Designing RLC circuits at specific frequencies for teaching use

Question

I need help designing simple circuits that resonate around specific frequencies. Basically I am looking for recommendations as to what size capacitor, inductor, and resistors I should get. Sorry if this is not the right forum - I am new to all of this!

We will use them to model neuronal resonance in an undergrad course. Each student group would get a breadboard + components, simple audio / function generator (adjusting input frequency) and measure resulting AC voltage with a multimeter. They will estimate the resonant frequency range by noting which input frequency produces the highest voltage response on the multimeter, and then change out components of the circuit to see how their properties affect this output.

I was hoping to create circuits that resonate around 8 Hz, 16 Hz, and anywhere between 30-35 Hz. These don't have to be exact.

Thanks for your help.

Answer 1

Assuming that you have an $RLC$ circuit, the resonant frequency will be $$ f_0 = \frac{1}{2\pi\sqrt{LC}} $$ so, theoretically, you can pick either $L$ or $C$ arbitrarily and then calculate the other for a given resonant frequency.

Unfortunately, you want circuits that are resonant at low frequencies. For reasonable values of $C$ you will need very large $L$. As an example of something similar you could look at the crossover networks used with subwoofer speakers. In the real world, high-value inductors also tend to have a high parasitic resistance, because they are made with many turns of wire. This will tend to make the resonance appear less ideal.

If you have an audio generator or function generator you may not be able to drive the low impedances that you will get at resonance. You will need $R$ to be at least 50Ω, perhaps several hundred ohms. For students to be able to observe a significant change in behavior at resonance, the total impedance of the $RLC$ should be significantly greater than $R$ when close, but not at, resonance. This will also push you to large inductors.

I suggest that you try calculating some values and then do some shopping to see what you can purchase. When I have done these lab exercises I used circuits that were resonant in the tens of kilohertz range, and the components were fairly easy to find and easy for students to work with.