A certain amplifier has a transfer characteristic given by: V o = 10 V i + 0.1 V

Question

A certain amplifier has a transfer characteristic given by:

Vo = 10 Vi + 0.1 Vi2

a) Find the Total Harmonic Distortion (THD) rating of this amplifier for a sinusoidal input voltage:

Vi (t) = cos (wt)

b) Repeat (a) above for:

Vi (t) = 10 cos (wt)

Hint: As cos2x = 1/2 + (1/2)cos(2x); this amplifier produces no third or higher harmonic distortion. Thus, D3 = 0, D4 = 0, ect...

Assume: THD denoted by D is given by:

D = (D22 + D32 + D42 + ...)

D2 = V2/V1; D3 = V3/V1; D4 = V4/V1 and so on.. V1, V2, V3, V4 are the amplitudes of the fundamental, second harmonic, third harmonic and forth harmonic.

Explanation / Answer

Vo= 10vi+0.1vi^2

(a) vin= coswt

Vo =10 coswt +0.1(coswt)^2

= 10coswt +0.1 [1+ cos(2wt)]/2

= 0.1/2 + 10coswt + 0.1cos(2wt)/2

Here v1= 10, V2 =0.1/2, v3 =0. And higher mode is zero.

D2 = v2/v1 = 0.01/2 , D3 =v3/v1=0,

THD =[D2^2 +D3^2]^0.5 = D2 = 1/2 = 0.005

(b) vin= 10 coswt

Vo =100 coswt +(coswt)^2

= 100coswt + [1+ cos(2wt)]/2

= 1/2 + 100coswt + cos(2wt)/2

Here v1= 100, V2 =1/2, v3 =0. And higher mode is zero.

D2 = v2/v1 = 0.005 , D3 =v3/v1=0,

THD =[D2^2 +D3^2]^0.5 = D2 = 1/2 = 0.005

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