency is maximized with the number of stages n = 2 (see FIG. 18). When the value of the step-up ratio E _o / E _d is 3 to 5, the efficiency is maximum at the number of stages n = 3 (see FIG. 18). When the value of the step-up ratio E _o / E _d is 6 to 9, the efficiency is maximum at the number of stages n = 4 (see FIG. 19). When the value of the step-up ratio E _o / E _d is 10 to 15, the efficiency is maximum when the number of stages n = 5 (see FIGS. 19 and 20). When the value of the step-up ratio E _o / E _d is 16 to 23, the efficiency is maximized with the number of stages n = 6 (see FIGS. 21 and 22). When the value of the step-up ratio E _o / E _d is 24 to 35, the efficiency is maximum at the number of stages n = 7 (see FIGS. 22, 23, and 24).

With reference to FIG. 11, some specific examples will be cited and described. When the resistance ratio r _nn /R=0.01, the following efficiency can be seen. The maximum efficiency when the step-up ratio E _o / E _d is 1.5 occurs when n = 1, and the value is approximately 98% (the calculated value is 97.7%, but the significant figure is 3 digits) If so, significant figures are the same below). The maximum efficiency value when the value of the step-up ratio E _o / E _d is 2 occurs when n = 1, and the value is approximately 96% (the calculated value is 95.8%). The maximum efficiency value when the value of the step-up ratio E _o / E _d is 3 occurs when n = 2, and the value is approximately 94% (the calculated value is 93.9%). The maximum efficiency value when the value of the step-up ratio E _o / E _d is 4 occurs when n = 3, and the value is approximately 92% (the calculated value is 92.4%). The maximum efficiency value when the value of the step-up ratio E _o / E _d is 5 occurs when n = 3, and the value is approximately 91% (the calculated value is 91.2%).

With reference to FIG. 12, some specific examples will be cited and described. The following efficiency can be seen when the resistance ratio r _nn /R=0.01. When the value of the step-up ratio E _o / E _d is 6, the maximum efficiency value occurs when n = 4, and the value is approximately 90% (the calculated value is 90.3%). When the value of the step-up ratio E _o / E _d is 7, the maximum efficiency value occurs when n = 4, and the value is approximately 90% (the calculated value is 89.6%). When the value of the step-up ratio E _o / E _d is 8, the maximum efficiency value occurs when n = 4, and the value is approximately 89% (the calculated value is 88.8%). The maximum efficiency value when the value of the step-up ratio E _o / E _d is 9 occurs when n = 5, and the value is approximately 88% (the calculated value is 88.2%). The maximum efficiency value when the value of the step-up ratio E _o / E _d is 10 occurs when n = 5, and the value is approximately 88% (the calculated value is 87.8%). Hereinafter, similarly, the maximum efficiency value for each of the values of the step-up ratio E _o / E _d of 10 to 35 can be read from FIGS. 13 to 17.

With reference to FIGS. 18 to 21, some specific examples will be cited and described. The following efficiency can be seen when the resistance ratio r _nn /R=0.005. When the value of the step-up ratio E _o / E _d is 1.5, the maximum efficiency value occurs when n = 1, and the value is approximately 99% (the calculated value is 98.9%). When the value of the step-up ratio E _o / E _d is 3, the maximum efficiency value occurs when n = 3, and the value is approximately 97% (the calculated value is 96.9%). When the value of the step-up ratio E _o / E _d is 6, the maximum efficiency value occurs when n = 4, and the value is approximately 95% (the calculated value is 95.1%). When the value of the step-up ratio E _o / E _d is 10, the maximum efficiency value occurs when n = 5, and the value is approximately 94% (the calculated value is 93.8%). The maximum efficiency value when the value of the step-up ratio E _o / E _d is 20 occurs when n = 6, and the value is approximately 92% (the calculated value is 92.0%).

With reference to FIGS. 22 to 24, some specific examples will be cited and described. The following efficiency can be seen when the resistance ratio r _nn /R=0.005. The maximum efficiency value when the value of the step-up ratio E _o / E _d is 25 occurs when n = 7, and the value is approximately 91% (the calculated value is 91.4%). The maximum efficiency value when the value of the step-up ratio E _o / E _d is 30 occurs when n = 7, and the value is approximately 91% (the calculated value is 91.0%). When the value of the step-up ratio E _o / E _d is 35, the maximum efficiency value occurs when n = 7, and the value is approximately 91% (the calculated value is 91.6%).

For the resistance ratio r _nn /R=0.01, the resistance ratio r _nn /R=0.005, and the resistance ratio r _nn /R=0.001 (not shown in FIGS. 11 to 24), the number of stages with the maximum efficiency Are summarized in Table 1. The leftmost column in Table 1 is the step-up ratio E _o / E _d . The second column is the number of stages n where the efficiency is the best in the resistance ratio r _nn /R=0.01, and the third column is the efficiency in the stages shown in the second column. The fourth column is the number of stages n where the efficiency is the best in the resistance ratio r _nn /R=0.005, and the fifth column is the efficiency in the number of stages shown in the fourth column. The sixth column is the number of stages n where the efficiency is the best in the resistance ratio r _nn /R=0.001, and the seventh column is the efficiency in the stages shown in the sixth column.

As described above, Equation (28) and Equation (29) are obtained by sequentially changing n (integer) using the step-up ratio E _o / E _d and the resistance ratio r _nn / R as parameters. From Equation (42), the step-up ratio E _o / E _d is fixed, n is changed to obtain the corresponding efficiency η _n , and the number n of stages with the highest efficiency can be obtained. However, in this case, it is possible to obtain the result of one row in Table 1 for the first time by repeatedly calculating by changing the value of the number of stages n corresponding to one step-up ratio E _o / E _d. It is. Therefore, as shown in the following formula (43), an extreme value where the result of partial differentiation of the efficiency η _n with respect to the number of stages n is 0, that is, the real number n corresponding to the efficiency η _n with the highest efficiency is directly obtained. You can also. Here, since only an integer is meaningful as the number of stages n, n (real number) obtained by Equation (43) is converted to an integer by rounding down, rounding up, or rounding off, thereby cascading the boost type switching power supply circuit. Find n (integer) which is the number of stages of connections. For example, when 3.3 is obtained as the value of n (real number) obtained by Expression (43), 3 is obtained as the value of n (integer) by rounding down and rounding. Is a desirable number of stages. Further, according to rounding up, 4 is obtained as the value of n (integer), and it can be seen that 4 stages is a desirable number of stages.

∂η _n / ∂n = ∂ [1 / << 1 + <[1- {1−4 × (r _nn / R) × (E _o / E _d ) ^{2 / n} } ^1/2 ] / {2 × (r _nn / R) × (E _o / E _d ) ^{1 / n} }> ² × (r _nn / R) >> ⁿ ] / （ ⁿ = 0 (43)

(Example)
How to use the above-described results shown in FIGS. 11 to 24 and Table 1 will be described with reference to examples.

  FIG. 25 is a block diagram of the power system 1 according to the embodiment. The power system 1 is a system for operating the communication device 17. As the power source, a solar cell 10, a commercial power system 14, and a battery 13 are used. An air conditioner (air conditioner) 18 for cooling these devices is connected to a DC (direct current) 400V (volt) bus line.

  What is obtained from the solar cell 10 is direct-current power whose voltage value changes in the range of DC 70 V to 300 V depending on the amount of sunlight. What is obtained from the battery 13 is DC 48V DC power. What is obtained from the commercial power system 14 is AC (AC) 200V AC power.

Voltage obtained from the solar cell 10 varies from DC70V~300V, but cascaded step-up switching power supply circuit 11 also the input voltage _{E d} is changed within a range of DC70V~300V maintain the output voltage _{E o} to 400V Used. Since it is obtained from the battery 13 is a DC power DC48V, cascaded step-up switching power supply circuit 12 to the input voltage _{E d} is the output voltage _{E o} is 400V at DC48V is used. Although not shown in FIG. 25, a step-down switching power supply circuit for charging the battery 13 is also used between the DC400V bus line and the battery 13. Since the communication device 17 operates at DC 48V, the step-down switching power supply circuit 16 is used between the DC 400V bus line and the communication device 17.

(About the cascaded boost type switching power supply circuit 11)
As the cascade connection boosting switching power supply circuit 11, a cascade connection boosting switching power supply circuit in which a plurality of boosting switching power supply circuits are connected in cascade is used. Here, when the voltage obtained from the solar cell 10 is DC 70 V (volts) and the desired output voltage is 400 V, the step-up ratio E _o / E _d = 400 V / 70 V = 5.7. Therefore, from FIG. 12, FIG. 19, or Table 1, the value of the number n of cascaded connections that maximizes the efficiency is 4. On the other hand, when the voltage obtained from the solar cell 10 is DC300V is because the boost ratio _{E o / E d = 400V /} 300V = 1.3, from 11, 18 or Table 1, the efficiency is maximized The value of the number n of cascade connections is 1. As described above, when the step-up ratio E _o / E _d = 400V / 70V = 5.7, the value of the cascade connection stage number n is set to 4 so that the efficiency is maximized. When E _o / E _d = 400V / 300V = 1.3, the value of the cascade connection stage number n may be set to 1 so that the efficiency is maximized.

Thus, if the input voltage E _d is varied rather than fixed, that is, the number of stages efficiency corresponding to the maximum value of the number of the efficiency corresponding to the minimum value of the input voltage becomes best when the input voltage becomes best is different in this case, from the viewpoint that it is changed according to the value of the number n of the cascade connected to the input voltage E _d it is to maximize efficiency. As how Hereinafter, alters the description if the value of the number n of the cascade connected to the input voltage E _d.

FIG. 26 is a circuit diagram of the cascaded boost type switching power supply circuit 11 that boosts the voltage obtained from the solar cell 10. The switch element control circuit 111 controls the switch element S ₁ , the switch element S ₂ , the switch element S ₃ , and the switch element S ₄ . Moreover, the voltage detection circuit 112 detects the voltage from the solar cell 10, detects the step-up ratio E _o / E _d = 400 V / (value of the voltage from the solar cell 10), and cascades to maximize the efficiency. The value of the connection stage number n is detected. The relationship between the value of the stage number n and the voltage from the solar battery 10 can be easily detected by storing it in advance in a ROM (not shown). Further, the number of stages of cascade connection is the number of stages according to the step-up ratio E _o / E _d = 400V / (minimum value of voltage from the solar cell 10), for example, (minimum value of voltage from the solar cell 10) is 70V. In some cases, a four-stage step-up switching power supply circuit is provided in advance.

For example, a (voltage values from the solar cell 10) is 300 V, the voltage detection circuit 112, when selecting a value of 1 for n stages, the switch element control circuit 111 only switching element S ₁ is switching operation The control is performed so that the switch elements S ₂ to S ₄ are always turned off by performing (on / off operation within a cycle). In this case, since the switching loss of the switching elements S ₂ to S _{4 and} the switching loss of the diodes D ₂ to D ₄ do not occur, the boosting switching power supply circuit of the second stage, the third stage, and the fourth stage The loss at is very small. Therefore, equivalently, only the first step-up switching power supply circuit contributes to boosting, so that 400 V can be obtained as the output voltage E _o as shown in Equation (3). The efficiency at this time is substantially shown by the mathematical formula (2).

Similarly, the voltage detection circuit 112, when selecting 2 as the value of the number n is, for example, switching element control circuit 111 switching element S ₁ and switching element S ₂ is so as to the switching operation, the switch element S ₃ and the switching element S ₄ performs control to always oFF. In this case, the switching loss of the switching element S ₃ and the switching element S _4, the switching loss of the diode D ₃ and the diode D ₄ is not generated, the third stage, the loss in the step-up switching power supply circuit of the fourth stage is very It will be small.

Similarly, the voltage detection circuit 112, when selecting 3 as the value of number n is, for example, switching element control circuit 111 switching element S ₁ and switching element S ₂ and the switching element S ₃ to the switching operation and so, switching element S ₄ performs control to always oFF. In this case, the switching loss of the switching element S _4, the switching loss of the diode D ₄ is not generated, the loss in the step-up switching power supply circuit of the fourth stage is very small.

Similarly, when the voltage detection circuit 112 selects 4 as the value of the number of stages n, the switch element control circuit 111 causes the switch elements S ₁ to S ₄ to perform a switching operation.

Note that when the value of the number n is 1, switching element for switching operation is not limited to the switching element S _1, may be any one of the other switching devices S _{2 ~} switching element S _4. When the value of the stage number n is 2, the number of switch elements to be switched may be any two of the switch elements S ₁ to S ₄ . Further, when the value of the number of stages n is 3, the number of switch elements to be switched may be any three of the switch elements S ₁ to S ₄ .

Here, the output voltage value is controlled as follows. The switch element control circuit 111 detects the output voltage from the output side to which the equivalent load resistance R is connected. Further, the switch element control circuit 111 detects the reference voltage E _Ref . Then, by feedback control, control is performed so that the output voltage value E _o matches the reference voltage E _Ref or the value obtained by dividing the output voltage value E _o matches the value of the reference voltage E _Ref .

When the strict constant voltage characteristic of the output voltage is not required, the switch element control circuit does not use the feedback control, and the switch element control circuit determines the OFF time of each switch element as the known input voltage _Ed and the desired output voltage. The feedforward control may be performed so as to obtain a predetermined fixed value corresponding to the ratio to _Eo, and the output voltage _Eo may be controlled to a desired voltage.

In FIG. 26, the step-up switching power supply circuit in the first stage includes a switch element S ₁ , an inductor L ₄₁ , a diode D ₁ , and a capacitor C ₄₁ . The step-up switching power supply circuit in the second stage includes a switch element S ₁ , an inductor L ₄₂ , a diode D ₁ , and a capacitor C ₄₂ . The step-up switching power supply circuit in the third stage includes a switch element S ₁ , an inductor L ₄₃ , a diode D ₁ , and a capacitor C ₄₃ . The fourth-stage (last stage) step-up switching power supply circuit includes a switch element S ₁ , an inductor L ₄₄ , a diode D ₁ , and a capacitor C ₄₄ .

In short, in the cascade connection boosting type switching power supply circuit 11, the value E _{o of the} output voltage output to the output side of the cascade connection boosting type switching power supply circuit is a constant value, and on the input side of the cascade connection boosting type switching power supply circuit. If the value E _d of the input voltage to be input is a variable value, the minimum value of the input voltage inputted to the input side, it satisfied the equation (28) described above, and the power is expressed by equation (29) Numerical efficiency eta _n is given by an integer n which maximizes or a step-up switching power supply circuit of the number given by the integer n to the value of power efficiency eta _n represented by the formula (42) is maximum n A cascade-connected step-up switching power supply circuit obtained by cascade connection is configured.

When the input voltage E _d is not fixed but changes, the following equation (44) is satisfied according to the value E _{d of the} input voltage input to the input side, and is expressed by the following equation (45). The number given by the integer k that maximizes the value of the power efficiency η _k to be obtained, or the integer obtained from Equation (42) is obtained, and the k switching elements are turned on / off, and (n−k) ) Control is performed to always turn off the individual switch elements.

E _o = (T _s / T _offk ) ^k × E _d × [1 / {1+ (T _s / T _offk ) ² × (r _nn / R)}] ^k (44)
η _k = (T _s / T _offk ) ^k × 1 / {1+ (T _s / T _offk ) ² × (r _nn / R)} ^k (45)

(Cascade connection boost type switching power supply circuit 12)
Next, the cascade connection boosting switching power supply circuit 12 (see FIG. 25) will be described. As the cascaded boosting switching power supply circuit 12 that boosts the voltage obtained from the battery 13, a cascaded boosting switching power supply circuit is used. Here, a constant value of the voltage obtained DC48V from the battery 13, the value of the input voltage E _d is a fixed value. Since the step-up ratio E _o / E _d = 400V / 48V = 8.3, as can be seen from FIG. 12, FIG. 19, or Table 1, the value of the cascade connection stage number n that maximizes the efficiency is 4. .

Therefore, the cascaded boosting switching power supply circuit 12 uses a four-stage cascaded boosting switching power supply circuit similar to the cascaded boosting switching power supply circuit 11 shown in FIG. 26, and all of the switch elements S ₁ to S ₄ . Is controlled to turn on and off in the switching cycle, and the highest efficiency can be obtained to obtain DC400V from DC48V. Here, instead of the solar cell 10 in the cascade connection boosting switching power supply circuit 11, the battery 13 is used in the cascade connection boosting switching power supply circuit 12.

As can be seen from FIGS. 12 and 19, when the step-up ratio E _o / E _d = 400 V / 48 V = 8.3, the value of the number of stages n is 4 even if the value of the number n of cascaded stages is set to 3. Since the reduction in efficiency is only small (within 1%) compared to the case of, the three-stage cascade connection instead of the four-stage cascade boost type switching power supply circuit in order to reduce the circuit scale and reduce the cost of the device A step-up switching power supply circuit can be used.

Further, as shown in Table _1, also vary with r _nn /R=0.01,r _nn /R=0.005,r _{nn /R=0.001,} the value of _{r nn} / R, It can be seen that the value of the number of cascaded stages that provides the best efficiency is not significantly different. Therefore, even if the efficiency of each stage varies at least in the range of the resistance ratio r _nn /R=0.01 to the resistance ratio r _nn /R=0.001, there is no significant difference in the number of stages for maximum efficiency. I understand.

The above-described example is an example of the embodiment, and the same is true even when the values of the output voltage E _o , the input voltage E _d , r _nn / R, and the boost ratio E _o / E _d are different from the example. Applicable within the scope of technical idea. Further, in an actual circuit, it is difficult to strictly match the efficiency of each stage connected in cascade, and variations occur. However, even when the efficiency of each stage varies, the embodiments within the scope of the same technical idea Can be applied.

(Modification of the embodiment)
Various modifications of the embodiment will be described below with reference to FIGS. 27, 28, 29, 30, 30, 31, 32, 33, and 34, and without referring to the drawings.

(First Modification of Embodiment)
FIG. 27 is a diagram showing an embodiment in which the timing for driving switch elements S ₁ to S ₃ in the circuit shown in FIG. 8 is different from that shown in FIG. In FIG. 10, the switch elements S ₁ to S ₃ are driven at the same timing. The switch elements S ₁ to S ₃ shown in FIG. 27 divide the period T _s into n parts, in this case, into three parts, and the phases are sequentially (360/3) ° (degrees) = 120 ° (degrees), Each of the switch elements S ₁ to S ₃ is driven by a shifted signal (a signal in which the timing at which the on state or the off state starts is shifted by a time corresponding to T _s / 3). That is, the switch element S ₁ is driven by the first drive signal (see reference sign S _{1 in} FIG. 27), the switch element S ₂ is driven by the second drive signal (see reference sign S _{2 in} FIG. 27), driving the switching element _{S 3} at a third driving signal (see reference numeral _{S 3} in FIG. 27). By doing in this way, the overlap time when the switch elements S ₁ to S ₃ are simultaneously turned on can be shifted, and the amount of ripple voltage generated at both ends of the equivalent load resistor R can be reduced.

Although the case where the number of stages n is 3 has been described with reference to FIG. 27, in the case of a general n stage, the phase of the on / off timing of each switch is shifted by (360 / n) degrees. By shifting the timing at which the on state or the off state starts by a time corresponding to T _s / n, an effect of reducing the amount of ripple voltage generated at both ends of the equivalent load resistance R can be obtained.

(Second Modification of Embodiment)
FIG. 28 is a diagram showing an embodiment in which the timings for driving the switch elements S ₁ to S ₃ in the circuit shown in FIG. 8 are different from those shown in FIG. 10 and FIG. For each switch element, the on-off state is reversed between the odd-numbered switch element and the even-numbered switch element. That is, when the switch element S1 of the _first boost circuit and the switch element S3 of the _third boost circuit are on, the switch element S2 of the _second boost circuit is turned off. So that it is controlled. As a result, the switch elements in adjacent stages do not turn on at the same time. As a result, the inductance value and capacitance value of each stage can be reduced.

Specifically, when the number n is three stages, as shown in FIG. 28, the switching element S ₁ and switching element S ₃ odd number of stages are driven in phase of the signal (first driving signal), the even switching element S ₂ of the stage phase relative to the signal for driving the switching elements of odd-numbered stage is driven by a 180-degree shift signal (second driving signal). By doing so, it is possible to prevent the overlap time during which the switch elements S ₁ to S ₃ are simultaneously turned on, and the equivalent load resistance R even if the inductance value and capacitance value of each stage are small. It is possible to reduce the amount of ripple voltage generated at both ends of the.

When the number of stages n is 4, for example, in the cascaded step-up switching power supply circuit 11 shown in FIG. 26, not only each of the switch elements S ₁ to S ₄ is driven by the same signal, but also the switch element S ₁ and a second drive signal switching element S ₃ the same signal (first driving signal) 180 degrees out of phase from the first drive signal and a switching element S ₂ and the switching element S ₄ to drive at different It can be driven.

  Referring to FIG. 28, when the number of stages is 3, the case where the number of stages is 4 has been described with reference to FIG. 26. Generally, when the number of stages is n, odd stages ( Drive by shifting the phase of the drive signal of the switch element in the cascade connection order of the odd-numbered stages and the drive signal of the switch element of the even-numbered stages (order of the cascade connection in the even-numbered stages) by 180 degrees Is done. That is, when the boost circuit of the first stage, the third stage,... Is on, the second boost circuit, the fourth stage,. ing.

(Third Modification of Embodiment)
FIG. 29 is a diagram showing not only a cascade connection but also a cascade connection boosting type switching power supply circuit formed by connecting stages of the same configuration in parallel. That is, the cathode of the cathode and the diode _{D 13} of the cathode and the diode _{D 12} of the diode _{D 11} is connected, the cathode of the cathode and the diode _{D 23} of the cathode and the diode _{D 22} of the diode _{D 21} is connected. That is, capacitors of the same stage (C ₃₁₁ and C ₃₁₂ and C ₃₁₃ , C ₃₂₁ and C ₃₂₂ and C ₃₂₃ , C ₃₃₁ , C ₃₃₂ and C ₃₃₃ ) are connected in parallel. In this way, it is possible to increase the power supplied to the equivalent load resistance R according to the number in parallel. Here, each stage of the switching elements connected in parallel (e.g., switching element S ₁₁ and the switch element S ₁₂ and a switching element S ₁₃₎ timing of on and off every one period of the may be the same but, in each stage By making the phase of the ON / OFF timing of the switch elements in the parallel direction different, the amount of ripple voltage generated at both ends of the equivalent load resistor R can be reduced even if the inductance value and capacitance value of each stage are small. it can.

FIG. 30 is a timing chart showing an example in which the on / off timing phases of the switch element S ₁₁ , switch element S ₁₂ , and switch element S ₁₃ (all refer to FIG. 29) are different in each stage connected in parallel. It is a figure shown by. As shown in FIG. 30, the switching elements S ₁₁ to S are divided by a signal obtained by dividing the period T _s into three and sequentially shifting the phase by 120 degrees (signals in which the timing at which the on state or the off state starts is shifted by T _s / 3). driving the respective switching elements S _13. That is, rise timing of on of the switching element S ₁₂ is so delayed 120 ° than rise timing of on of the switching element S _11, rise timing of on of the switching element S ₁₃ is a switch element S ₁₂ on 120 ° behind the start-up timing. By doing so, the amount of ripple voltage generated at both ends of the equivalent load resistance R can be reduced by shifting the overlapping time when the switch elements S ₁₁ to S ₁₃ are simultaneously turned on. Here, the time length off31 switch element _{S 11} is turned off, the time length off32 switch element _{S 12} is turned off, the switching element _{S 11} is the time length off33 made off, is the same time.

The phase of the switch element S ₂₁ , the switch element S ₂₂ , the switch element S ₂₃ group, the switch element S ₃₁ , the switch element S ₃₂ , and the switch element S ₃₃ group is sequentially shifted by 120 degrees in each group. The amount of ripple voltage can be reduced by driving the switch element with the received signal.

  29 and 30, the case where the number of parallel connections is three has been described. Generally, when the number of parallel connections is m, the parallel direction is incremented by (360 / m) degrees. By shifting the phase of the signal that drives each of the switch elements, an effect of reducing the amount of ripple voltage generated across the equivalent load resistor R can be obtained.

  In short, the on / off timing phase of each switch is shifted in the series direction of cascaded boost switching power supply circuits, and the on / off timing of each switch in the parallel direction of boosted switching power supply circuits connected in parallel. By shifting the phase, the power supplied to the equivalent load resistor can be increased, and the amount of ripple voltage can be reduced. That is, the series and parallel connection of the step-up switching power supply circuit can reduce the amount of ripple voltage generated at both ends of the equivalent load resistance even if the inductance value and capacitance value of each stage are small.

(Fourth Modification of Embodiment)
As described above, when attention is paid to the efficiency, it is possible to obtain an appropriate number of cascade connection stages with the highest efficiency based on the formula (29) or the formula (42). However, in terms of the device price of the switching power supply circuit, the smaller the number of stages, the lower the price. Therefore, in consideration of the balance between the efficiency of the cascaded boost type switching power supply circuit and the device price, the cascaded boost type switching is based on the formula (29), formula (46), and formula (47) below. A power supply circuit can also be configured. Here, i is an integer such that i <n, and η _i is the efficiency of the cascaded boost type switching power supply circuit in which the number of cascaded stages is i. The allowable reduction amount ε is an allowable reduction amount of efficiency and is determined in advance. Here, the value of the allowable reduction amount ε of the predetermined efficiency is desirably 1%, and most desirably 0.5%. With such a reduction amount, there is no great difference in the loss amount of each stage, and it does not depart from the purpose of improving the efficiency of the cascaded boost type switching power supply circuit. R _ii is the i-th equivalent loss resistance.

η _n = 1 / {1+ (T _s / T _offn ) ² × (r _nn / R)} ⁿ (29)

η _i = 1 / {1+ (T _s / T _offi ) ² × (r _ii / R)} ⁱ (46)

η _n −η _i <ε (47)

  In other words, the cascade connection switching power supply circuit of the fourth modification example allows n to be reduced in efficiency within a predetermined allowable range while the number of stages of the cascade connection boost type switching power supply circuit that maximizes the efficiency is n. This is an i-stage (i <n) cascaded boost type switching power supply circuit. In this way, the balance between efficiency and price can be optimized.

(Fifth Modification of Embodiment)
In the above-described cascaded step-up switching power supply circuit 11 shown in FIG. 26, all the off times of the switch elements S ₁ to S ₄ are controlled according to the output voltage, but the change of the equivalent load resistance R When the amount of change in T _s / T _offn is small, not all of the switch elements S ₁ to S ₄ are used for voltage control according to the change in the load, but a part of the switches The element can be used for controlling a voltage according to a change in load. Even in this case, it is possible to produce the same operation and effect as in the cascaded boost type switching power supply circuit 11 in which the switch element OFF time is controlled according to the output voltage.

The drive signal shown in FIG. 31 indicates another drive signal for driving the circuit shown in FIG. As shown in FIG. 31, among the _four switch elements S ₁ to S ₄ , three switch elements (for example, switch element S ₁ to switch element S ₃ ) are equivalent load resistance R. It is driven by a drive signal having a fixed width (refer to the reference symbol T _{fix in} FIG. 31) regardless of the fluctuation of. Only the drive signal for driving one switch element (for example, the last-stage switch element S ₄ ) is controlled with a variable width (see the symbol T _{var in} FIG. 31) according to the variation of the equivalent load resistance R. Is. Here, for example, the time T _offn obtained by Expression (29) may be used as the off time T _fix of the fixed width signal, and the off time T _var and length of the variable width signal may be used. A close signal may be appropriately selected.

Such control can be performed by adopting another switch element control circuit (not shown) instead of the switch element control circuit 111 (see FIG. 26). In another switching element control circuit, a drive signal of a fixed width time T _fix (fixed width T _fix ) is generated, and a variable width of the output voltage value E _o is matched with the reference voltage E _Ref by feedback control. A drive signal having a time T _var (variable width T _fix ) is generated. In the drive signal shown in FIG. 31, the phase difference between the odd-numbered stage drive signal and the even-numbered stage drive signal is different by 180 ° (degrees). However, the switch elements S ₁ to S with the same phase signal. ₄ may be driven.

As described above, the combination of the drive signal having the fixed width T _fix as the off time and the drive signal having the variable width T _var as the off time can simplify the configuration of the switch element control circuit. Furthermore, since the order of the control loop characteristics can be reduced, the control characteristics can be stabilized.

(Sixth Modification of Embodiment)
In the first modification of the embodiment, the odd-numbered switch elements are driven by in-phase signals, and the even-numbered switch elements are driven by signals that are 180 degrees out of phase with respect to the signals that drive the odd-numbered switch elements. Thus, the time when the adjacent switch elements are turned on does not overlap. However, when (T _s / T _off ) is 2 or less (such a case may occur when the load becomes extremely large or power supply efficiency is poor), adjacent switch elements There will be a situation in which the time when is turned on overlaps. The sixth modification of the embodiment is effective in such a case.

As described above, in the case of a constant boosting ratio _E o / _{E d is, T off1 <T off2 <T} off3 ····· <T offn ( _{However, T OFFN} off corresponding to n is 4 or more Time). Therefore, considering the balance between the purpose of reducing the inductance value and capacitance value of each stage so that the adjacent switch elements do not overlap each other and the efficiency of the cascaded step-up switching power supply circuit. Thus, the cascaded step-up switching power supply circuit can be configured based on the mathematical formula (28), the mathematical formula (29), the mathematical formula (48), and the following mathematical formula (49). Here, p is an integer such that p> n, and η _p is the efficiency of the cascaded step-up switching power supply circuit in which the number of cascaded stages is p. The allowable reduction amount ε is an allowable reduction amount of efficiency and is determined in advance. Here, the value of the allowable reduction amount ε of the predetermined efficiency is desirably 1%, and most desirably 0.5%. With such a reduction amount, there is no great difference in the loss amount of each stage, and it does not depart from the purpose of improving the efficiency of the cascaded boost type switching power supply circuit. Note that r _pp is the equivalent loss resistance at the p-th stage. In the fourth modification of the embodiment, i <n, whereas in the sixth modification of the embodiment, both are different in that p> n.

_{E o = (T s / T} offn) n × E d × [1 / {1+ (T s / T offn) 2 × (r nn / R)}] n (28)

η _n = 1 / {1+ (T _s / T _offn ) ² × (r _nn / R)} ⁿ (29)

η _p = 1 / {1+ (T _s / T _offp ) ² × (r _pp / R)} ^p (48)

η _n −η _p <ε (49)

That is, in the sixth modification of the embodiment, one end of the inductor, one end of the switch element, and one end of the diode are connected, the other end of the inductor and the other end of the switch element are input, and the other end of the diode is A capacitor is connected between the other end of the switch element, and there are a plurality of step-up switching power supply circuits formed with both ends of the capacitor as the output side. A cascade connection boosting type switching power supply circuit obtained, wherein the output power output to the output side of the last stage of the cascade connection boosting type switching power supply circuit and the input power input to the input side of the cascade connection boosting type switching power supply circuit Is the power efficiency η _n and the resistance value corresponding to the loss of the last boost switching power supply circuit of the cascaded boost switching power supply circuit is r _nn Where R is the value of the equivalent load resistance connected to the output side of the cascaded step-up switching power supply circuit, and Eo is the value of the output voltage output to the output side of the cascaded step-up switching power supply circuit. The value of the input voltage input to the input side of the type switching power supply circuit is E _d, and the allowable reduction amount of the predetermined efficiency given in advance is the allowable reduction amount ε, satisfying Equation (28) and expressed by Equation (29) The number of p-stage cascade connection stages corresponds to a positive number p larger than the integer n _where the value of the power efficiency η _n to be maximized. Then, the difference between the power efficiency eta _p of power efficiency eta _n and p cascaded step-up switching power supply circuit is smaller than the allowable amount of decrease epsilon.

Further, in addition to Equation (29), Equation (48), and Equation (49), in the minimum amount where the magnitude of the equivalent load resistance R is expected (in the maximum amount where the amount of power supplied to the load is expected) It is desirable that the condition of Expression (50) is weighted so that two switch elements in two adjacent stages are not turned on at the same time. In this case, switching element control _circuit monitors the magnitude of _{T s /} T _offp, until _{T s /} T offp> 2 conditions are met, and thus increasing the number of stages p is controlled. Note that the number of cascade connection of the step-up switching power supply circuit is set in advance to p stages or more, and more than the number of switch elements corresponding to the required number of stages are used in an OFF state.

T _s / T _offp > 2 (50)

(Seventh Modification of Embodiment)
FIG. 32 is a diagram showing an embodiment in which the timing for driving the switch element in the circuit shown in FIG. 8 is different from that shown in FIG. 10, FIG. 27, and FIG. FIG. 32 is a diagram illustrating an ON state of switch elements for the (q−1) -stage and the q-stage, which are two adjacent stages, in an arbitrary number of stages in a cascade-connected step-up switching power supply circuit obtained by cascade connection of n stages. It is a figure which shows the timing of turning off.

In Figure 32, (q-1) shows the timing stage of the switching element S _q-1 on and off in the upper, illustrating the timing of on and off of the switching element S _q of q-th stage to the lower stage. In FIG. 32, a switch element control circuit (not shown) detects the OFF timing of the switch element _Sq-1 . Then, the switch element control circuit turns on the switch element S _q after the time T _d has elapsed since the switch element S _q-1 was turned off. In this way, when the switch element of the next stage has a delay characteristic by turning on the switch element of the next stage after a predetermined time _Td has elapsed after the switch element of the adjacent previous stage is turned off In addition, the switch element S _q-1 and the switch element S _q are not simultaneously turned on.

(Eighth Modification of Embodiment)
FIG. 33 and FIG. 34 are diagrams showing a cascaded boost type switching power supply circuit having loads corresponding to a plurality of different voltages. In FIG. 33, the input voltage is E _d , and the output voltage supplied to the load 131 is the cascade connection boost type switching power supply circuit 101 whose output voltage is E _{o1 and} the cascade connection boost type switching power supply circuit where the output voltage supplied to the load 132 is E _o2 102 and a cascaded boost type switching power supply circuit 103 whose output voltage supplied to the load 133 is E _o3 . 34, the input voltage is E _d , the output voltage supplied to the load 131 is a cascade connection boosting switching power supply circuit 201 whose output voltage is E _o1 , and the cascade connection boosting type switching power supply circuit whose output voltage is supplied to the load 132 is E _o2. 202 and a cascade-connected step-up switching power supply circuit 203 whose output voltage supplied to the load 133 is E _o3 . In the circuits shown in FIGS. 33 and 34, the relationship of output voltage E _o1 <output voltage E _o2 <output voltage E _o3 is established. The reference voltage E _Ref1 corresponds to the output voltage E _o1 , the reference voltage E _Ref2 corresponds to the output voltage E _o2 , and the reference voltage E _Ref3 corresponds to the output voltage E _o3 .

In the circuit shown in FIG. 33, the cascaded boost type switching power supply circuit 101 has the maximum number of stages according to the input voltage E _d and the output voltage E _o1 . The number of stages has the maximum efficiency according to the output voltage E _o1 and the output voltage E _o2, and the cascaded step-up switching power supply circuit 103 has the maximum efficiency according to the output voltage E _o2 and the output voltage E _o3. The number of stages becomes.

In the circuit shown in FIG. 34, the cascaded step-up switching power supply circuit 201 has the maximum number of stages according to the input voltage E _d and the output voltage E _o1 . According to the input voltage E _d and the output voltage E _o2 , the number of stages is maximized, and the cascaded boost type switching power supply circuit 203 has the maximum efficiency according to the input voltage E _d and the output voltage E _o3. The number of stages becomes.

  It is naturally possible to adopt a new embodiment in which two or more of the various embodiments described above are combined.

DESCRIPTION OF SYMBOLS 1 Power system, 10 Solar cell, 11, 12, 101, 102, 103, 201, 202, 203 Cascade connection boost type switching power supply circuit, 13 Battery, 14 Commercial power system, 16 Step-down switching power supply circuit, 17 Communication equipment, 18 Air conditioner, 111, 121, 122, 123, 141, 142, 143 Switch element control circuit, 112 Voltage detection circuit, C ₁₁ , C ₂₁ , C ₂₂ , C ₃₁ , C ₃₂ , C ₃₃ , C ₄₁ , C ₄₂ , _{C 43, C 44, C n1} , C n2, C nn capacitor (capacitance _{values), D 1, D 11,} D 12, D 13, D 2, D 21, D 22, D 23, D 3, D 4 _{diodes, E} 1, _E 2, voltage, _{E d} input voltage (input voltage _{value), E o, E o1,} E o2, E o3 output current (Output voltage _{value), E} o / E _d up _{ratio, L 1, L 11, L} 21, L 22, L 31, L 32, L 33, L 41, L 42, L 43, L 44 inductors, R equivalent Load resistance, r ₁₁ , r ₂₁ , r ₂₂ , r ₃₁ , r ₃₂ , r ₃₃ , r ₄₁ , r ₄₂ , r ₄₃ , r ₄₄ , r _nn (loss) resistance, r _nn / R resistance ratio, E _Ref , E _Ref1 , E _Ref2 , E _Ref3 reference voltage, S ₁ , S ₁₁ , S ₁₂ , S ₁₃ , S ₂ , S ₂₁ , S ₂₂ , S ₂₃ , S ₃ , S ₃₁ , S ₃₂ , S ₃₃ , S ₄ switch _{element, T off1, T off2, T} off3, T fix, T var, off time, _{T s} period

Claims (8)

One end of the inductor, one end of the switch element, and one end of the diode are connected, the other end of the inductor and the other end of the switch element are input sides, and the other end of the diode and the other end of the switch element are between A step-up switching power supply circuit formed with both ends of the capacitor as output sides, and having a plurality of step-up switching power supply circuits.
The n-stage boosting switching power supply circuit is connected to the first stage by sequentially connecting the output side of the boosting switching power supply circuit in one stage and the input side of the boosting switching power supply circuit in another stage. Cascade connection from the step-up switching power supply circuit to the n-th step-up switching power supply circuit,
By setting all the switching cycle of the switching elements of the step-up switching power supply circuit in each of the n stages to T _s and all the switching elements off time to T _offn , the first stage The value of the resistance corresponding to the loss of the step-up switching power supply circuit or the value of the resistance corresponding to the loss of the step-up switching power supply circuit in the n-th stage is set to r _nn .
The ratio of the output power output to the output side of the nth step-up switching power supply circuit and the input power input to the input side of the first step-up switching power supply circuit is defined as power efficiency η _n
The value of the equivalent load resistance connected to the output side of the nth step-up switching power supply circuit is R,
The value of the output voltage output to the output side of the nth step-up switching power supply circuit is E _o ,
The value of the input voltage input to the input side of the first step-up switching power supply circuit is E _d ,
A cascade-connected step-up switching power supply circuit that cascade-connects the step-up switching power supply circuits having the number of stages given by an integer n that satisfies the following formula 1 and has the maximum power efficiency η _n represented by the following formula 2.
_{E o = (T s / T} offn) n × E d × [1 / {1+ (T s / T offn) 2 × (r nn / R)}] n ······· Formula 1
η _n = 1 / {1+ (T _s / T _offn ) ² × (r _nn / R)} ^n. The switch element OFF time T _offn is set to a length corresponding to a value E _{o of the} output voltage detected from the output side of the nth step-up switching power supply circuit , and the output voltage is controlled. 2. A cascaded step-up switching power supply circuit according to 1. The value of the output voltage output to the output side of the nth step-up switching power supply circuit is 400 volts,
The value of the input voltage inputted into the input side of the step-up switching power supply circuit of the first stage is 48 volts, the value of the integer n is 3 or 4, according to claim 1 or claim 2 Cascade connection boost type switching power supply circuit. As the value E _o of the output voltage outputted to the output side of the step-up switching power supply circuit of the n-th stage is a constant value, according to claim 2 for controlling the time T _OFFN off of the switching element Cascade connection step-up switching power supply circuit. Wherein n value E _o of the output voltage outputted to the output side of the step-up switching power supply circuit of the stage is a constant value, the input voltage input to the input side of the step-up switching power supply circuit of the first stage When the value _Ed of the variable is a variable value,
In the minimum value E _d of the input voltage inputted to the input side, satisfies the equation 1, the value of the power efficiency eta _n of the above formula 2 is several given by the integer n which maximizes the step-up switching power supply circuit constitutes a cascade step-up switching power supply circuit which is obtained by connecting the n stages in cascade,
Depending on the value E _d of the input voltage inputted into the input side of the step-up switching power supply circuit of the first stage, satisfy the following equation 3, and the maximum value of power efficiency eta _k represented by the following formula 4 Find the number given by the integer k
Wherein said n instead that all the off-time of the switching element and the T _OFFN, time off and on-off control as T _OFFk for the integer k and the same number of k switching elements, ( The cascaded step-up switching power supply circuit according to claim 1, wherein control is performed to always turn off (n−k) (where n> k) switch elements.
E _o = (T _s / T _offk ) ^k × E _d × [1 / {1+ (T _s / T _offk ) ² × (r _nn / R)}] ^k.
η _k = 1 / {1+ (T _s / T _offk ) ² × (r _nn / R)} ^k. 2. The ON / OFF control timing of the odd-numbered switch elements of the n-stage boosting switching power supply circuit and the ON / OFF control timing of the even-numbered switch elements have a phase difference of 180 degrees. The cascaded boost type switching power supply circuit according to claim 5 . Wherein n m-number of step-up switching power supply circuit to the capacitor of each stage of the step-up switching power supply circuit of the stage is formed by parallel connection,
Said having connected in parallel the m of the control timing of the on and off states of the switching elements of the step-up switching power supply circuit (360 / m) degrees by the phase difference, cascaded according to claims 1 to 5 Step-up switching power supply circuit. One end of the inductor, one end of the switch element, and one end of the diode are connected, the other end of the inductor and the other end of the switch element are input sides, and the other end of the diode and the other end of the switch element are between A step-up switching power supply circuit formed with both ends of the capacitor as output sides, and having a plurality of step-up switching power supply circuits.
The n-stage boosting switching power supply circuit is connected to the first stage by sequentially connecting the output side of the boosting switching power supply circuit in one stage and the input side of the boosting switching power supply circuit in another stage. Cascade connection from the step-up switching power supply circuit to the n-th step-up switching power supply circuit,
The step-up boosting power supply circuit of each of the n stages is made equal by repeating all the ON / OFF cycles of the switching elements, and by making all the switching elements OFF times equal to each other. The resistance value corresponding to the loss of the switching power supply circuit of the type or the resistance value corresponding to the loss of the boosting switching power supply circuit of the n-th stage are all represented as r _nn .
The ratio of the output power output to the output side of the nth step-up switching power supply circuit and the input power input to the input side of the first step-up switching power supply circuit is defined as power efficiency η _n
The value of the equivalent load resistance connected to the output side of the nth step-up switching power supply circuit is R,
The value of the output voltage output to the output side of the nth step-up switching power supply circuit is E _o ,
The value of the input voltage input to the input side of the first step-up switching power supply circuit is E _d ,
A real number _n that maximizes power efficiency η _n that satisfies the following formula 5 is obtained, and the real number n is rounded down, rounded up, or rounded up or rounded up, and the number of stages of the step-up switching power supply circuit equal to the integer value obtained is cascaded. Cascade connection boost type switching power supply circuit.
∂η _n / ∂n = ∂ [1 / << 1 + <[1- {1−4 × (r _nn / R) × (E _o / E _d ) ^{2 / n} } ^1/2 ] / {2 × (r _nn / R) × (E _o / E _d ) ^{1 / n} }> ² × (r _nn / R) >> ⁿ ] / ∂n = 0.

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