Calculate %age 2nd Harmonic Distortion in Voltage Amplifier

[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%= 0.0408No frequency has been given. So in am unsure.

All help is appreciated.

Thanks

 

[Dr. Courtney]

I'm not sure what the question is.

 

[rude man]

I'm not sure what the question is.

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

 

[rude man]

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

That part is right.

fundamental
98*0.01=0.98 v

OK

harmonic
2*2*0.01^2 = 0.004 v

No no.

No frequency has been given. So in am unsure.

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 ...

 

[topcat123]

Thanks for your reply.

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)

 

[topcat123]

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

 

[rude man]

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

because your instructor wants to see if you're on your toes!

 

[rude man]

Thanks for your reply.
vo = 98 sin(x) + 2 sin(x)^2

don't understand what you mean by this equation.
*****************************************************

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

not quite right

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

well, finish the problem after you correct the equation before this one: "harmonic distortion = amplitude of nth harmonic / amplitude of fundnamental".

 

[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

 

[rude man]

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

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).

 

[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%

 

[rude man]

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%

Very good!

 

[topcat123]

Thank you for all your help..

 

[rude man]

Thank you for all your help..

My pleasure!