RU2110140C1 - Adjustable arc filter - Google Patents

Abstract

FIELD: radio engineering; selective radio electronic, including microelectronic, devices. SUBSTANCE: filter has first and second resistors 1, 2, first and second operational amplifiers 3, 4 third and fourth resistors 5, 6, third operational amplifier 7, fifth, sixth, seventh, and eighth resistors 8-11, fourth operational amplifier 12, first and second capacitors 13, 14 first and second numeric-control conductors 15, 16, ninth, tenth, eleventh, and twelfth resistors 17-20. EFFECT: extended operating frequency range and enlarged functional capabilities. 3 cl, 4 dwg , 2 tbl

Description

 The invention relates to radio engineering and can be used in selective radio-electronic devices, including microelectronic.

 A device is known "Universal active filter" (Germany, Pat. N 3213513, class H 03 H 11/04, published in the bulletin "Inventions in the USSR and abroad" N 10, 1983), containing the summing unit and the first integrating unit, covered by negative frequency-independent feedback through the first attenuator, the second integrating block covered by the summing block and the first integrating block negative frequency-independent feedback through the second attenuator, the input signal being fed to the non-inverting input of the summing block, and the output as a filter is the output of the summing unit or the output of the first or second integrating unit.

 The signs of this device, which coincide with the features of the proposed technical solution, are attenuators and integrating units.

 The reasons that impede the achievement of the technical result are the great dependence of the frequency and quality factor (attenuation) of the pole at a high frequency due to the influence of the gain areas of operational amplifiers.

 Also known is an "Active RC filter" (USSR, A.S. N 1381689, published. 15.03.88, bull. N 10), containing the first adder, the output of which through the first and second integrators and the first attenuator are connected in series to the first non-inverting the input of the second adder, and through the second attenuator connected to the second non-inverting input of the first adder, the output of the second integrator through the third attenuator is connected to the first inverting input of the first adder, the output of the first integrator through the fourth attenuator is connected to the inverting at the input of the second adder, the fifth attenuator is connected to the second non-inverting input of the first adder, between the output of the first adder and its second inverting input, as well as between the output of the first integrator and the input of the fifth attenuator, correction elements with the transfer function of the first-order aperiodic link are included, the first non-inverting input the first adder is the input, and the output of the second adder is the output of the device.

 The signs of this device, which coincide with the features of the proposed technical solution, are attenuators and integrators.

 The reasons that impede the achievement of the technical result are the high sensitivity of the frequency and the Q factor at high frequency due to the influence of the amplification areas of operational amplifiers, as well as the high power consumption (the device contains six operational amplifiers), as well as limited functionality.

 The closest solution in technical essence to the proposed device is "Universal filter of the second order with independently adjustable characteristics" (In the book.: Titze U., Schenk K. Semiconductor circuitry: Reference manual. Translated from German.- M.: Mir, 1982 ; p.224, Fig. 13.37), containing four operational amplifiers, eight resistors and two capacitors, the first and second resistors are connected between the inverting inputs and outputs of the first and second operational amplifiers, the third and fourth resistors are connected by the first outputs to the inverting input of the first operational amplifier, the second output of the fourth resistor is connected to the output of the third operational amplifier, the fifth resistor is connected to the output of the fourth operational amplifier by the first output, the sixth resistor is connected between the output of the first and inverting input of the second operational amplifiers, the seventh resistor is connected between the output of the second and inverting the input of the third operational amplifier, the eighth resistor is connected between the output of the third and the inverting input of the fourth operational amplifier amplifiers, the first and second capacitors are connected to the inverting inputs and outputs of the third and fourth operational amplifiers, respectively, while the non-inverting inputs of the operational amplifiers are connected to a common bus, the second output of the fifth resistor is connected to the inverting input of the second operational amplifier, and the second output of the third resistor is the input of the device , device outputs are operational amplifier outputs.

 The reason that impedes the achievement of the required technical result is the narrow frequency range of the device due to the influence of the area of operational amplifiers.

 The problem to which the invention is directed is to expand the range of operating frequencies.

The technical result that can be obtained by carrying out the invention:
extended frequency range of work;
advanced functionality.

 To achieve a technical result in a tunable ARC filter containing four operational amplifiers, eight resistors and two capacitors, the first and second resistors connected between the inverting inputs and outputs of the first and second operational amplifiers, respectively, the third and fourth resistors are connected to the inverting input of the first operational amplifier, the second output of the fourth resistor is connected to the output of the third operational amplifier, the fifth resistor is connected to the output by the first output to the fourth operational amplifier, the non-inverting input of the second operational amplifier is connected to a common bus, and the output of the filter is one of the outputs of the operational amplifiers; additionally introduced the first and second digitally controlled conductances included respectively between the output of the second and non-inverting inputs of the third operational amplifiers and between the outputs of the third and non-inverting inputs of the fourth operational amplifiers, the first output of the fourth resistor connected to the inverting input of the third operational amplifier, the second output of the fifth resistor connected to the second terminal of the third and with the first terminals of the sixth and seventh resistors, the second terminal of the seventh resistor is connected to the common th bus, the eighth resistor is connected to the output of the fourth operational amplifier by the first output and the second output to the inverting inputs of the second and fourth operational amplifiers, the first capacitor is connected between the output of the first operational amplifier and the non-inverting input of the third operational amplifier, and the second capacitor is connected between the output of the second operational amplifier and non-inverting inputs of the first and fourth operational amplifiers, the second output of the sixth resistor is the first input of the filter.

 To achieve a technical result, which is to expand the functionality (due to the implementation of the inputs of the lowpass, highpass, bandpass and notch filters with phase inversion and without phase inversion), the ninth and tenth resistors are introduced, and the ninth resistor is connected by the first output to the inverting input of the first operational amplifier and the second is the second input of the filter, the tenth resistor is connected by the first output to the inverting input of the second operational amplifier, and the second is the third input of the filter.

To achieve a technical result, which consists in increasing the stability of the quality factor, the non-inverting input of the fourth operational amplifier is connected to the non-inverting input of the first operational amplifier through a resistive voltage divider consisting of the eleventh and twelfth resistors, the first output of the eleventh resistor connected to the non-inverting input of the fourth operational amplifier, and the second - to the first output of the twelfth resistor and to the non-inverting input of the first operational gain I, the second terminal of the twelfth resistor connected to a common bus. The possibility of achieving a technical result is due to the following conclusions:
the expansion of the frequency range of the device’s work is achieved by introducing new connections between the elements, due to which the proposed device has a higher pole frequency compared to the prototype device, ceteris paribus, or the pole parameters deviate less from the calculated value, which is especially important for tunable filters;
the expansion of the functionality of this technical solution is achieved by introducing additional resistors and additional inputs, which allows the device to implement various types of filters (low-pass filter, high-pass filter, PF and RF) with independently adjustable parameters: frequency and quality factor of the pole, scale transfer coefficient, as well as additionally signal inversion;
the stability of the Q factor of the pole is improved by introducing an additional resistive voltage divider, the choice of the transmission coefficient of which ensures almost complete compensation of the influence of the gain areas of operational amplifiers on the pole attenuation.

 The presence of a causal relationship between the totality of the implemented features of the invention and the achieved technical result is given when considering the operation of a tunable ARC filter.

 Figure 1 shows a functional diagram of a tunable ARC filter; figure 2-diagram of the voltage divider; figure 3-circuit diagram and its signal graph; figure 4 is a schematic diagram of the device of the prototype and its signal graph.

 The tunable ARC filter contains (see FIG. 1) the first 1 and second 2 resistors, the first 3 and second 4 operational amplifiers, the third 5 and fourth 6 resistors, the third operational amplifier 7, fifth 8, sixth 9, seventh 10 and eighth 11 resistors, the fourth operational amplifier 12, the first 13 and second 14 capacitors, the first 15 and second 16 digitally-controlled conductivity, ninth 17, tenth 18, (eleventh 19 and twelfth 20 resistors (in Fig. 2)).

 The tunable ARC filter contains the first 1 and second 2 resistors that are connected between the inverting inputs and outputs of the first 3 and second 4 operational amplifiers, respectively, the third 5 and fourth 6 resistors are connected by the first conclusions to the inverting input of the first operational amplifier 3, the second output of the fourth resistor is connected to the output of the third operational amplifier 7, the fifth resistor 8 is connected with the first output to the output of the fourth operational amplifier 12, a non-inverting input of the second operational amplifier 4 sub is connected to the common bus, and the filter output is one of the outputs of operational amplifiers 3, 4, 7, or 12, the first capacitor 13 is connected between the output of the first operational amplifier 3 and the non-inverting input of the third operational amplifier 7, and the second capacitor 14 is connected between the output of the second operational amplifier 4 and non-inverting inputs of the first 3 and fourth 12 operational amplifiers, the first 15 and second 16 digitally-controlled conductivities included respectively between the output of the second 4 and the non-inverting input of the third 4 and non-inverting the input of the third 7 operational amplifiers and between the output of the third 7 and the non-inverting input of the fourth 12 operational amplifiers, while the first output of the fourth resistor 6 is connected to the inverting input of the third operational amplifier 7, the second output of the fifth resistor 8 is connected to the second output of the third 5 and with the first conclusions the sixth 9 and seventh 10 resistors, the second terminal of the seventh resistor 10 is connected to a common bus, the eighth resistor 11 is connected to the output of the fourth operational amplifier 12 by the first terminal, and to the second terminal the inverting input of the second 4 and fourth 12 operational amplifiers, the second output of the sixth resistor 9 is connected to the first input of the device; the first terminal of the ninth resistor 17 is connected to the inverting input of the first operational amplifier 3, and the second terminal of the ninth resistor 17 is connected to the second input of the device, the first terminal of the tenth resistor 18 is connected to the inverting input of the second operational amplifier 4, and the second terminal of the tenth resistor 18 is connected to the third input devices.

 To increase stability, quality factor between the non-inverting input of the fourth operational amplifier 12 and the non-inverting input of the first operational amplifier 3, a voltage divider is included, consisting of the eleventh 19 and twelfth 20 resistors, the first conclusions of which are connected to the non-inverting input of the first operational amplifier 3, and the second conclusions of the eleventh 19 and twelfth of 20 resistors are connected respectively to the non-inverting input of the fourth operational amplifier 12 and to a common bus.

 The tunable ARC filter works as follows.

 An input harmonic signal is supplied to one of the inputs of the device, passes through it, and enters the outputs of the tunable ARC filter.

где F_ij(p) - передаточная функция с i-го входа на j-й выход;
M_ij - масштабный коэффициент передачи с i-то входа на j-й выход;
A_ij - числитель передаточной функции с i-го входа на j-й выход;
B(p) - знаменатель передаточных функций.As a result, the tunable ARC filter implements the transfer function

where F _ij (p) is the transfer function from the i-th input to the j-th output;
M _ij is the scaled transmission coefficient from the i-th input to the j-th output;
A _ij is the numerator of the transfer function from the i-th input to the j-th output;
B (p) is the denominator of the transfer functions.

- коэффициенты передач резистивных делителей напряжения).To analyze the properties of a tunable ARC filter, the graph method was used. A graph of a tunable ARC filter circuit (see FIG. 3b, where the numbers with indices "+" or "-" indicate non-inverting or inverting inputs OY, and the numbers without indices indicate their outputs; μ ₃ , μ ₄ , μ ₇ and μ ₁₂ - gains respectively of the first 3, second 4, third 7 and fourth 12 operational amplifiers; R ₁ , R ₂ , R ₅ , R ₆ , R ₈ , R ₉ , R ₁₀ and R ₁₁ - resistance of the first 1, second 2, third 5, fourth 6, fifth 8, sixth 9, seventh 10 and eighth 11 resistors; C ₁₃ and C ₁₄ - capacitances of the first 13 and second 14 capacitors; τ ₁ = R ₁₅ C ₁₃ ; τ ₂ = R ₁₆ C ₁₄ - time constants RC-circuits; R ₁₅ and R ₁₆ - tsifroupravlyaemyh conductivities are equivalent resistance 15 and 16, respectively;

- gear ratios of resistive voltage dividers).

.Since the main properties of the tunable ARC filter are the properties of the poles of the transfer function, we define their parameters. To do this, we write the expression for the denominator of the function according to the Mason formula:

.

и пренебрегая членами второго и более высоких порядков малости (т.е. пропорциональных

) после алгебраических преобразований, а также заменяя

, где П_i - площадь усиления i-го операционного усилителя, получим

.Multiplying by a factor

and neglecting the terms of the second and higher orders of smallness (i.e., proportional

) after algebraic transformations, and also replacing

where P _i is the gain area of the i-th operational amplifier, we obtain

.

.As П _i → ∞, we obtain the expressions for the denominator of the transfer function of the tunable ARC filter with ideal OY

.

затухание полюса

;
Q_p - добротность полюса.Where do we find idealized pole parameters
pole frequency

pole attenuation

;
Q _p is the quality factor of the pole.

.Since the deviation of idealized poles usually varies near the frequency of the pole, where the sensitivity of the frequency response of the filter has a maximum value, the equality p ² = -ω $\genfrac{}{}{0ex}{}{\text{2}}{\text{p}}$ , and p ³ = -pω $\genfrac{}{}{0ex}{}{\text{2}}{\text{p}}$ . Then the polynomial of the denominator of the third degree is converted to the polynomial of the second degree

.

.From the last relation we find the relative changes in the parameters of the poles

.

.Carrying out a similar analysis of the circuit of the prototype device, the graph of which is shown in FIG. 4, we get

.

.From relations (9) and (10) for the proposed device with τ ₁ = τ ₂ Q _p = 10 (in this case, k ₁ = k ₃ = 0.45; β = 0.045); γ = 1; R ₆ / R ₁ = 1; R ₁₁ / R ₁₂ = 1; P ₃ = P ₄ = P ₇ = P ₁₂ = P we get

.

Из сопоставления выражений (13) и (14) следует, что отклонение частоты из-за влияния площади усиления ОУ у предлагаемого устройства в 1,7 раза, а отклонение затухания полюса в 25 раз меньше, чем у прототипа, и, следовательно, во столько же раз повышается стабильность параметров, или при одинаковой стабильности во столько же раз расширяется диапазон рабочих частот.With similar ratios between the elements and parameters for the circuit of the prototype device at τ ₁ = τ ₂ Q _p = 10 (with R ₂ / R ₅ = 1; R ₂ / R ₆ = 0.1; R ₁ / R ₃ = R ₁ / R ₄ = 1) P ₁ = P ₂ = P ₃ = P ₄ = P from expressions (11) and (12) we obtain

From a comparison of expressions (13) and (14), it follows that the frequency deviation due to the influence of the gain area of the op amp of the proposed device is 1.7 times, and the deviation of the pole attenuation is 25 times less than that of the prototype, and therefore the same time the stability of the parameters increases, or with the same stability, the range of operating frequencies is expanded by the same amount.

Откуда, при указанных выше соотношениях между элементами, находим
γ ≈ 0,9.
Таким образом, при полученном значении γ затухание полюса практически не зависит от площади усиления и имеет максимальную стабильность. Однако, чтобы при введении делителя не изменялись идеализированные параметры перестраиваемого ARC-фильтра, необходимо выполнение условия: R₂₀>>R₁₆, которое на практике легко реализуется.To increase the stability of the pole attenuation between the inverting inputs of the fourth operational amplifier 12 and the third operational amplifier 3, a voltage divider is included (Fig. 2), consisting of resistors 19 and 20 and allowing changing the value of γ until the condition δd _p (П) = 0, i.e., .

Where, with the above ratios between the elements, we find
γ ≈ 0.9.
Thus, at the obtained value of γ, the pole attenuation is practically independent of the gain area and has maximum stability. However, to prevent the idealized parameters of the tunable ARC filter from changing when introducing the divider, the following conditions must be met: R ₂₀ >> R ₁₆ , which is easily implemented in practice.

 The expressions for the numerators of the transfer functions (1) of the tunable ARC filter from the i-th input to the j-th output are obtained according to the Mason formula from the graph of the diagram of Fig. 3, are given in table. one.

 As can be seen from the table. 1, a tunable ARC filter implements from the corresponding inputs to the corresponding outputs the transfer functions of low and high frequency filters, as well as band and notch filters with phase inversion (“-” sign) and without inversion (“+” sign). The presence of the same functions with and without inversion allows the construction of high-order filters with multi-loop feedback without using additional op-amps, which usually play the role of inverters.

 The expressions for the scale factors of the transfer function (1) are given in table. 2.

To adjust the frequency of the pole, digital-controlled conductivities having equivalent resistances R ₁₅ and R _{16 are used} . Digitally-controlled conductivities are a set of resistors and electronic keys, on the control electrodes of which digital codes are supplied. Closing, the electronic keys change the time constants τ ₁ and τ ₂ , this leads to a change in the frequency of the pole and, accordingly, to the rearrangement of the filter.

 In a non-reconfigurable version of the device, the digitally-controlled conductivity can be replaced with constant resistors.

 Thus, due to the introduction of new elements and the relationships between them, an increase in the frequency stability and pole attenuation was achieved, and the functionality of the ARC filter was expanded compared to the prototype.

Claims (3)

 1. A tunable ARC filter containing four operational amplifiers, eight resistors and two capacitors, the first and second resistors connected between the inverting inputs and outputs of the first and second operational amplifiers, respectively, the third and fourth resistors with the first conclusions connected to the inverting input of the first operational amplifier, the second output of the fourth resistor is connected to the output of the third operational amplifier, the fifth resistor is the first output connected to the output of the fourth operational amplifier, the non-inverting input of the second operational amplifier is connected to a common bus, and the output of the filter is one of the outputs of the operational amplifiers, characterized in that the first and second digital-controlled conductivities are added, connected respectively between the output of the second and non-inverting input of the third operational amplifiers and between the output of the third and non-inverting input fourth operational amplifiers, while the first output of the fourth resistor is connected to the inverting input of the third operational amplifier For the second output of the fifth resistor - with the second output of the third and with the first conclusions of the sixth and seventh resistors, the second output of the seventh resistor is connected to a common bus, the eighth resistor is connected to the output of the fourth operational amplifier by the first output, and the second output to the inverting inputs of the second and fourth operational amplifiers, the first capacitor is connected between the output of the first operational amplifier and the non-inverting input of the third operational amplifier, and the second capacitor is connected between the output of the second operation a non-inverting input of the fourth operational amplifier, which is connected to the non-inverting input of the first operational amplifier, the second output of the sixth resistor is the first input of the filter.  2. The ARC filter according to claim 1, characterized in that the ninth and tenth resistors are inserted into it, the first output of the ninth resistor is connected to the inverting input of the first operational amplifier, and the second output of the ninth resistor is the second input of the filter, while the first output of the tenth resistor connected to the inverting input of the second operational amplifier, and the second output of the tenth resistor is the third input of the filter.  3. The ARC filter according to claim 2, characterized in that the non-inverting input of the fourth operational amplifier is connected to the non-inverting input of the first operational amplifier through an input voltage divider made on the eleventh and twelfth resistors, the first terminals of which are connected to the non-inverting input of the first operational amplifier, and the second terminals of the eleventh and twelfth resistors are connected respectively to the non-inverting input of the fourth operational amplifier and to the common bus.

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