Harmonic Distortion/Non-linear /amplitude distortion

 Harmonic Distortion/Non-linear /amplitude distortion

The presence of unwanted frequency components in the output which are harmonics of the input frequency is called harmonic distortion .When a sinusoidal signal is applied to a transistor ,non-linearity occurs.Some portion of the signal is amplified more than the other portion


$I_c=K_1I_b$(linear circuit)
with harmonic distortion $I_c=K_1I_b+K_2I_B^2+K_3I_B^3....$ 
if $I_b$ is sinusoidal  $I_b=I_bcosωt$
$I_c=K_1I_bcosωt+K_2I_B^2I_bcos^2ωt+K_3I_B^3cos^3ωt....$ 
$=K_1I_bcosωt+K_2I_B^2[\frac{1+cos2ωt}{2}]....$ 
$=K_1I_bcosωt+\frac{1}{2}K_2I_B^2+\frac{1}{2}K_2I_B^2[cos2ωt]....$
  $=B_1cosωt+B_0+B_2cos2ωt....$
$D_2=\frac{B_2}{B_1}(2^{nd})$      $D_3=\frac{B_3}{B_1}(3^{rd})$     $D_4=\frac{B_4}{B_1}(4^{th})$
Total harmonic distortion=$\sqrt{D^2_2+D^2_3+D^2_4....}$