Hello.
How to calculate, using maths and definitions, the THD of this signal: A sine with a small dent at the crossovers.
S(t) = 0 for 0 < t < D where D is much smaller than T
S(t) = sin omega*t for D < t < T/2 where omega is 2*pi/T
S(t) = 0 for T/2 < t < T/2 + D
S(t) = sin omega*t for T/2 + D < t < T
Using LTspice simulations I find THD = 25*( D/T )^2
In this simulation I used a 1000 HZ SINE combined with a PULSE with values of D like 0.1u 0.2u 0.5u 1u 2u 5u 10u 20u 50u
These simulations gave me a THD that perfectly fits with 25*( D/T )^2
Here is the issue.
I was enable to prove this result with maths
(instead of simulations ).
I started computing the RMS value of the error signal (the dents at the crossovers)
With sin omega*t = omega*t ( valid for t << T )
I don' t get the 25*( D/T )^2 result, I do get a fonction of D/T, so far so good, but I don't get the right exponant. It seems my approach is wrong.
Is there a signal theory / maths guru who can give the proof that for such a signal S(t) ( with D << T ) we have THD = 25*( D/T )^2
