# Total harmonic distortion (THD) of a circuit

Where $V_{sin}$ is sinusoidal with frequency $f_{1} = 1 kHz$.

The THD is defined as the sum of the power of all harmonics (except the fundamental) divided by the power of the fundamental harmonic.

I calculated $V_{out}$ wrt $\omega$ and the time-averaged power from there. Then I tried evaluating this power at frequencies $f_{(n)} = n \cdot 1 kHz$ and calculating the THD from this, but I can't make this sum.

This question was in a 3h exam, and it was worth 10%, so it should take around 18min to do. It can't be that complex numerically.

I'm most interested in the process of solving this over the actual answer. Thanks in advance.

• The circuit is perfectly linear, i.e you have no non-linear effect going on in there, so there should be no THD. What's more, the source only outputs a single, fixed frequency signal. Did you mean attenuation for higher, or lower harmonics? Jun 25 '18 at 15:55
• @aconcernedcitizen Wow you are absolutely right. So the THD = 1, then. I didn't realize capacitors were linear. Mainly it was its impedance that confused me (1/jwC): it varies with frequency, but doesn't "create" any new frequency. Thank you! Solved. Jun 25 '18 at 16:15
• No, THD will be zero @AsierR. Jun 25 '18 at 16:18
• You're right, THD = 0. @Andyaka Jun 25 '18 at 16:38
• Some real-world capacitors are non-linear, that non-linearity being explained as electric-field forces cause a thickness variation in the dielectric. Jun 26 '18 at 15:54