# RLC voltage at resonance

I did a small simulation for a RLC circuit as here : How does one compute the maximal voltage attained for this resonance?

At resonance, the final voltage on the resistor is precisely what the input sinewave amplitude is. This is because inductive and capacitive reactances totally cancel to zero in an AC analysis.

This then tells you the current flowing through all series components so, use ohms law (for impedances) to calculate the voltage on L and C individually. At resonance they will be the same amplitude and, if their individual reactances are greater than the resistor, you will see that the voltages are larger than the incoming sinewave.

In an off-resonance scenario you calculate the net impedance of the capacitor and inductor (zero at resonance as previously mentioned) and use Pythagoras to determine the voltage across the resistor then proceed as above.

I leave the complete answer for you to solve.

use the impedance ratio of the voltage divider to determine the Transfer function (f). Then multiply this by your input signal.

## edit

I must assume now( since you are young and assume too much and forgot to include specs) that you are modulating an ideal voltage source 0 ohms at the theoretical resonant frequency with an AM signal from 0 to 100% and you ask how to determine the output amplitude when then input is unknown. SO we can look at ratios.

We know that X(fo) impedance for a series LC resonant frequency = 0 Ohms

We see your ideal LC circuit ( no DCR in L or ESR in C and no significant (yet real) parasitic capacitance Cp in the inductor,L) with a 1 Ohm load. Yet inspite of this 1 Ohm load with an 0 ohm source and 0 ohm resonant frequency and assuming the generator is exactly at this amplitude. We should expect the transfer function to be unity. Any error in the above assumptions leads to less than unity gain or "attenuation"

Without know your assumptions and errors, one can only guess.

The relevant factors are the Q of the series filter which determines envelope rise time. You ought to know how to calculate resonant frequency from ωo=1/√(LC) and impedance ratio Q at ωo.

From the signal we see a modulation effect of the envelope which declines at te end of the trace. This carrier modulation for a high Q circuit may be the beat frequency of the error of your input signal frequency and your actual resonant frequency.

( from mental calculations) I previously estimate the Q @ 125 which means your signal generator error must be << 1/125 . Q is defined as the resonant f/-3dB BW so if Q is 125 or so ( U do the math) then your sig. gen must be < 0.1% error to reach >90% of the input.

Since it is now obvious to me that your signal generator has more than 0.1% error from envelope wavelength relative to the signal frequency ~125kHz , by number of cycles to ramp up and then ramp down from error f I could calculate your attenuation and estimate your input signal.

But the rigorous method is to perform Calculations with Input signal and transfer function from impedance of each part using the same methods as KVL for divider ratios. The input signal voltage, frequency and impedance are essential in the Vin(t) or Vin(f).