CN112989729A

CN112989729A - Circuit design and modeling method of balanced high-temperature superconducting receiver

Info

Publication number: CN112989729A
Application number: CN202110204243.7A
Authority: CN
Inventors: 高翔; 李焕新; 代贤乐; 卜祥元; 安建平; 刘珩
Original assignee: Beijing Institute of Technology BIT
Current assignee: Beijing Institute of Technology BIT
Priority date: 2021-02-23
Filing date: 2021-02-23
Publication date: 2021-06-18
Anticipated expiration: 2041-02-23
Also published as: CN112989729B

Abstract

The invention relates to a circuit design and modeling method of a balanced type high-temperature superconducting receiver, belonging to the technical field of microwave and terahertz communication and high-temperature superconducting. The method comprises a circuit design of a balanced high-temperature superconducting receiver and a receiver modeling method; step 1, circuit design of a balanced type high-temperature superconducting receiver comprises MgO chip circuit design and alumina PCB circuit design and is connected through a bonding tape; the MgO chip circuit design comprises a 3dB branch bridge network, an impedance matching, a Josephson junction with a direct current bias circuit, a fan-shaped choke filter and a fifth-order choke filter; the design of the aluminum oxide PCB circuit comprises a bias three-way circuit and an intermediate frequency signal mixing circuit; and 2, modeling the balanced high-temperature superconducting receiver, including establishing a multiport network interweaving model and obtaining an analytical expression of conversion gain and noise temperature of the superconducting receiver. The designed circuit has the advantages of small volume, low cost, low noise, extremely wide medium-frequency band, high frequency upper limit and low power requirement.

Description

Circuit design and modeling method of balanced high-temperature superconducting receiver

Technical Field

The invention relates to a circuit design and modeling method of a balanced type high-temperature superconducting receiver, belonging to the technical field of microwave and terahertz communication and high-temperature superconducting.

Background

Compared with a conventional semiconductor terahertz receiver, the superconducting receiver has the advantages of low noise, extremely wide middle-frequency band, high frequency upper limit, low power requirement and the like; compared with a low-temperature superconducting receiver, the high-temperature superconducting receiver needs a smaller and cheaper low-temperature facility, and has a good application prospect as a front-end device of a terahertz communication system. However, the received rf signal typically has high spurious tones and amplitude noise generated by the frequency doubling amplification network, which severely degrades the performance of the hts receiver. Compared with a unijunction or series junction type high-temperature superconducting receiver, the balanced type high-temperature superconducting receiver has the capability of eliminating local oscillation stray sound and amplitude noise, and can effectively solve the problem caused by radio frequency receiving signals. Due to the complexity of the balanced high-temperature superconducting receiver circuit and the modeling theory thereof, no effective balanced high-temperature superconducting receiver circuit and the modeling theory thereof are published or researched in China at present.

In view of the above, it is desirable to provide a circuit design and a modeling method for a balanced high-temperature superconducting receiver.

Disclosure of Invention

The invention aims to provide a circuit design and a modeling method of a balanced type high-temperature superconducting receiver, aiming at the problem that the noise resistance of the receiver is poor due to the fact that the existing high-temperature superconducting receiver lacks a balanced type circuit and a modeling method.

In order to achieve the above purpose, the present invention adopts the following technical scheme.

The circuit design and modeling method of the balanced type high-temperature superconducting receiver comprises the circuit design of the balanced type high-temperature superconducting receiver and the modeling method of the balanced type high-temperature superconducting receiver;

step 1, circuit design of a balanced type high-temperature superconducting receiver comprises MgO chip circuit design and alumina PCB circuit design, and the MgO chip circuit design and the alumina PCB circuit design are connected through an adhesive tape;

the MgO chip circuit is a high-temperature superconducting microstrip circuit and comprises a 3dB branch bridge network, an impedance matching circuit, two Josephson junctions with direct-current bias circuits, a fan-shaped choke filter, a five-order choke filter and an adhesive tape;

the aluminum oxide PCB circuit comprises a bias three-way circuit and a mixing circuit of intermediate frequency signals;

step 1 specifically comprises the following substeps:

step 1.1 design MgO chip circuit, including the following substeps:

step 1.1.1, designing a 3dB branch bridge network as an orthogonal coupling circuit of a radio frequency signal and a local oscillator signal, finishing orthogonal coupling of the radio frequency signal and the local oscillator signal, and enabling signal energy after the orthogonal coupling to be evenly distributed into two paths of radio frequency signals to be output;

step 1.1.2, designing a quarter-wavelength high-low impedance line for impedance matching, respectively arriving two josephson junctions with two paths of radio frequency signals and local oscillation signals after orthogonal coupling for frequency mixing, and outputting two paths of intermediate frequency signals;

wherein the impedance match is between the 3dB branching bridge network and the two Josephson junctions;

step 1.1.3, designing direct current bias circuits of the two Josephson junctions by adopting a fan-shaped choke filter to ensure that the two Josephson junctions work normally;

the fan-shaped choke filter is used for preventing the intermediate frequency signals, the local oscillator signals and the radio frequency signals from flowing to a direct current offset;

step 1.1.4, designing a fifth-order choke filter, so that two paths of intermediate frequency signals generated by mixing at two Josephson junctions can reach a dc/IF gasket, and the gasket is connected with an aluminum oxide PCB circuit through a radial stub;

the dc/IF gasket and the radial stub form a bonding tape, and the bonding tape connects the MgO chip circuit with the alumina PCB circuit;

step 1.2, designing an aluminum oxide PCB circuit, which specifically comprises the following substeps:

step 1.2.1, designing two bias tee circuits for testing characteristics of the Josephson junction and the circuits;

wherein each bias three-way circuit comprises two 500 omega resistors and a 100-nF capacitor;

step 1.2.2, designing a mixing circuit of intermediate frequency signals, and carrying out in-phase superposition on the two paths of intermediate frequency signals generated in the step 1.1.2 in the mixing circuit;

the local oscillation stray sound and the amplitude noise are just reversely added and offset through the step 1.2.2;

the mixing circuit of the intermediate frequency signal is a broadband multi-section Wilkinson, and the range of the central working frequency is as follows: 5GHz-15 GHz;

step 2, a modeling method of a balanced type high-temperature superconducting receiver is a modeling method based on time-frequency separation and network interleaving processing, and specifically comprises the following steps:

step 2.1, establishing a multiport network interleaving model, which specifically comprises the following substeps:

step 2.1.1 establishing a model middle part comprising two identical Josephson junctions, wherein the two Josephson junctions are driven by two independent thermal noise currents;

wherein each josephson junction is a parallel resistor circuit;

step 2.1.2 two reverse bias currents I by providing bias currents to the Josephson junctions_b1And I_b2Establishing a left end of a model by two circuit networks for providing local oscillator signals and a local oscillator coupling network;

wherein a circuit network for providing local oscillator signals comprises only an impedance Z_lo1Another circuit network for providing a local oscillator signal includes an impedance Z_lo2And the local vibration source voltage V_los(ii) a Impedance matrix for local oscillator coupling network

Description is given;

step 2.1.3, establishing the right ends of models comprising two radio frequency signal generating circuits, a radio frequency signal coupling network, an intermediate frequency signal generating circuit, a mirror image signal coupling network and two mirror image signal generating circuits;

wherein a radio frequency signal generating circuit comprises an impedance Z_rf1And a radio frequency signal source voltage V_rfsThe other radio-frequency signal generating circuit includes only an impedance Z_rf2(ii) a RF signal coupling network consisting of impedance matrix

Description is given; intermediate frequency signal coupling network composed of impedance matrix

Description is given; intermediate frequency signal generating circuit consisting of_ifForming; mirror signal coupling network consisting of an impedance matrix

Description is given; two mirror image signal generating circuits are respectively composed of impedance Z_im1And Z_im2Forming;

step 2.2, obtaining an analytical expression of conversion gain and noise temperature of the balanced type high-temperature superconducting receiver according to the multi-port network interweaving model established in step 2.1, and specifically comprising the following substeps:

step 2.2.1, according to the nonlinear relation of the high-temperature superconducting Josephson junctions and the kirchhoff current law, combining a circuit in the middle part of the model, establishing a time domain nonlinear Josephson equation set according to the kirchhoff current law, and solving the equation set to obtain time domain normalization junction voltage v of two Josephson junctions₁(τ) and v₂(τ)；

One end of the time domain nonlinear Josephson equation set is superconducting current of the high-temperature superconducting Josephson junction and junction resistance R flowing through_jThe other end is the sum of the current of the direct current signal flowing into the high-temperature superconducting Josephson junction, the current of the local oscillator signal and the current of the noise; the superconducting current of the high-temperature superconducting Josephson junction is the critical current I of the junction_jProduct of a sine function of the difference in superconducting phase from the junction;

step 2.2.2 normalization of the time domain resulting voltage v₁(τ) and v₂(tau) performing Fourier transform and retaining voltage components v at the frequencies of the direct current and the local oscillator signals respectively_{bq_0}、v_{loq_0}And the rest components are discarded;

step 2.2.3, selecting direct current and local oscillator current with different amplitudes, repeating steps 2.2.1 and 2.2.2, and respectively calculating the mean value of the direct current voltage and the local oscillator voltage components<v_{bq_0}>、<v_{loq_0}>Variance, variance<(δv_{bq_0})²>、<(δv_{loq_0})²>Covariance of<(δv_{bq_0})(δv_{loq_0})>And the module square difference of the local oscillator voltage<|δv_{loq_0}|²>；

Wherein q is 1, 2; k ranges from 2 to 20;<v_{bq_0}>represents v_{bq_0}The average value of (a) of (b),<v_{loq_0}>represents v_{loq_0}The mean value of (a);<(δv_{bq_0})²>represents v_{bq_0}The variance of (a) is determined,<(δv_{loq_0})²>represents v_{loq_0}The variance of (a) is determined,<(δv_{bq_0})(δv_{loq_0})>represents v_{bq_0}And v_{loq_0}The covariance of (a);<|δv_{loq_0}|²>represents v_{loq_0}The difference of the mode squares of (a);

step 2.2.4 combining the model left-end local oscillation coupling network, establishing an equation set according to kirchhoff voltage law, and solving to obtain local oscillation source voltage V_losAnd local oscillator voltage<v_lo1>Local oscillator current i_lo1、i_lo2Local oscillator coupling network impedance A_lo12、B_lo11、B_lo12The relationship between the two, then the local vibration source power P is obtained_losAnd the local vibration source voltage V_losCritical current I of high-temperature superconducting Josephson junction_jJunction resistance R of high-temperature superconducting Josephson junction_jImpedance Z_lo2The relationship between;

wherein, the step 2.2.4 is used for adjusting the local vibration source power P under the condition that other parameters are known_losRealizing local oscillator current i_lo1、i_lo2A change in (b);

step 2.2.5 combining the circuit and the coupling network at the right end of the model to establish a radio frequency voltage v_rf1、v_rf2Intermediate frequency voltage v_if1、v_if2Mirror voltage v_im1、v_im2And radio frequency current i_rf1、i_rf2If current i_if1、i_if2Mirror current i_im1、i_im2A set of equations relating the impedance of the first and second electrodes, the set of equations being defined by a static impedance matrix

And a radio frequency source voltage vector v_sigEstablishing;

wherein an impedance matrix

The element of (A) is obtained by the current operation of the circuit at the right end of the model and each impedance of the coupling network;

wherein, the radio frequency source voltage vector v_sigImpedance of circuit and coupling network including right end of model and radio frequency signal source voltage V_rfs；

Step 2.2.6 obtaining the radio frequency voltage v in combination with the middle part of the model_rf1、v_rf2Intermediate frequency voltage v_if1、v_if2Mirror voltage v_im1、v_im2And radio frequency current i_rf1、i_rf2If current i_if1、i_if2Mirror current i_im1、i_im2Another system of equations for the relationship between the expression by a dynamic impedance matrix

And noise vector

Establishing;

wherein, the operation reason of the step 2.26 is that: compared with the direct current signal and the local oscillator signal at the left end of the model, the radio frequency signal, the intermediate frequency signal and the image signal at the right end of the model are very small and can be regarded as small signals;

step (ii) of2.2.6, specifically: for the mean value of the direct current voltage and the local oscillator voltage obtained in the step 2.2.3<v_{bq_0}>、<v_{loq_0}>Take the full differential (<v_{bq_0}>、<v_{loq_0}>Are all DC current i_bqAnd local oscillator current i_loqWherein q is 1, 2), then taking the sum of the radio frequency signal and the image signal as the differential of the local oscillator, taking the intermediate frequency signal as the differential of the direct current to be brought into a full differential equation, and obtaining a dynamic impedance matrix according to the principle that the real parts and the imaginary parts at the two ends of the equal signal are correspondingly equal

Wherein the noise vector

Is the variance obtained in step 2.2.3<(δv_{bq_0})²>、<(δv_{loq_0})²>Covariance of<(δv_{bq_0})(δv_{loq_0})>And the module square difference of the local oscillator voltage<|δv_{loq_0}|²>；

Step 2.2.7 step 2.2.5 and step 2.2.6 respectively establish an equation set, and calculating to obtain the radio frequency current i according to the established equation set_rf1、i_rf2If current i_if1、i_if2And a mirror current i_im1、i_im2The intermediate frequency current i is obtained according to the relevant theory of circuit analysis by combining the circuit at the right end part of the model and the coupling network_ioAnd then obtaining an analytical expression of the conversion gain and the noise temperature of the balanced type high-temperature superconducting receiver according to the related definitions of the conversion gain and the noise temperature.

Advantageous effects

The invention provides a circuit design and modeling method of a balanced type high-temperature superconducting receiver, which comprises the circuit design of the balanced type high-temperature superconducting receiver and the modeling method of the balanced type high-temperature superconducting receiver, and compared with the existing circuit design application and modeling method, the circuit design and modeling method has the following beneficial effects:

1. the circuit design of the balanced type high-temperature superconducting receiver skillfully superposes the in-phase signals generated by mixing two Josephson junctions, and local oscillation stray sound and amplitude noise are just reversely added and offset, so that compared with a unijunction or serial junction type high-temperature superconducting receiver, the balanced type high-temperature superconducting receiver can effectively reduce the noise temperature of the receiver and improve the frequency conversion gain of the receiver; the high-temperature superconducting receiver has much smaller volume and lower cost than the low-temperature superconducting receiver; the superconducting receiver has the advantages of low noise, extremely wide medium-frequency band, high frequency upper limit, low power requirement and the like; the high-temperature superconducting receiver has a very good application prospect in the field of terahertz communication with high frequency and fast attenuation;

2. the modeling method of the balanced type high-temperature superconducting receiver makes up the vacancy of a theoretical modeling technology in the research of the balanced type high-temperature superconducting receiver, and lays a design and application foundation for the development and the use of the balanced type high-temperature superconducting receiver;

3. the performance prediction of the balanced high-temperature superconducting receiver is realized by performing electromagnetic simulation design on a circuit of the balanced high-temperature superconducting receiver, extracting relevant impedance, and applying a modeling method of the balanced high-temperature superconducting receiver to design the direct current IV characteristic of the circuit to enable G_recMaximum amount of T_recOptimum DC bias I as low as possible_b1Optimal power P of LO signal_losAnd IF frequency and G_recAnd T_recThe method predicts the relation of the balance type high-temperature superconducting receiver, provides an engineering application mode of the modeling method of the balance type high-temperature superconducting receiver, and further embodies the importance of the modeling method of the balance type high-temperature superconducting receiver to the balance type high-temperature superconducting receiver.

Drawings

FIG. 1 is a balanced high temperature superconducting receiver circuit design;

FIG. 2 is a diagram of S parameter amplitude of the MgO chip circuit of the balanced high temperature superconducting receiver at the frequency of the radio frequency signal;

FIG. 3 is a diagram of the S parameter phase of the MgO chip circuit of the balanced high temperature superconducting receiver at the frequency of the RF signal;

FIG. 4 is the current distribution diagram of the RF signal at 0 and 90 degrees phase for the MgO chip circuit of the balanced high temperature superconducting receiver;

FIG. 5 is a graph of S parameter amplitude at the RF signal frequency for an alumina PCB circuit for a balanced high temperature superconducting receiver;

FIG. 6 is a current distribution diagram of a balanced HTS receiver with a phase of 0 at 10GHz IF;

FIG. 7 is a model diagram of a method for modeling a balanced high temperature superconducting receiver;

FIG. 8 is a schematic diagram of a four-port network model;

FIG. 9 is a DC IV curve prediction diagram of two Josephson junctions when no local oscillator signal is added to the balanced high temperature superconducting receiver at different temperatures;

FIG. 10 is a DC IV curve prediction diagram of two Josephson junctions when the balanced high temperature superconducting receiver loads local oscillator signals at different temperatures;

FIG. 11 is a diagram of the prediction of the relationship between the conversion gain and noise temperature of a balanced HTS receiver at different temperatures and DC offset;

FIG. 12 is a diagram of the prediction of the relationship between the conversion gain and noise temperature of a balanced HTS receiver at different temperatures and the local oscillator signal power;

FIG. 13 is a diagram of a conversion gain and noise temperature versus IF frequency prediction for a balanced HTS receiver at different temperatures;

illustration of the drawings:

in FIG. 2, (a) is a three-dimensional view and (b) is a top view;

the circuit comprises a 1-MgO chip, a 2-aluminum oxide PCB, a 3-adhesive tape, a 4-high temperature superconducting microstrip circuit, a 5-orthogonal coupling network, a 6-Josephson junction, a 7-quarter wavelength high-low impedance line, an 8-five-order choke filter, a 9-dc/IF gasket, a 10-GND gasket, an 11-fan choke filter, a 12-bias three-way circuit, a 13-500 omega resistor, a 14-100-nF capacitor and a 15-intermediate frequency signal mixed circuit.

Detailed Description

The circuit design and modeling method of a balanced high temperature superconducting receiver according to the present invention will be further explained and described in detail with reference to the accompanying drawings and embodiments.

Example 1

The circuit design of the balanced high-temperature superconducting receiver designed by the embodiment corresponds to the step 1 of the invention content, and as shown in fig. 1, the circuit design comprises an MgO chip 1 and an alumina PCB2 which are connected through an adhesive tape 3.

Corresponding to the step 1.1 of the invention content, an MgO chip 1 is designed, the main design content is a high-temperature superconducting microstrip circuit 4, firstly, an orthogonal coupling network 5 combined by a 3dB branch bridge is designed to be used as an orthogonal coupling circuit of a radio frequency signal and a local oscillator signal, the orthogonal coupling of the radio frequency signal and the local oscillator signal is completed, and the coupled signal energy is evenly distributed into two paths of signal output. And then designing a quarter-wavelength high-low impedance line 7 for impedance matching, so that the two coupled radio frequency signals, the local oscillator signal and the local oscillator signal respectively reach two Josephson junctions 6 for frequency mixing. And then, the fan-shaped choke filter 11 and the GND gasket 10 are used as direct current bias circuits of the two Josephson junctions to ensure the normal work of the two Josephson junctions. The fan-shaped choke filter 11 functions to prevent the intermediate frequency signal, the local oscillator signal, and the radio frequency signal from flowing to the GND pad 10. The fifth order choke filter 8 is then designed so that only the two intermediate frequency signals resulting from mixing at the two josephson junctions 6 reach the dc/IF pads 10, which are connected by radial stubs and the circuitry of the alumina PCB 2.

After the design is finished, the performance indexes of the MgO chip 1 circuit are as follows: when electromagnetic simulations are performed with RF (radio frequency) and LO (local oscillator signal) ports as

ports

1 and 2, respectively, and symmetric josephson junctions 6 as

ports

3 and 4 in fig. 1, as shown in fig. 2 and 3, the reflection parameter S11 is less than-10 dB over a wide frequency range of 550GHz to 650 GHz. In addition, the transmission coefficient S21 between the radio frequency port and the LO port is smaller than-15 dB within the range of 570-623 GHz, and reaches about-35 dB peak value at 596GHz, which shows that the port isolation performance is good. In addition, the coefficients S31 and S41 are of similar magnitude (about-3.6 dB at 600 GHz), differ by nearly 90 ° throughout the frequency band, showing the broadband characteristics of the terahertz orthogonal coupling network 5. Fig. 4 is a current distribution diagram of the radio frequency signal at 0 ° and 90 ° phases. It can be seen that the radio frequency current splits equally into two paths in quadrature phase relationship and then couples into the two josephson junctions 6 separately, while being well isolated from the other ports and pads.

Corresponding to step 1.2 of the invention, an alumina PCB2 is designed, the circuit mainly designed with the intermediate frequency and direct current signals, first, two bias tee circuits 12 are designed for testing the characteristics of the josephson junction and the circuit, each bias tee includes two 500 Ω resistors and a 100-nF capacitor. And then designing a broadband multi-section Wilkinson power divider with the center frequency of 10GHz as a mixing circuit 15 of intermediate frequency signals, and finally realizing that the two paths of intermediate frequency signals generated at the two Josephson junctions 6 are superposed in the same phase in the mixing circuit, and local oscillation stray sound and amplitude noise are just added and offset in the reverse direction.

After the design is completed, the performance of the circuit of the balanced type high-temperature superconducting receiver is as follows: when electromagnetic simulation is performed with the IF (intermediate frequency signal) port as port 1 and the symmetric josephson junctions as

ports

2, 3 in fig. 2, as shown in fig. 5, 6. FIG. 5 shows that due to the good broadband characteristic of the multi-stage Wilkinson power divider, the bandwidth of the available intermediate frequency signal is 3-18 GHz, and the reflection parameter S is₁₁Less than-10 dB. In addition, the transmission parameters S of the band₂₁And S₃₁Are all about-4 to-5 dB. As can be seen in fig. 6, except for the dc-biased GND pad 10 and the terahertz quadrature coupling network 5 and the RF (radio frequency signal) and LO (local oscillator signal) ports, the current from the IF (intermediate frequency signal) port flows through all the relevant components or microstrip lines on the MgO chip 1 and the alumina PCB 2. Furthermore, the currents on the two branches associated with the two josephson junctions 6 have the same amplitude and phase. The results of the two graphs show that the system has good intermediate frequency signal transmission and isolation characteristics.

The above analysis shows that the circuit performance of the balanced high-temperature superconducting receiver designed by the embodiment completely meets the design requirements, and finally the purpose that two paths of intermediate frequency signals are superposed in phase in a hybrid circuit and local oscillation stray sound and amplitude noise are just added and offset in reverse direction can be achieved, so that the noise temperature of the receiver is reduced, and the conversion gain of the receiver is improved.

The dimension H, L, W labeled in FIG. 1 is determined based on the overall dimensions of the circuitry of the balanced HTS receiver; l is_MgO、W_MgOAre determined according to the circuit size of the MgO chip 1; l is_Alu、W_AluAre determined by the circuit dimensions of the alumina PCB 2.

Example 2

The modeling method of the balanced type high-temperature superconducting receiver provides a powerful tool for the frequency mixing analysis and the performance prediction of the balanced type high-temperature superconducting receiver, and establishes a multiport network interweaving model;

in specific implementation, the working process of the multiport network interleaving model established in step 2.1 is as follows:

1) local oscillator coupling network outputs local oscillator current I_lo1And I_lo2To two josephson junctions, respectively;

2) radio frequency signal coupling network output end radio frequency current I_rf1And I_rf2Respectively reaching two Josephson junctions;

3) local oscillator current I_lo1And radio frequency current I_rf1Non-linear mixing at a josephson junction; local oscillator current I_lo2And radio frequency current I_rf2Non-linear mixing at a josephson junction;

4) intermediate frequency signal I produced after mixing at two Josephson junctions_if1And I_if2Respectively expressed and outputted by an intermediate frequency signal coupling network and an intermediate frequency signal generating circuit to generate an image signal I_im1And I_im2Respectively expressed by a mirror image signal coupling network and two mirror image signal generating circuits;

1. corresponding to the step 2.2.1, a time domain nonlinear Josephson equation set is established, and the equation set is solved to obtain time domain normalized junction voltage v of two Josephson junctions₁(τ) and v₂(τ)。

As shown in the modeling model of the balanced high-temperature superconducting receiver in fig. 1, two josephson junctions are driven by using direct current, local oscillator signals and noise sources, and a time domain nonlinear josephson equation set is established according to the nonlinear relation of the high-temperature superconducting josephson junctions and kirchhoff current law:

wherein h is Planck constant, R_jIs the junction impedance of the Josephson junction, e is the charge of a single photon, phi₁、φ₂Superconducting phase difference, I, of two Josephson junctions_jIs the critical current of the Josephson junction, I_b1、I_b2DC biasing of two Josephson junctions, respectively_lo1、I_lo2The complex half amplitude value delta I of the current of the local oscillation signals loaded on the two Josephson junctions_n1And δ I_n2The autocorrelation function is the current noise temperature for two josephson junctions:

wherein k is Boltzmann constant, and T is Josephson junction temperature.

Equations (1) and (2) are written in normalized form:

2. corresponding to step 2.2.2, by pairing v₁(τ)＝dφ₁(τ)/d τ and v₂(τ)＝dφ₂(τ)/d τ, performing Fourier transform to obtain voltage components at the frequencies of the direct current and the local oscillator signals:

v_{bq_0}＝<v_{bq_0}>+δv_{bq_0} (5)

v_{loq_0}＝<v_{loq_0}>+δv_{loq_0} (6)

wherein v is_{bq_0}Is a direct voltage, v_{loq_0}Q is 1 or 2.

3. Corresponding to the step 2.2.3, selecting direct current signal current and local oscillator current with different amplitudes, repeating the process for K times, and obtaining the following formula according to the knowledge of mathematical statistics:

wherein q is 1, 2; k ranges from 2 to 20;<v_{bq_0}>represents v_{bq_0}The average value of (a) of (b),<v_{loq_0}>represents v_{loq_0}The mean value of (a);<(δv_{bq_0})²>represents v_{bq_0}The variance of (a) is determined,<(δv_{loq_0})²>represents v_{loq_0}The variance of (a) is determined,<(δv_{bq_0})(δv_{loq_0})>represents v_{bq_0}And v_{loq_0}The covariance of (a);<|δv_{loq_0}|²>represents v_{loq_0}The modulus variance of (c).

4、Corresponding to the step 2.2.4, solving to obtain the local vibration source voltage V_losAnd local vibration source power P_losIs described in (1).

(i) due to the constraint of the local oscillator coupling network on the left side of the model_{lo1_0},<v_{lo1_0}>) And (i)_{lo2_0},<v_{lo2_0}>) The results of the calculations of (a) cannot be simultaneously valid. Suppose (i)_{lo1_0},<v_{lo1_0}>) Effective, in combination with i_{lo2_0}And<v_{lo2_0}>the relation between i_lo2And<v_lo2>the relationship between them.

Introducing a polynomial to approximate i_lo2And<v_lo2>the relationship of (1), namely:

using the least squares method and_{lo2_0},<v_{lo2_0}>) Value data set of (x respectively)₁,x₂,…,x_N]^TAnd [ y₁,y₂,…,y_N]^T) Obtaining:

wherein,

in addition to equation (13), there is another constraint on i using the local oscillator coupling network_lo2And<v_lo2>the equation of (c).

Considering that the local oscillator coupling network is a four-port network, as shown in fig. 8, the impedance matrix of the model can be represented as:

from the definition of the circuit and network impedance matrix shown in fig. 8, it can be seen that:

simultaneous equations (19) and (20) yield:

also according to the definition of the impedance matrix, v₃、v₄Can be expressed as:

simultaneous equations (21) and (22) yield:

wherein:

according to the formulas (19) to (25), the correlation variable (v) is set_s1＝0,v_s2＝v_los,i₃＝-i_lo1,i₄＝-i_lo2,v₃＝<v_lo1>,v₄＝<v_lo2>,z₁＝z_lo1,z₂＝z_lo2,

And

) Obtaining:

wherein,

derived from formula (26):

combining equation (13) to obtain equation (29)<v_lo2>Comprises the following steps:

obtaining i in equation (30) by using MATLAB software_lo2And further find v_losAnd P_los：

v_los＝(<v_lo1>+B_lo11i_lo1+B_lo12i_io2)/A_lo12 (31)

5. Corresponding to step 2.2.5, a radio frequency voltage v is established_rf1、v_rf2Intermediate frequency voltage v_if1、v_if2Mirror voltage v_im1、v_im2And radio frequency current i_rf1、i_rf2If current i_if1、i_if2Mirror current i_im1、i_im2The system of equations for the relationship between.

Similar to the derivation of equation (26), the RF circuit and coupling network variables (v) at the right end of the model are set_s1＝v_rfs,v_s2＝0,i₃＝-i_rf1,i₄＝-i_rf2,v₃＝v_rf1,v₄＝v_rf2,z₁＝z_rf1,z₂＝z_rf2,

) And mirror circuit and coupling network variable (v)_s1＝0,v_s2＝0,i₃＝-i_im1,i₄＝-i_im2,v₃＝v_im1,v₄＝v_im2,z₁＝z_im1,z₂＝z_im2,

) Obtaining:

wherein,

the current and voltage of the intermediate frequency coupling network are:

the combination of formulae (33), (34), (40) yields:

or is as follows:

6. corresponding to step 2.2.6, the radio frequency voltage v is obtained under the restriction of small signals_rf1、v_rf2Intermediate frequency voltage v_if1、v_if2Mirror image electricityPressure v_im1、v_im2And radio frequency current i_rf1、i_rf2If current i_if1、i_if2Mirror current i_im1、i_im2Another set of equations for the relationship between:

or

Wherein,

and

wherein q is 1 or 2.

The equations (46) to (51) are derived as follows:

according to the process of solving the time domain nonlinear josephson equation system, the following results are obtained:

<v_bq>＝f_1q(i_bq,|i_loq|) (52)

<v_loq>＝i_loqf_2q(i_bq,|i_loq|) (53)

wherein q is 1, 2.

The equations (52) and (53) are differentiated by:

according to the generalized frequency mixing theory, the voltage (current) of the radio frequency signal and the voltage (current) of the image signal can be regarded as the differential of the voltage (current) of the local oscillator signal; the voltage (current) of the intermediate frequency signal can be seen as the differential of the direct voltage (current).

di_loq＝i_rf exp(jΩ_ifτ)+i_imexp(-jΩ_ifτ) (58)

d<v_loq>＝v_rf exp(jΩ_ifτ)+v_imexp(-jΩ_ifτ) (59)

Substituting equations (56) to (57) into equations (54) and (55) yields:

therefore, equations (46) to (51) can be obtained.

7. And corresponding to the step 2.2.7, solving an analytical expression of the conversion gain and the noise temperature of the balanced type high-temperature superconducting receiver.

According to formulae (43) and (45), we obtain:

by setting up

According to formulae (43) and (45), we obtain:

then there are:

introducing a matrix

Obtaining:

the normalized rf signal source power is:

p_rfs＝|v_rfs|²/2Re(z_rf1) (70)

receiver conversion gain G_mixComprises the following steps:

to obtain the receiver noise temperature, the signal term is made equal to the noise term in equation (42). Then there are:

due to input power p_rfsAlso from T_mixDenoted by f Δ Ω/T, the receiver noise temperature is:

example 3

The performance prediction of the balanced high-temperature superconducting receiver can effectively predict the direct current IV characteristic, noise and conversion performance of the receiver.

Aiming at the balanced high-temperature superconducting receiver circuit designed in the example 1, electromagnetic simulation design is carried out, and radio-frequency signals, local oscillator signals, image signals and self-impedance and mutual impedance of an intermediate-frequency coupling network are extracted from the electromagnetic simulation of the circuit design; then, the junction resistance R of the Josephson junction at different temperatures is measured by two bias tee circuits 12_jAnd critical current I_j(ii) a Finally, the above values are substituted into the examples2, calculating the direct current IV characteristic, noise and conversion performance of the receiver by using MATLAB software, as shown in fig. 9, 10, 11 and 12.

It can be seen in figure 9 that both josephson junctions 6 exhibit non-linear shunting phenomena. From 20K to 60K, superconducting critical current I_jDecreases with increasing operating temperature, junction resistance R_jIt is determined by the slope of the linear segment of the IV curve and remains constant at 4.4 Ω. Due to R of two junctions at the same temperature_jAnd I_jThe values are the same and the polarity of the bias current is opposite, so the IV curve is symmetrical on the V-0 axis.

In FIG. 10, when the HTS receiver loads the local oscillator signal (f) through the coupling network_lo＝600GHz、P_losApproximant to-27 dBm), I_jPartially suppressed, a series of sharp-edged sharp steps appeared in the IV curve. First order Charperot voltage V₁And local oscillator signal frequency f_LOConform to V₁＝Φ₀f_LOTheoretical relationship of (phi)₀Is a quantum of magnetic flux). Corresponding inhibition I_jThe difference in value and the sharp current step height is due to the incomplete balancing of the amplitudes of the coupling network.

In FIG. 11, gain G is converted_recAnd noise temperature T_recWith bias DC I_b1And the bias current is changed and reaches an extreme value under the optimal bias direct current, and the bias current is smaller at a higher working temperature. This is because the optimum bias current is typically between the 0 th and 1 st order sharp of the IV curve shown in fig. 10. Furthermore, the optimum conversion gain G increases when the operating temperature T increases from 20K to 60K_recAnd noise temperature T_recCan be degraded in part due to the lower dynamic resistance (R) at higher temperatures_ddV/dI) affects the impedance matching between the josephson junction and the intermediate frequency signal output network.

In fig. 12, the local oscillator signal power P is low under the corresponding optimum bias current condition_losThe influence on the performance of the receiver is weaker than that of the bias direct current, and the phenomenon is more obvious particularly at lower working temperature. And the best local oscillator signal powerRate P_losAlmost independent of temperature, much lower than that required for schottky diode receivers. At radio frequency f_rf603GHz and local oscillator frequency f_loAt 600GHz, the optimum G_recAnd T_rec(at the optimum local oscillator signal power P_losDC bias I_b1And I_b2With the proviso) are-2.5 dB and 865K at 20K, about-8 dB and 1550K at 40K, and about-18.4 dB and 5880K at 60K.

In fig. 13, the proposed modeling method shows great flexibility and efficiency in dealing with many complex network-related problems contained in the high-temperature superconducting receiver body circuit, and the conversion gain G is simulated at the LO frequency of the local oscillator signal of 600GHz_recAnd noise temperature T_recRanges of-1.5 to-4.5 dB and 845K to 995K at 20K, -7.9dB to-9.6 dB and 1500K to 1740K at 40K, -17.7dB to-21 dB and 5690K to 6530K at 60K, and 1 to 18GHz for the available intermediate frequency range.

The foregoing merely represents embodiments of the present invention, which are described in some detail and detail, and therefore should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various changes and modifications without departing from the system concept, and all of them fall into the protection scope of the present patent. Therefore, the protection scope of this patent shall be subject to the appended claims.

Claims

1. A circuit design and modeling method for a balanced high-temperature superconducting receiver is characterized in that: the method comprises the steps of designing a circuit of a balanced high-temperature superconducting receiver and modeling the superconducting receiver;

step 1 specifically comprises the following substeps:

step 1.1 design MgO chip circuit, including the following substeps:

step 2, modeling is carried out on the balanced type high-temperature superconducting receiver, and time-frequency separation and network interweaving processing are specifically adopted, wherein the modeling comprises the following steps:

step 2.1.2 by providing two inversions of the bias current for the Josephson junctionTo bias current I_b1And I_b2Establishing a left end of a model by two circuit networks for providing local oscillator signals and a local oscillator coupling network;

Wherein q is 1, 2;<v_{bq_0}>represents v_{bq_0}The average value of (a) of (b),<v_{loq_0}>represents v_{loq_0}The mean value of (a);<(δv_{bq_0})²>represents v_{bq_0}The variance of (a) is determined,<(δv_{loq_0})²>represents v_{loq_0}The variance of (a) is determined,<(δv_{bq_0})(δv_{loq_0})>represents v_{bq_0}And v_{loq_0}The covariance of (a);<|δv_{loq_0}|²>represents v_{loq_0}The difference of the mode squares of (a);

And a radio frequency source voltage vector v_sigEstablishing;

wherein an impedance matrix

And noise vector

Establishing;

wherein the noise vector

2. The circuit design and modeling method for the balanced high-temperature superconducting receiver according to claim 1, wherein: in step 1.1.2, the impedance match is located between the 3dB branching bridge network and the two josephson junctions.

3. The circuit design and modeling method for the balanced high-temperature superconducting receiver according to claim 2, wherein: in step 1.1.3, the fan-shaped choke filter is used for preventing the intermediate frequency signals, the local oscillator signals and the radio frequency signals from flowing to a direct current offset; in step 1.1.4, the dc/IF gasket and the radial stub form a bonding tape, and the bonding tape connects the MgO chip circuit and the alumina PCB circuit; the local oscillation stray sound and the amplitude noise are just reversely added and offset through the step 1.2.2.

4. The circuit design and modeling method for the balanced high-temperature superconducting receiver according to claim 3, wherein: in step 1.2.1, each bias tee circuit includes two 500 Ω resistors and a 100-nF capacitor.

5. The circuit design and modeling method for the balanced high-temperature superconducting receiver according to claim 4, wherein: in step 1.2.2, the mixing circuit of the intermediate frequency signal is a broadband multi-section Wilkinson, and the range of the central working frequency is as follows: 5GHz-15 GHz.

6. The circuit design and modeling method for the balanced high-temperature superconducting receiver according to claim 5, wherein: in step 2.1.1, each josephson junction is a resistor parallel connection circuit; in step 2.1.2, a circuit network providing local oscillator signals comprises only impedance Z_lo1Another circuit network for providing a local oscillator signal includes an impedance Z_lo2And the local vibration source voltage V_los(ii) a Impedance matrix for local oscillator coupling network

A description is given.

7. The circuit design and modeling method for the balanced high-temperature superconducting receiver according to claim 6, wherein: in step 2.1.3, a radio frequency signal generating circuit includes an impedance Z_rf1And a radio frequency signal source voltage V_rfsThe other radio-frequency signal generating circuit includes only an impedance Z_rf2(ii) a RF signal coupling network consisting of impedance matrix

Description is given; two mirror image signal generating circuits are respectively composed of impedance Z_im1And Z_im2And (4) forming.

8. The circuit design and modeling method for the balanced high-temperature superconducting receiver according to claim 7, wherein: in step 2.2.1, one end of the time domain nonlinear Josephson equation set is the superconducting current of the high temperature superconducting Josephson junction and the junction resistance R_jThe other end is the sum of the current of the direct current signal flowing into the high-temperature superconducting Josephson junction, the current of the local oscillator signal and the current of the noise; the superconducting current of the high-temperature superconducting Josephson junction is the critical current I of the junction_jThe product of the sine function of the difference in superconducting phase of the junction.

9. The circuit design and modeling method for the balanced high-temperature superconducting receiver according to claim 8, wherein: in step 2.2.3, the value range of K is 2 to 20; step 2.2.4 is effected by adjusting the local source power P in the case that other parameters are known_losRealizing local oscillator current i_lo1、i_lo2Is changed.

10. The circuit design and modeling method for the balanced high-temperature superconducting receiver according to claim 9, wherein: the operational reasons for step 2.2.6 are: compared with the direct current signal and the local oscillator signal at the left end of the model, the radio frequency signal, the intermediate frequency signal and the image signal at the right end of the model are very small and can be regarded as small signals;

step 2.2.6, specifically: for the mean value of the direct current voltage and the local oscillator voltage obtained in the step 2.2.3<v_{bq_0}>、<v_{loq_0}>Take the full differential (<v_{bq_0}>、<v_{loq_0}>Are all DC current i_bqAnd local oscillator current i_loqWherein q is 1, 2), then taking the sum of the radio frequency signal and the image signal as the differential of the local oscillator, taking the intermediate frequency signal as the differential of the direct current to be brought into a full differential equation, and obtaining a dynamic impedance matrix according to the principle that the real parts and the imaginary parts at the two ends of the equal signal are correspondingly equal