Syms and solver help

Hello all,

I am taking a resonant converters class and I am trying to use MATLAB to solve an equation that relates frequency and Load to a duty cycle for a converter I am looking at. I entered my equation below and when I didn't have success getting the solver to work( I am pretty sure that for my Rl min of 5 ohms and the frequency of 400,000Hz, I should get a D = 0.5), I tried to plot it as well, but I didn't succeed in that either. Could anyone help me understand my issues with the solver and also why I can't plot this?

(sorry for not including C before

C = 2.533e-8
f = 400e3;
Rl_min = 5;

syms D
S = double(solve((2*pi*f*C*Rl_min) == 1/(2*pi)*(1-2*pi^2*(1-D)^2-cos(2*pi*D)+(2*pi*(1-D)+sin(2*pi*D))^2/(1-cos(2*pi*D))),D))

y1 = (2*pi*f*C*Rl_min);
y2 = (1/(2*pi)*(1-2*pi^2*(1-D)^2-cos(2*pi*D)+(2*pi*(1-D)+sin(2*pi*D))^2/(1-cos(2*pi*D))));
x = linspace(0,1);

plot(x,y1,x,y2)

Answer 1

[Star Strider]

The code apparently works (although ‘C’ is missing, and since double does not allow for symbolic variables to be present, ‘S’ will be empty). To see ‘S’ with symbolic variables, use vpa instead of double.

As for the plots, try this:

C = 2.533e-8;
f = 400e3;
Rl_min = 5;

syms D
S = double(solve((2*pi*f*C*Rl_min) == 1/(2*pi)*(1-2*pi^2*(1-D)^2-cos(2*pi*D)+(2*pi*(1-D)+sin(2*pi*D))^2/(1-cos(2*pi*D))),D))

y1 = (2*pi*f*C*Rl_min);
y2 = (1/(2*pi)*(1-2*pi^2*(1-D)^2-cos(2*pi*D)+(2*pi*(1-D)+sin(2*pi*D))^2/(1-cos(2*pi*D))));
x = linspace(0,1);

figure
fplot(y1,[0 1])
hold on
fplot(y2,[0 1])
hold off
set(gca,'YScale','log')
grid

EDIT — (26 Mar 2021 at 00:43)

With the addition of a value for ‘C’:

S =
    -2.264999999973986e+02    

Since ‘S’ does not have a symbolic solution, likely because ‘D’ is also an argument to the trigonometric functions.

The plots change a bit, however the code does not.

[Matthew Myers]

Thank you Star Strider,

I appreciate the help plotting. When I plot the answer, it matches well with my initial guess of 0.5. And I think the answer should be between 0 and 1, but I can't get the symbolic answer to match the intersection of the plot like expected. Is there a reason that these answers can be different?

[Star Strider]

My pleasure!

Using vpasolve with an initial guess (here 0.1):

S = double(vpasolve((2*pi*f*C*Rl_min) == 1/(2*pi)*(1-2*pi^2*(1-D)^2-cos(2*pi*D)+(2*pi*(1-D)+sin(2*pi*D))^2/(1-cos(2*pi*D))),D, 0.1))

produces:

S = 
   0.500001183648597

.

[Matthew Myers]

Sorry, I forgot to accept this answer. Thank you for the help Start Strider, I appreciate it!

-Matthew

[Star Strider]

As always, my pleasure!

Thank you for returning to Accept it!