CS201074B1 - Active ac filter - Google Patents

Description

The invention relates to an active RC filter with arbitrarily adjustable transmission function coefficients for use in frequency selective systems, for correctors, in particular for use in telecommunications and control and measurement technology.

The process of miniaturization and integration of electronic circuits brings with it new problems. Integrated circuit filters cannot contain inductors in the form of coils in their structure. There are already a number of methods for the synthesis of induction-free filters. They generally use active function blocks such as gyrators, impedance converters, operational amplifiers, etc.

With these function blocks, integrated circuit filters can be implemented.

In telecommunications technology, in regulation and possibly in measurement technology, there are selective circuits and correctors with very different transmission functions. Synthesis of active RC circuits implementing given transfer functions is often very lengthy and complicated. It is necessary to decompose the transfer function, to realize the double-sided RC from elements of a double-sided matrix, etc. Also the capacitor values are very different. With current types of active filters implementing higher order transfer functions, it is not possible to set individual coefficients of polynomials in the transfer function by one element. The diversity of capacitor capacitance values creates difficulties in manufacturing and in adjusting transmission circuit parameters.

The above drawbacks are overcome by an active RC filter with a defined polynomial of the transfer function, consisting of a frequency-dependent divider consisting of resistors, capacitors and operational amplifiers, according to the invention. Its essence is that multiple inductors or multiple capacitors are connected in the frequency-dependent divider. The multiple inductors or multiple capacitors are in the form of at least a two-pole replacement. External resistors are connected in parallel to the external terminals of the active RC filter, each of which is connected between two mutators.

Furthermore, it is expedient according to the invention if the multiple inductors and the multiple capacitors are formed by mutators which comprise frequency-dependent converters sequentially connected to an external resistance branch.

According to another feature, the mutators are formed by operational amplifier chains whose outputs are connected via resistors to the first inputs of the operational amplifiers and via capacitors to the second inputs of the operational amplifiers. The second inputs of the preceding operational amplifiers are connected to the first inputs of the subsequent operational amplifiers and the reference center terminals of these operational amplifiers are interconnected.

The four-pole multiple inductance replacement is determined by the product of cascading matrices of the form:

- - - 1 0 X 1 ^R n X 1 0 and 1 ^and nV ⁿ 0 1 0 1 ^{0 H} n P ⁿ 0 1 ^H n p ⁿ

where the constant given by the mutator design, p is the complex frequency a

R _n is a resistance transformed to multiple inductance.

/ n /

According to another aspect of the invention, adjacent mutants L '' R are replaced by a mutator one based on the formula:

p • - * 1 0 1 0 1 0 0 -1 -1 / n-1 / X 0 1 with 0 1 ^H n-1 P 'N π p ^H n P L - -

The RC active filter according to the invention preferably consists of higher order mutators, implemented in canonical form, consisting of sequentially shifting the same frequency-dependent converters into an external resistance branch.

010 7

Multiple inductors or multiple capacitors are connected as elements in a frequency-dependent divider which, for example in the case of a low-pass filter, has a voltage transmission in the form of:

^{An / P /} Ro + p Lx ⁷¹⁷ + p ² L2 / 2 / + ... + _p ⁿ 7n7 “ _{_} ____________________ ^R o____________________% ^{+ p H} 1 ^R l ⁺ P ^{2 and} 2 ^H 2 ⁺ ··· ⁺ P ^{n R} n where A / p / - ^ 2 is the voltage transfer from input to output, ^U 1

R _q is the resistance in the frequency-dependent divider,

L ^ ⁷ * ⁷ is a multiple inductance, is the mutant constant L · ⁷ ^ ⁷ R of the second kind a

R ^ is a resistance that transforms with multiple L ⁷ * ⁷ R into multiple inductance.

An advantage of the active RC filter according to the invention is that it allows the realization of any transfer function so that one external resistor can be set to one coefficient of the transfer function polynomial, independently of the others. A further advantage of the invention is that the capacitor chip values within each mutator may all be the same. The advantage is also that the individual components of the filter, the L ^z 'R mutators, can themselves constitute a universal kit for the implementation of active RC circuits. Another advantage is the possibility of realizing the c / n / mutator

G by simply interchanging the input and output terminals. This mutator makes it possible to realize a multi-axis capacitor of uumitance:

Y / P / = C ^{/ n /} p ^n.

The RC active filter circuit of the present invention can be implemented using hybrid micro electronic technology, wherein the mutators form separate hybrid function blocks. Reactants are created by capacitors inside the mutators. These capacitors can be inserted into hybrid mutator circuits as monolithic chips. Resistance values that determine the magnitude of the corresponding constant in the polynomial of the transfer function are set either by variable resistors or by fixed resistances of a calculated value, connected to the terminals of the imitators. '

It follows from the principle of operation that the active RC filter can be implemented for any terminating impedances.

201 074

The connection of an active RC filter with arbitrarily adjustable transfer function coefficients according to the invention will be described in more detail with reference to the accompanying drawings, in which Fig. 1 represents a block diagram of an active RC filter according to the invention. Fig. 3 shows a method of simulating a multiple inductor with a two-pole replacement; Fig. 4 shows a method of simulating a multiple inductor with a four-pole replacement;

Fig. 5 shows the principle of implementing an active RC filter with multiple inductors according to the invention;

Fig. 6 represents the replacement of multiple inducers in an active RC filter by type 2 mutators according to the invention;

Fig. 7 shows the principle of quadrupole replacement of multiple inductors according to the invention;

Fig. 8 is a simplified schematic of an active RC filter;

(n) Fig. 9 is a null model of the mutant in species 'R 2';

Fig. 10 shows a method of replacing the nullors in a model using operational amplifiers; Fig. 11 represents another embodiment of a type 2 mutant R;

Fig. 12 shows the principle of implementing an active RC with multiple capacitors according to the invention;

Fig. 13 shows the principle connection of the RC active filter, in which the multiple capacitors are replaced by j / n /

G, loaded with conductors G _R.

The frequency-dependent active filter divider RC 1 consists of a series connection of multiple inductors and a resistance R _Q. Each single multiple inductor of impedance given by the relation

Z / p / = L. ^{/ n /} p ⁿ according to the invention consists of a type 2 mutator R loaded with a resistance R. This arrangement converts the load resistor R from the output terminals to the input terminals to a multiple inductor l / ⁿ /. The mathematical expression of the mutant R of the second species is given by the relation

0

A =, where A is the cascade matrix, k _n is the mutator constant given by the realization and p = s + j ^ is the complex frequency.

/ n /

The conversion of the resistance R from the output to the input of the mutator L ^{/ n /} B can be expressed by the relation ^z i ^{/ p /} = V ” ^{H 1} ρ ^{Π L / n /} '

L ^{/ n /} = K _n R, where Z ^ / p / is the input impedance of the resistively loaded mutator l / ^{n //} R.

The series inductor of the multiple inductors according to the invention makes it possible to realize a dependent divider which represents an active RC 1 filter.

Giant. 1 shows an example of a block arrangement of an active low pass filter RC 1. Transfer function coefficients ^U 2

A '/ p / = uu ¹ ζ' ~ ζρ ~ '5ρ ⁵ '^;'···^; ^ ρ ⁵ '

TT where: A / p / = 2 is the no-load voltage transfer, ^K i are the polynomials of the transfer function and p jtA .; The basic building block in the RC 1 active filter is the so-called multiple inductor or multiple capacitor. Both elements and their impedance respectively. admittances are shown in Fig. 2. In a practical device, the multiple inductor and the like capacitor can be replaced by a resistively loaded mutant of the type I / ^{n / Z} R of Fig. 3. The mutator has a cascade matrix ri ^C L ^{/ n /} -R

H _n p ⁿ

The load resistance R _n is transformed into an input according to the formula:

Z- / p / = H p ⁿ R, ^H n ^r n ' ^{l / n /} - "n ^B " · where Zj / p / is the input conductivity of the mutator R loaded by the external resistance R _n a

H _n is the constant of the mutator given by its construction.

toi O-fy

Fig. 4 shows the so-called quadrupole replacement by a multiple inductor. This connection can be characterized by the product of cascade matrices

1 0 0 1 of 1 0 ^H n 1 X 1 0 •and 3 O 1 1 0 «« V ⁰ 1 «Η P” _ _ - - _

The RC 1 active filter according to the invention can be realized by a frequency-dependent divider utilizing multiple inductors or capacitors. FIG. 5 shows a low pass filter whose transmission function is shown in FIG. 1. By suitable arrangement of multiple inductors in the divider, both bandpass and high pass filter can be realized. In the practical connection, it is possible to apply multiple reactances using resistively loaded mutators / FIG. 6 /. In FIG. 7 'shows the use of the so-called quadrupole replacement of multiple inductors. According to the invention, adjacent pairs of mutators can be replaced by one (see pair A in Fig. 7). Wiring is greatly simplified. In FIG. 8, the resulting outer 5 and FIG.

connection of active filter RG 1. Polynomial coefficients oe can be set by resistors R _q to R _n · ^{Au / P /} Ux Rq + p + p ² L2 + ... + p ⁿ L _n ^{/ n /}

_Q + R p + R p Hi ^ Hg Rg + ... + ... P ^N H _N R _N / N /

Fig. 9 and Fig. 11 show the possibilities of realization of mutants in the R 2 type. Nulors can be replaced by the operational amplifiers 2 according to Fig. 10.

Fig. 12 and Fig. 13 show an example of a low pass filter with multiple capacitors which are again used in a frequency-dependent divider.

Claims (3)

An active RC filter having a defined transfer function polynomial, consisting of a frequency-dependent divider consisting of resistors, capacitors and operational amplifiers, characterized in that multiple inductors (L ^z ') or multiple capacitors / C ^z ' are connected in the frequency-dependent divider. which are formed in the form of at least two-pole replacement, with external resistors (R ^) connected in parallel to the external terminals of the active filter RC (1), each connected between two mutators (L ^of 'R or C ^{/ n /} Q) /. 201 074 2. An RC active filter according to claim 1, characterized in that the multiple inductors (1 / ^{n //} R or C ^ G) which comprise frequency-dependent converters successively connected to an external resistance branch (R ^). RC active filter according to claim 1, characterized in that the mutators (1 / ⁿ / R or C ^ ^{n //} C) are formed by chains of operational amplifiers (2), the outputs of which are connected via resistors (R ^) to the first the inputs of the operational amplifiers (2) and through the capacitors (C ^) to the second inputs of the operational amplifiers (2), the second inputs of the preceding operational amplifiers (2) being connected to the first inputs of the subsequent operational amplifiers (2) / 2 / are interconnected.