DE2317644B2 - Circuit arrangement for the representation of a large number of transfer functions of quadrupoles by active RC filters provided with two operational amplifiers - Google Patents

Description

State of the art

In the course of the increasing spatial densification of electrical circuit arrangements, it will always be more difficult to accommodate passive filters equipped with coils and capacitors. Especially in circuits For low frequencies it is therefore desirable to largely replace coil filters with RC filters. For low requirements, passive RC filters with no significant difficulties are sufficient for this prepare.

To meet higher requirements, it is known to use low-pass filters (DT-AS 12 23 075). Resonance filter (DT-AS 12 62 466), all passes (DT-AS 19 58 140) and optionally high or low passes (DT-AS 16 16 412) as to display active RC filters. The German Offenlegungsschrift 19 54 543 also has a Circuit arrangement in RC technology as known after, which is used to implement all of the above-mentioned types of filters suitable is.

Another circuit of this type with two op-amps is in the IEEE Spectrum magazine. January 1969, p. 56 (Fig. 19) and 57 described and illustrated.

From the Literaturstcllc in Electronics Letters, June 1972, Vol. 8. No. 11, p. 288 (Fig. 1 c) and 289 an arrangement with three operational amplifiers is known in which the inverting inputs are connected to one another and the outputs are connected via Real or capacitive conductance values are connected to the inputs of the respective following operational amplifier, the output of the last operational amplifier being connected to the input circuit of the first operational amplifier.

These and other known active RC networks have a tendency to and have some self-excitation the serious disadvantage of the low temporal constancy of a transfer function set once. The dependence of the same on the temperature, the operating voltages and the aging of the active and passive components have so far caused considerable difficulties and required additional ones technical effort that was not reflected in the structure of the filter itself.

The already mentioned circuit arrangement according to German patent application 19 54 543 is for Representation of some filter types is very complex and leaves only the compromises in the dimensioning to that an increase in the resonance quality a decrease in the constancy and an improvement in the Constancy causes a reduction in the quality of the resonance

task

The invention is based on the object a circuit arrangement with a minimum expenditure of components for active RC filters that are suitable for representing a large number of transfer functions and that have a high degree of temporal constancy same guaranteed. This object is achieved by the invention specified in claim I.

advantages

In the circuit arrangement according to the invention, the influence of the 'gain factor and the Transit frequency of the two operational amplifiers to the resonance frequencies and the bandwidths of the Filters vanishingly small. The stability of the resonance frequencies and the bandwidths is essential only given by the constancy of the RC elements. Therefore the constancy is the one after this Circuitry built-up filter without additional stabilization measures as well as with passive LC filters, and it becomes possible to achieve high slopes by being close to the band limits to achieve lying poles.

When dimensioning the filters, as in Electronics Letters. June 1972. Fig. Ic. shown Arrangement the capacitance values free, z. B. from a standard series, be selected and be of the same size. Changes in resistance and capacitance values for setting damping poles have no effect Influence on their resonance sharpness. In addition, the adjustment of the resonance frequencies, the bandwidths and possibly the attenuation pole frequencies in the finished filter simply by changing the resistance values possible. This simplifies the structure in monolithic and hybrid integration technology.

As from the following exemplary embodiments As can be seen, the structure of the circuit arrangement is the same for all filter types. To convert to a other Filtcrart only an exchange of guide values is necessary, whereby it can also happen that one or more conductance values with the value zero no longer appear as a component. This is it is possible to produce the basic structure using integrated technology and your respective filter type accordingly to sound.

Since the output impedance of the circuit arrangement is a good approximation equal to zero, is as in other known active RC filters, the use of the Stufentcchn.k is possible.

Explanation of exemplary embodiments of the inventive scarf

_wn g _S9 arrangement are based on the F i g. 1 to 8

purifies. It shows
pig. I the basic principle of the invention

Circuit arrangement,

ρ j g. 2 the execution example of a low pass,
pig. 3 the transfer function of the low pass

according to F i g · 2 and the representation of the pole in FIG

complex plane,

F i g. 4 shows the embodiment of a bandpass filter, FIG. 5 the embodiment of a high pass, 6 shows the embodiment of a band pass

with a positive-real zero,

the establishment of F i g. 7 the embodiment of an all-pass,
F i g. 8 the exemplary embodiment of a low-pass filter with s damping pole,

In the basic circuit diagram according to FIG. 1, two operational amplifiers V ₁ and V ₁ , each with an inverting and a non-inverting input, are connected to one another via a network which contains the conductance values Y ₁ "to Y _6h . The input variable is specified _{with U 0} and the output variable with U _1. Assuming ideal operational amplifiers, the voltage transfer function of the circuit arrangement is a function of the complex frequency s

FlS) = A =

_W obei Y ₁ = Yia ^Y +> b and Y ₆ = Y + _ba Y is _OH.

To represent certain filter types, real ty = G), capacitive (Y = sC) or parallel connections of geeller and capacitive conductance values (Y ^ G ^ sC) can be used instead of the general complex conductance values.

The network of the low pass according to FIG. 2 contains the conductance values Y _la = G ₁ , Y _n , = 0, Y ₂ = G ₂ , Y ₃ = sC ^. γ ₄ = G ₄ , Y ₅ = G ₅ + sC ₅ , Y _ba = 0 and Y ₆ , = G _n .

The transfer function of the filter is then:

U ₁ (G ₁ + G ₂ ) G ₄ G ₁ ,

⁼ "U ₀ " ~~ 5 ² C ₃ C ₅ G ₁ + 7CjG ₅ Ci ₁ + G ₂ G ₄ G ₁ , "

This expression is meant to refer to the form

As with the resonant circuit, quality 0 is an important variable here too. It is defined by Q = «> - _r h and results from: -> the relationship

0 =

were brought.

Here, K is a constant factor (basic attenuation of the filter), b the 3 dB bandwidth and <■>., The resonance frequency.

The sizes b and <·) “. are shown in the diagrams of FIG. 3 for better explanation. In the complex representation, Im (s) is the imaginary and Re (s) the real axis of the diagram.

Another transformation of the transfer function by division with C ^ C ₅ G ₁ results

r [S) -

G ₂ G ₄ G ₁ ,

With the ratio of the conductance values .I ₂₁ - G ₂ G ₁ and the time constants T ₅₅ = C ₅ G ₅ . 7 _U = C, G ₄ and T ₅₆ = Cj / G ,, results

'.14' 5h

b = ~ v-

'55

Accordingly, the quality is determined by the resistance and capacity ratios.

The dimensions of a low-pass filter according to FIG. 2 is done as follows.

The resonance frequency o and the bandwidth b are given. For example, « ₂₁ = I and T ₃₄ = T _{56 is selected} . Then T ₃₄ = T ₅₆ = 1 ι ··, and T ₅₅ = Ϊ b.

After freely choosing the capacitance _{values for C 3} and C ₅ , the remaining values are Ci ₄ = C, T ₃₄ =; ,, C, G ₆ =, -, C ₅ and G ₅ = HC ₅ . Because, <- ,, = 'l. is G ₁ = G- ,. The value of G or G ₂ can be freely selected.

After the completion of the filter dimensioned according to the above instructions, the adjustment takes place, the resonance frequency being set by changing the ratio a ,, (G ₁ -Ci ₂ ) or the conductance values of G ₄ or G _n without changing the bandwidth, and the bandwidth is readjusted by changing the conductance Ci ₅ without changing the resonance frequency.

This shows that the resonance frequency and the bandwidth are only dependent on passive components. The change in the values of G _; or C '<by I "ο results in a change in the bandwidth before likewise ΓΌ. and the change in the values of G _x Ci _2. G _4. Ci ,,. C, or C ₅ by 1" »causes a shift in the resonance frequency by about ' ₂ "4. According to this, this low-pass filter behaves like a passive LC filter.

When calculating the low pass, ideal operational amplifiers were assumed. At the dcrz.ci available operational amplifiers, this assumption is justified because it affects the filter properties only then occurs. when the resonance.frcquen reaches the order of magnitude of the transit frequencies de operational amplifier.

The calculation of other filter types can analogously in the for the low-pass filter according to FIG. 2 specified manner.

F i g. 4 shows how, according to the basic circuit diagram of FIG. 1 shows a bandpass filter. The network for this contains the conductance values Y ₁ "= G ₁ , Y _{1 b} = 0, Y ₂ = G ₂ , Y ₃ = G ₃ , Y ₄ = sQ, Y ₅ = G ₅ , Y ₆₀ = sC ₆ and Y ₆ "= G ₆ , and the transfer function is:

5C ₄ G ₆ (G, + G ₂ )

U ₀ VG ₂ C ₄ C ₆ + s C ₄ G ₆ G ₂ + G ₁ C ₃ G ₅ '

Ut_

1 + «

12th

s ² + - = - s +

"12

TT '43 '(

where « ₁₂ = G ₁ ZG ₂ , T ₆₆ = CJG ₆ . T ₄₃ = C ₄ G ₃ and T ₆₅ = CJG ₅ .

The network for the high pass according to FIG. 5 has the conductance values Y ₁₀ = G ₁ , Y _ih = 0. Y ₂ = G ₂ , Y ₃ = G ₃ . Y ₄ = sC ₄ , Y ₅ = G ₅ , Y _6a = G ₆ and Y ₆₁ , = sC ₆ . The transfer function is

F (s) =

S ² C ₄ C ₆ ( C ₊ G ₂ ) s ² C ₄ C ₆ G ₂ + s C ₄ G ₆ G ₂ + G, G ₃ G ₅

J 4- f. S + _T 'V

'66 '43 ^J 65

For a bandpass filter with a positive-real zero according to FIG. 6 the following conductance values are to be used in the circuit: Y _ia = sC ,, Y _{1 b} = G ₁ . V ₂ = G ₂ , V ₃ = G ₃ , Y ₄ = G ₄ , Y ₅ = 5C ₅ , Y ₆₀ = G ₆ and Y ₆ "= 0.

If « ₄₃ = GJG ₃ . T _n = C _x IG ^ T _n = C _x IG ₂ and T ₅₆ = C ₅ / Gf, set, the result is the transfer function

s C ₅ G ₁ Gj-G ₁ G ₄ G ₆

F sharp) =

F (s) =

S ¹ C ₁ C ₅ G ₃ + a C ₅ G ₁ G ₃ + G ₂ G ₄ G ₆

s -

"43

«43

While the influences of the transit frequencies of both operational amplifiers, if taken into account must be, in the circuit arrangements according to

the F i g. 2, 4 and 5 compensate each other, so are they can be neglected in this arrangement if «43 = 1 is chosen.

As the basic circuit diagram according to FIG. I can be used to represent an all-pass is shown in FIG. 7 to be seen. The conductance values used are Y _lfl = 0, Y ₁₆ = G ₁ , Y ₂ = G ₂ , Y ₃ = G ₃ , Y ₄ = SC *, Y ₅ = G ₅ , Y ₆₀ = G ₆ and Y _ftfc = sC ₆ , and the transfer function is

S ² C ₄ C ₆ G ₂ + SC ₄ G ₂ G ₆ + G ₁ G ₃ G ₅

"12

T ₆₆

"12

¹ fth ^J Λ <1

T ₅₆

_{If «I2} = GJG ₂ = 1 is chosen in this arrangement, it behaves like an all-pass.

F i g. 8 shows how a low-pass filter with a damping pole

can be built up if the conductance values Y _x "= G ₁ .

Y ₁₁₁ = SC ₁ . Y ₂ = G ₂ , Y ₃ = G ₃ , Y ₄ = G ₄ , Y ₅ = SC ₅ , Y ₆₀ = O and Y _6k = G ₆ can be used. The relationship applies to the transfer function

+ G ₆ G ₄ (G ₂₊ G ₁ )

.s ² C ₁ C ₅ G ₃ + sC ₅ G ₁ G ₃ + G ₂ G ₄ G ₆

J, «43 (il2-r Π

s ²

S ₊

«43

where «43 = G ₄ IG ₃ and« ₁₂ = GJG ₂ .

In this relation the numerator polynomial is of the type s ² + (I ₀ and therefore has purely imaginary zeros with S ₀ = ± j ^ a _0. Such zeros are comparable to those that generate LC suction circles of infinite quality enters the zero ebe nIf be i a frequency / ₀ = 5 ₀ 2RR on. where S ₀ = ^1/1 / LC. from g transmission function of the active J? C filter according to F i. 8 it can be seen that when Changes to all resistance and capacitance values, the zeros remain imaginary and only the zero frequencies change.This favorable property does not occur in previously known RC networks.

For this purpose 4 sheets of drawings

Claims (1)

Claim: Circuit arrangement for displaying a large number of transfer functions of quadrupole S through active RC filters of the second degree, provided with two operational amplifiers, in which the output variable to ground is taken from the output of the second operational amplifier, characterized in that the input variable (LZ ₀ ) is referred to ground via a voltage divider consisting of real and / or capacitive conductance values (conductance values Y _{1 a} and ^ j _n Y _6a ^and Y ₆ b) is connected to the non- inverting inputs of the two operational amplifiers (V ₁ and V ₂ ) so that the inverting inputs are connected to each other are connected and that via the inputs of both. Operational amplifiers (K ₁ and K _{2 ) a series circuit (V 2} and Y ₃ , Y ₄ and Y ₅ ) consisting of two real and / or capacitive conductance values, whereby the connection point of the conductance values of the first series circuit (Y ₂ and Vj) is applied the output of the second operational amplifier (K ₂ ) and that of the conductance values (Y ₄ and Y ₅ ) of the second series circuit are connected to the output of the first operational amplifier (K ₁ ).