RU2830068C1 - Tunable band-pass active rc filter - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: invention relates to means used to select a signal source spectrum. Tunable band-pass active RC-filter additionally contains the third and the fourth inverting operational amplifiers. First outputs of the third, fourth and seventh resistors are connected to the inverting input of the third operational amplifier. Second output of the third resistor is connected to the output of the first operational amplifier. Second leads of the fourth and fifth resistors are connected to the output of the third operational amplifier. First leads of the fifth resistor and the first capacitor are connected to the inverting input of the fourth operational amplifier. Second leads of the sixth and eighth resistors, the second capacitor and the output of the filter are connected to the output of the fourth operational amplifier. Non-inverting inputs of the second, third and fourth operational amplifiers are connected to the common filter base. Fourth resistor is in form of a tunable memristor. First and third resistors are adjustable.

EFFECT: possibility of independent readjustment of the main filter parameters: resonance frequency, pole quality factor and filter transfer coefficient at resonance frequency.

1 cl, 3 tbl, 7 dwg

Description

The invention relates to means used to isolate the spectrum of a signal source, for example, when processing by analog-to-digital converters. Bandpass active RC filters are among the common analog devices that determine the quality indicators of many radio engineering systems during digital signal processing.

An active RC filter is known (patent RU 2694134, IPC H03H 11/1252, "Band-pass ARC filter on two operational amplifiers with pole frequency increase and independent adjustment of the main parameters", published 09/07/2019). The filter comprises an input and an output of the device, a first operational amplifier, the output of which is connected to the output of the device, a first resistor connected between the output and the inverting input of the first operational amplifier, second and third series-connected resistors connected between the inverting input of the first operational amplifier and the common power supply bus, a first capacitor connected between the common node of the series-connected second, third resistors and the non-inverting input of the first operational amplifier, a fourth resistor, the first terminal of which is connected to the output of the first operational amplifier, a fifth resistor, the first terminal of which is connected to the common power supply bus, a sixth resistor, the first terminal of which is connected to the inverting input of the first operational amplifier, a seventh resistor, the first terminal of which is connected to the input of the device, the second terminals of the sixth and seventh resistors are connected to the inverting input of the second operational amplifier, and an eighth resistor is connected between the output and the inverting input of the second operational amplifier, the non-inverting input of the second operational amplifier is connected to the common power supply bus, the output of the second operational amplifier connected through the ninth resistor to the second terminal of the fourth resistor, which is connected to the non-inverting input of the first operational amplifier and the second terminal of the fifth resistor through the second capacitor.

A significant disadvantage of the bandpass filter is that it does not provide independent reconfiguration of the main parameters of the circuit: resonant frequency, pole quality factor and transfer coefficient. This complicates the calculation of the parameters of the circuit elements of a reconfigurable bandpass active RC filter.

An active RC filter is known (patent RU No. 2718830 IPC H03H 11/12, "Second-order bandpass filter with independent adjustment of the main parameters", published 2019.11.25). The filter comprises an input and an output of the device, first and second differential operational amplifiers, first, second and third series-connected resistors connected between the output of the second differential operational amplifier connected to the output of the device and a common power source bus, wherein the common node of the first and second series-connected resistors is connected to the inverting input of the second differential operational amplifier, and the common node of the second and third series-connected resistors is connected to the non-inverting input of the second differential operational amplifier via the first capacitor, fourth and fifth series-connected resistors connected between the output of the first differential operational amplifier and the input of the device, wherein the inverting input of the first differential operational amplifier is connected to the inverting input of the second differential operational amplifier via the sixth resistor, and the non-inverting input of the first differential operational amplifier is connected to the common power source bus, the output of the first differential operational amplifier is connected to the non-inverting input of the second differential operational amplifier via the series-connected second capacitor and seventh resistor, wherein the common node of the series-connected second capacitor and The seventh resistor is connected to the common bus of the power supply through the eighth resistor and is connected to the output of the device through the third capacitor.

A significant disadvantage of the bandpass filter is that the circuit uses an excessive number of elements, which complicates the independent adjustment of the main filter parameters: resonant frequency, pole quality factor, and transmission coefficient at the resonant frequency.

A tunable active RC filter is known (patent RU No. 2722752, IPC H03H 11/12, “Band-pass filter with independent adjustment of pole frequency, pole attenuation and transmission coefficient”, published on 11/12/2019), which is the closest in technical essence to the claimed technical solution. The filter comprises an input and an output of the device, first and second differential operational amplifiers, first and second series-connected resistors connected between the input of the device and the output of the second differential operational amplifier, the common node of which is connected to the inverting input of the second differential operational amplifier, the non-inverting input of which is connected to the common power supply bus, the eighth resistor is connected between the non-inverting input of the first differential operational amplifier and the common power supply bus, the output of the first differential operational amplifier is connected to the output of the device, the output of the second differential operational amplifier is connected to the inverting input of the first differential operational amplifier through a series-connected first capacitor and a fourth resistor, the output of the first differential operational amplifier is connected to the non-inverting input of the first differential operational amplifier through series-connected sixth and seventh resistors, the common node of which is connected to the common node of the series-connected first capacitor and fourth resistor through a fifth resistor, the output of the device is connected to the inverting input of the first differential operational amplifier through the second capacitor and is connected to the inverting input of the second differential operational amplifier through the third resistor.

A significant disadvantage of a bandpass filter is the complexity of performing an iterative (step-by-step) process of adjusting the main parameters of the circuit, since when adjusting one of the filter parameters, for example, attenuation or resonant frequency, another parameter of the amplitude-frequency characteristic changes - the transmission coefficient in the passband. Therefore, the adjustment of each filter parameter must be repeated several times, which significantly complicates the implementation of a tunable bandpass active RC filter.

The objective of the claimed invention is to expand the technical capabilities of measuring equipment by independently adjusting the parameters of a bandpass active RC filter.

The technical result that can be obtained by implementing the claimed technical solution consists in the possibility of independent restructuring of the main parameters of the filter: resonant frequency, pole quality factor and filter transmission coefficient at the resonant frequency, while the restructuring of the pole quality factor can be performed using an adjustable memristor.

In order to achieve the technical result in a tunable bandpass active RC filter containing first and second inverting operational amplifiers, eight resistors and two capacitors, wherein the first terminals of the first, second and eighth resistors are connected to the inverting input of the first operational amplifier, and the second terminals of the first and second resistors are connected to the filter input and the output of the first operational amplifier, the first terminals of the sixth resistor and second capacitor are connected to the inverting input of the second operational amplifier, and the second terminals of the second capacitor and seventh resistor are connected to the output of the second operational amplifier, the non-inverting input of the first operational amplifier is connected to the common base of the filter, the third and fourth inverting operational amplifiers are additionally introduced, wherein the first terminals of the third, fourth and seventh resistors are connected to the inverting input of the third operational amplifier, and the second terminals of the third and fourth resistors are connected to the outputs of the first and third operational amplifiers, the first terminals of the fifth resistor and first capacitor are connected to the inverting input of the fourth operational amplifier, and their second terminals are connected to the outputs of the third and fourth operational amplifiers, the second terminals of the sixth, eighth resistors and the filter output are connected to the output of the fourth operational amplifier, the non-inverting inputs of the second, third and fourth operational amplifiers are connected to the common base of the filter, while the fourth resistor is made in the form of a tunable memristor, and the first and third resistors are adjustable.

The essence of the claimed technical solution is explained by the following graphic materials: Fig. 1 shows a diagram of a tunable bandpass active RC filter; Fig. 2 is a block diagram of a bandpass filter; Fig. 3 is a model of a tunable memristor; Fig. 4 is the frequency characteristics of a bandpass filter with a tunable resonant frequency when using a memristor; Fig. 5 is the frequency characteristics of a bandpass filter with an adjustable pole quality factor; Fig. 6 is the frequency characteristics of a bandpass filter with a tunable transmission coefficient; Fig. 7 is the impulse response of a bandpass filter.

The tunable bandpass active RC filter (Fig. 1) comprises first 1 and second 2 inverting operational amplifiers, eight resistors and two capacitors, wherein the first terminals of the first 5, second 6 and eighth 7 resistors are connected to the inverting input of the first 1 operational amplifier, and the second terminals of the first 5 and second 6 resistors are connected to the input 8 of the filter and the output of the first 1 operational amplifier, respectively, the first terminals of the sixth 14 resistor and second 15 capacitor are connected to the inverting input of the second 2 operational amplifier, and the second terminals of the second 15 capacitor and seventh 11 resistor are connected to the output of the second 2 operational amplifier, the non-inverting input of the first 1 operational amplifier is connected to the common base of the filter, and also comprises third 3 and fourth 4 inverting operational amplifiers, wherein the first terminals of the third 9, fourth 10 and seventh 11 resistors are connected to inverting input of the third 3 operational amplifier, and the second terminals of the third 9 and fourth 10 resistors are connected to the outputs of the first 1 and third 3 operational amplifiers, respectively, the first terminals of the fifth 12 resistor and first 13 capacitor are connected to the inverting input of the fourth 4 operational amplifier, and their second terminals are connected to the outputs of the third 3 and fourth 4 operational amplifiers, the second terminals of the sixth 14, eighth 7 resistors and the output 16 of the filter are connected to the output of the fourth 4 operational amplifier, the non-inverting inputs of the second 2, third 3 and fourth 4 operational amplifiers are connected to the common base of the filter, wherein the fourth 4 resistor is made in the form of an adjustable memristor, and the first 1 and third 3 resistors are also adjustable.

The transfer function of the claimed tunable active RC filter has the form

Where circular resonant frequency;

pole quality factor;

And time constants;

filter transmission coefficient at resonant frequency.

The circuit diagram of the bandpass active RC filter is shown in Fig. 1. Fig. 2 shows the block diagram of the filter, which shows the two negative feedbacks used in the circuit. The first feedback The first and third operational amplifiers are included, as well as the first active RC integrator, implemented on the fourth operational amplifier. In the second feedback - the third operational amplifier and two active RC integrators implemented on the second and fourth operational amplifiers. At resonant frequencies the filter in the second 2 node of the circuit (Fig. 2) sums the signals of the first that coincide in phase and the second feedback, which allows the implementation of a tunable bandpass filter circuit with the required transfer function

The bandpass filter works as follows:

When applying a DC voltage (f=0) to the filter input, the gain factors of the second and fourth inverting operational amplifiers become infinitely large. To ensure the operation of these amplifiers in a linear mode, it is necessary to maintain the voltage at their inputs close to zero, then the output voltage of the bandpass filter will be minimal. At an infinitely high frequency of the input voltage, the reactances of the first and second capacitors will be minimal, i.e. the second and fourth inverting operational amplifiers are covered by 100% negative feedback, and therefore practically do not amplify the signals. Thus, the voltage at the filter output will be close to zero. At frequencies other than those considered, the gain factor The filter gain is determined by the ratio of the resistances of the eighth and first resistors. The transfer coefficient The filter can be independently adjusted over a wide range by changing the resistance of the first resistor. Pole quality factor filter varies widely by adjusting the resistance of the third resistor. The resonant frequency in the described circuit is adjusted by changing the resistance of the fourth resistor, which can be made in the form of an adjustable memristor (Fig. 3). The memristor used is characterized by an active resistance which is shown in the diagram (Fig. 1) as the resistance of the fourth resistor. A memristor is a passive element of an electric circuit, the resistance of which depends on the value of the current passed through it. The memristor consists of a thin film (50 nm) of titanium dioxide between two metal contacts 5 nm thick (Fig. 3). In the titanium dioxide film there are two layers, one of which is depleted (Doped) and has a small number of oxygen atoms. Oxygen vacancies are charge carriers, so the depleted layer has low resistance and is conductive. The oxygen-saturated layer (Undoped) has enormous resistance to current. The properties of such a memristor can be demonstrated using a simple model based on the mechanism of ion drift under the action of an applied voltage. The total resistance of the device under consideration can be represented as the sum of the resistances of two variable resistors connected in series. One of the resistors (the conducting region) has low resistance another resistor - much higher resistance When voltage is applied to the metal contacts of the memristor (Fig. 3),

charged ions begin to drift and the boundary between the two regions shifts. Thus, the film resistance as a whole depends on the amount of charge that has passed through it in a certain direction, and the charge value is reversible when the direction of the current changes. The dependence of the voltage on the memristor on the current flowing through it is determined by the expression

Where width of the alloyed region [0,D]; total width of the memristor structure; voltage on the memristor; current through the memristor; low resistance of the doped region of the memristor; high resistance of the undoped region of the memristor.

In the circuit of a tunable active RC filter (Fig. 1), the active resistance is memristor can be changed by selecting the appropriate active resistance of the undoped regionin the SPICE memristor model libraryLTspice software simulator.

Fig. 4 shows the amplitude-frequency characteristics (AFC) of a tunable bandpass active RC filter with an adjustable resonant frequency. which can be changed by selecting the appropriate resistance of the undoped region of the memristor

Table 1

n 1 10 1,408 4,0623 9,6956 2 15 1,506 3,3111 14,594 3 20 2,2505 2,8349 19,908 4 25 2,5195 2,5435 24,731 5 30 2,7553 2,3026 30,177 6 40 3,1768 1,9885 40,462 7 50 3,5837 1,7824 50,362

Table 1 provides a description of the frequency characteristics taken at seven resistances of the undoped region. memristor. The table shows the results of the resonant frequency calculations pole quality factor and active resistance of the memristor

The study of the frequency characteristics of the bandpass filter established that when choosing different resistances of the undoped region of the memristor differing by 5 times, the resonant frequency changed by 2.545 times, while the pole quality factor changed by 2.279 times, and the resistance of the memristor - by 5.194 times. The obtained calculation results show that when regulating the resistance of the undoped region of the memristor, changes in the resistance of the memristor and the resonant frequency of the filter are ensured in wide ranges.

Fig. 5 shows the amplitude-frequency characteristics (AFC) of a filter with adjustable pole Q-factor. when the resistance of the resistor changes Table 2 shows the results of the resonant frequency calculations. and pole quality factor from which it follows that when regulating the resistance of the resistor 4 times the pole quality factor independently changed by 3.899 times, and the resonant frequency by 0.17%.

Table 2

n 1 30 2,252 526.31 4,2794 2 45 2,249 352.25 6,3846 3 60 2,249 269.04 8,3605 4 80 2,249 198.49 11,330 8 120 2,253 135.36 16,648

Fig. 6 shows the amplitude-frequency characteristics (AFC) of a bandpass filter with an adjustable transmission coefficient. when the resistance of the resistor changes Table 3 shows the results of the resonant frequency calculations. pole quality factor and the transmission coefficient from which it follows that when the resistance of the resistor changes 16 times independent regulation of the transmission coefficient is provided filter by 27.1 dB. At the same time, the values of the pole quality factor and resonant frequency changed only by 9.5% and 0.2%, respectively.

Table 3

n 1 5 2,249 806.94 2,781 18.09 2 10 2,253 796.85 2,826 12.07 3 20 2,064 635,66 3,047 6.04 4 40 2,255 803.86 2,805 0.03 8 80 2,251 802.97 2,804 -9.51

Fig. 7 shows the impulse response. bandpass filter (Fig. 1) taken at the resistance of the undoped region memristor. Results of studies of the amplitude-frequency characteristic of the filter, namely the pole quality factor and resonant frequency under the considered mode were presented in Table 1 and Fig. 4. The pole quality factor of the filter according to the oscillogram of the impulse response can be found using the formula

where U1m=313.88 mV and U2m=101.96 mV are the first two amplitude values of the impulse response (Fig. 7).

It should be noted that the calculations of the pole quality factor by frequency and temporary characteristics differ slightly - by 1.46%.

In the impulse response graph window The calculations of the resonant frequency are presented performed in the LTspice program.

It can be noted that the calculations of the resonant frequency based on the frequency and time characteristics differ slightly - by 1.78%.

Thus, the presented experimental studies confirm the possibility of independent restructuring of the main filter parameters: resonant frequency, pole quality factor and filter transmission coefficient at the resonant frequency, while the restructuring of the pole quality factor can be performed using an adjustable memristor.

Claims (1)

A tunable bandpass active RC filter comprising first and second inverting operational amplifiers, eight resistors and two capacitors, wherein the first terminals of the first, second and eighth resistors are connected to the inverting input of the first operational amplifier, and the second terminals of the first and second resistors are connected to the filter input and the output of the first operational amplifier, the first terminals of the sixth resistor and second capacitor are connected to the inverting input of the second operational amplifier, and the second terminals of the second capacitor and seventh resistor are connected to the output of the second operational amplifier, the non-inverting input of the first operational amplifier is connected to the common base of the filter, characterized in that a third and fourth inverting operational amplifiers are additionally introduced, wherein the first terminals of the third, fourth and seventh resistors are connected to the inverting input of the third operational amplifier, and the second terminals of the third and fourth resistors are connected to the outputs of the first and third operational amplifiers, respectively, the first terminals of the fifth resistor and first capacitor are connected to the inverting input of the fourth operational amplifier, and their second terminals are connected to the outputs of the third and fourth operational amplifiers, respectively, the second terminals of the sixth, eighth resistors and the filter output are connected to the output of the fourth operational amplifier, the non-inverting inputs of the second, third and fourth operational amplifiers are connected to the common base of the filter, while the fourth resistor is made in the form of a memristor, and the first and third resistors are adjustable.