# How to find the expression for theta1?

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safi58 on 22 Apr 2017
Answered: Manuela Gräfe on 24 Apr 2017
theta1=2*atan((2*tan(theta2/2)*tan(gama/2 - theta2/2) + (4*tan(theta2/2)^2 - 4*M^2*tan(theta2/2)^2 - 4*M^2*tan(gama/2 - theta2/2)^2 - M^2*gama^2*l^2 - 8*M^2*tan(theta2/2)*tan(gama/2 - theta2/2) - 4*M^2*gama*l*tan(theta2/2) - 4*M^2*gama*l*tan(gama/2 - theta2/2) - M^2*gama^2*l^2*tan(theta2/2)^2*tan(gama/2 - theta2/2)^2 + 2*M^2*gama^2*l^2*tan(theta2/2)*tan(gama/2 - theta2/2) + 4*M^2*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)^2 + 4*M^2*gama*l*tan(theta2/2)^2*tan(gama/2 - theta2/2) + 4)^(1/2) - 2)/(2*tan(theta2/2) + 2*M*tan(gama/2 - theta2/2) + 2*M*tan(theta2/2) + M*gama*l - M*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)) - (2*tan(theta2/2)*tan(gama/2 - theta2/2))/(2*tan(theta2/2) + 2*M*tan(gama/2 - theta2/2) + 2*M*tan(theta2/2) + M*gama*l - M*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)))
Can anyone help me to find an expression for theta1 in terms of thetac where
theta2=thetac-theta1
Manuela Gräfe on 24 Apr 2017
Hi, umme mumtahina.
I see you are working with the LLC converter and the IEEE document (Optimal design methodology for LLC Resonant Converter... by Zhijian Fang etc.).
I am looking for the same solution at the moment for my bachelor thesis and I was wondering if you could provide me your MATLAB code? So I 'don't have to annoy Walter Roberson with the same issues. Please contact me via private message.

John D'Errico on 22 Apr 2017
Nope. Wanting magic to happen is not sufficient. I am quite confident that there is no way to untangle the implicit function you will get when you eliminate theta2.
Having theta1 inside and out of all of those terms will make it impossible to solve.
If you have values for all of the other variables, then you can use a root finder, but expect multiple solutions to exist.
safi58 on 23 Apr 2017
Edited: Walter Roberson on 23 Apr 2017
k1=0.423;
k_1=0.423;
F=1.05;
gama=pi/F
thetac=2.98;
theta2=thetac-theta1;
l=0.218;
M=0.95;
Can you please tell me how can I find theta1 using these values?
Walter Roberson on 23 Apr 2017
syms theta1 theta2 gama M l
eqn = theta1 == 2*atan((2*tan(theta2/2)*tan(gama/2 - theta2/2) + (4*tan(theta2/2)^2 - 4*M^2*tan(theta2/2)^2 - 4*M^2*tan(gama/2 - theta2/2)^2 - M^2*gama^2*l^2 - 8*M^2*tan(theta2/2)*tan(gama/2 - theta2/2) - 4*M^2*gama*l*tan(theta2/2) - 4*M^2*gama*l*tan(gama/2 - theta2/2) - M^2*gama^2*l^2*tan(theta2/2)^2*tan(gama/2 - theta2/2)^2 + 2*M^2*gama^2*l^2*tan(theta2/2)*tan(gama/2 - theta2/2) + 4*M^2*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)^2 + 4*M^2*gama*l*tan(theta2/2)^2*tan(gama/2 - theta2/2) + 4)^(1/2) - 2)/(2*tan(theta2/2) + 2*M*tan(gama/2 - theta2/2) + 2*M*tan(theta2/2) + M*gama*l - M*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)) - (2*tan(theta2/2)*tan(gama/2 - theta2/2))/(2*tan(theta2/2) + 2*M*tan(gama/2 - theta2/2) + 2*M*tan(theta2/2) + M*gama*l - M*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)));
F=1.05;
gama=pi/F
thetac=2.98;
theta2=thetac-theta1;
l=0.218;
M=0.95;
seqn = subs(eqn);
sol = vpasolve(seqn);
or
F=1.05;
gama=pi/F
thetac=2.98;
l=0.218;
M=0.95;
eqn = @(theta1) (2*atan((-2*tan(-(1/2)*thetac+(1/2)*theta1)*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)+(4*tan(-(1/2)*thetac+(1/2)*theta1)^2-4*M^2*tan(-(1/2)*thetac+(1/2)*theta1)^2-4*M^2*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)^2-M^2*gama^2*l^2+8*M^2*tan(-(1/2)*thetac+(1/2)*theta1)*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)+4*M^2*gama*l*tan(-(1/2)*thetac+(1/2)*theta1)-4*M^2*gama*l*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)-M^2*gama^2*l^2*tan(-(1/2)*thetac+(1/2)*theta1)^2*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)^2-2*M^2*gama^2*l^2*tan(-(1/2)*thetac+(1/2)*theta1)*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)-4*M^2*gama*l*tan(-(1/2)*thetac+(1/2)*theta1)*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)^2+4*M^2*gama*l*tan(-(1/2)*thetac+(1/2)*theta1)^2*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)+4)^(1/2)-2)/(-2*tan(-(1/2)*thetac+(1/2)*theta1)+2*M*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)-2*M*tan(-(1/2)*thetac+(1/2)*theta1)+M*gama*l+M*gama*l*tan(-(1/2)*thetac+(1/2)*theta1)*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1))+2*tan(-(1/2)*thetac+(1/2)*theta1)*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)/(-2*tan(-(1/2)*thetac+(1/2)*theta1)+2*M*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)-2*M*tan(-(1/2)*thetac+(1/2)*theta1)+M*gama*l+M*gama*l*tan(-(1/2)*thetac+(1/2)*theta1)*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)))) - theta1;
sol = fzero(eqn, rand())

Manuela Gräfe on 24 Apr 2017
Hi, umme mumtahina.
I see you are working with the LLC converter and the IEEE document (Optimal design methodology for LLC Resonant Converter... by Zhijian Fang etc.).
I am looking for the same solution at the moment for my bachelor thesis and I was wondering if you could provide me your MATLAB code? So I 'don't have to annoy Walter Roberson with the same issues. Please contact me via private message.