# How to decide the resonant frequency

I have a circuit of the following form.

Circuit diagram:

How do I decide the resonant frequency ?

What is the criteria here to select the resonant frequency ?

Background: I am testing the transfer function for the system, and I need to know what is the proper value of "w" (omega) I can use.

Please let me know if anyone has the knowledge on this.

Thanks.

• Have spice make you a bode plot? Run a signal generator into the input and measure the output as a function of frequency. I trust the inductors aren't coupled. – George Herold Aug 30 '16 at 16:20
• @GeorgeHerold...Please let me know how did you think it is not coupled. I want to know. Regards – cppiscute Aug 30 '16 at 16:22

First find the equivalent impedance of your circuit using, e.g., Thevenin theorem. This impedance will depend on $\omega$. The resonant frequency(ies) is(are) the value(s) of $\omega$ that makes the reactive part of the impedance zero.
• I use a computer algebra system to help doing the calculations. In my case, it's maxima, but I think Mathematica and even Matlab also do the same thing. Basically I write the impedance for each element and combine them manually in series or parallel. Although it's not automated it does help a lot in the calculations. For example, for your example, it took me less than 5 mins to find that the resonant frequencies are $\omega=0$ and $\omega=1/C_1(L_1+L_3)$. – hcabral Sep 6 '16 at 13:49
• The full denominator of the Thevenin impedance is $j\omega^2C_1C_2R_1 + \omega C_2(1 -\omega^2C_1(L_1 + L_3))$. – hcabral Sep 6 '16 at 13:52
• Please scrape off the $\omega=0$ resonant frequency. $\omega=0$ actually zeroes the full denominator, which means the impedance is infinite and the load will not get anything. – hcabral Sep 6 '16 at 14:00
• OK, hold on because in my hurry I forgot $R_L$. – hcabral Sep 6 '16 at 14:22