RU2598330C2 - Higher (k-th) order two-terminal circuit simulator - Google Patents

Abstract

FIELD: radio engineering and communications.

SUBSTANCE: invention relates to radio engineering and communication and can be used in designing active RC-filters, as well as in pulse equipment devices and automatic control devices for adjustment and compensation of transition processes. K-order two-terminal circuit simulator contains k operational amplifiers with input circuits of two serially connected complex resistances, as well as required connections between them.

EFFECT: increased accuracy of setting capacitance, inductive and resistive full output resistances of 9th order two-terminal circuit during simulation.

1 cl, 4 dwg, 1 tbl

Description

The invention relates to electronics and communications and can be used to create active RC filters, as well as in devices of pulsed technology and automatic control for regulation and compensation of transients.

Known simulator of inductance with switched capacitors (copyright certificate SU 1145460). The simulator contains an operational amplifier with a capacitive negative feedback circuit made on the capacitor, the first and second resistor simulators, two links, each of which contains an additional operational amplifier with a capacitive negative feedback circuit made on the capacitor, a capacitor, the first and second additional resistor simulators moreover, the simulators are made on switched capacitors. However, the known simulator is able to simulate only first-order inductances.

Known imitators of higher-order two-terminal devices, made on dependent voltage sources controlled by current and voltage (Philippow E., Reinhard M. Beitrag zur Theorie Kunstlicher Elemente hoherer Ordnung // IWK Tech. Hochschule Ilmenau, 1981., Philippow E., Druckner P. Anwendung kunstlicher Elemente hoherer Ordnung in selektiven Schaltungen // 23IWK Tech. Hochschule Ilmenau 1978 - Vortragsreie B2 - s. 33-37). However, the implementation of such simulators of higher order dvukhpolosnykh turns out to be difficult, and their frequency characteristics differ from those obtained with a rigorous mathematical description.

The closest in technical essence to the claimed device solution is a simulator of a two-terminal higher (k-th) order, which is a serial connection of k links in the form of integrators (E. Filippov, V. Kachan. Mathematical description and stability of circuits with high-order artificial elements / / University proceedings. Energy. 1983. No. 8. P. 24-27). Such a higher-order two-terminal circuit contains errors that occur during integration, and with an increase in the number of integrators, the error increases. In addition, the well-known imitator of a two-terminal network has instability, for the elimination of which it is necessary to adjust one or another circuit parameter for each link.

The objective of the invention is to provide a simulation of inductive, capacitive and resistive two-terminal devices of any order.

The technical result consists in increasing the accuracy of setting capacitive, inductive and resistive total output resistances of the two-terminal higher (9th) order during simulation.

The specified technical result is achieved by the fact that a two-terminal simulator of order k contains a serial connection of k links, according to the solution, each link contains an operational amplifier and a circuit of two series-connected complex resistances connected between the non-inverting and inverting inputs of the operational amplifier, with each link except k go, the non-inverting input of the operational amplifier is connected to the inverting input of the operational amplifier of the subsequent link, the common connection point is set of the resistors connected to the output of the operational amplifier of the next link, and the common connection point of the complex resistances of the k-th link is connected to the output of the operational amplifier of the first link, while the first output of the two-terminal is connected through the integrated resistance to the inverting input of the operational amplifier of the first link, and the second output of the two-terminal with non-inverting input of the operational amplifier of the k-th link.

The invention is illustrated by drawings, where in FIG. 1 shows an electrical diagram of the inventive simulator of a two-terminal k-th order; in FIG. 2 is a circuit diagram of a 3rd order two-terminal simulator with inductive output impedance, FIG. 3 is a circuit diagram of a 3rd order bipolar simulator with capacitive output resistance, FIG. 4 - experimentally obtained frequency dependence of the output impedance of a third-order two-terminal network with inductive resistance.

A two-terminal simulator of order k equipped with first and second outputs is assembled in the form of a series connection of k links, each of which contains an operational amplifier and a circuit of two series-connected complex resistances connected between the non-inverting and inverting inputs of the operational amplifier. Each link except the kth non-inverting input of the operational amplifier is connected to the inverting input of the operational amplifier of the next link, and the common point of connection of complex resistances is connected to the output of the operational amplifier of the next link. The common connection point of the complex resistances of the k-th link is connected to the output of the operational amplifier of the first link. The first output of the two-terminal is connected through the integrated resistance to the inverting input of the operational amplifier of the first link, and the second output of the two-terminal is connected to the non-inverting input of the operational amplifier of the k-th link.

и $$Z_2^{(i)}$$

, а полное выходное сопротивление Z имитатора двухполюсника высшего (k-го) порядка рассчитывается по формуле (1).To simplify the formula for calculating the total output impedance of a simulator of a two-terminal higher (kth) order, the complex resistances of the circuit of the ith link are indicated as $$Z_{\mathrm{one}}^{(i)}$$

and $$Z_2^{(i)}$$

, and the total output resistance Z of the simulator of a two-terminal higher (k-th) order is calculated by the formula (1).

и полные выходные проводимости

имеют резистивный характер, а у двухполюсников нечетного (k = 3, 5, 7, …) порядка полные выходные сопротивления имеют индуктивный или емкостный характер. Table 1 shows the second-ninth order two-terminal parameters calculated by formula (1). All bipolar even (k = 4, 6, 8, ...) orders have full output resistances

and full conductivity outputs

have a resistive character, and for two-terminal odd (k = 3, 5, 7, ...) orders of magnitude, the total output resistances are inductive or capacitive in nature.

и

выбраны резисторы с сопротивлением R $$(Z_1^{(1)}=Z_1^{(2)}=Z_1^{(3)}=Z_0=R)$$

, а в качестве комплексных сопротивлений $$Z_2^{(1)},Z_2^{(2)},Z_2^{(3)}$$

- конденсаторы c емкостью C $$(Z_2^{(1)}=Z_2^{(2)}=Z_2^{(3)}=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$j\omega C$}\right.)$$

, где j - мнимая единица, $$\omega$$

- частота. Тогда в соответствии с формулой (1) полное выходное сопротивление двухполюсника принимает вид: As an example in FIG. 2 shows an electric circuit of a third-order two-terminal simulator with inductive output impedance. So that the total output impedance of the two-terminal is inductive, as complex resistances $$Z_{\mathrm{one}}^{(\mathrm{one})},Z_{\mathrm{one}}^{(2)},Z_{\mathrm{one}}^{(3)}$$

and

resistors with resistance R selected $$(Z_{\mathrm{one}}^{(\mathrm{one})}=Z_{\mathrm{one}}^{(2)}=Z_{\mathrm{one}}^{(3)}={\mathrm{<figure-callout\; id="0"\; label="Z"\; filenames="00000029.png"\; state="\{\{state\}\}">Z</figure-callout>}}_0=R)$$

as well as complex resistances $$Z_2^{(\mathrm{one})},Z_2^{(2)},Z_2^{(3)}$$

- capacitors with capacitance C $$(Z_2^{(\mathrm{one})}=Z_2^{(2)}=Z_2^{(3)}=\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{$j\omega C$}\right.)$$

where j is the imaginary unit, $$\omega$$

- frequency. Then, in accordance with formula (1), the total output impedance of a two-terminal device takes the form:

,

,

- индуктивность имитированного двухполюсника третьего порядка. Where $$L^{(3)}={\omega }^2{C}^3{R}^{\mathrm{four}}$$

- inductance of a simulated two-terminal third order.

выбирают конденсаторы c емкостью C $$(Z_1^{(1)}=Z_1^{(2)}=Z_1^{(3)}=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$j\omega C$}\right.)$$

, а в качестве комплексных сопротивлений $$Z_2^{(1)},Z_2^{(2)},Z_2^{(3)}$$

и $$Z_0$$

- резисторы с сопротивлением R $$(Z_2^{(1)}=Z_2^{(2)}=Z_2^{(3)}=Z_0=R)$$

. Тогда в соответствии с формулой (1) полное выходное сопротивление двухполюсника принимает вид: As a second example in FIG. 3 shows an electric circuit of a simulator of a 3-order bipolar with a capacitive output resistance. So that the total output impedance of a two-terminal device is capacitive as complex resistances $$Z_{\mathrm{one}}^{(\mathrm{one})},Z_{\mathrm{one}}^{(2)},Z_{\mathrm{one}}^{(3)}$$

choose capacitors with capacitance C $$(Z_{\mathrm{one}}^{(\mathrm{one})}=Z_{\mathrm{one}}^{(2)}=Z_{\mathrm{one}}^{(3)}=\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{$j\omega C$}\right.)$$

as well as complex resistances $$Z_2^{(\mathrm{one})},Z_2^{(2)},Z_2^{(3)}$$

and $$Z_0$$

- resistors with resistance R $$(Z_2^{(\mathrm{one})}=Z_2^{(2)}=Z_2^{(3)}={\mathrm{<figure-callout\; id="0"\; label="Z"\; filenames="00000029.png"\; state="\{\{state\}\}">Z</figure-callout>}}_0=R)$$

. Then, in accordance with formula (1), the total output impedance of a two-terminal device takes the form:

, $$Z={(-\mathrm{one})}^{3}R\frac{{(\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{$j\omega C$}\right.)}^3}{{\mathrm{<figure-callout\; id="3"\; label="R"\; filenames="00000029.png"\; state="\{\{state\}\}">R</figure-callout>}}^3}=\frac{\mathrm{one}}{j{\omega }^3{C}^3{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="00000029.png"\; state="\{\{state\}\}">R</figure-callout>}}^2}=\frac{\mathrm{one}}{j\omega C^{(3)}}$$

,

- емкость имитированного двухполюсника третьего порядка (k = 3).Where $$C^{(3)}={\omega }^2{C}^3{R}^2$$

- the capacity of a simulated third-order two-terminal network (k = 3).

Concrete example

1% и четыре резистора с одинаковыми номиналами 1 кОм

5%. Теоретическое значение индуктивности

на частоте 100 Гц составило 0.4 мкГн, на частоте 1 кГц - 40 мкГн. При имитации двухполюсника 3-го порядка с емкостным выходным сопротивлением выбирались три одинаковых конденсатора с номиналом 100 нФ

1% и четыре одинаковых резистора с номиналом 10 кОм

5%. Теоретическое значение емкости

на частоте 100 Гц составляет 40 нФ, на частоте 1 кГц - 4 мкФ. Для имитации двухполюсника 4-го порядка с резистивным сопротивлением

использованы четыре одинаковых конденсатора с номиналом 10 нФ

1% и пять резисторов с одинаковыми номиналами 10 кОм

5%. Теоретическое значение

на частоте 100 Гц составило 0.156 Ом, а на частоте 1 кГц - 1560 Ом.The fourth-order bipolar simulator is a combination of two LF412CH integrated circuits, each of which contains two operational amplifiers, a set of resistors of type C2-14-0.125 and capacitors of type K71-7. This design allows you to simulate two-terminal from the second to fourth order when you turn on the appropriate number of operational amplifiers. Three operational amplifiers were used to simulate 3rd order bipolar devices. When simulating a third-order two-terminal with an inductive output resistance, three identical capacitors with nominal values of 10 nF were selected

1% and four resistors with the same ratings of 1 kOhm

5%. The theoretical value of inductance

at a frequency of 100 Hz, it was 0.4 μH; at a frequency of 1 kHz, it was 40 μH. When simulating a third-order two-terminal with capacitive output resistance, three identical capacitors with a nominal value of 100 nF were selected

1% and four identical 10 kΩ resistors

5%. The theoretical value of capacity

at a frequency of 100 Hz is 40 nF, at a frequency of 1 kHz - 4 microfarads. To simulate a 4th order bipolar with resistive resistance

used four identical capacitors with a nominal value of 10 nF

1% and five resistors with the same ratings of 10 kOhm

5%. Theoretical value

at a frequency of 100 Hz it was 0.156 Ohms, and at a frequency of 1 kHz - 1560 Ohms.

представлен на фиг. 4. Относительная погрешность отклонения измеренных значений индуктивности $$L^{(3)}$$

от расчетных значений возрастала с частотой и для частот от 100 Гц до 5 кГц не превышала 5%.An experimental study of the frequency dependences of the total output resistances of simulated two-terminal devices was carried out on a SK4-56 spectrum analyzer operating in the mode of measuring the amplitude-frequency characteristics of four-terminal devices. To this end, the serial connection of a simulator of one of the higher order two-terminal and additional resistance was connected to the output of the SK4-56 frequency-modulated oscillation generator, and a two-terminal simulator was connected to the input connector of the SK4-56 device. An amplitude-frequency characteristic appeared on the analyzer screen, and the value of the vertical deflection of the beam was proportional to the total input impedance of the two-terminal simulator. An example of an experimentally obtained frequency dependence for a third-order inductance $$L^{(3)}$$

shown in FIG. 4. The relative error of the deviation of the measured values of the inductance $$L^{(3)}$$

from the calculated values increased with frequency and for frequencies from 100 Hz to 5 kHz did not exceed 5%.

Claims (1)

A two-terminal simulator of order k containing a series connection of k links, characterized in that each link contains an operational amplifier and a circuit of two series-connected complex resistances connected between the non-inverting and inverting inputs of the operational amplifier, with each link except the kth non-inverting input the operational amplifier is connected to the inverting input of the operational amplifier of the next link, the common connection point of the complex resistances is connected to the output of the opera an amplifier of the next link, and the common connection point of the complex resistances of the k-th link is connected to the output of the operational amplifier of the first link, while the first output of the two-terminal is connected through the integrated resistance to the inverting input of the operational amplifier of the first link, and the second output of the two-terminal is connected to a non-inverting input of the operational amplifier k-th link.

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