10. Circuit synthesis-wideband matching circuit design method based on simplified real frequency
Chapters 1-9 in the Overview of Network Synthesis and Simplified Real Frequency Theory Learning introduced some basic concepts and experimental methods of SRFT, and finally came to another ultimate use of SRFT, the design of broadband matching circuits.
1. Some previous reviews and summaries
Some cases of circuit synthesis have been given before, but these cases must be based on S parameters in the form of analytical functions. In more general cases, it is difficult for us to complete the design based on this. We often need to based on the impedance to be matched. Design the actual circuit:
5. Circuit synthesis – super cool – directly synthesize the microstrip circuit diagram based on S11 parameters
Based on the expression of the given S11 parameter, the corresponding microstrip circuit diagram is synthesized. Note that the S11 parameter expression here needs to be in analytical form (that is, it must be in the form of a function expression)
6. Circuit synthesis-design of SRFT microstrip line-cut Byshev low-pass filter based on simplified real frequency
Circuit synthesis is performed based on the Chebyshev function, and the circuit synthesis is performed directly based on the target parameters to obtain the corresponding microstrip circuit. The corresponding theory and operation steps are given (with Matlab code)
7. Circuit synthesis – SRFT microstrip line Butterworth low-pass filter design based on simplified real frequency
Conduct circuit synthesis based on the Butterworth function, directly conduct circuit synthesis based on the target parameters to obtain the corresponding microstrip circuit, and provide the corresponding theory and operation steps (with Matlab code)
8. Circuit synthesis-bandpass filter design based on simplified real frequency SRFT microstrip line
Conduct circuit synthesis based on Butterworth and Chebyshev functions, directly conduct circuit synthesis based on target parameters to obtain the corresponding bandpass microstrip circuit, and provide the corresponding theory and operation steps (with Matlab code)
2. Simplified real frequency broadband matching circuit design method theory
Impedance matching is actually the matching of the S11 circuit. Given the impedance value that needs to be matched to design a microstrip circuit, it is actually given the S11 parameters of some frequency points to synthesize the circuit diagram. The only thing we need is tofit the analytical expression of S11 in the Richard domain based on the S11 parameters at some frequency points.
This fitting process can also be regarded as an optimization process, which is to make the analytical expression as close as possible to the known S11 parameters. The basic process is the same as 9. Circuit synthesis – microstrip circuit design based on arbitrary amplitude-frequency response of simplified real frequency, so I won’t go into details here.
3. Simplified real frequency wideband matching circuit Matlab code and simple verification
Case: To match 10 ohms to 50 ohms within 2.1-5.1GHz, just set several discrete frequency points and target impedance in the code:
% Set the frequency point to be controlled f_target=[2.1 2.7 3.3 3.9 4.5 5.1]*1e9; % Set the corresponding impedance to be controlled and normalize it z_target=[10 10 10 10 10 10]/Z0;
The theme of the code is as follows (download the detailed code from the top link):
clear
clc
close all
global Z0
globalfreq_solve
% Use 1GHZ microstrip line, control up to 3GHz, characteristic impedance 50 ohms
f=4e9;
fe=4e9;
Z0=50;
%Use k cascaded microstrip lines for design
k=6;
%There is no zero point at DC
q=0;
%Initialize the coefficient of H
h=-1.*ones(1,k);
we=2*pi*fe;
tau=pi/2/we;
%speed of light
c=299792458;
ele_l=360*tau*f;
l=ele_l/360*c/f;
disp(['Here is implemented using a microstrip line with a power-off length of',num2str(f/1e9),'GHz of',num2str(ele_l),'°']);
% Set the frequency point to be controlled
f_target=[2.1 2.7 3.3 3.9 4.5 5.1]*1e9;
% Set the corresponding impedance to be controlled and normalize it
z_target=[10 10 10 10 10 10]/Z0;
% Convert to S11 parameters
s11_target=(z_target-1)./(z_target + 1);
% Define optimization variables
x0=h;
% Call optimization with no transformer
A = [];
b = [];
Aeq = [];
beq = [];
lb = [];
ub = [];
% opt=optimset('Display','off');
% warning('off');
[x,fval] = fmincon(@(x)objective_Z(x,fe,q,k,l,f_target,s11_target),x0,A,b,Aeq,beq,lb,ub,[]);
disp(['error is ',num2str(fval)])
% warning('on');
h=x;
h(k + 1)=0;
% Calculate other parameters based on h obtained from optimization
[G,H,F,g]=SRFT_htoG(h,q,k);
tau=pi/2/we;
%Solution frequency range, unit GHz
f_start=2;
f_stop=5;
f_step=0.1;
%Solution range
freq_solve=[f_start:f_step:f_stop]*1e9;
%Calculate the phase shift constant beta at different frequencies
beta=2*pi*freq_solve/c;
%Convert to lambda domain
lamda=1j*tan(beta*l);
num_h=0;
for i=1:1:length(h)
num_h=num_h + h(i).*lamda.^(length(h)-i);
end
num_g=0;
for i=1:1:length(g)
num_g=num_g + g(i).*lamda.^(length(g)-i);
end
num_f=(1-lamda.^2).^(k/2);
S11=num_h./num_g;
SimthChart(3)=figure(3);
wxp_smithplot=smithplot(S11,'GridType','Z');
legend(['th',num2str(1),'harmonic']);
dcm_obj = datacursormode(SimthChart(3));
set(dcm_obj,'UpdateFcn',@myupdatefcn_smith1);
wxp_smithplot.Marker = {<!-- -->' + '};
% Comprehensively obtain the required microstrip circuit
[Z_imp]=UE_sentez(h,g);
Z_imp=Z_imp.*Z0;
disp(Z_imp)
The result of running is as follows:
It can be seen from the Smith chart that the matching is good and the error is small. Construct the ADS circuit diagram with the source impedance set to 10 ohms:
The simulation results of ADS are as follows, which shows that the matching is perfect and the design is reasonable:
4. Simplify the matching design of real frequency power amplifier
Simplifying the real frequency is very useful in the design of power amplifiers. For the matching circuit of the power amplifier, the best frequencies at different frequency points are at different impedance points. For example, the best source impedance and load impedance of CGH40006S are as follows:
The SRFT circuit design is based on the optimal impedance value above. The design code is as follows (source matching and load matching can be changed by modifying the comments. Two optimization methods are provided, and modification comments are provided to switch):
clear
clc
close all
global Z0
globalfreq_solve
% Use 1GHZ microstrip line, control up to 3GHz, characteristic impedance 50 ohms
f=4e9;
fe=4e9;
Z0=50;
%Use k cascaded microstrip lines for design
k=5;
%There is no zero point at DC
q=0;
%Initialize the coefficient of H
h=-1.*ones(1,k);
we=2*pi*fe;
tau=pi/2/we;
%speed of light
c=299792458;
ele_l=360*tau*f;
l=ele_l/360*c/f;
disp(['Here we use a microstrip line with a power-off length of',num2str(f/1e9),'GHz of',num2str(ele_l),'° for implementation']);
% Set the frequency point to be controlled, source matching
f_target=[2.1 2.7 3.3 3.9 4.5 5.1]*1e9;
% Set the corresponding impedance to be controlled and normalize it
z_target=[20-1j*12 20-1j*8 18-1j*4 7-1j*3 6-1j*7 10-1j*10]/Z0;
% % Set the frequency point to be controlled, load matching
% f_target=[2.1 2.7 3.3 3.9 4.5 5.1]*1e9;
% % Set the corresponding impedance to be controlled and perform normalization
% z_target=[28 + 1j*14 26 + 1j*15 20 + 1j*13 19 + 1j*9 16 + 1j*7 15 + 1j*5.5]/Z0;
% % Set the frequency point to be controlled
% f_target=[2.1 2.7 3.3 3.9 4.5 5.1]*1e9;
% % Set the corresponding impedance to be controlled and perform normalization
% z_target=[10 10 10 10 10 10]/Z0;
% Convert to S11 parameters
s11_target=(z_target-1)./(z_target + 1);
%Choose one of two optimization methods
OPTIONS=optimset('MaxFunEvals',20000,'MaxIter',50000,'Algorithm','levenberg-marquardt');
x=lsqnonlin('objective_Z',x0,[],[],OPTIONS,fe,q,k,l,f_target,s11_target);
%Choose one of two optimization methods
% A = [];
% b = [];
% Aeq = [];
% beq = [];
%lb = [];
%ub = [];
% % opt=optimset('Display','off');
% % warning('off');
% [x,fval] = fmincon(@(x)objective_Z(x,fe,q,k,l,f_target,s11_target),x0,A,b,Aeq,beq,lb,ub,[]);
% disp(['error is ',num2str(fval)])
% % warning('on');
h=x;
h(k + 1)=0;
% Calculate other parameters based on h obtained from optimization
[G,H,F,g]=SRFT_htoG(h,q,k);
tau=pi/2/we;
%Solution frequency range, unit GHz
f_start=2;
f_stop=5;
f_step=0.1;
%Solution range
freq_solve=[f_start:f_step:f_stop]*1e9;
%Calculate the phase shift constant beta at different frequencies
beta=2*pi*freq_solve/c;
%Convert to lambda domain
lamda=1j*tan(beta*l);
num_h=0;
for i=1:1:length(h)
num_h=num_h + h(i).*lamda.^(length(h)-i);
end
num_g=0;
for i=1:1:length(g)
num_g=num_g + g(i).*lamda.^(length(g)-i);
end
num_f=(1-lamda.^2).^(k/2);
S11=num_h./num_g;
SimthChart(3)=figure(3);
wxp_smithplot=smithplot(S11,'GridType','Z');
legend(['th',num2str(1),'harmonic']);
dcm_obj = datacursormode(SimthChart(3));
set(dcm_obj,'UpdateFcn',@myupdatefcn_smith1);
wxp_smithplot.Marker = {<!-- -->' + '};
% %------------------------------------
% Comprehensively obtain the required microstrip circuit
[Z_imp]=UE_sentez(h,g);
Z_imp=Z_imp.*Z0;
disp(Z_imp)
The running results are as follows:
Construct the ADS simulation circuit diagram of input matching. Note that this is input matching, and the input and output order of the microstrip line needs to be reversed (the first section of the microstrip line is 49.6156 ohms, and so on):
In the picture above, port 1 is connected to the 50 ohm port, and port 2 is connected to the gate of the transistor. The simulation observes S22 to determine the matching result. The matching effect is very good:
The above design is input matching. Next, we will design the output matching circuit. We also modify the comments based on the above code and then synthesize it:
The matching effect is average and basically meets the requirements. In fact, the issue of over-fitting also needs to be considered here, so I won’t go into details here. Build an output matching circuit based on this result:
Port 1 is connected to the drain of the transistor, port 2 is connected to the 50 ohm port, and the simulation results of S11 are observed as follows, consistent with the theory:
