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Structure and content of harmonics created by a differentiated pwm waveform?

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Sparks_nz

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Hi,
Id like to ask what type and structure of harmonics are produced from a pwm waveform (being modulated) that has been differentiated, so it is then essentially alternating narrow spikes of bipolar nature.
If the pwm modulation causes the negative going spike to cyclically deviate about from its center 50% position (due to the modulation) then what type of harmonics are produced - as opposed to when there is no modulation happening, and the source is essentially a fixed 50% duty cycle square wave.
I presume that a differentiated square wave produces only odd harmonics, and that the decay of these n harmonics at 1/n is somewhat cancelled by the frequency response boost of the differentiating process.
I would like to know what the change in harmonic content is when the pwm is happening.
 

In a rough estimation you get constant magnitude of the harmonic series with +/- fm sidebands. Also a certain amount of odd components because the duty cycle isn't strictly symmetrical.
 

depends on the effective width of the spikes ( in the real world ), the rounded ness at the peaks, the slopes of the rise and fall times ....
 

Yes, constant magnitude would be achieved with ideal delta pulses, in reality the harmonic series is multiplied by the spectrum of the pulse.
 

Thank you for the replies. Im sorry, but I am not sure what you are meaning in regards my question relating to the pwm being active, and therefore the negative spike cyclically moving in relation to the positive spikes. I presume the active pwm modulation alters the normal harmonic distribution of odd harmonics. (for a standard diff'd sq wave scenario). Does this mean that some even harmonics are created, and is there a rule to the amount and structure of these altered harmonics at specific duty cycles - in similar style to the graph Ive attached for standard pwm harmonics verses duty cycle % (but without the even harmonics due to the differentiation process).

pwm_harmonics.jpg
 
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The signal will be differentiated across any coupling
capacitance to any "victim".

The harmonic content is proprtional to the edge dV/dt
which is why "soft switching" is a thing.

You have "bundles" of edge harmonics repeating at
2X fSW and a smattering of 1/on-time and 1/off-time
fundamental and harmonic as well. And intermods
galore as your powertrain is chock full of rectifying
elements.
 

The signal will be differentiated across any coupling
capacitance to any "victim".

The harmonic content is proprtional to the edge dV/dt
which is why "soft switching" is a thing.

You have "bundles" of edge harmonics repeating at
2X fSW and a smattering of 1/on-time and 1/off-time
fundamental and harmonic as well. And intermods
galore as your powertrain is chock full of rectifying
elements.
Thanks for the replies. I have bought a small pwm gen board with fully adjustable duty cycle, so I can see the effect of duty cycle changes on the waveform's harmonics.
 

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