JPS628967B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a lossless floating inductance circuit used in an active RC filter.

Recently, active RC filters using IC amplifiers have become widely used in place of LC filters and mechanical filters.

Along with this, for example, low-sensitivity double-terminated passive LC
Various so-called direct simulation configuration methods have been considered in which the L portion of the ladder circuit is replaced with an equivalent inductance circuit realized by active elements and RC elements.

However, many of the conventional methods that employ these methods require a large number of operational amplifiers, resulting in high consumption.
It had disadvantages in terms of power and price.

Therefore, it is an object of the present invention to provide a lossless floating inductance circuit that can reduce power consumption and cost by minimizing the number of operational amplifiers and capacitors used.

By the way, first, the principle of this invention will be explained using a two-port circuit shown in FIG. That is, in the two-port circuit shown in the figure, 1-1' and 2-2' are the input and output ports, respectively, and V ₃ , V ₄ , ......Vn are the standards of nodes 3, 4 ......n in circuit N. This is the voltage from the ground point. Here, circuit N consists of several VCVS with differential input, single-ended output, and infinite gain.
(Voltage-Controlled Voltage Sources) and passive elements floating from the ground point.

According to such a configuration, the voltage Vj at any node can be expressed as follows.

Also, from Hilberman's theorem, holds true. On the other hand, if we apply the nodal equation to nodes 1 and 2, is obtained. Because there are no elements directly connected to the ground point at nodes 1 and 2. becomes. Therefore, by substituting equations (1), (2), and (4) into equation (3), we get is obtained. Therefore, [Y] of the two-port circuit in Figure 1
queue If expressed as follows, it can be seen that the following relationships hold: Y ₁₂ = −Y ₁₁ , Y ₂₁ = −Y ₂₂ (7).

An embodiment of the present invention that satisfies this principle will be described with reference to FIG.

In Figure 2, T ₁ is one terminal, and this terminal
T ₁ is connected to the inverting input terminal of the first operational amplifier OP ₁ via a conductance G 1 and to the non-inverting input terminal of the same amplifier OP ₁ via _a conductance G ₄ . This operational amplifier OP ₁ has a series circuit of a capacitor C and a conductance G ₂ connected between the inverting input terminal and the output terminal, and the non-inverting input terminal is connected to the other terminal T ₂ via the conductance G ₄ . There is. Further, this operational amplifier OP ₁ has an output terminal connected to the one terminal T ₁ via a conductance G ₆ and a second terminal via a conductance hG ₇ .
Connect to the inverting input terminal of operational amplifier OP ₂ . This amplifier OP ₂ converts the inverting input terminal into a conductance
Connect to the other terminal T ₂ via G ₇ and G ₉ , and connect the non-inverting input terminal to the capacitor C and conductance.
It is connected to the common connection point of _G2 and also to the terminal _T2 via conductance _G3 . Further, this operational amplifier OP ₂ has its output terminal connected to the common connection point of the conductances G ₇ and G ₉ .

However, in such a circuit, now the terminal
When the voltages of T ₁ and T ₂ are respectively V ₁ and V ₂ , the voltage at any node, that is, the input voltage V of the operational amplifier OP ₁ ,
Output side voltage V ₀ , output side voltage of operational amplifier OP ₂
V ₀ ' and the voltage V ₅ at the common connection point of the capacitor C and the conductance G ₂ can be respectively derived from the above-mentioned Hilberman's theorem as shown below.

Here, t ₁ =1/2+h/2・G ₁ −G ₃ /2+(hG ₃ /G ₂
-1) G ₁ /2sC 〓〓〓〓
_t2 =1/2(1+ _G3 / _G2 - _G1 / _G2 )-1/2(
1+G ₃ /G ₂ )G ₁ /sC t ₃ =1/2−G ₁ /2sC Therefore, the 2-port [Y] determinant of the circuit shown in FIG. 2 satisfies the above-mentioned equation (7). From equations (8) and (9), it can be derived as follows.

However, h is a positive constant.

Here, to make the circuit in Figure 2 a lossless floating inductance, in equations (10) and (10'), if the desired inductance is Leq, then Y ₁₁ = -Y ₁₂ = Y ₂₂ It is necessary to set =-Y ₂₁ =1/sLeq(11).

By the way, in equation (10), the sum of the first three terms must be zero, and the term multiplied by 1/sC must be equal to 1/sLeq.

The same holds true for equation (10').

Here, let Leq=C/mG ² (11)′. However, m is a positive constant and G is a constant having the dimension of conductance, which can be freely selected as long as it satisfies (11').

Therefore, from equations (10), (10′), (11), and (11′), is obtained, which allows m, h, G ₁ , G ₂ ,
By determining G ₃ , G ₄ , G ₆ , G ₇ , G _{9 ,} etc., a lossless floating inductance can be formed. That is, if the value of C is determined, the value of mG ² is determined from equation (11'), so the number of constants to be determined is the above nine, and since there are four conditional expressions in equation (12), there are nine constants. Five of the constants can be arbitrarily determined.
As an example, if we calculate a specific value while taking the circuit's dynamic range into consideration, we will obtain the following value.

m=1, G ₁ = G ₂ = G ₄ = G/2 G ₃ = 3 G/2 G ₆ = G ₇ = G h = 7/10 G ₉ = 5 G Therefore, according to such a floating inductance circuit, each conductance and constant h
A lossless floating inductance can be obtained by setting .
Further, in this case, the circuit can be reduced to the minimum number of parts, consisting of only two operational amplifiers and one capacitor, so that the power consumption can be reduced accordingly, and the cost can also be reduced. Additionally, experiments have shown that the dynamic range of this circuit is approximately 1.5 times larger than that of other circuits.

As described above, according to the present invention, it is possible to reduce power consumption and cost by minimizing the number of operational amplifiers and capacitors, and to provide a lossless floating inductance circuit.

[Brief explanation of the drawing]

FIG. 1 is an explanatory diagram for explaining the principle of the invention, and FIG. 2 is a circuit diagram showing an embodiment of the invention. 〓〓〓〓
G ₁ , G ₂ , G ₃ , G ₄ , G ₆ , G ₇ , G ₉ ... conductance, OP ₁ , OP ₂ ... operational amplifier, C ... capacitor. 〓〓〓〓

Claims (1)

[Claims] 1. One terminal _T1 is connected to the inverting input terminal of the first operational amplifier via conductance _G1 and to the non-inverting input terminal of the first operational amplifier via conductance _G4 . A series circuit of a capacitor C and a conductance G ₂ is connected between the inverting input terminal and the output terminal of this first operational amplifier, and the non-inverting input terminal is connected to the other terminal T ₂ through the conductance G ₄ .
and connect the output terminal of this first operational amplifier to the above one terminal T ₁ via conductance G ₆
and the inverting input terminal of the second operational amplifier through conductance hG ₇ , and the inverting input terminal of the second operational amplifier is connected to the other one through conductance G ₇ and G ₉ . Connect to terminal T ₂ ,
The non-inverting input terminal is connected to the common connection point of the capacitor C and the conductance _G2 , and is also connected to the other terminal _T2 through the conductance _G3 , and the output terminal of this second operational amplifier is connected to the above-mentioned terminal. It is connected to the common connection point of conductances G ₇ and G ₉ , and each of the above conductances G ₁ , G ₂ , G ₃ , G ₄ ,
G ₆ , G ₇ , G ₉ are G ₁ + G ₄ + (1 + G ₁ / G ₂ ) G ₆ = G ₃ / G ₂ G ₆ 1/2 (1 + G ₃ / G ₂ ) G ₁ G ₆ = mG ² G ₃ +G ₄ +(1+hG ₁ /G ₂ )G ₉ =hG ₃ /G ₂ G ₉ [(hG ₃ /G ₂ −1)G ₉ −G ₃ ]G ₁ /2=mG ² (however, h and m is a positive constant G is a constant having the dimension of conductance) A floating inductance circuit characterized by satisfying the above relationship.