Wrong resonant frequency in RLC series circuit analysis

Hello all,

I'm currently doing a RLC series circuit analysis and want to draw a bode plot. As I calculated, the resonant frequency should be at around 30 MHz, but I got more than 100MHz in the plot. Following is my simple code.

clear all

syms L C R 

R = 98.7814e-3;
L = 65.265e-9;
C = 436.876e-12;

Z = tf([L*C,R*C,1],[C,0]);
bode(Z,{40,5e8});
grid on

Does anybody have ideas what's wrong with my code? Thanks in advance!

Runze

Answer 1

[Sarvesh Kale]

Hi Runze Zhang,

You have given the numerator and denominator polynomials in wrong order to the tf function, the tf function takes the numerator input polynomial coefficients first and then denominator, for more help check

https://in.mathworks.com/help/control/ref/tf.html

R = 98.7814e-3;
L = 65.265e-9;
C = 436.876e-12;

%  V is voltage transfer function, output across capacitor 
V = tf([1],[L*C,R*C,1]); % tf numerator and denominator order changed 
bode(Z,{40,5e8});
grid on

The value of your resonant frequency will depend on your L, and C values, In my opinion the values entered by you are not practical as resistances in the order of milli ohms are not present in standard resistance charts, this applies to your capacitor and inductor values too, you must look at the chart values.

The resonant frequency of series RLC circuit is 1/sqrt(L*C), after substituting the values entered by you for L and C we can see that the Voltage graph peaks at the same frequency(1/sqrt(L*C)) shown in the graph .

The following equation will graph the Impedance of the circuit according to me, so in order to calculate the resonant frequency, you have to mark the point where the phase is 0 deg. since at this point the impedance will be purely resistive and this will be your resonant frequency. Again this is also equal to 1/sqrt(L*C)

Z = tf([L*C,R*C,1],[C,0]);
bode(Z,{40,5e8});
grid on

I hope this answers your query

Thank you.

[Runze Zhang]

Thanks for your answer! Yes, you are absolutely right. Actually I saw my mistake, I misunderstood the unit rad/s as Hz. My calculation is 30HMz and that frequency is nearly 200Mrad/s. They are actually the same and probably I have to transfer the unit of rad/s to Hz. But anyway, your answer really helps.