CN112699627B - Method for improving Ton/Toff circuit architecture by continuous function compensation method - Google Patents
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Abstract
The invention relates to a method for improving a Ton/Toff circuit architecture by a continuous function compensation method, which takes key element parameters or related system design variables thereof as input variables, generates compensation quantity by using a continuous function meeting specific conditions and compensates upper and lower limit thresholds. The principle of the circuit architecture is as follows: a compensation quantity theta related to an element parameter x is introduced for delta, and a relation between theta and x is used for compensating a function theta (x) to meet specific requirements. The method takes key element parameters or related system design variables thereof as input variables, generates compensation quantities by using continuous functions meeting specific conditions, and compensates upper and lower limit thresholds, so that the contradiction can be relieved by properly sacrificing ripple characteristics only by increasing extremely low cost, and good ripple characteristics can be kept when the contradiction is not sharp, thereby widening the application range of a product and providing possibility for specific optimization design of a scheme.
Description
Technical Field
The invention relates to the technical field of electronic circuits and integrated circuits, in particular to a method for improving a Ton/Toff circuit architecture by a continuous function compensation method.
Background
The working principle of Ton/Toff circuit architecture is shown in the attached figure 1: the target parameter has an equivalent relation with a certain parameter in the system, and the parameter in the system is respectively increased linearly and decreased linearly by switching the on and off states of a power switch in the system, so that only a lower limit threshold VL and an upper limit threshold VH need to be set for the parameter, when the parameter reaches VL, the switch is switched to the on state, and the parameter starts to rise linearly; when the parameter reaches VH, the switch is switched to off state, and the parameter starts to decrease linearly, so that the cycle is repeated, and the average value Va of the parameter is equal to (VH + VL)/2, that is, the parameter only needs to be selected as the control parameter, and the desired target parameter can be obtained by setting VH and VL thereof.
The duty cycle T of this circuit architecture depends on the sum of the time (Ton) for the control parameter to rise from VL to VH and the time (Toff) for the control parameter to fall from VH to VL, hence this architecture is referred to as Ton/Toff architecture. While the duty cycle of other architectures is determined in other ways. The Ton/Toff architecture is not only simple in circuit implementation, but also has some advantages that other architectures do not have, and therefore becomes the preferred architecture in some applications.
Let Δ be the difference between the upper and lower limits, for the Ton/Toff architecture, the equation holds: VH-Va | VL-Va | - Δ/2, and Δ/2 represents the maximum degree to which the parameter deviates from the average, characterizing the ripple characteristics of the parameter.
Since the parameters vary linearly during on, off, the time required for the change is determined entirely by the rising slope sr, the absolute value of the falling slope sf:
Ton＝Δ/sr (1)；
Toff＝Δ/sf (2)；
T＝Ton+Toff＝Δ/sr+Δ/sf (3)；
f＝1/T＝(sr+sf)/Δ (4)；
wherein T is the switching period of the system, and f is the switching frequency of the system.
The rising and falling slopes sr and sf of Ton/Toff are necessarily related to the parameter values of a certain key element in the system, so that a designer can design a scheme of the system. Taking a common voltage boosting constant current output Ton/Toff practical application circuit using an inductor as an energy storage unit as an example, the target parameter is an average output current, the controlled parameter is an inductor current, and the parameter of an element determining a change slope of the inductor current is an inductance.
Suppose that the parameter x of a certain element a in the system determines the absolute value of the rise and fall slope of the controlled parameter:
sr＝sr(x) (5)；
sf＝sf(x) (6)；
note that in practical applications, the condition of x >0 is always satisfied, i.e., the element parameter does not take a negative value or 0. To obtain stability, sr (x) and | sf (x) | must both be strictly monotonic functions of x, i.e., dsr/dx, dsf/dx are either constantly positive or constantly negative. The practically optional elements sr (x) and sf (x) must have the same monotonicity, and if the rising slope increases with increasing x, the absolute value of the falling slope also increases with increasing x. Further, there is a simple correspondence between sf (x) and sr (x):
sf (x) ═ sr (x), where k >0 (7);
this has the following:
f(x)＝(1+k)sr(x)/Δ (8)；
df/dx＝(1+k)dsr/dx/Δ (9)；
since k >0, dsr/dx is always positive or negative, and Δ is a constant, the frequency f is also a monotonic function of the element parameter x.
The switching frequency f of the system determines the switching loss of the system, affects the working efficiency and heating of the system, and cannot be too high, so that a limiting condition is provided for the value of the element parameter x. The contradiction between the switching frequency f and the element parameter x sometimes becomes a major design challenge for the Ton/Toff circuit architecture.
Taking a very common voltage boosting constant current output Ton/Toff practical application circuit using an inductor as an energy storage unit as an example, the rising and falling slope of the inductor current is an inverse function of the inductance: sr is α/L, sf is β/L, where α and β are constants determined only by operating conditions of input, output, and the like of the system, and L is an inductance.
Therefore, f is (α + β)/L/Δ, i.e. the system switching frequency f is in inverse proportion to the inductance L, and if the switching frequency is decreased (thereby decreasing the switching loss and heat generation of the system), the inductance can only be increased, but a larger inductance not only means an increase in the procurement cost of components, but also means that the physical size and height of the inductor have to be increased in order to make the dc on-resistance and the rated current index of the inductor meet the requirements, which increases the PCB area and product height of the final product, and is not feasible in applications (such as LED lamp heads and the like) where the system size and space height are very limited. However, if the inductance is not increased, the system has to operate at a higher switching frequency, which may cause severe switching loss and heat generation, and thus, such a product with a narrow space faces a severe heat dissipation challenge.
Although increasing the upper and lower limit values Δ can alleviate the above-mentioned contradiction, the ripple characteristics (the difference between the highest value and the lowest value and the average value) of the control parameters become worse. Therefore, when the contradiction between element selection and switch heating is not sharp, the obtained ripple characteristic of the same product is poor, and the same product cannot be applied to application occasions with high ripple characteristic requirements, so that the application range of the product is limited.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method for improving a Ton/Toff circuit architecture by a continuous function compensation method, which can effectively relieve the contradiction between the switching loss and heating of a system and the parameter value of a key element on one hand, and relieve the contradiction by sacrificing some ripple characteristics when the contradiction is not harmonious; and on the other hand, the realization capability of design optimization is provided, when the acceptable value range of the key element parameters is wider, the optimized selection can be performed between the system conversion efficiency and the target parameter ripple characteristics, and the defects of the prior art are effectively overcome.
The above object of the present invention is achieved by the following technical solutions:
a method for improving the structure of Ton/Toff circuit by continuous function compensation method, using key element parameter or its related system design variable as input variable, using continuous function meeting specific condition to generate compensation quantity, compensating the upper and lower threshold values;
the circuit architecture principle is as follows: introducing a compensation quantity theta related to an element parameter x for delta, wherein the relation between theta and x is a compensation function theta (x) meeting specific requirements;
if f and x are monotonically increasing, i.e., for any x >0, df (x)/dx >0, the compensation function θ (x) only needs to satisfy the following three conditions in the region of x >0 at the same time:
(4) θ (x) is a continuous function, i.e., θ (x) is everywhere derivable;
(5) theta (x) is a strictly monotonically increasing function, i.e., d theta/dx >0 is constant for x > 0;
(6) the compensation intensity cannot change the monotonic polarity of f (x), i.e., the compensated df/dx is still constant > 0; recording the difference between the compensated upper limit and lower limit as:
Δ’＝Δ+θ(x) (10)；
then there are:
f(x)＝(1+k)sr/Δ’＝(1+k)sr/[Δ+θ(x)] (11)；
thereby:
df/dx＝(1+k)dsr/dx/[Δ+θ(x)]-(1+k)sr(x)*dθ/dx/[Δ+θ(x)]2 (12)；
for any x >0, there is dsr/dx >0 and d θ/dx >0, and the df/dx after the compensation is still positive, so the | df/dx | after the compensation is necessarily smaller than before the compensation, which means that the system switching frequency f is slowed down with the change rate of the element parameter x, and the conflict between f and x is alleviated.
The present invention in a preferred example may be further configured to: if f and x are monotonically decreasing, only the requirement of the compensation function needs to be modified to the following three:
(1) θ (x) is a continuous function, i.e., θ (x) is everywhere derivable;
(2) θ (x) is a strictly monotonic function whose monotonic polarity is the same as f (x);
(3) the compensation intensity cannot change the monotonic polarity of f (x).
The present invention in a preferred example may be further configured to: taking the rising slope sr as an argument, according to the aforementioned equation:
Δ’＝Δ+θ(sr) (13)；
f(sr)＝(1+k)sr/[Δ+θ(sr)] (14)；
df/dsr＝(1+k)/[Δ+θ(sr)]-(1+k)sr*dθ/dsr/[Δ+θ(sr)]2 (15)；
they are equivalent to the expression with x as an argument.
The present invention in a preferred example may be further configured to: the continuous functions used for compensation purposes further comprise linear functions, exponential functions and logarithmic functions, and the linear functions, the exponential functions and the logarithmic functions all take the sr as an argument.
In summary, the invention includes at least one of the following beneficial technical effects:
1. the circuit is simple to realize, and only little cost needs to be added.
2. The method can effectively relieve the contradiction between the switching loss and heating of the system and the parameter value of the key element, and when the contradiction is not reconciled, the contradiction is relieved by sacrificing some ripple characteristics.
3. The realization capability of design optimization is provided, and when the acceptable value range of the key element parameters is wide, the optimized selection can be carried out between the system conversion efficiency and the target parameter ripple characteristics.
Drawings
FIG. 1 is a diagram illustrating the operation of a conventional Ton/Toff circuit architecture.
FIG. 2 is a diagram of the linear compensation function of the present invention.
FIG. 3 is a graph of a linear function of the rising slope generated by the integration circuit of the present invention with a fixed time.
FIG. 4 is a graph of the exponential compensation function of the present invention.
FIG. 5 is a graph of the log-offset function of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention discloses a method for improving a Ton/Toff circuit architecture by a continuous function compensation method, which takes key element parameters or related system design variables thereof as input variables, generates compensation quantity by using a continuous function meeting specific conditions, and compensates upper and lower limit thresholds;
the principle of the circuit architecture is as follows: introducing a compensation quantity theta related to an element parameter x for delta, wherein a relation between theta and x is a compensation function theta (x) meeting specific requirements;
if f and x are monotonically increasing, i.e., for any x >0, df (x)/dx >0, the compensation function θ (x) only needs to satisfy the following three conditions in the region of x >0 at the same time:
(7) θ (x) is a continuous function, i.e., θ (x) is everywhere derivable;
(8) theta (x) is a strictly monotonically increasing function, i.e., d theta/dx >0 is constant for x > 0;
(9) the compensation intensity cannot change the monotonic polarity of f (x), i.e., the compensated df/dx is still constant > 0; recording the difference between the compensated upper limit and lower limit as:
Δ’＝Δ+θ(x) (10)；
then there are:
f(x)＝(1+k)sr/Δ’＝(1+k)sr/[Δ+θ(x)] (11)；
thereby:
df/dx＝(1+k)dsr/dx/[Δ+θ(x)]-(1+k)sr(x)*dθ/dx/[Δ+θ(x)]2 (12)；
for any x >0, there is dsr/dx >0 and d θ/dx >0, and the df/dx after the compensation is still positive, so the | df/dx | after the compensation is necessarily smaller than before the compensation, which means that the system switching frequency f is slowed down with the change rate of the element parameter x, and the conflict between f and x is alleviated.
If f and x are in a monotone decreasing relation, only the requirement of the compensation function needs to be modified into the following three:
(4) θ (x) is a continuous function, i.e., θ (x) is everywhere derivable;
(5) θ (x) is a strictly monotonic function whose monotonic polarity is the same as f (x);
(6) the compensation intensity cannot change the monotonic polarity of f (x).
The rising slope sr is used as an independent variable, so that the analysis is more intuitive, and a compensation function is more convenient to find. According to the preceding equations:
Δ’＝Δ+θ(sr) (13)；
f(sr)＝(1+k)sr/[Δ+θ(sr)] (14)；
df/dsr＝(1+k)/[Δ+θ(sr)]-(1+k)sr*dθ/dsr/[Δ+θ(sr)]2 (15)；
they are equivalent to the expression with x as an argument.
The continuous functions used for compensation purposes also include linear functions, exponential functions and logarithmic functions, all of which take sr as an argument.
(1) Linear function:
the compensation signal θ and the rising slope sr are in a linear relationship, as shown in fig. 2, the function can be expressed as:
θ(sr)＝m*sr+b (16)；
where m >0, b is arbitrarily taken, but is usually 0. Assuming that b is 0, substituting equation (16) into equations (14) and (15) above, we can obtain:
f(sr)＝(1+k)sr/[Δ+m*sr] (17)；
df/dsr＝(1+k)/[Δ+m*sr]-(1+k)m*sr/[Δ+m*sr]2＝(1+k)Δ/[Δ+m*sr]2 (18)；
it is readily demonstrated that formula (18) is constantly less than the uncompensated df/dsr ═ 1+ k)/Δ.
The circuit generation of linear functions is many, for example, as shown in FIG. 3, using a fixed time T0(T0<An integrating circuit of ton (min)) integrates the inductor current il (T), so that y (sr) ═ T can be obtained0Sr. The output v of the integrator is a linear function of slope, and the simplest circuit to produce a fixed-time integrator is the R-C integrator, whose integration time T is0＝RC。
(2) Exponential function:
the compensation signal θ is exponentially related to the slope of the rise and fall, and as shown in fig. 4, the function can be expressed as:
θ(sr)＝k*esr (19)；
wherein k > 0. The exponential compensation can be realized by an exponential amplifier, the sr information can be taken out by the integrating circuit, and then the sr information is processed by the exponential amplifier, and details are not described again in the present invention.
(3) Logarithmic function:
the compensation signal θ is logarithmically related to the slope of the rise and fall, and as shown in fig. 5, the function can be expressed as:
θ(sr)＝k*ln(sr) (20)；
wherein k > 0. The logarithmic compensation can be realized by a logarithmic amplifier, sr information can be taken out by an integrating circuit and then processed by the logarithmic amplifier, and details are not described in the invention.
The implementation principle of the embodiment is as follows: the invention is a Ton/Tof circuit architecture which takes key element parameters or related system design variables thereof as input variables, generates compensation quantities by using continuous functions meeting specific conditions and compensates upper and lower limit thresholds, can relieve the contradiction by properly sacrificing ripple characteristics only by increasing extremely low cost, and can keep good ripple characteristics when the contradiction is not sharp, thereby widening the application range of a product and providing possibility for specific optimization design of a scheme.
An improved Ton/Toff circuit structure for compensating upper and lower threshold values by using compensation quantity generated by key element parameters or related system design variables is characterized in that the compensation function is a continuous function of the key element parameters or related system design variables.
On one hand, the contradiction between the system switching loss and heating and the value of key element parameters can be effectively relieved, and when the contradiction is not reconciled, the contradiction is relieved by sacrificing some ripple characteristics; and on the other hand, the realization capability of design optimization is provided, when the acceptable value range of the key element parameters is wider, the optimized selection can be performed between the system conversion efficiency and the target parameter ripple characteristics, and the defects of the prior art are effectively overcome.
The embodiments of the present invention are preferred embodiments of the present invention, and the scope of the present invention is not limited by these embodiments, so: all equivalent changes made according to the structure, shape and principle of the invention are covered by the protection scope of the invention.
Claims (4)
1. A method for improving the structure of Ton/Toff circuit by continuous function compensation method is characterized in that: taking key element parameters or related system design variables thereof as input variables, generating compensation quantities by using continuous functions meeting specific conditions, and compensating upper and lower limit thresholds;
the circuit architecture principle is as follows: Δ — VH-VL is the difference between the upper and lower limits;
since the parameters vary linearly during on, off, the time required for the change is determined entirely by the rising slope sr, the absolute value of the falling slope sf:
Ton＝Δ/sr (1)；
Toff＝Δ/sf (2)；
T＝Ton+Toff＝Δ/sr+Δ/sf (3)；
f＝1/T＝(sr+sf)/Δ (4)；
wherein T is the switching period of the system, and f is the switching frequency of the system;
further, there is a simple correspondence between sf (x) and sr (x):
sf (x) ═ sr (x), where k >0 (7);
this has the following:
f(x)＝(1+k)sr(x)/Δ (8)；
df/dx＝(1+k)dsr/dx/Δ (9)；
since k >0, dsr/dx is constantly positive or negative, Δ is a constant that is constant, the frequency f is also a monotonic function of the element parameter x;
introducing a compensation quantity theta related to an element parameter x for delta, wherein the relation between theta and x is a compensation function theta (x) meeting specific requirements;
if f and x are monotonically increasing, i.e., for any x >0, df (x)/dx >0, the compensation function θ (x) only needs to satisfy the following three conditions in the region of x >0 at the same time:
(1) θ (x) is a continuous function, i.e., θ (x) is everywhere derivable;
(2) theta (x) is a strictly monotonically increasing function, i.e., d theta/dx >0 is constant for x > 0;
(3) the compensation intensity cannot change the monotonic polarity of f (x), i.e., the compensated df/dx is still constant > 0;
recording the difference between the compensated upper limit and lower limit as:
Δ’＝Δ+θ(x) (10)；
then there are:
f(x)＝(1+k)sr/Δ’＝(1+k)sr/[Δ+θ(x)] (11)；
thereby:
df/dx＝(1+k)dsr/dx/[Δ+θ(x)]-(1+k)sr(x)*dθ/dx/[Δ+θ(x)]2(12)；
for any x >0, there is dsr/dx >0 and d θ/dx >0, and the df/dx after the compensation is still positive, so the | df/dx | after the compensation is necessarily smaller than before the compensation, which means that the system switching frequency f is slowed down with the change rate of the element parameter x, and the conflict between f and x is alleviated.
2. The method of claim 1, wherein the method comprises the steps of: if f and x are monotonically decreasing, only the requirement of the compensation function needs to be modified to the following three:
(1) θ (x) is a continuous function, i.e., θ (x) is everywhere derivable;
(2) θ (x) is a strictly monotonic function whose monotonic polarity is the same as f (x);
(3) the compensation intensity cannot change the monotonic polarity of f (x).
3. The method of claim 2, wherein the method comprises the steps of: taking the rising slope sr as an argument, according to the aforementioned equation:
Δ’＝Δ+θ(sr) (13)；
f(sr)＝(1+k)sr/[Δ+θ(sr)] (14)；
df/dsr＝(1+k)/[Δ+θ(sr)]-(1+k)sr*dθ/dsr/[Δ+θ(sr)]2(15)；
they are equivalent to the expression with x as an argument.
4. The method of claim 3, wherein the method further comprises the steps of: the continuous functions used for compensation purposes further comprise linear functions, exponential functions and logarithmic functions, and the linear functions, the exponential functions and the logarithmic functions all take the sr as an argument.
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| CN1271473A (en) * | 1997-08-11 | 2000-10-25 | 系统通用公司 | Adaptative slope compensator for current mode power converter |
| JP2008067533A (en) * | 2006-09-08 | 2008-03-21 | Sony Corp | Switching power supply circuit |
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