# Amplifier Harmonic Distortion

Discussion in 'Homework Help' started by harry99932, Dec 31, 2010.

1. ### harry99932 Thread Starter Member

Dec 30, 2010
38
2
Hi guys,
Hope you can help, ive got an assignment question im stuck on and im not sure if its my understanding or my maths skills letting me down! Im guessing from the equation below the soloution will be the fundamental frequency at a certain voltage i.e Vin*98, plus a harmonic of
(2/k)*Vi) would that be right? Just need a poke in the right direction! cheers in advance guys

A voltage amplifier ideally should have the input-output relationship of
vo = 100vi but in practice the relationship is;

Vout= Vin (98+((2/k)*Vi)
where k = 1 × 103 V.

(a) Determine the expression for the output voltage when a 10 mV
(peak), 800 Hz, sinusoidal input signal is applied to the amplifier.

(b) Sketch the frequency spectrum of the output voltage

2. ### mik3 Senior Member

Feb 4, 2008
4,846
65
I think the equation for Vout should be:

$Vout=Vin(98+\frac{2}{k}Vin)$ (1)

(a) says that Vin=$10^{-3}cos(2\pi800t)$ (2)

submit (2) into (1) to find question (a)

for (b) show amplitude vs frequency of the resultant sinewaves (or cos)

3. ### harry99932 Thread Starter Member

Dec 30, 2010
38
2
Ok thats the point i got to before sorry if i didnt make that clear, what im struggling with is actually "doing" that equation if that makes sense lol im imagining i should get several parts to the answer i.e the fundamental frequency at the highest amplitude then a harmonic at a lower amplitude and so on for the spectrum of the output but looking at that equation you have Vin multiplied by the second part giving an answer at just the fundamental frequency?

Sorry if this is ridiculously simple, ive been working hard on my maths since i got into electronics but i dont find it easy lol!

4. ### harry99932 Thread Starter Member

Dec 30, 2010
38
2
For instance plumbing the value for Vin straight into the above formula in a scientific calculator gives 0.09720325229124??

(10^(-3)*cos(2*pi*800))*(98+(2/10^(-3)*10^(-3)*cos(2*pi*800)))

5. ### shteii01 AAC Fanatic!

Feb 19, 2010
3,702
555
When you expand the part inside parenthesis, you will have cos(A)cos(A), this product of cosines is then expanded into 0.5[cos(A-A)+cos(A+A)]. Together with other parts, it looks to me, you will have 0 Hz, 800 Hz and 1600 Hz.

6. ### harry99932 Thread Starter Member

Dec 30, 2010
38
2
And hey presto my non mathematical mind lets me down again what kind of a fool forgets to expand brackets

thank you kinds sirs il go away and try again

Nov 25, 2009
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