# 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

This circuit only uses linear components. Ideal resistors, capacitors, and inductors are linear components meaning, their behavior is independent of the amplitude of the voltage and current.

As such this circuit is unable to generate harmonics. For that there would need to be a non-linear component present. For example a diode or a transistor.

So the answer is: THD = 0

Obviously this is a question to test your knowledge of the relation between (non) linear circuits and distortion of signals.