# Harmonic distortion

1. Sep 4, 2015

### topcat123

A voltage amplifier ideally should have the input-output relationship of
vo = 100vi but in practice the relationship is vo = vi(98 + 2vi).
Calculate the %age second harmonic distortion present in the amplifier’s
output for a sinusoidal input of 10 mV r.m.s

% harmonic distortion = amplitude of nth harmonic / amplitude of fundnamental

fundnamental
98*0.01=0.98 v

harmonic
2*2*0.01^2 = 0.004 v

%= 0.0408

No frequency has been given. So in am unsure.

All help is appreciated.

Thanks

2. Sep 5, 2015

### Dr. Courtney

I'm not sure what the question is.

3. Sep 5, 2015

### rude man

Calculate the %age second harmonic distortion present in the amplifier’s
output for a sinusoidal input of 10 mV r.m.s

4. Sep 5, 2015

### rude man

That part is right.
OK
No no.
Frequency is irrelevant. So is the 10mV input magnitude.
You're not comparing fundamental and 2nd harmonic amplitudes. But you must.
Hint: there is a relation in trig between sin2(x) and cos(2x). Use that ...

5. Sep 5, 2015

### topcat123

sin^2(x) = ½(1 - cos(2x))

vo = 98vi + 2vi^2

so vi = sin(x)

vo = 98 sin(x) + 2 sin(x)^2

vo = 98 sin(x) + 4 sin^2 (x)

vo = 98 sin + 2(1 - cos(2x)) = 98 sin + 2 - 2 cos(2x)

6. Sep 5, 2015

### topcat123

why have i been provided with the "output for a sinusoidal input of 10 mV r.m.s" if it is irrelevant?

7. Sep 5, 2015

8. Sep 5, 2015

9. Sep 5, 2015

### topcat123

I am a bit stuck

vo=98 sin(x)+(2 sin(x)^2

vo=98 sin(x)+4(1/2(1- cos(2x))

Is this correct

10. Sep 5, 2015

### rude man

No. Why are you squaring the "2" in "vo=98 sin(x)+(2 sin(x)^2?
BTW I assume you meant "vo=98 sin(x)+(2 sin(x))^2"
which is vo=98 sin(x) + 4sin2(x)
which is still wrong; see my first sentence.

In case you need it,
(sin(x))2 is commonly written as sin2(x).

11. Sep 7, 2015

### topcat123

Looked again at my learning material and I don’t need to sq the 2. Don’t know where I got that one.

Vo=98sin(x)+2sin^2(x) =98sin(x)+2(1/2(1-cos(2x))

=1+98sin(x)-1cos(2x)

fundamental = 98mV

second harmonic = 1mV

with a d.c. term of 1mV

So "harmonic distortion = (amplitude of nth harmonic / amplitude of fundamental)x100".

%harmonic distortion= (1/98)x100=1.02%

12. Sep 7, 2015

### rude man

Very good!

13. Sep 8, 2015

### topcat123

Thank you for all your help..

14. Sep 8, 2015

My pleasure!