I figured the problem out. The paper has a small syntax in their system of equations. Therefore, MATLAB cannot give the result that I want. The mistake was at equation 2 that Vin should be -Vin. Also, instead of using my own parameters, I used the paper's parameters, and everything just works perfectly. Thanks all for helping me this out.
Below is the code that works for me. The modification includes:
1) Correct the error in the equation system
2) Use parameters in the paper instead
3) Add the range for all parameters as positive numbers
clear;clc; close all;
Vo = 48; Po = 7200; figure;
N = 18; Lm = 111.4e-6; Lr = 19.18e-6;
Cr = 20.25e-9; Co = 1e-3;
Zr1 = sqrt(Lr/Cr); wr1 = 1/sqrt(Lr*Cr);
fr1 = wr1/(2*pi); Tr1 = 1/fr1;
Zr2 = sqrt((Lr + Lm)/Cr); wr2 = sqrt(1/((Lr + Lm)*Cr));
fr2 = wr2/(2*pi); Tr2 = 1/fr2;
select = 1;
Q1 = 0.1831; Q2 = 0.3662;
if (select == 1)
Q = Q1;
else
Q = Q2;
end
Rac = Zr1/Q; Ro = Rac*(pi^2)/8/(N^2);
%% Below Resonance
syms I1 V1 I2 V2 deltaT1 deltaT2 fs
Vin = 800;
eq1 = (I1 + I2) -(N*Vo/Lm)*deltaT1;
eq2 = (-V1 - Vin + N*Vo)^2 +(I1*Zr1)^2 - (V2 - Vin + N*Vo)^2 - (I2*Zr1)^2 ;
eq3 = deltaT1 - ((pi - atan(I2*Zr1/(V2-Vin+N*Vo)) + atan(I1*Zr1/(V1+Vin-N*Vo)))/wr1);
eq4 = (V1 - Vin)^2 +(I1*Zr2)^2 - (V2 - Vin)^2 - (I2*Zr2)^2 ;
eq5 = deltaT2 - ((atan(I1*Zr2/(Vin - V1)) - atan(I2*Zr2/(Vin - V2)))/wr2);
eq6 = (Vo*(deltaT1 + deltaT2)/(N*Ro)) - (V1+V2)*Cr - (deltaT1*(I1-I2))/2;
eqs = [eq1,eq2,eq3,eq4,eq5,eq6];
range = [0, Inf; % I1
0, Inf; % V1
0, Inf; % I2
0, Inf; % V2
0, Inf; % deltaT1
0, Inf]; % deltaT2
[I1,V1,V2,I2,deltaT1,deltaT2] = vpasolve(eqs,[I1,V1,V2,I2,deltaT1,deltaT2],range)
I1 =
8.483487211088991203528612806318
V1 =
253.64132442119089964849356851349
V2 =
163.29575706350444322315252328323
I2 =
7.4427274570926256928348488481962
deltaT1 =
0.0000020534494375410093334689879526685
deltaT2 =
0.00000022936567635361382499350827474835
fs = 1/(deltaT1*2 + deltaT2*2)
fs =
219027.81217659331611383356783722