DE2317644C3 - Circuit arrangement for the representation of a large number of transfer functions of quadrupole terminals through active RC filters provided with two operational amplifiers - Google Patents

Description

In the circuit arrangement according to H. Extension 30, the influence of the gain factor and the

_QfQ ". . _T ... transit frequency of the two operational amplifiers

btana the lechnuc _{DJE Resonanzfreque} s n _Z and the bandwidths of the

In the course of the increasing spatial compression, the filter is vanishingly small. The stability of the resoelectric circuit arrangements is always nanzfrequenzen and the bandwidths is essentially more difficult to accommodate passive filters equipped with coils and capacitors 35 borrowed only by the constancy of the RC elements. Especially in scarfs. Therefore, the constancy of the low frequencies according to this line is therefore desirable to largely replace circuitry-built filters without an overcoil filter with RC filters. Additional stabilization measures are just as good as For low requirements, passive LC filters are sufficient for this, and it is possible to use high RC filters that do not cause any significant difficulties ₄₀ edge steepnesses through close to the band limits. to achieve lying poles.

In order to meet higher requirements, it is known that when dimensioning the filter, as in

Low-pass filter (DT-AS 12 23 075), resonance filter (DT- der in Electronics Letters, June 1972, Fig. Ic, ge

AS 12 62 466), all-passes (DT-AS 19 58 140) and optional arrangement, the capacity values freely, e.g. B. off

wise high or low passes (DT-AS 16 16 412) are selected as 45 of a standard series and are of the same size,

to display active RC filters. The German open changes of resistance and capacitance values

Legendschrift 19 54 543 also indicates a setting of damping poles have no

Circuit arrangement in RC technology is known to have an influence on the sharpness of resonance. Besides, the

according to the implementation of all of the above filter adjustment of the resonance frequencies, the bandwidths

species is suitable. 50 and possibly the damping pole frequencies at

Another circuit of this type with two op- erated filters simply by changing the resistance amplifiers is possible in the journal IEEE Specstand values. This simplifies the trum, January 1969, p. 56 (Fig. 19) and 57 described structure in monolithic and in hybrid integration and pictured. tion technology.

Through the reference in Electronics Letters, 55 As from the exemplary embodiments below

June 1972, Vol. 8, No. 11, p. 288 (Fig. 1 c) and 289 is shown, the structure of the Schallungsanordnunj

an arrangement with three operational amplifiers is the same for all filter types. To switch to a <

knows, in which the inverting inputs with each other other Filtcrart is just an exchange of Leit

connected and the outputs are necessary via real or capacitive values, whereby it can also occur

zitive master values to the inputs of the following 60 that one or more master values with the value NuI

Operational amplifiers are connected, the no longer appearing as a component. This is

Output of the last operational amplifier at which it is possible to use the basic structure in integrated technil

Establish the input circuit of the first operational amplifier and correspond to the respective filter type «

lies. to peel.

This and other known active RC network 65 Since the output impedance of the circuit arrangement

works tend to be self-excited and have a good approximation of zero. is like be

the serious disadvantage of other known active RC filters that are less time-consuming

Consistency of a one-time set transmission of the step technology is possible.

Explanation of the invention

Embodiments of the circuit arrangement according to the invention are shown on the basis of FIG. 1 to 8 explained. It shows

F i g. 1 the basic principle of the circuit arrangement according to the invention,

F i g. 2 shows the exemplary embodiment of a low-pass filter, FIG. 3 the transfer function of the low pass according to FIG. 2 and the representation of the pole in the complex plane,

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

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

In the basic circuit diagram according to FIG. 1, two operational amplifiers K 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 a} to Y ₆₆ . The input variable is _{indicated with U 0} and the output variable with l /. Assuming ideal operational amplifiers, the voltage transfer function of the circuit arrangement is a function of the complex frequency s

Y ₁ Y, Y ₅ +

and Y ₀ = Y _6a + Y _bb .

where Y ₁ = Yj ₀ +

To represent certain filter types, real (Y = G), capacitive (Y = sC) or parallel connections of real 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 ₁₆ = 0, Y ₂ = G ₂ , Y ₃ = sC ^, Y ₄ = G ₄ , Y ₅ = G ₅ + sC ₅ , Y _6a = 0 and Y ₆ , = G ₆ .

The transfer function of the filter is then:

F {s) =

(G ₁ + G ₂ ) G ₄ G ,,

U ₀ .S ² C ₃ C ₅ G ₁ + .SC ₃ G ₅ G ₁ + G ₂ G ₄ G _b This expression is intended to refer to the form

F (s) ■ = K

to be brought.

K is a constant factor (basic attenuation of the filter), b is the 3 dB bandwidth and r. » _{x is} the resonance frequency.

The sizes b and «> _m are for better explanation in the diagrams of FIG. 3 shown. 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 ₃ C ₅ G results

F (x) =

he c;

With the ratio of the conductance values u ₂₁ = GJG ₁ and the time constants T ₅₅ = C ₅ / G _s . T ₃₄ = CJG ₄ and T ₅₆ = C ₅ / G _h results

b = -

6o

ί-5

As with the oscillating circuit, the quality Q is also an important variable here. It is defined by Q = O _x Jb and results from the relationship

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

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

Given are the resonance frequency <; _x and the bandwidth b. For example, « ₂₁ = 1 and

= T ₅₆ . Then T ₃₄ = T ₅₆ =

After the free choice of capacitance _{values for C 3} and C ₅ , the remaining values result in G ₄ = C ₃ / T ₃ A - "',,. C ₃₁ G ₆ = ii _x , C ₅ and G ₅ = frC _5. Because ^ ₂₁ = 1, G ₁ = G _2. The value of G or G ₂ can be chosen freely.

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 n _n (G _x , G ₂ ) or the conductance values of G ₄ or G ₆ without changing the bandwidth, and the Bandwidth is readjusted by changing the conductance G 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 ₅ or C ₅ by 1% results in a change in the bandwidth of also 1%, and the change in the values of G ₁ , G ₂ , G ₄ . G ₆ , C ₃ or C ₅ by 1% causes a shift in the resonance frequency by about,%. Accordingly, this low-pass filter behaves like a passive LC-Filicr.

When calculating the low pass, ideal operational amplifiers were assumed. With the currently This assumption is justified because it affects the filter properties only then occurs. if the resonance frequency is in the order of magnitude of the transil frequency Operational amplifier arrives.

The calculation of other filter types can be carried out in the same way as for the low-pass filter according to FIG. 2 specified Way to be done.

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 V ₁ ″ = Gj, V _{1 b} = 0, y ₂ = G ₂ , Y ₃ = G ₃ , V ₄ = sC ₄ , V ₅ = G ₅ , V _6n = sC ₆ and V ₆ , = G ₆ , and the transfer function is;

" U ₀

S ¹ G ₂ C ₄ C ₆ + sC ₄ G ₀ G ₂ + G ₁ G ₃ G ₅

the F i g. 2, 4 and 5 mutually compensate for each other, they are negligible in this arrangement if "43 ⁼ 1" is selected.

As the basic circuit diagram according to FIG. 1 can be used to represent an all-pass is off F i g. 7 to be seen. The guide values used are

= 0, V ₁ "= G ₁ , V ₂ = G ₂ , V ₃ = G ₃ ,
= G ₅ , V ₆₀ = G ₆ and Y _6b = sC ₆ , and
function is

V ₄ = sC ₄ , V ₅ the trans

S ² C ₄ C ₆ G ₂ + SC ₄ G ₂ G ₆ + G ₁ G ₃ G _$

'66

S ² H-

S +

where u _l2 = GJG ₂ , T ₆₆ = CJ G _b , T ₄₃ = CJG ₃ , and T ₆₅ = C ₆ / G ₅ .

The network for the high pass according to FIG. 5 has the conductance values V ₁₀ = G ₁ , Y ₁ "= 0, Y ₂ = G ₂ , Y ₃ = G ₃ , V ₄ = sC ₄ , V ₅ = G ₅ , V ₆₀ = G ₆ and Y ₆₁ , = 5C ₆ . The transfer function is

_{F (s) =} -S ² C ₄ C ₆ (G _{1 +} G ₂ )

^rys) S ² C ₄ C ₆ G ₂ + SC ₄ G ₆ G ₂ + G ₁ G ₃ G ₅

"12

T ₄₃ T 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: V _1n = sC _u V ₁₁ , = G ₁ , V ₂ = G ₂ , V ₃ = G ₃ , V ₄ = G ₄ , V ₅ = sC ₅ , Y _ba = G ₆ and V _6b = 0. Becomes _{a 43} = _{GJG 3} , T _n = CJG ₁ . T ₁₂ = CJG ₂ and T ₅₆ = CJG ₆ set, the result is the transfer function

_{F (} ν SC ₅ G ₁ G ₃ - G ₁ G ₄ G ₆

^{t [S)} S ² C ₁ C ₅ G ₃ + SC ₅ G ₁ G ₃ + G ₂ G ₄ G ₁ , "

1
T ₁₁

"43 T ₅₆

S ² + ^ r-

While the influences of the transit frequencies of both operational amplifiers, if they have to be taken into account, can be found in the circuit arrangements according to «12

T ₃₄ T ₅₆

5 1- - i "Ι" _DD

' 66 ' 34 '56

_{If «12} = G ₁ JG 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 V ₁ "= G ₁ , Y ₁₁₁ = SC ₁ , V ₂ = G ₂ , V ₃ = G ₃ , V ₄ = G ₄ , Y ₅ = SC ₅ , Y (, _a = O and V ₆₁ , = G _6. The relationship applies to the transmission functions

F (s) =

S ² C ₁ C ₅ G ₃ + G ₆ G ₄ (G ₂ + G ₁ )

S ² C ₁
C ² C ₅ G ₃ +
, "43 (« sC ₅
12 + G ₁ G ₃
D. Ts ₆ + G ₂ G ₄ G ₆ T ₅₆ S ² + ¹ Il «43 T ₁ ,

where U ₄₃ = G ₄ / G ₃ and « ₁₂ = G ₁ ZG ₂ .

In this relation the numerator polynomial is of the type s ² + O ₀ and therefore has purely imaginary zeros with s ₀ = ± 7 | / iv Such zeros are comparable to those that generate LC suction circles of infinite quality. In the case of an LC suction circuit, the zero point also occurs at a frequency / ₀ = S ₀ / 2.-. where S ₀ =] / l / LC . From the transfer function of the active RC filter according to FIG. 8 it can be seen that when all resistance and capacitance values change, the zeros remain imaginary and only the zero frequencies change. This (favorable property does not occur in the previously known KC networks.

For this purpose 4 sheets of drawings

Claims (1)

function. The dependence of these on the temperature Claim: temperature, operating voltages and aging of the active and passive components prepared so far Circuit arrangement to represent a lot of considerable difficulties and required additional number of transfer functions of quadrupole 5 technical effort involved in the structure of the filter itself did not appear due to active with two operational amplifiers. See RC filter of the second degree, in which the already mentioned circuit arrangement according to output variable to ground the output of the German Offenlegungsschrift 19 54 543 is taken from the second operational amplifier, representation of some Filier types very complex and characterized in that the io leaves with the dimensioning only compromises input [U ₀₎ to ground with respect to each, that increasing the Resonanzgiite down-a of real and / or capacitive conductance reduction of constancy and the improvement of the existing voltage divider (conductances Y _la and constancy be a reduction in the Resonanzgiite - Y _lb , Y _6a and Y _6b ) to the non-inverting things,
outputs of the two operational amplifiers (K ₁ and 15 K ₂ ) is connected, that the inverting inputs task inputs are connected to one another and that via the inputs of the two operational amplifiers The invention is based on the _{object of adding a series circuit (K 1} and K ₂ ) each consisting of two real and / or capacitive components to a switching circuit (V ₂ 20 processing arrangement door active RC filters create that and V ₃ , Y ₄ and Y ₅ ), the connection function being suitable for representing a large number of transfer points of the conductance values of the first series circuit and a high temporal con (Y ₂ and Y ₃ ) at the output of the second operation of the same guaranteed. This task is solved by the ion amplifier (K ₂ ) and the conductance values (Y ₄ and by the invention specified in claim 1 ge-Y ₅ ) of the second series circuit at the output of the * 5,
first operational amplifier (K ₁ ) is connected. advantages