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=\(\sqrt{D^2_2+D^2_3+D^2_4....}\)MathJax example
\( I_c=K_1I_b\)(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=\(\sqrt{D^2_2+D^2_3+D^2_4....}\)
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