# What is the structure and type of harmonics generated by a very differentiated square wave (i.e bipolar spikes)?

this question is in two parts. Firstly, can you please tell me what the structure and amplitude distribution is of harmonics generated by a differentiated square wave of 50% duty cycle, where the time constant is very short, producing alternating bipolar spikes of short duration? I know a square wave produces odd order harmonics that decay in amplitude by 1/n, but not sure if the above does - or has even order harmonics as well? Secondly, what change to the harmonic series and amplitudes occurs for duty cycles tending towards 0% or 100%, from 50%, as if the source was PWM'd by a lower freq signal. Thanks.

• Symmetrical signals don't have even harmonics Mar 31, 2023 at 20:23
• Just combine (multiply) the harmonic structure of the square wave with the frequency response of a differentiator. Hint: the differentiator's frequency response rises with frequency. Alternatively, just compute the harmonic series of the PWM signal directly, using the Fourier Transform. Mar 31, 2023 at 20:24