RU2490780C2 - Method for amplitude, phase and frequency modulation of high-frequency signals and multifunctional apparatus for realising said method - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: disclosed method is aimed at providing amplitude, phase and frequency modulation according to the law of variation of the amplitude of a low-frequency control signal with a long linear section of frequency modulation characteristics using one nonlinear element in frequency modulation mode and with a given ratio of the modules and phase difference of the transfer function in two states, characterised by two amplitude values of the low-frequency control signal in amplitude and phase modulation mode.

EFFECT: efficient compact devices for amplitude, phase and frequency modulation using a lumped parameter reactive base.

2 cl, 5 dwg

Description

The invention relates to the fields of radio communications, radar, radio navigation and electronic warfare and can be used to provide amplitude, phase and frequency modulation.

A known method of amplitude, phase and frequency modulation of a high-frequency signal, based on the frequency modulation mode by converting the energy of a constant voltage source into energy of a high-frequency signal, organizing external positive feedback between the load and the control electrode of the first nonlinear element, fulfilling the excitation conditions in the form of amplitude balance and balance phases determining respectively the amplitude and frequency of the generated high-frequency signal, and the matching conditions of the first a linear element with a load, changing the frequency of the generated high-frequency signal by changing the phase balance by changing the parameter of the second non-linear element included in the selective load, according to the law of changing the amplitude of the low-frequency control (primary, information) signal (see Gonorovsky I.S. signals - M .: “Bustard.” - 2006, p. 434-437). In the mode of amplitude and phase modulation, the source of the high-frequency signal is connected to the input of the device and its amplitude and phase are changed.

A device for amplitude and phase modulation and frequency modulation of a high-frequency signal is known, consisting of a constant voltage source that establishes a working point in the middle of a quasilinear section of the current-voltage characteristic of a transistor, a four-terminal reactive load, in the form of a parallel oscillatory circuit, which includes a varicap connected to a control signal source , RC circuits of the external positive feedback between the load and the control electrode of the transistor, while the meters of the circuit, transistor and varicap are selected from the condition of ensuring the specified amplitude and frequency range of the generated high-frequency signal according to the law of the amplitude of the low-frequency control (primary, information) signal (see Gonorovsky IS Radio-technical circuits and signals - M .: “Bustard” . - 2006, p. 434-437). In the mode of amplitude and phase modulation, the source of the high-frequency signal is connected to the input of the device and its amplitude and phase are changed. The principle of operation of this device is as follows. In the frequency modulation mode, when a constant voltage (current) source is turned on, due to an abrupt change in the amplitude, oscillations arise in the entire circuit, the spectrum of which occupies the entire frequency radio range. The amplitudes of these oscillations decay quickly. However, due to the presence of a positive feedback circuit, the oscillation with a frequency equal to the resonant frequency of the oscillating circuit is supplied to the control electrode of the transistor, which, by matching with the reactive four-terminal device, starts to operate in the amplification mode until the amplitude of this oscillation increases to the level at which saturation mode (amplitude limits). There is a stationary mode. In this mode, a change in the capacitance of a varicap under the action of a control signal leads to a change in the frequency of the generated signal according to the law of change in the amplitude of the low-frequency signal. In the mode of amplitude and phase modulation, the source of the high-frequency signal is connected to the input of the device and its amplitude and phase are changed under the action of the control signal in the general case according to an uncontrolled law, since the device is synthesized only by the criterion of ensuring frequency modulation.

The closest in technical essence and the achieved result (prototype) is a method of amplitude, phase and frequency modulation of a high-frequency signal, based in the frequency modulation mode on converting the energy of a constant voltage source into the energy of a high-frequency signal, organizing internal feedback in the first nonlinear element by using as of a bipolar nonlinear element with negative differential resistance, the fulfillment of the excitation conditions in the form of a balance amplitudes and phase balance, respectively determining the amplitude and frequency of the generated high-frequency signal, and the conditions for matching the first non-linear element with the load, changing the frequency of the generated high-frequency signal by changing the phase balance by changing the parameter of the second non-linear element included in the selective load, according to the law of changing the low-frequency amplitude control (primary, informational) signal (see Gonorovsky I.S. Radio engineering circuits and signals - M .: “Bustard”. - 2006, p. 414-417, 434-437).). In the mode of amplitude and phase modulation, the source of the high-frequency signal is connected to the input of the device and its amplitude and phase are changed.

The closest in technical essence and the achieved result (prototype) is a device of amplitude, phase and frequency modulation of a high-frequency signal, consisting of a constant voltage source that sets the operating point in the middle of the falling section of the current-voltage characteristics of a bipolar nonlinear element with negative differential resistance, reactive four-terminal, load in in the form of a parallel oscillatory circuit with the varicap turned on, connected to the source I control its signal, while the parameters of the circuit, the bipolar nonlinear element and the varicap are selected from the condition of providing the specified amplitude and frequency range of the generated high-frequency signal according to the law of the amplitude of the low-frequency control (primary, information) signal (see Gonorovsky I.S. Radio engineering circuits and signals - M.: “Bustard.” - 2006, p. 414-417, 434-437). The principle of operation of this device is as follows. In the frequency modulation mode, when a constant voltage (current) source is turned on, due to an abrupt change in the amplitude, oscillations arise in the entire circuit, the spectrum of which occupies the entire frequency radio range. The amplitudes of these oscillations decay quickly. However, due to the presence of internal feedback in a bipolar nonlinear element, a negative differential resistance arises in the section with a falling current-voltage characteristic, which, by matching with a reactive four-terminal, compensates for losses in the circuit. Due to this, the oscillation with a frequency equal to the resonant frequency of the oscillatory circuit is amplified until the amplitude of this oscillation increases to a level at which the amplitude goes beyond the falling section of the current-voltage characteristic. There is a stationary mode. In this mode, a change in the capacitance of a varicap under the action of a control signal leads to a change in the frequency of the generated signal according to the law of change in the amplitude of the low-frequency signal. In the mode of amplitude and phase modulation, the source of the high-frequency signal is connected to the input of the device and its amplitude and phase are changed.

The disadvantage of this method and device is the presence of two nonlinear elements, one of which works as an amplifier and a limiter, and the second is used in the frequency modulation mode to change the frequency of the generated high-frequency signal and a small linear section of the modulation characteristic due to the smallness of the linear section of the capacitance-voltage characteristic of the varicap. In addition, it does not indicate how it is necessary to choose the values of the parameters of both four-terminal networks, at which the excitation mode and the stationary mode occur. This question arises especially sharply when designing generation and frequency modulation devices in the HF and UHF bands, on which the reactive components of the parameters of nonlinear elements must be taken into account. Currently, the classical theory of radio circuits does not take this into account. In the mode of amplitude and phase modulation, the main disadvantage is the change in the amplitude and phase of the high-frequency signal according to an uncontrolled law, but they must be changed according to the law of change in the amplitude of the low-frequency control signal.

Thus, the main disadvantage of all known methods and devices for modulating the parameters of a high-frequency signal is the inability to effectively perform amplitude, phase and frequency modulation using one device according to the law of changing the amplitude of the low-frequency control signal.

The technical result of the invention is the provision of amplitude, phase and frequency modulation using one device according to the law of changing the amplitude of the low-frequency control signal with an increased linear portion of the frequency modulation characteristic when using one nonlinear element in the frequency modulation mode and with a given ratio of modules and phase difference of the transfer function in two states characterized by two values of the amplitude of the low-frequency control signal in the amplitude mode and phase modulation, which allows you to create efficient compact devices of amplitude, phase and frequency modulation when using a reactive basis with lumped parameters.

1. The specified result is achieved by the fact that in the method of amplitude, phase and frequency modulation of a high-frequency signal, based on the interaction of high-frequency and low-frequency signals with a multifunctional device of amplitude, phase and frequency modulation of a high-frequency signal, made of a nonlinear element matching the four-terminal and load, and the frequency modulation mode converts the energy of a constant voltage source into the energy of a high-frequency signal, organizes the internal reverse coupling in a nonlinear element by using a bipolar nonlinear element with negative differential resistance as it, the conditions for the excitation of the stationary generation mode in the form of a balance of amplitudes and phase balance, which respectively determine the amplitude and frequency of the generated high-frequency signal, and the conditions for matching the nonlinear element with the load using matching quadripole, change the frequency of the generated high-frequency signal by changing the phase balance according to the law of the amplitude of the low-frequency control signal, in the amplitude and phase modulation mode, change the amplitude and phase of the input high-frequency signal under the influence of the low-frequency control signal, in addition to the input of the four-terminal into the transverse circuit, a complex two-terminal is connected, in the frequency modulation mode, the frequency of the generated high-frequency signal is changed and the matching conditions are satisfied for due to a change in the resistance of a bipolar nonlinear element connected between the four-terminal and the load in the transverse circuit, according to the law of changing the amplitude of the low-frequency control signal, and providing a stationary generation mode in the form of equal to zero the denominator of the transmission coefficient over the entire range of changes in the resistance of a bipolar nonlinear element from the amplitude of the low-frequency control signal and for a given first range of changes in the frequency of the generated signal, in the mode amplitude and phase modulation change the amplitude and phase of the output high-frequency signal according to the law of low-frequency amplitude change of a different control signal by implementing the specified ratios of the modules and the phase differences of the transfer function of the multifunction device in two states determined by two values of the amplitude of the low-frequency signal in a given second frequency range, by choosing the optimal frequency characteristics of the four-terminal parameters from the conditions for ensuring the physical feasibility of the above operations in accordance with the following mathematical expressions

; a, b, c, d - элементы классической матрицы передачи четырехполюсника; α, β, γ - оптимальные частотные зависимости отношений соответствующих элементов классической матрицы передачи четырехполюсника в обоих режимах; d - оптимальная частотная зависимость соответствующего элемента классической матрицы передачи четырехполюсника в обоих режимах; r₀, x₀ - заданная частотная зависимость действительной и оптимальная частотная зависимость мнимой составляющих сопротивления комплексного двухполюсника в первом диапазоне изменения частоты в режиме частотной модуляции; r_н, x_н - заданные частотные зависимости действительной и мнимой составляющих сопротивления нагрузки в первом диапазоне изменения частоты в режиме частотной модуляции; r, x - заданные зависимости действительной и мнимой составляющих сопротивления двухполюсного нелинейного элемента от частоты в первом диапазоне изменения частоты и амплитуды низкочастотного управляющего сигнала в режиме частотной модуляции; r_0a, x_0a - заданные частотные зависимости действительной и мнимой составляющих сопротивления комплексного двухполюсника во втором диапазоне изменения частоты в режиме амплитудной и фазовой модуляции; r_нa, x_нa - заданные частотные зависимости действительной и мнимой составляющих сопротивления нагрузки во втором диапазоне изменения частоты в режиме амплитудной и фазовой модуляции; g_1,2, b_1,2 - заданные зависимости действительной и мнимой составляющих проводимости двухполюсного нелинейного элемента в двух состояниях, определяемых двумя значениями амплитуды низкочастотного управляющего сигнала, от частоты во втором диапазоне изменения частоты в режиме амплитудной и фазовой модуляции; m₂₁, φ₂₁ - заданные частотные зависимости отношения модулей и разности фаз передаточных функций в двух состояниях, определяемых двумя значениями амплитуды низкочастотного управляющего сигнала, во втором диапазоне изменения частоты в режиме амплитудной и фазовой модуляции; остальные обозначения имеют смысл промежуточных обозначений в интересах упрощения математических выражений. $$x_0=x_{0a}\pm \sqrt{{\left(E-E_a\right)}^2+\left(F-F_a\right)\left(D-D_a\right)}$$

; a, b, c, d - elements of the classical quadrupole transmission matrix; α, β, γ are the optimal frequency dependences of the relations of the corresponding elements of the classical quadrupole transmission matrix in both modes; d is the optimal frequency dependence of the corresponding element of the classical quadrupole transmission matrix in both modes; r ₀ , x ₀ - the given frequency dependence of the real and the optimal frequency dependence of the imaginary components of the resistance of a complex two-terminal network in the first frequency range in the frequency modulation mode; r _n , x _n - given frequency dependences of the real and imaginary components of the load resistance in the first frequency range in the frequency modulation mode; r, x are the given dependences of the real and imaginary components of the resistance of a bipolar nonlinear element on frequency in the first range of the frequency and amplitude of the low-frequency control signal in the frequency modulation mode; r _0a , x _0a - given frequency dependences of the real and imaginary components of the resistance of a complex two-terminal network in the second frequency range in the amplitude and phase modulation mode; r _na , x _na are the given frequency dependences of the real and imaginary components of the load resistance in the second frequency range in the amplitude and phase modulation mode; g _1,2 , b _1,2 - given dependences of the real and imaginary components of the conductivity of a bipolar nonlinear element in two states, determined by two values of the amplitude of the low-frequency control signal, on the frequency in the second frequency range in the amplitude and phase modulation mode; m ₂₁ , φ ₂₁ are the given frequency dependences of the ratio of the modules and the phase difference of the transfer functions in two states determined by two values of the amplitude of the low-frequency control signal in the second frequency range in the amplitude and phase modulation mode; the remaining notation has the meaning of intermediate notation in the interests of simplifying mathematical expressions.

2. The specified result is achieved by the fact that in a multifunctional device of amplitude, phase and frequency modulation of a high-frequency signal, consisting of a constant voltage source, a bipolar nonlinear element with negative differential resistance, a four-terminal reactive, a load and a low-frequency control signal source, in addition to a reactive four-terminal input complex two-terminal, two-pole non-linear element is connected between the output of the four-terminal and the load narrow in the transverse circuit, the source of the low-frequency control signal is connected to a bipolar nonlinear element, the imaginary component of the resistance of the source of the high-frequency signal is implemented by a series oscillatory circuit with parameters L ₁ , C ₁ parallel to the capacitance C ₀ , the reactive four-terminal is made in the form of a U-shaped connection of three two-terminal circuits made in the form of two series-connected parallel circuits of elements with parameters L _1k , C _1k , L _2k , C _2k , the values of these parameters defined in accordance with the following mathematical expressions:

; a, b, c, d - элементы классической матрицы передачи четырехполюсника; α, β, γ - оптимальные значения отношений соответствующих элементов классической матрицы передачи четырехполюсника в обоих режимах на заданных четырех частотах ω_n=2πf_n; n=1, 2, 3, 4 - номер частоты; d - оптимальные значения соответствующего элемента классической матрицы передачи четырехполюсника в обоих режимах на заданных четырех частотах; r_0n, x_0n - заданные значения действительной и оптимальные значения мнимой составляющих сопротивления комплексного двухполюсника на заданных первых трех частотах в режиме частотной модуляции; r_нn, x_нn - заданные значения действительной и мнимой составляющих сопротивления нагрузки на заданных первых трех частотах в режиме частотной модуляции; r_n, x_n - заданные значения действительной и мнимой составляющих сопротивления двухполюсного нелинейного элемента на заданных первых трех частотах и соответствующих трех значениях амплитуды низкочастотного управляющего сигнала в режиме частотной модуляции; r_0an, x_0an - заданные значения действительной и мнимой составляющих сопротивления комплексного двухполюсника на заданной четвертой частоте в режиме амплитудной и фазовой модуляции; r_нan, x_нan - заданные значения действительной и мнимой составляющих сопротивления нагрузки на заданной четвертой частоте в режиме амплитудной и фазовой модуляции; g_1n,2n, b_1n,2n - заданные значения действительной и мнимой составляющих проводимости двухполюсного нелинейного элемента в двух состояниях, определяемых двумя значениями амплитуды низкочастотного управляющего сигнала, на заданной четвертой частоте в режиме амплитудной и фазовой модуляции; m_21n, φ_21n - заданные значения отношения модулей и разности фаз передаточных функций в двух состояниях, определяемых двумя значениями амплитуды низкочастотного управляющего сигнала, на заданной четвертой частоте в режиме амплитудной и фазовой модуляции; x_1n, x_2n, x_3n - оптимальные значения сопротивлений двухполюсников П-образного соединения трех двухполюсников на заданных четырех частотах; k=1, 2, 3 - номера двухполюсников П-образного соединения; остальные обозначения имеют смысл промежуточных обозначений в интересах упрощения математических выражений. На фиг.1 показана схема многофункционального устройства амплитудной, фазовой и частотной модуляции высокочастотных сигналов (прототип), реализующего способ-прототип. На фиг.2 показана структурная схема предлагаемого многофункционального устройства амплитудной, фазовой и частотной модуляции высокочастотных сигналов по п.2., реализующая предлагаемый способ по п.1. $$x_{0n}=x_{0an}\pm \sqrt{{\left(E-E_a\right)}^2+\left(F-F_a\right)\left(D-D_a\right)}$$

; a, b, c, d - elements of the classical quadrupole transmission matrix; α, β, γ are the optimal values of the ratios of the corresponding elements of the classical four-terminal transmission matrix in both modes at the given four frequencies ω _n = 2πf _n ; n = 1, 2, 3, 4 - frequency number; d are the optimal values of the corresponding element of the classical quadrupole transmission matrix in both modes at given four frequencies; r _0n , x _0n are the given values of the real and optimal values of the imaginary components of the resistance of the complex two-terminal network at the given first three frequencies in the frequency modulation mode; r _nn , x _nn - set values of the real and imaginary components of the load resistance at the given first three frequencies in the frequency modulation mode; r _n , x _n - set values of the real and imaginary components of the resistance of the bipolar nonlinear element at the given first three frequencies and the corresponding three values of the amplitude of the low-frequency control signal in the frequency modulation mode; r _0an , x _0an - set values of the real and imaginary components of the resistance of a complex two-terminal network at a given fourth frequency in the mode of amplitude and phase modulation; r _нan , x _нan - set values of the real and imaginary components of the load resistance at a given fourth frequency in the amplitude and phase modulation mode; g _{1n, 2n} , b _{1n, 2n} - set values of the real and imaginary components of the conductivity of a bipolar nonlinear element in two states, determined by two values of the amplitude of the low-frequency control signal, at a given fourth frequency in the amplitude and phase modulation mode; m _21n , φ _21n are the set values of the ratio of the modules and the phase difference of the transfer functions in two states determined by two values of the amplitude of the low-frequency control signal at a given fourth frequency in the amplitude and phase modulation mode; x _1n , x _2n , x _3n - the optimal values of the resistance of the two-terminal U-shaped connection of three two-terminal at a given four frequencies; k = 1, 2, 3 - numbers of two-terminal U-shaped connections; the remaining notation has the meaning of intermediate notation in the interests of simplifying mathematical expressions. Figure 1 shows a diagram of a multifunctional device for amplitude, phase and frequency modulation of high-frequency signals (prototype) that implements the prototype method. Figure 2 shows the structural diagram of the proposed multifunctional device of the amplitude, phase and frequency modulation of high-frequency signals according to claim 2., Which implements the proposed method according to claim 1.

Figure 3 shows a diagram of a four-terminal network in the form of a U-shaped link included in the proposed device, a diagram of which is presented in figure 2.

Figure 4 shows a diagram of the first, second and third reactive bipolar included in the four-terminal, a diagram of which is presented in figure 3.

Figure 5 shows a diagram of the formation of a two-terminal, characterizing the imaginary component of the resistance of the source of the high-frequency signal.

The prototype device (Figure 1), which implements the prototype method, contains a non-linear element-1 with negative differential resistance, connected to a voltage source-2 with low internal resistance, matching filtering device-3 (reactive four-terminal), the load is in the form of an oscillatory contour on the elements L-4, R-5, C (t) -6. The controlled capacitance C (t), implemented by varicap-6, is connected to the source of the low-frequency control (information) signal-7. The principle of operation of the device for generating and modulating high-frequency signals (prototype) that implements the prototype method is as follows.

When you turn on the DC voltage source (2), due to the abrupt change in the amplitude, oscillations arise in the entire circuit, the spectrum of which occupies the entire frequency radio range. The amplitudes of these oscillations decay quickly. However, due to the presence of internal feedback, in a bipolar nonlinear element, for example, tunnel diode-1, a negative differential resistance arises in the section with a falling current-voltage characteristic, which, by matching with a reactive four-terminal-3, compensates for losses in the circuit L-4, R- 5, C (t) -6. Due to this, the oscillation with a frequency equal to the resonant frequency of the oscillatory circuit is amplified until the amplitude of this oscillation increases to a level at which the amplitude goes beyond the falling section of the current-voltage characteristic. There is a stationary mode. In this mode, a change in the capacitance of the varicap C (t) -6 under the action of the control signal of the source-7 leads to a change in the frequency of the generated signal according to the law of the amplitude of this signal. This is the frequency modulation mode. In the amplitude and phase modulation mode in a different frequency range, the amplitude and phase of the output high-frequency signal changes under the influence of the low-frequency control signal in the general case according to an uncontrolled law.

The remaining disadvantages of the prototype method and device for its implementation are described above.

The proposed device according to claim 2 (figure 2), which implements the proposed method according to claim 1, contains a non-linear element-1 with negative differential resistance z _n = r _n + jx _n at a given carrier frequency, connected to a source of low-frequency control voltage with a constant component-9 with low internal resistance and connected at high frequency to the transverse circuit between the output of the four-terminal network (matching filtering device (SFU)) - 3 and load-10 with resistance z _нn = r _нn + jx _нn at a given carrier frequency. The four-terminal-3 is made in the form of a U-shaped connection of three two-terminal (Fig. 3) with resistances x _1n - 11, x _2n - 12, x _3n - 11. A complex two-terminal-8 with resistance z _0n = r is connected to the input of the four-terminal-3 _0n + jx _0n at a given carrier frequency that simulates the resistance of a source of high-frequency oscillations in the frequency modulation mode (in the analysis and synthesis, instead of a source of a high-frequency signal, a short-circuit jumper must be taken into account) that occur when the low-frequency control voltage source is switched on with a constant component-9 at the time of an abrupt change in the amplitude of its voltage and the resistance of the source of the input high-frequency signal in the amplitude and phase modulation mode. The imaginary component of the resistance of the source of high-frequency oscillations is formed by a two-terminal network from a sequential oscillatory circuit connected in parallel with the capacitance. The synthesis of this two-terminal device was carried out according to the criterion of ensuring all modes using a single device (see below). Synthesis of a four-terminal network (selection of resistance values -11, 12. 13 of the first, second, and third two-terminal U-shaped connections (Figure 3) at four given frequencies (n = 1, 2, 3, 4 - frequency number) and the scheme for the formation of these two-terminal of two parallel parallel circuits connected in series (Figure 4) and the values of the circuit parameters), the criterion was used to ensure the balance of amplitudes and phase balance by implementing the denominator of the transmission coefficient of the multifunction device in the frequency demodulation mode on p three of four frequencies of a given frequency range of the generated signal and three values of the amplitude of the low-frequency control signal, respectively, and according to the criterion for ensuring the given ratios of the modules and phase differences of the transfer function at the fourth (carrier) frequency of the input high-frequency harmonic signal and two values of the amplitude of the low-frequency control signal in the mode amplitude and phase modulation.

The proposed device operates as follows. In the frequency modulation mode, when the low-frequency control voltage source with a constant component of 9 is turned on, oscillations occur over the entire circuit due to the abrupt change in the amplitude, the spectrum of which occupies the entire frequency radio frequency range. The amplitudes of these oscillations decay quickly. However, due to the presence of internal feedback, in a bipolar nonlinear element, for example, tunnel diode-1, a negative differential resistance arises in the section with a falling current-voltage characteristic, which, due to the synthesis of four-terminal-3 by a given criterion, compensates for losses in the entire circuit. The amplitude of the oscillation with a given frequency is amplified to a certain level and then limited. The synthesis of four-terminal-3 was carried out according to the criterion for the coincidence of the real frequency dependences of the resistances of the first-11 and second-12 two-terminal at four frequencies with optimal characteristics that provide a change in the frequency of the generated signal according to the law corresponding to the law of change in the amplitude of the variable component of the signal (low-frequency control signal) of source-9 . Due to this, the oscillation with a given carrier frequency is amplified until the amplitude of this oscillation increases to a level at which the amplitude goes beyond the falling section of the current-voltage characteristic. There is a stationary mode. In this mode, the change in the real and imaginary components of the resistance of the nonlinear element-1 under the action of the variable component of the signal source-9. leads to a change in the frequency of the generated signal according to the law of change in the amplitude of this signal. Source-9 can be replaced by two sources - a source of constant voltage and a source of low-frequency control signal. In the amplitude and phase modulation mode, the specified ratios of the modules and the phase differences of the transfer function are provided at two values of the amplitude of the low-frequency control signal and at the carrier frequency of the input high-frequency harmonic signal. A continuous change in the amplitude of the low-frequency control signal from one state to another provides modulation of the amplitude and phase of the output high-frequency harmonic signal according to the law of change in the amplitude of the low-frequency control signal at the carrier frequency.

Let us prove the feasibility of implementing these properties.

Suppose that, in the frequency modulation mode, the dependences of the resistance of an imaginary signal source Z ₀ = r ₀ + jx ₀ , the load Z _n = r _n + jx _n , and the conductivity of a nonlinear element y = g + jb on frequency are known. In addition, the dependences of the real and imaginary components of the conductivity of a nonlinear element on the amplitude of the control low-frequency signal are known. Thus, each given value of the amplitude of the low-frequency signal corresponds to a certain value of the real and imaginary components of the conductivity of the nonlinear element at a given frequency. For simplicity of writing, the arguments ω = 2πf (circular frequency) and U, I (voltage or current amplitude of the low-frequency signal) are omitted.

A nonlinear element is characterized by the following transfer matrix:

$$A_{n\mathrm{uh}}=\left[\begin{array}{cc}\mathrm{one}& 0\\ y& \mathrm{one}\end{array}\right].\left(\mathrm{one}\right)$$

Taking into account the reciprocity condition (x ₁₂ = -x ₂₁ ), the SFU can be characterized by a resistance matrix

$$X=\left[\begin{array}{cc}j{x}_{\mathrm{eleven}}& -j{x}_{21}\\ j{x}_{21}& j{x}_{22}\end{array}\right]\left(2\right)$$

and the corresponding classical transfer matrix:

$$A_{\mathrm{from}f\mathrm{at}}=\left[\begin{array}{cc}\frac{x_{\mathrm{eleven}}}{x_{21}}& j\frac{\left|x\right|}{x_{21}}\\ -j\frac{\mathrm{one}}{x_{21}}& -\frac{x_{22}}{x_{21}}\end{array}\right],\left(3\right)$$

- определитель матрицы (2).Where $$\left|x\right|=-x_{\mathrm{eleven}}{x}_{22}-x_{21}^2$$

is the determinant of the matrix (2).

Multiply the transfer matrix of the reactive four-port network by the transfer matrix of the nonlinear element. Given Z ₀ , Z _n [: Feldstein A.L., Yavich L.R. Microwave four-terminal and eight-terminal synthesis. M .: Svyaz, 1971. p. 34-36] we obtain the expression for the normalized classical transmission matrix of the generation device and frequency demodulation:

$$A_{\mathrm{at}}=\left[\begin{array}{cc}\sqrt{\frac{Z_n}{Z_{\mathrm{about}}}}\left(\frac{x_{\mathrm{eleven}}}{x_{21}}+jy\frac{\left|x\right|}{x_{21}}\right)& j\frac{\left|x\right|}{x_{21}}\cdot \frac{\mathrm{one}}{\sqrt{Z_0{Z}_H}}\\ -\left(j\frac{\mathrm{one}}{x_{21}}+y\frac{x_{22}}{x_{21}}\right)\cdot \sqrt{Z_0{Z}_H}& -\frac{x_{22}}{x_{21}}\cdot \sqrt{\frac{Z_0}{Z_H}}\end{array}\right].\left(\mathrm{four}\right)$$

Using the known relations between the elements of the classical transfer matrix and the elements of the scattering matrix, taking into account (4), we obtain the expression for the transfer coefficient of the multifunction device in the amplification mode (the first generation stage):

$$S_{21}=\frac{2x_{21}\sqrt{Z_O{Z}_H}}{Z_H\left(x_{\mathrm{eleven}}-j{Z}_O\right)+\left(\mathrm{one}+Z_{H}y\right)\left(j\left|x\right|-Z_O{x}_{22}\right)}.\left(5\right)$$

.A physically realized transfer function is related to the transfer coefficient by a simple relation: $$H=\frac{\mathrm{one}}{2}\sqrt{\frac{z_n}{z_0}}{S}_{21}$$

.

The condition for ensuring the stationary generation mode (the condition of the balance of amplitudes and phase balance) corresponds to the equality of the denominator of the transmission coefficient to zero (5). After dividing the complex equation formed from this equality into real and imaginary parts, we get a system of two equations:

$$x_{\mathrm{eleven}}{r}_n-x_{22}\left(x_{0}B-r_{0}A\right)-\left|x\right|B+r_n{x}_0+r_0{x}_n=0;x_{\mathrm{eleven}}{x}_n-x_{22}\left(x_{0}A-r_{0}B\right)+\left|x\right|A+x_0{x}_n-r_0{r}_n=0\left(6\right)$$

where A = 1 + r _n gx _n b; B = r _n b + x _n g.

The solution to system (6) has the form of interconnections between the elements of the quadrupole resistance matrix:

$$x_{\mathrm{eleven}}=D{x}_{22}+E-{\mathrm{<figure-callout\; id="0"\; label="x"\; filenames="00000092.png"\; state="\{\{state\}\}">x</figure-callout>}}_0;x_{21}=\pm \sqrt{-D{x}_{22}^2-2x_{22}+F},\left(7\right)$$

; $$E=\frac{r_0\left[-x_{н}+b\left(r_{н}^2+x_{н}^2\right)\right]}{r_{н}+g\left(r_{н}^2+x_{н}^2\right)}$$

; $$F=\frac{-r_0\left(x_{н}^2+r_{н}^2\right)}{r_{н}+g\left(r_{н}^2+x_{н}^2\right)}$$

Where $$D=\frac{r_0\left({\left(\mathrm{one}+r_{n}g-x_{n}b\right)}^2+{\left(r_{n}b+x_{n}g\right)}^2\right)}{r_n+g\left(r_n^2+x_n^2\right)}$$

; $$E=\frac{r_0\left[-x_n+b\left(r_n^2+x_n^2\right)\right]}{r_n+g\left(r_n^2+x_n^2\right)}$$

; $$F=\frac{-r_0\left(x_n^2+r_n^2\right)}{r_n+g\left(r_n^2+x_n^2\right)}$$

Based on the use of the known relations between the elements of the resistance matrix and the elements of the classical transmission matrix in the interests of further considerations, we write the relationships (7) in terms of the elements of the classical transmission matrix:

$$\alpha =\gamma \left(x_0-E\right)-D;\beta =F\gamma -E-{\mathrm{<figure-callout\; id="0"\; label="x"\; filenames="00000092.png"\; state="\{\{state\}\}">x</figure-callout>}}_0,\left(8\right)$$

, $$\beta =\frac{b}{d}$$

, $$\gamma =\frac{c}{d}$$

, a, b, c, d - элементы классической матрицы передачи.Where $$\alpha =\frac{a}{d}$$

, $$\beta =\frac{b}{d}$$

, $$\gamma =\frac{c}{d}$$

, a, b, c, d - elements of the classical transmission matrix.

The obtained relationships (8), taking into account the given frequency dependences r ₀ , x ₀ , r _n , x _n , r, x, are optimal approximating functions of the frequency dependences of the corresponding ratios of the elements of the classical SFU transmission matrix according to the criterion for ensuring frequency modulation.

Suppose that in a mode of the amplitude and phase modulation depending known source of resistance high harmonic signal _0a z = r + jx _{0a 0a,} load _nA z = r + jx _{nA nA} and conductivity managed nonlinear element y _1,2 = g _1,2 + jb _{1 2} in two states determined by two levels of control action, from frequency. The frequency band in this mode is different from the frequency band in the frequency modulation mode.

It is required to determine the frequency characteristics of the SFU and two-terminal parameters forming the four-terminal network, the minimum number of elements and the values of the parameters of the matching filtering device (SFU) on the reactive elements, in which the switching of the controlled element from one state to another would unambiguously lead to a change in the module and phase of the transfer coefficient according to the following law:

$$S_{21}^I=m_{21}\left(cos{\varphi }_{21}+jsin{\varphi }_{21}\right)S_{21}^{III}\left(9\right)$$

; $${\varphi }_{21}={\varphi }_{21}^I-{\varphi }_{21}^{II}$$

; $$M=\frac{1-m_{21}}{1+m_{21}},m_{21}<1$$

; $$M=\frac{m_{21}-1}{m_{21}+1},m_{21}>1$$

; $$\Delta \varphi =\frac{{\varphi }_{21}}{2}$$

- требуемые частотные зависимости отношения модулей, разности фаз коэффициентов передачи $$S_{21}^I$$

, $$S_{21}^{II}$$

в двух состояниях управляемого нелинейного элемента, коэффициента амплитудной модуляции и девиации фазы. При m₂₁=1 имеем чисто фазовую модуляцию, а при φ₂₁=0 - амплитудную.where $$m_{21}=\left|S_{21}^I\right|/\left|S_{21}^{II}\right|$$

; $${\varphi }_{21}={\varphi }_{21}^I-{\varphi }_{21}^{II}$$

; $$M=\frac{\mathrm{one}-m_{21}}{\mathrm{one}+m_{21}},m_{21}<\mathrm{one}$$

; $$M=\frac{m_{21}-\mathrm{one}}{m_{21}+\mathrm{one}},m_{21}>\mathrm{one}$$

; $$\Delta \varphi =\frac{{\varphi }_{21}}{2}$$

- the required frequency dependencies of the ratio of the modules, the phase difference of the transmission coefficients $$S_{21}^I$$

, $$S_{21}^{II}$$

in two states of a controlled nonlinear element, amplitude modulation coefficient and phase deviation. For m ₂₁ = 1, we have pure phase modulation, and for φ ₂₁ = 0, we have amplitude modulation.

Given the reciprocity condition (x ₁₂ -x ₂₁ ), the SFU can be characterized by a resistance matrix (2) and the corresponding classical transmission matrix (3).

The controlled element in the first and second states is characterized by the following transfer matrix:

$$A_{\mathrm{at}\mathrm{uh}}^{\mathrm{1,2}}=\left[\begin{array}{cc}\mathrm{one}& 0\\ {\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="00000092.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,2}}& \mathrm{one}\end{array}\right].\left(10\right)$$

Multiply matrices (3) and (10). Given Z ₀ , Z _n we find the normalized transfer matrix of the entire device:

$$A_{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="00000092.png"\; state="\{\{state\}\}">y</figure-callout>}}^{\mathrm{1,2}}=\left[\begin{array}{cc}\sqrt{\frac{Z_n}{Z_{\mathrm{about}}}}\left(\frac{x_{\mathrm{eleven}}}{x_{21}}+\mathrm{<figure-callout\; id="1"\; label="j\; y"\; filenames="00000092.png"\; state="\{\{state\}\}">j\; </figure-callout>}{y}_{}{}_{\mathrm{1,2}}\frac{\left|x\right|}{x_{21}}\right)& j\frac{\left|x\right|}{x_{21}}\cdot \frac{\mathrm{one}}{\sqrt{Z_0{Z}_H}}\\ -\left(j\frac{\mathrm{one}}{x_{21}}+{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="00000092.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,2}}\frac{x_{22}}{x_{21}}\right)\cdot \sqrt{Z_0{Z}_H}& -\frac{x_{22}}{x_{21}}\cdot \sqrt{\frac{Z_0}{Z_H}}\end{array}\right].\left(\mathrm{eleven}\right)$$

Therefore, the expression for the transmission coefficient of the multifunction device in the amplitude and phase modulation mode in two states will be:

$$S_{21}^{\mathrm{1,2}}=\frac{2x_{21}\sqrt{Z_O{Z}_H}}{Z_H\left(x_{\mathrm{eleven}}-j{Z}_O\right)+\left(\mathrm{one}+{\mathrm{<figure-callout\; id="1"\; label="Z\; H\; y"\; filenames="00000092.png"\; state="\{\{state\}\}">Z\; </figure-callout>}}_H{y}_{}{}_{\mathrm{1,2}}\right)\left(j\left|x\right|-Z_O{x}_{22}\right)};\left(12\right)$$

To obtain the relationships between the elements of the resistance matrix (2), which are optimal according to the criterion for ensuring the required law of change in the amplitude and phase of the transmitted signal, we substitute (12) in (9). After dividing the complex equation into real and imaginary parts, we get a system of two equations, the solution of which has the form of the relationship between the elements of the resistance matrix:

$$x_{\mathrm{eleven}}=D_a{x}_{22}+E_a-x_{0a};x_{21}=\pm \sqrt{-D_a{x}_{22}^2-2E_a{x}_{22}+F_a},\left(13\right)$$

'Where $$D_a=\frac{r_{0a}\left(B_{\mathrm{one}}^2+A_{\mathrm{one}}^2\right)}{\left(r_{{}_{na}}^2+x_{{}_{na}}^2\right)\left[m_{21}^2{g}_{\mathrm{one}}+g_2-m_{21}cos{\varphi }_{21}\left(g_{\mathrm{one}}+g_2\right)+m_{21}sin{\varphi }_{21}\left(b_{\mathrm{one}}-b_2\right)\right]+r_{na}\left(\mathrm{one}+m_{21}^2\right)-2r_{na}{m}_{21}\cos {\varphi }_{21}}$$

''

; $$E_a=\frac{-r_{0a}\left\{\left(r_{na}^2+x_{na}^2\right)\left[m_{21}sin{\varphi }_{21}\left(g_{\mathrm{one}}-g_2\right)+m_{21}cos{\varphi }_{21}\left(b_{\mathrm{one}}+b_2\right)-b_2-b_{\mathrm{one}}{m}_{21}^2\right]+x_{na}\left(\mathrm{one}+m_{21}^2\right)-2x_{na}{m}_{21}cos{\varphi }_{21}\right\}}{\left(r_{na}^2+x_{na}^2\right)\left[m_{{}_{21}}^2{g}_{\mathrm{one}}+g_2-m_{21}cos{\varphi }_{21}\left(g_{\mathrm{one}}+g_2\right)+m_{21}sin{\varphi }_{21}\left(b_{\mathrm{one}}-b_2\right)\right]+r_{na}\left(\mathrm{one}+m_{21}^2\right)-2r_{na}{m}_{21}cos{\varphi }_{21}}$$

;

; A₁=g₂x_нa+b₂r_нa-m₂₁cosφ₂₁(g₁x_нa+b₁r_нa)-m₂₁sinφ₂₁(1+g₁r_нa-b₁x_нa); $$F_a=\frac{E_a^2+r_{0a}^2}{-D_a}$$

; A ₁ = g x ₂ + b _{2 nA nA} -m r cosφ _{21 21} (g ₁ x + b _{1 nA} r _nA) -m sinφ _{21 21} (1 + g ₁ r x ₁ -b _{nA nA);}

B ₁ = 1 + g ₂ r _n -b ₂ x _n -m ₂₁ cosφ ₂₁ (1 + g ₁ r _n -b ₁ x _n ) + m ₂₁ sinφ ₂₁ (g ₁ x _n + b ₁ r _n ).

Based on the use of the known relations between the elements of the resistance matrix and the elements of the classical transmission matrix in the interests of further considerations, we write the relationships (13) in terms of the elements of the classical transmission matrix (the order of the resulting equations decreases):

$$\alpha =\gamma \left(x_{0a}-E_a\right)-D_a;\beta =F_a\gamma -E_a-x_{0a},\left(\mathrm{fourteen}\right)$$

Relations (14) are also approximating functions of the frequency dependences of these elements by criterion (9).

In order for the same device to perform the functions of an amplitude, phase, and frequency modulator, it is sufficient that the optimal relationships (8) and (14) are pairwise equal (the solutions obtained for the frequency modulation mode and for the amplitude and phase modulation mode are stitched together) . From these equalities and conditions of physical realizability (reciprocity conditions (α + βγ) d ² = 1), restrictions on the frequency characteristics of two more elements of the classical transmission matrix and the imaginary component of the resistance of the signal source follow:

$$\gamma =\frac{E_a-E+x_{0a}-x_0}{F_a-F}=\frac{D-D_a}{E_a-E-x_{0a}+x_0};d=\frac{\mathrm{one}}{\pm \sqrt{\alpha +\beta \gamma }};x_0=x_{0a}\pm \sqrt{{\left(E-E_a\right)}^2+\left(F-F_a\right)\left(D-D_a\right)}.\left(\mathrm{fifteen}\right)$$

Relationships (8), (15) or (14), (15) in addition, mean that for the implementation of the approximating functions of the frequency dependences of the parameters of the four-terminal network, the SFU must contain at least three independent two-terminal networks, the frequency dependences of the resistances of which must be determined from the solution systems of three equations formed on the basis of relationships (8), (15) or (14), (15). To do this, it is necessary to take a sample typical SFU scheme, find the transfer matrix of this scheme and the elements α, β, γ found in this way (the element d is dependent on the reciprocity condition), expressed through the parameters of the scheme, substitute in (8), (15) or (14), (15) and solve the formed system of three equations with respect to the resistances of the selected three two-terminal networks. The frequency characteristics of the other parameters r _0, r _n, x _n, r, x, r _0a, x _0a, r _nA, x _nA, g _1.2, b _1,2 and the remaining two-terminal SibFU (if the number of two-poles greater than three) may be selected arbitrarily or on the basis of any other physical considerations.

In accordance with the above algorithm, expressions are obtained for finding optimal approximations of the frequency dependences of the resistances of the first, second, and third two-terminal SFUs in the form of a U-shaped connection of three reactive two-terminal devices:

$$x_{\mathrm{one}n}=\frac{\beta }{\mathrm{one}+Q};x_{2n}=\frac{-\beta }{Q};x_{3n}=\frac{\beta }{\alpha +Q};Q=\pm \sqrt{\alpha +\beta \gamma },\left(16\right)$$

where n = 1, 2 ... are the numbers of the interpolation frequencies. The root expression in (16) is always positive; Index n must also be entered into the other given and calculated quantities

r _0n , r _нn , x _нn , r _n , x _n , r _0an , x _0an , r _нan , x _нan , r _1n.2n , x _{1n, 2n} , x _0n and others.

To ensure that the optimal frequency dependences of the two-terminal resistances (16) coincide with the real frequency characteristics, it is necessary to form two-terminal with resistances x _1n , x _2n , x _3n from at least N (the number of interpolation frequencies) of the reactive elements, find expressions for their resistances, equate them the optimal values of the two-terminal resistances at the given frequencies determined by formulas (16) and solve the system of N equations formed in this way with respect to the N selected reactive element parameters in. This is an interpolation method. The values of the parameters of the remaining elements can be chosen arbitrarily or on the basis of any other physical considerations, for example, from the condition of physical realizability. Let each of the two-terminal networks with resistances x _1n , x _2n , x _{3n be} formed from two parallel-connected parallel circuits L _1k , C _1k , L _2k , C _2k (k = 1, 2, 3 is the number of the two-terminal network (Fig. 4)). For N = 4, we compose three systems of four equations:

A similar problem must be solved with respect to ensuring that the optimal frequency dependence (15) of the imaginary component x _{0 of the} resistance of the complex two-terminal (signal source resistance) coincides with the actual frequency characteristics at three frequencies in the frequency modulation mode. Let the two-terminal network with the imaginary component x _{0 of} resistance be formed from a sequential oscillatory circuit with parameters L ₁ , C ₁ parallel connected to the capacitance C ₀ (Fig. 5). We compose a system of three equations:

At the fourth frequency, the imaginary component of the resistance of the signal source in the amplitude and phase modulation mode can take an arbitrary value x _0a .

The implementation of the optimal approximations of the frequency characteristics of the two-terminal circuits of the four-terminal network in the form of a U-shaped link (16) using (18) and the optimal approximations of the frequency characteristics x ₀ (15) using (20) provides an increase in the frequency range of the generated signal, since it implements the condition of balance of amplitudes and phase balance at three frequencies of a given modulation characteristic or a given range of frequency changes in the frequency modulation mode. This allows for a reasonable choice of the positions of the first three preset frequencies relative to each other to expand the linear portion of the modulation characteristic. In the amplitude and phase modulation mode, the specified ratios of the modules and the phase difference of the transfer function in two states, determined by two values of the amplitude of the low-frequency control signal, at the carrier frequency of the high-frequency harmonic signal, will be realized. With a reasonable choice of two values of the amplitude of the low-frequency control signal and with a continuous change in the amplitude of the low-frequency control signal from the first value to the second, the amplitude and phase modulation mode will be implemented according to the law of change of the amplitude of the low-frequency control signal at the carrier frequency.

The proposed technical solutions have an inventive step, since it does not explicitly follow from the published scientific data and the known technical solutions that the claimed sequence of operations (performing a four-terminal reactive in the form of the above three connected three-terminal devices, forming the first, second and third two-terminal devices from the series connected two parallel loops, the choice of values of their parameters from the condition of providing a stationary mode of generation at three s the given frequencies when changing the state of a nonlinear bipolar element with negative differential resistance, connected between the output of the reactive four-terminal and the load in the transverse circuit, connecting the complex two-terminal to the input of the reactive four-terminal, forming a two-terminal, which characterizes the imaginary component of the resistance of the complex two-terminal, from a series oscillatory circuit connected in parallel with capacity), provides modulation of the frequency of the generated signal and according to the law of changing the amplitude of the low-frequency signal in the frequency modulation mode, it also implements a given ratio of modules and a given phase difference of the transfer function in two states determined by two values of the amplitude of the low-frequency control signal, and modulation of the amplitude and phase of the high-frequency signal at the fourth frequency according to the law of change of amplitude low-frequency control signal with continuous change from the first value to the second.

The proposed technical solutions are practically applicable, since active semiconductor diodes (Gunn diodes, tunnel diodes, avalanche-span diodes, etc.), inductances and capacitances formed in the claimed reactive four-terminal circuit can be used for their implementation. The values of the parameters of the inductances and capacitances of the oscillatory circuits can be uniquely determined using mathematical expressions given in the claims.

The technical and economic efficiency of the proposed method and device consists in providing frequency modulation of a high-frequency signal in one frequency band and amplitude and phase modulation in another frequency band according to the law of changing the amplitude of a low-frequency signal using one device by optimizing the values of the parameters of the reactive elements according to the criterion of ensuring the listed functions , which reduces the nomenclature of radio devices and unifies them in the interests of production.

Claims (2)

1. The method of amplitude, phase and frequency modulation of a high-frequency signal based on the interaction of high-frequency and low-frequency signals with a multifunctional device of amplitude, phase and frequency modulation of a high-frequency signal made of a nonlinear element matching a four-terminal network and a load, and in the frequency modulation mode, the energy of a constant source is converted voltage into the energy of a high-frequency signal, organize internal feedback in a nonlinear element by using If a bipolar nonlinear element with negative differential resistance is used as it, the excitation conditions of the stationary generation mode are fulfilled in the form of a balance of amplitudes and phase balance, which respectively determine the amplitude and frequency of the generated high-frequency signal, and the conditions for matching the nonlinear element with the load using the matching four-port network change the frequency of the generated high-frequency signal by changing the phase balance according to the law of changing the amplitude of the low-frequency control of the signal, in the amplitude and phase modulation mode, the amplitude and phase of the input high-frequency signal are changed under the action of a low-frequency control signal, characterized in that a complex two-terminal network is connected to the input of the four-terminal network in the transverse circuit, in the frequency modulation mode, the frequency of the generated high-frequency signal is changed and the matching conditions are satisfied for due to changes in the resistance of a bipolar nonlinear element connected between the four-terminal and the load in the transverse circuit, according to the law of varying the amplitude of the low-frequency control signal, and ensuring a stationary generation mode in the form of equal to zero the denominator of the transmission coefficient over the entire range of changes in the resistance of a bipolar nonlinear element from the amplitude of the low-frequency control signal and for a given first range of changes in the frequency of the generated signal, in the amplitude and phase modulation mode change the amplitude and phase of the output high-frequency signal according to the law of changing the amplitude of the low-frequency control signal by re analysis of the given ratios of modules and phase differences of the transfer function of the multifunctional device in two states, determined by two values of the amplitude of the low-frequency signal, on a given second frequency variation range by choosing the optimal frequency characteristics of the four-terminal parameters from the conditions for ensuring the physical realizability of the above operations in accordance with the following mathematical expressions
α = γ (x ₀ -E) -D = γ (x _0a -E _a ) -D _a ; β = Fγ-Ex ₀ = F _a γ-E _a -x _0a ; $$\gamma =\frac{E_a-E+x_{0a}-x_0}{F_a-F}=\frac{D-D_a}{E_a-E-x_{0a}-x_0},$$

Where $$D=\frac{r_0\left({\left(\mathrm{one}+r_{n}g-x_{n}b\right)}^2+{\left(r_{n}b+x_{n}g\right)}^2\right)}{r_n+g\left(r_n^2+x_n^2\right)};$$

$$E=\frac{r_0\left[-x_n+b\left(r_n^2+x_n^2\right)\right]}{r_n+g\left(r_n^2+x_n^2\right)}$$

; $$F=\frac{-r_0\left(x_n^2+r_n^2\right)}{r_n+g\left(r_n^2+x_n^2\right)}$$

; $$d=\frac{\mathrm{one}}{\pm \sqrt{\alpha +\beta \gamma }}$$

;
$$D_a=\frac{r_{0a}\left(B_{\mathrm{one}}^2+A_{\mathrm{one}}^2\right)}{\left(r_{{}_{na}}^2+x_{{}_{na}}^2\right)\left[m_{21}^2{g}_{\mathrm{one}}+g_2-m_{21}cos{\varphi }_{21}\left(g_{\mathrm{one}}+g_2\right)+m_{21}sin{\varphi }_{21}\left(b_{\mathrm{one}}-b_2\right)\right]+r_{na}\left(\mathrm{one}+m_{21}^2\right)-2r_{na}{m}_{21}\cos {\varphi }_{21}}$$

;
$$E_a=\frac{-r_{0a}\left\{\left(r_{na}^2+x_{na}^2\right)\left[m_{21}sin{\varphi }_{21}\left(g_{\mathrm{one}}-g_2\right)+m_{21}cos{\varphi }_{21}\left(b_{\mathrm{one}}+b_2\right)-b_2-b_{\mathrm{one}}{m}_{21}^2\right]+x_{na}\left(\mathrm{one}+m_{21}^2\right)-2x_{na}{m}_{21}cos{\varphi }_{21}\right\}}{\left(r_{na}^2+x_{na}^2\right)\left[m_{{}_{21}}^2{g}_{\mathrm{one}}+g_2-m_{21}cos{\varphi }_{21}\left(g_{\mathrm{one}}+g_2\right)+m_{21}sin{\varphi }_{21}\left(b_{\mathrm{one}}-b_2\right)\right]+r_{na}\left(\mathrm{one}+m_{21}^2\right)-2r_{na}{m}_{21}cos{\varphi }_{21}}$$

;
$$F_a=\frac{E_a^2+r_{0a}^2}{-D_a}$$

; A ₁ = g x ₂ + b _{2 nA nA} -m r cosφ _{21 21} (g ₁ x + b _{1 nA} r _nA) -m sinφ _{21 21} (1 + g ₁ r x ₁ -b _{nA nA);}
B ₁ = 1 + g ₂ r _n -b ₂ x _n -m ₂₁ cosφ ₂₁ (1 + g ₁ r _n -b ₁ x _n ) + m ₂₁ sinφ ₂₁ (g ₁ x _n + b ₁ r _n ); $$\alpha =\frac{a}{d};$$

$$\beta \frac{b}{d};$$

$$\gamma =\frac{c}{d};$$

$$x_0=x_{0a}\pm \sqrt{{\left(E-E_a\right)}^2+\left(F-F_a\right)\left(D-D_a\right)}$$

; a, b, c, d - elements of the classical quadrupole transmission matrix; α, β, γ are the optimal frequency dependences of the relations of the corresponding elements of the classical quadrupole transmission matrix in both modes; d is the optimal frequency dependence of the corresponding element of the classical quadrupole transmission matrix in both modes; r ₀ , x ₀ - the given frequency dependence of the real and the optimal frequency dependence of the imaginary components of the resistance of a complex two-terminal network in the first frequency range in the frequency modulation mode; r _n , x _n - given frequency dependences of the real and imaginary components of the load resistance in the first frequency range in the frequency modulation mode; r, x are the given dependences of the real and imaginary components of the resistance of a bipolar nonlinear element on frequency in the first range of the frequency and amplitude of the low-frequency control signal in the frequency modulation mode; r _0a , x _0a - given frequency dependences of the real and imaginary components of the resistance of a complex two-terminal network in the second frequency range in the amplitude and phase modulation mode; r _on , x _on - given frequency dependences of the real and imaginary components of the load resistance in the second frequency range in the amplitude and phase modulation mode; g _1,2 , b _1,2 - given dependences of the real and imaginary components of the conductivity of a bipolar nonlinear element in two states, determined by two values of the amplitude of the low-frequency control signal, on the frequency in the second frequency range in the amplitude and phase modulation mode; m ₂₁ , φ ₂₁ are the given frequency dependences of the ratio of the modules and the phase difference of the transfer functions in two states determined by two values of the amplitude of the low-frequency control signal in the second frequency range in the amplitude and phase modulation mode; the remaining notation has the meaning of intermediate notation in the interests of simplifying mathematical expressions. 2. A multifunctional device for amplitude, phase and frequency modulation of a high-frequency signal, consisting of a constant voltage source, a bipolar nonlinear element with negative differential resistance, a reactive four-terminal device, a load, and a source of a low-frequency control signal, characterized in that a complex two-terminal, two-pole device is connected to the input of the reactive four-terminal device a nonlinear element is connected between the output of the four-terminal network and the load in the transverse circuit, the source bottom the frequency control signal is connected to a bipolar non-linear element, the imaginary component of the resistance of the source of the high-frequency signal is implemented by a series oscillatory circuit with parameters L ₁ , C ₁ parallel connected to the capacitance C ₀ , the reactive four-terminal is made in the form of a U-shaped connection of three two-terminal, made in the form of two connected in parallel with the circuit element parameters _{L 1k, C 1k, L 2k} , C _2k, the values of these parameters are determined according to the following yuschimi mathematical expressions
$$L_{\mathrm{one}}=\frac{x_{01}{\omega }_{\mathrm{one}}-x_{02}{\omega }_2}{\left(x_{02}{\omega }_2{C}_0-\mathrm{one}\right)\left({\omega }_{\mathrm{one}}^2-{\omega }_2^2\right)\left(\mathrm{one}-{\omega }_{\mathrm{one}}{x}_{01}{C}_0\right)};$$

$$C_{\mathrm{one}}=\frac{\left({\omega }_{\mathrm{one}}^2-{\omega }_2^2\right)\left[\mathrm{one}+{\omega }_{\mathrm{one}}{\omega }_2{x}_{01}{x}_{02}{C}_0^2-C_0\left(x_{01}{\omega }_{\mathrm{one}}+x_{02}{\omega }_2\right)\right]}{{\omega }_{\mathrm{one}}{\omega }_2\left[\left({\omega }_2^2-{\omega }_{\mathrm{one}}^2\right)x_{01}{x}_{02}{C}_0+{\omega }_{\mathrm{one}}{x}_{02}-x_{01}{\omega }_2\right]}$$

;
$$C_0=\frac{{\omega }_3{x}_{03}\left({\omega }_{\mathrm{one}}^2-{\omega }_2^2\right)+{\omega }_2{x}_{02}\left({\omega }_3^2-{\omega }_{\mathrm{one}}^2\right)+{\omega }_{\mathrm{one}}{x}_{01}\left({\omega }_2^2-{\omega }_3^2\right)}{{\omega }_2{\omega }_3{x}_{02}\left({\omega }_3^2-{\omega }_2^2\right)x_{03}+{\omega }_{\mathrm{one}}{\omega }_3{x}_{01}\left({\omega }_{\mathrm{one}}^2-{\omega }_3^2\right)x_{03}+{\omega }_{\mathrm{one}}{\omega }_2{x}_{01}\left({\omega }_2^2-{\omega }_{\mathrm{one}}^2\right)x_{02}}$$

;
$$L_{\mathrm{one}k}=\frac{e_{\mathrm{one}}{x}_{k2}+h_{\mathrm{one}}{x}_{k\mathrm{one}}}{{\omega }_{\mathrm{one}}{\omega }_2\left({\omega }_{\mathrm{one}}^2-{\omega }_2^2\right)\left(B-A\right)}$$

; $$L_{2k}=\frac{e_2{x}_{k2}+h_2{x}_{k\mathrm{one}}}{{\omega }_{\mathrm{one}}{\omega }_2\left({\omega }_{\mathrm{one}}^2-{\omega }_2^2\right)\left(B-A\right)}$$

; $$C_{\mathrm{one}k}=\frac{A}{L_{\mathrm{one}k}}$$

; $$C_{2k}=\frac{B}{L_{2k}}$$

,
Where $$B=\frac{-y\pm \sqrt{y^2-\mathrm{four}xz}}{2x}$$

; $$A=\frac{a_{\mathrm{one}}B+b_{\mathrm{one}}}{c_{\mathrm{one}}B+d_{\mathrm{one}}}=\frac{a_{2}B+b_2}{c_{2}B+d_2}$$

;
x = a ₂ c ₁ - a ₁ c ₂ ; y = a ₂ d ₁ + b ₂ c ₁ - a ₁ d ₂ -b ₁ c ₂ ; z = b ₂ d ₁ -b ₁ d ₂ ;
$$e_{\mathrm{one}}={\omega }_{\mathrm{one}}\left(\mathrm{one}-{\omega }_2^{2}B\right)\left(\mathrm{one}+A^2{\omega }_{\mathrm{one}}^2{\omega }_2^2-A\left({\omega }_{\mathrm{one}}^2+{\omega }_2^2\right)\right)$$

; $$h_{\mathrm{one}}=-{\omega }_2\left(\mathrm{one}-{\omega }_{\mathrm{one}}^{2}B\right)\left(\mathrm{one}+A^2{\omega }_{\mathrm{one}}^2{\omega }_2^2-A\left({\omega }_{\mathrm{one}}^2+{\omega }_2^2\right)\right)$$

;
$$e_2=-{\omega }_{\mathrm{one}}\left(\mathrm{one}-{\omega }_2^{2}A\right)\left(\mathrm{one}+B^2{\omega }_{\mathrm{one}}^2{\omega }_2^2-B\left({\omega }_{\mathrm{one}}^2+{\omega }_2^2\right)\right)$$

; $$h_2={\omega }_2\left(\mathrm{one}-{\omega }_{\mathrm{one}}^{2}A\right)\left(\mathrm{one}+B^2{\omega }_{\mathrm{one}}^2{\omega }_2^2-B\left({\omega }_{\mathrm{one}}^2+{\omega }_2^2\right)\right);$$

$$a_{\mathrm{one}}={\omega }_{\mathrm{one}}{\omega }_2{\omega }_{\mathrm{four}}^2{x}_{k\mathrm{four}}\left({\omega }_2^2-{\omega }_{\mathrm{one}}^2\right)+{\omega }_{\mathrm{one}}{\omega }_2^2{\omega }_{\mathrm{four}}{x}_{k2}\left({\omega }_{\mathrm{one}}^2-{\omega }_{\mathrm{four}}^2\right)+{\omega }_{\mathrm{one}}^2{\omega }_2{\omega }_{\mathrm{four}}{x}_{k\mathrm{one}}\left({\omega }_{\mathrm{four}}^2-{\omega }_2^2\right)$$

;
$$b_{\mathrm{one}}={\omega }_{\mathrm{one}}{\omega }_2{x}_{k\mathrm{four}}\left({\omega }_{\mathrm{one}}^2-{\omega }_2^2\right)+{\omega }_{\mathrm{one}}{\omega }_{\mathrm{four}}{x}_{k2}\left({\omega }_{\mathrm{four}}^2-{\omega }_{\mathrm{one}}^2\right)+{\omega }_2{\omega }_{\mathrm{four}}{x}_{k\mathrm{one}}\left({\omega }_2^2-{\omega }_{\mathrm{four}}^2\right)$$

;
$$c_{\mathrm{one}}=\left[{\omega }_{\mathrm{four}}^3{x}_{k\mathrm{four}}\left({\omega }_2^2-{\omega }_{\mathrm{one}}^2\right)+{\omega }_2^3{x}_k{}_2\left({\omega }_{\mathrm{one}}^2-{\omega }_{\mathrm{four}}^2\right)+{\omega }_{\mathrm{one}}^3{x}_{k\mathrm{one}}\left({\omega }_{\mathrm{four}}^2-{\omega }_2^2\right)\right]{\omega }_{\mathrm{one}}{\omega }_2{\omega }_{\mathrm{four}};$$

$$d_{\mathrm{one}}=\left[{\omega }_{\mathrm{four}}{x}_{k\mathrm{four}}\left({\omega }_{\mathrm{one}}^2-{\omega }_2^2\right)+{\omega }_2{x}_{k2}\left({\omega }_{\mathrm{four}}^2-{\omega }_{\mathrm{one}}^2\right)+{\omega }_{\mathrm{one}}{x}_{k\mathrm{one}}\left({\omega }_2^2-{\omega }_{\mathrm{four}}^2\right)\right]{\omega }_{\mathrm{one}}{\omega }_2{\omega }_{\mathrm{four}}$$

;
$$a_2={\omega }_{\mathrm{one}}{\omega }_2{\omega }_3^2{x}_{k3}\left({\omega }_2^2-{\omega }_{\mathrm{one}}^2\right)+{\omega }_{\mathrm{one}}{\omega }_2^2{\omega }_3{x}_{k2}\left({\omega }_{\mathrm{one}}^2-{\omega }_3^2\right)+{\omega }_{\mathrm{one}}^2{\omega }_2{\omega }_3{x}_{k\mathrm{one}}\left({\omega }_3^2-{\omega }_2^2\right);$$

$$b_2={\omega }_{\mathrm{one}}{\omega }_2{x}_{k3}\left({\omega }_{\mathrm{one}}^2-{\omega }_2^2\right)+{\omega }_{\mathrm{one}}{\omega }_3{x}_{k2}\left({\omega }_3^2-{\omega }_{\mathrm{one}}^2\right)+{\omega }_2{\omega }_3{x}_{k\mathrm{one}}\left({\omega }_2^2-{\omega }_3^2\right);$$

$$c_2=\left[{\omega }_3^3{x}_{k3}\left({\omega }_2^2-{\omega }_{\mathrm{one}}^2\right)+{\omega }_2^3{x}_k{}_2\left({\omega }_{\mathrm{one}}^2-{\omega }_3^2\right)+{\omega }_{\mathrm{one}}^3{x}_{k\mathrm{one}}\left({\omega }_3^2-{\omega }_2^2\right)\right]{\omega }_{\mathrm{one}}{\omega }_2{\omega }_3;$$

$$d_2=\left[{\omega }_3{x}_{k3}\left({\omega }_{\mathrm{one}}^2-{\omega }_2^2\right)+{\omega }_2{x}_{k2}\left({\omega }_3^2-{\omega }_{\mathrm{one}}^2\right)+{\omega }_{\mathrm{one}}{x}_{k\mathrm{one}}\left({\omega }_2^2-{\omega }_3^2\right)\right]{\omega }_{\mathrm{one}}{\omega }_2{\omega }_3;$$

$$x_{\mathrm{one}n}=\frac{\beta }{\mathrm{one}+Q}$$

; $$x_{2n}=\frac{-\beta }{Q}$$

; $$x_{3n}=\frac{\beta }{\alpha +Q}$$

; $$Q=\pm \sqrt{\alpha +\beta \gamma }$$

; α = γ (x _0n -E) -D = γ (x _0an -E _a ) -D _a ;
β = Fγ-Ex _0n = F _a γ-E _a -x _0an ; $$\gamma =\frac{E_a-E+x_{0an}-x_{0n}}{F_a-F}=\frac{D-D_a}{E_a-E-x_{0an}+x_{0x}}$$

; $$\alpha =\frac{a}{d}$$

; $$\beta =\frac{b}{d}$$

; $$\gamma =\frac{c}{d}$$

; $$d=\frac{\mathrm{one}}{\pm \sqrt{\alpha +\beta \gamma }}$$

;
$$D=\frac{r_{0n}\left({\left(\mathrm{one}+r_{nn}{g}_n-x_{nn}{b}_n\right)}^2+{\left(r_{nn}{b}_n+x_{nn}{g}_n\right)}^2\right)}{r_{nn}+g_n\left(r_{nn}^2+x_{nn}^2\right)};$$

$$E=\frac{r_{0n}\left[-x_{nn}+b_n\left(r_{nn}^2+x_{nn}^2\right)\right]}{r_{nn}+g_n\left(r_{nn}^2+x_{nn}^2\right)}$$

; $$F=\frac{-r_{0n}\left(x_{nn}^2+r_{nn}^2\right)}{r_{nn}+g_n\left(r_{nn}^2+x_{nn}^2\right)}$$

; $$F_a=\frac{E_a^2+r_{0an}^2}{-D_a}$$

;
$$D_a=\frac{r_{0an}\left(B_{\mathrm{one}}^2+A_{\mathrm{one}}^2\right)}{\left(r_{nan}^2+x_{nan}^2\right)\left[m_{21n}^2{g}_{\mathrm{one}n}+g_{2n}-m_{21n}cos{\varphi }_{21n}\left(g_{\mathrm{one}n}+g_{2n}\right)+m_{21n}sin{\varphi }_{21n}\left(b_{\mathrm{one}n}-b_{2n}\right)\right]+r_{nan}\left(\mathrm{one}+m_{21n}^2\right)-2r_{nan}{m}_{21n}cos{\varphi }_{21n}}$$

$$E_a=\frac{-r_{0an}\left\{\left(r_{nan}^2+x_{nan}^2\right)\left[m_{21n}\sin {\phi }_{21n}\left(g_{\mathrm{one}n}-g_{2n}\right)+m_{21n}\cos {\phi }_{21n}\left(b_{\mathrm{one}n}+b_{2n}\right)-b_{2n}-b_{\mathrm{one}n}{m}_{21n}^2\right]+x_{nan}\left(\mathrm{one}+m_{21n}^2\right)-2x_{nan}{m}_{21n}\cos {\phi }_{21n}\right\}}{\left(r_{nan}^2+x_{nan}^2\right)\left[m_{{}_{21n}}^2{g}_{\mathrm{one}n}+g_{2n}-m_{21n}\cos {\phi }_{21n}\left(g_{\mathrm{one}n}+g_{2n}\right)+m_{21n}\sin {\phi }_{21n}\left(b_{\mathrm{one}n}-b_{2n}\right)\right]+r_{nan}\left(\mathrm{one}+m_{21n}^2\right)-2r_{nan}{m}_{21n}\cos {\phi }_{21n}};$$

A ₁ = g _2n x _nan + b _2n r _{nan-m 21n} cosφ _21n (g _1n x _nan + b _1n r _nan ) -m _21n sinφ _21n (1 + g _1n r _nan- b _1n x _nan );
B ₁ = 1 + g _2n r _нn -b _2n x _нn -m _21n cosφ _21n (1 + g _1n r _нn -b _1n x _нn ) + m _21n sinφ _21n (g _1n x _нn + b _1n r _нn );
$$x_{0n}=x_{0an}\pm \sqrt{{\left(E-E_a\right)}^2+\left(F-F_a\right)\left(D-D_a\right)}$$

; a, b, c, d - elements of the classical quadrupole transmission matrix; α, β, γ are the optimal values of the ratios of the corresponding elements of the classical four-terminal transmission matrix in both modes at the given four frequencies ω _n = 27πf _n ; n = 1, 2, 3, 4 - frequency number; d are the optimal values of the corresponding element of the classical quadrupole transmission matrix in both modes at given four frequencies; r _0n , x _0n are the given values of the real and optimal values of the imaginary components of the resistance of the complex two-terminal network at the given first three frequencies in the frequency modulation mode; r _nn , x _nn - set values of the real and imaginary components of the load resistance at the given first three frequencies in the frequency modulation mode; r _n , x _n - set values of the real and imaginary components of the resistance of the bipolar nonlinear element at the given first three frequencies and the corresponding three values of the amplitude of the low-frequency control signal in the frequency modulation mode; r _0an , x _0an - set values of the real and imaginary components of the resistance of the complex two-terminal network at a given fourth frequency in the mode of amplitude and phase modulation; r _nan , x _nan - set values of the real and imaginary components of the load resistance at a given fourth frequency in the amplitude and phase modulation mode; g _{1n, 2n} , b _{1n, 2n} - set values of the real and imaginary components of the conductivity of a bipolar nonlinear element in two states, determined by two values of the amplitude of the low-frequency control signal, at a given fourth frequency in the amplitude and phase modulation mode; m _21n , φ _21n are the set values of the ratio of the modules and the phase difference of the transfer functions in two states determined by two values of the amplitude of the low-frequency control signal at a given fourth frequency in the amplitude and phase modulation mode; x _1n , x _2n , x _3n - the optimal values of the resistance of the two-terminal U-shaped connection of three two-terminal at a given four frequencies; k = 1, 2, 3 - numbers of two-terminal U-shaped connections; the remaining notation has the meaning of intermediate notation in the interests of simplifying mathematical expressions.

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