DE1541972C3 - Electric filter circuit - Google Patents

Description

Establish zero pairs of the filter transfer function.

This task is performed with an electrical filter circuit using an operational amplifier, which has a push-pull terminal pair in its input and / or its output and the fed back via a frequency-selective network consisting only of resistors and capacitors is solved according to the invention in that the network lying in the negative feedback path contains at least one bridge circuit, of which two branches by the interconnection of at least a resistor with at least one capacitor and the other two branches through the pair of push-pull terminals of the operational amplifier are formed, and that the resistors and capacitors formed branches of this bridge circuit in such a way in the frequency dependence of their Impedance are different that this, as known per se, a pair of zeros Attenuation function of the transmission attenuation is set.

One branch of the bridge preferably contains a series circuit and another branch of the bridge contains a parallel circuit of resistors and capacitors.

Particularly favorable conditions, namely the achievement of a pole pair and a zero pair with only a resistor-capacitor bridge circuit can be achieved if in one of the Bridge branches a tap is provided which connects to an output terminal of the output terminal pair the filter circuit is connected and defines a pair of poles of the damping function.

A further development of the invention is characterized in that the operational amplifier both an input having a push-pull behavior and an output having a push-pull behavior and has the highest possible level of common mode rejection, and that in the negative feedback path lying network contains two bridge circuits, one of which is connected to the input and the other is formed in connection with the output of the operational amplifier, and that each of the Bridge circuits defines a pair of zeros for the damping function. Here you can also form a pair of poles by arranging a tap in one of the bridge circuits.

Another development of the invention is characterized in that in the entrance and / or Output two parallel-connected bridge circuits are provided, each of which only one is in the negative feedback path and the other to a terminal of an associated terminal pair the filter circuit and serves to form a pair of poles.

It is also advantageous to add high-order filters through the daisy chain connection of four-pole filters realize, which are designed according to the invention.

The invention is explained in more detail below using exemplary embodiments.

When designing active RC filters, it is important to use a given transfer function as much as possible to realize few capacitors, since these are much more expensive in an integrated design than Resistors and transistors.

In this regard, the known RC bridge (Fig. 1) is a favorable circuit for generating either a pole pair or - used as a negative feedback quadrupole - a zero pair. You only need two capacitors for each pair. An integrated push-pull amplifier, also called an operational amplifier, is used as the active element.

The F i g. 2 shows the structure of a basic filter element, which has a pair of zeros and a pair of poles as Realized partial factor of a transfer function.

Higher grade filters are then obtained by daisy chaining several basic filter links. For a low-pass filter of the order 2n + 1 with η + 1/2 poles of the echo attenuation in the pass band and η + 1/2 poles of the operational attenuation in the stop band, one therefore needs η amplifier units with An capacitors.

The four poles of the bridge are connected to a constant voltage (CZ ₁ ) on the input side, since the output resistance of the amplifier with negative feedback is zero.

Most four-pole terminals are short-circuited on the output side (R _a = O). The negative feedback quadrupoles (I), which generate the zeros, are _{loaded with the very low input resistance of the (own) negative feedback amplifier (Z 1} = 0). The blocking four-poles (II), which generate the poles of the transfer function, are short-circuited by the input resistance of the next amplifier unit (z ₂ = 0). Only the quadrupole II at the end of the entire filter is expediently loaded with a resistor R _a. This allows you to force an additional zero on the negative real frequency axis.

The transfer function of the short-circuited bridge (Fig. 1, R ₁₁ = 0) is

JJj ₌ R ₁ (I + PC ₂ R ₂ )

P + σ ,,,

(p + σ ₀ - } ω _ο ) (ρ + σ ₀ + j O) ₀ )

Here σ ₀ ± jm _{0 means} the position of the zero or Pole pair is therefore to be regarded as a given. a, " can be selected arbitrarily, but must be the same for the two bridges belonging to an amplifier unit (I" and II). (It then falls out of the overall transfer function.)

The size of the switching elements can easily be determined from equation (1). One finds

Negative coupling bridge I:

σ ² , - 2 σ ₀ c

σ ₀

Q ι =

σο

1 / C ₂ = σ ,,, R ₂ ;
6ο barrier bridge II (<r ₀ = 0; ω ₀ = ω _4. ):

R -A + "Mr
1 / Q ₁₁ = L ₊ JiL) R ₂ ,

\ ^σ ,,, J

XIC ₁ = O _1n R ₂ .

10 4 1 y

The transfer function of the amplifier unit (FIG. 2) is then

Λ _ Qi P ² + 2σ _ο ρ + σ ² , + </> l

I ₁ + p (2R _a + R ₂ ) C ₂ R ₁ + p ² C ₁ R ₁ C ₂ R ₂ R ₁₁ R ₁₁ (I + p ² C ₁ R ₁ C ₂ R ₂ )

(2)

^v = T \ _ ^a - + ^σ -
R ₁ = (1 + v ² ) R ₂ ,

a "-

+ v ² ) _R.

2 ^ 2>

1 / C ₁ = (v + ^ jw _s R ₂ ,
1 / C ₂ = Vw ₃ R ₂ .

Sensitivity to .RC changes

As a measure of the detuning, which should remain as small as possible, we use accordingly

(7 ₀ C ₁ R ₁ + C ₂ R ₂ - C ₂ R ₁

J ₂ C ₁ 1, ρ ϊ- O) ₅

The associated pole-zero point plan is shown in FIG. 3. For the balanced bridge loaded with a resistor (Fig. 1, R ₁₁ φ 0), which is used as the last link in the amplifier chain if a filter with an odd ordinal number (n = 3.5.7) with a zero (a ") On the reg. If the real frequency axis is to be built, the transfer function is obtained

The zero a “ is given. However, the other root a _m must not fall below a minimum value if the following formulas for the switching elements, which are obtained from equation (2), should result in positive, real values:

When calculating the switching elements of an amplifier unit that implements a given pair of poles and zeros, the value a _m - the zero of the transfer function of the bridges - remained freely selectable. It is of interest what influence this parameter has on the sensitivity of the bridges to fluctuations in the switching elements.

The zero pairs correspond in the transfer function Factors of the shape (see Fig. 3)

P ² +

sin b

C ₁ R ₁ C ₂ R ₂

C ₁ R ₂ VC ₁ R ₂

After performing the differentiation, we bet
C ₁ R ₁ + C ₂ R ₂ = C ₂ R ₁

that is, we restrict ourselves to the case that the zeros are close to the imaginary frequency axis (σ ₀ <c fi) for changes. is particularly vulnerable. For abbreviation, the size is introduced:

υ =

then applies

One can see from this: For υ = 1 (σ ² , = al + (d ^2. ) The detunings of C and R have the same weight. If one has to reckon with significantly larger detunings of C than of R , then

moderate to make υ <1. For the case - = - = 1%,

-5- = 0.1%, for example, results in the most favorable measurement: ν = j / ÖTT [σ ,,, = 10 (al + wq)]. The F i g. 4 shows how this is expressed in the impedance curve of the two bridge branches.

In the previous exemplary embodiment, a zero and a pole pair of the transfer function of a filter with the help of two RC bridge circuits, one of which is in a chain with connected to the amplifier and generates the pair of poles, while the other is used to generate the pair of zero points is fed back to the input of the amplifier.

In a further development of the invention, however, it is possible to produce a pair of poles and zero points with only one bridge circuit, that is to say with only two capacitors, if the bridge resistance R _{1 is} subdivided. The structure of the amplifier unit is shown in FIG. 5. The transfer function can take the following form:

U ₀ [1

+ ρ / (σ ₀ + J

U _n

if the following conditions are met:
R _e = r ² / (R + r) ά r (R <: r).

R ₁ C ₁ C ₂ (R ₂ -R) = 1 / α

For the shape of the transfer curve, e.g. B. for the formation of damping or reinforcement peaks, the variable sin ö = - ^ - is obviously decisive. If this remains constant, ie if σ ₀ and (i change to the same extent, only the frequency scale is influenced, while the curve character is retained. We want to regard this change as less critical.

R ₁ C ₁ C ₂ (R ₂

C ₁ + C ₂ (K ₂ - R- R ₁ - R ₁ RIr) = 0,
RR ₁

R ₁ C ₁ + C ₂ (R ₂ +

The position of the zero point: n ₀ ± j «j" and the pole: ± j (»" are given. The size of the switching elements can then be determined on the basis of equation (I).

To set up a grade 2 low-pass filter with η poles of the echo attenuation in the pass band and η poles of the operational attenuation in the stop band, η amplifier units are connected directly in a chain, with the input resistance R _{e of} the following unit coinciding with the output resistance r of the preceding unit.

For low-pass filters with an odd ordinal number (2 h + 1) one needs a zero a " on the neg. Real frequency axis. It arises when the input resistance R _{1 of} the first amplifier unit is replaced by the RC element from FIG.

It applies here

U ^ J ₁ = RJl + PC ₀ RJA) = RJ \ + ρ Ο,

C ₀ = 4 / R _e a ".

For example, for a low-pass filter of degree m , m capacitors are required, not more than a normal LC low-pass filter contains. In place of each coil there are five resistors and an integrated standard amplifier. The two balancing resistors of the amplifier output are included in the five resistors. All other components of the amplifier do not need to be particularly constant or precisely adjusted.

The circuit according to FIG. 5 can also be used as a high-pass filter if the negative feedback is not derived from x but from y and the amplifier output is connected to χ . The input circuit according to FIG. 6, if it is applied, must then be redesigned accordingly.

A band filter behavior can be achieved, for example, by daisy-chaining at least one high-pass filter and achieve at least one low-pass filter.

Numerical example for a low pass

/, = 4.775 kHz K = 3 · 10 ⁴ ),.
/ ₀ = 4.416 kHz K = 2.77443 · 10 ⁴ ),
<7 ₀ /2.t = 0.19OkHz (σ ₀ = 0.11918 · 10 ⁴ )

A switching element can be freely selected, for the rest one can then find

R =
R ₁ =

& 2 =

C ₁ =

0.0773 kQ,
12.763 kC2,
14,597k £ 2,
Ik £ 2,

7.9375 nF,
8.4186 nF.

The circuit can also be dimensioned for much higher frequencies; This also applies to the other remarks on circuits according to the invention. It is then only possible to act Stray capacities to be taken into account.

For the filter circuit according to FIG. 5 can be used regardless of whether it is a high-pass or Low-pass filter is to derive a basic circuit diagram as shown in FIG. 7 together with the associated frequency plan indicates.

If the operational amplifier has a push-pull input, this way of switching, as shown in FIG. 8 shows, can also be used in the same way in the input. In this In this case, it is advisable, as indicated, to have two separate resistors in the input of the operational amplifier to be provided, which then, so to speak, belong to the two other branches of the bridge or essentially form these branches.

Is the individual operational amplifier according to a combination of the soundings according to the 7 and 8, a bridge circuit is arranged upstream and a bridge circuit is arranged downstream, so can one can realize either a high pass or a low pass of a higher degree. It is, however, an advantage also possible, one bridge for a high pass formation and the other bridge for a low pass formation to use. One then obtains with a basic filter element containing only one operational amplifier a band pass filter.

For this purpose 4 sheets of drawings

509 535/154

Claims (7)

Patent claims: 1. Electrical filter circuit using an operational amplifier which has a push-pull terminal pair in its input and / or its output and which is counter-coupled via a frequency-selective network consisting only of resistors and capacitors, characterized in that the network (I) lying in the negative feedback path at least contains a bridge circuit, of which two branches are formed by the interconnection of at least one resistor with at least one capacitor (R ₁ , C ₁ ; R ₂ , C ₂ ) and the other two branches are formed by the pair of push-pull terminals of the operational amplifier, and that the resistors and capacitors formed branches of this bridge circuit are so different in the frequency dependence of their impedance that thereby, as known per se, a pair of zeros of the damping function of the transmission loss is determined (FIG. 2 in conjunction with FIG. 1). 2. Electrical filter circuit according to claim 1, characterized in that a bridge branch a series connection and another bridge arm a parallel connection of resistors and includes capacitors (e.g. I in Figure 2). 3. Electrical filter circuit according to claim 1, characterized in that a tap (R) is provided in one of the bridge branches (R ₂ , C ₂ ) on a resistor, which is connected to an output terminal of the output terminal pair of the filter circuit and defines a pair of poles of the damping function (Fig. 5). 4. Electrical filter circuit according to claim 1, characterized in that the operational amplifier a push-pull input and a push-pull output and that the network lying in the negative feedback path has two bridge circuits of which one in connection with the input and the other in connection with the Output of the operational amplifier is formed and that each of the bridge circuits has a zero pair the damping function (Fig. 7, 8). 5. Electrical filter circuit according to claim 4, characterized in that at least one the bridge circuits a tap is provided, which is used to form a pole pair (Fig. 7 and Fig. 8, respectively). 6. Electrical filter circuit according to claim 1, characterized in that two connected in parallel Bridge circuits (I, H) are provided, of which only one (I) is in the negative feedback path and the other (II) to a terminal of an associated terminal pair the filter circuit and serves to form a pair of poles (Fig. 2). 7. Electrical filter circuit according to one of the preceding claims, characterized by the use as a chain link in a chain circuit to form such basic filter links of higher grade filters. The invention relates to an electrical filter circuit using an operational amplifier, which has a push-pull terminal pair in its input and / or its output and the .5 negative feedback via a frequency-selective network consisting only of resistors and capacitors is. For filter circuits for use in electrical communications engineering and, above all, also ίο the Runkfunktechnik have been provided so far, in which the lowest possible loss Capacitors and coils are the frequency-determining switching elements. Due to the general Tendency to the devices of electrical communications engineering and broadcasting technology in their outer To make dimensions as small as possible, designs have been introduced in recent years that one could summarize under the term »microminiaturization« (cf. for example the book "Microminiaturization", Pergamon Press 1962). Coils of the conventional type are used for these designs spatially too expensive. There are therefore electrical circuits have been developed in which the previously by Coils realized inductances through circuits with the same effect, apart from capacitors and Resistors still contain transistors are replaced. Known circuits of this type are, for example, in the journal "Proceedings IEE", Vol. 112, No. 5, May 1965, pages 901-914. The transistors are mostly in shape so-called operational amplifier provided and the microminiaturization brings with it that Efforts are made to use as few capacitors as possible on the one hand and as few operational amplifiers as possible on the other to spend for the implementation of a predetermined profile of the transmission loss of a filter. The one for the transmission properties Such four-pole filter poles become decisive poles and zeros of the damping function for the sake of clarity and simpler mathematical treatment represented in the so-called complex frequency plane. Even if this is the way of representation is used below in the explanation of the invention, there is no need to go into more detail here on this, because it is a mathematical method of treatment that is well known to a person skilled in the art acts. For example, explanations in this regard can be found in the book by F e 1 d t keller "Introduction to the theory of high-frequency band filters", 5th edition, Hirzel Verlag, Stuttgart, im Chapter 41, in the book by B ο d e “Network Analysis and Feedback Amplifier Design «, pp. 18 to 30, and in the pocket book of high frequency technology by Meinke-Gundlach, 2nd edition, pp. 1135 and 1136. In the journal Proc. IEEE ", Oct. 1965, pp. 1648 to 1649, an active RC network is also specified, in which an operational amplifier is used as the active element. In this known circuit However, there is only a single admittance in the negative feedback path, that of the positive output the entrance is returned. The invention is based on the problem of filter circuits of the type described in the introduction with the least possible amount of operational amplifiers and capacitors high predetermined number of pole and / or