non-lineair distortion

[mobile-it]

I need help from you guys concerning the following:

I can write the output as following

Uo = aUi + b (Ui)² + c(Ui)³ + ...

where Ui is the input signal and Uo is the output signal.

When I apply as Ui = E Sin (wt) I get the following amplitudes for the harmonics:

1 harmonic : aE
2 harmonic : 1/2 bE²
3 harmonic: 1/4 cE³
...

can someone explain how I can find this amplitudes????

Another thing is when I apply

Ui = E1 sin(w1t) + E2 sin(w2t) how can I find the intermodulationfrequenties and their amplitudes???

Thank you very much!

 

[lladnar23]

Use the following trig identities:
cos^2(x) = 1/2(1+cos(2x))
cos^3(x) = 1/4(3cos(x)+cos(3x))
cos(x)cos=1/2(cos(x+y)+cos(x-y))

 

[mobile-it]

Ok, but then I have another question: do you now how to find the solution for sin^5(x)=.... sin(5x)

So I need a formula for sin^n =....sin(nx)

 

[VSWR]

See https://mathworld.wolfram.com/TrigonometricPowerFormulas.html