Harmonic Distortion Power Amplifier Graph

**Harmonic distortion in power amplifiers**

Output signal variations of less than 360° of the signal cycle are considered to have distortion. This means that the output signal is no longer just an amplified version of the input signal but in some ways a distorted or changed from that of the_jnput. The poor quality of music coming from radio or hi-fi system with the music or voice no longer sounding like that which was originally recorded or transmitted is the result of distortion. A good amplifier should not only give an enlarged version of the input signal at the output, but should also provide a faithful reproduction of the input waveforms. One type of distortion that is common to most of the amplifiers is called the **amplitude ****or *** harmonic distortion,*which is caused due to non-linearity of the active device employed for amplification. The active device (semiconductor device or tube) used for amplification may not increase equally all portions of the input signal over its positive and negative excursions. Harmonic distortion increases as we go from class A operation to class C operation.

Even in class A operation some distortion occurs.(When non-linear distortion is present, the output waveform contains components of frequencies~which are harmonics (integer multiples) of the input signal frequency. There may be present second, third and higher order harmonic components, but the most important in terms of the amount of distortion for the classes of operation we will consider is the second harmonic. For a signal occuring in class A B or class B, the distortion may be mainly even harmonics of which the second harmonic component is the greatest. ‘

An instrument such as a spectrum analyzer permits the measurement of the harmonics present in the signal by providing a display oT the fundamental component of signal and a number of harmonics on a CRT screen. Similarly a wave analyzer instrument allows a more precise measurement of the harmonic components of a distorted signal by filtering out each of these components and providing a reading of these components, one at a time. In any case the technique of considering any distorted signal as containing a fundamental component and harmonic components is practical and useful.

**Determination of Second Harmonic Distortion**

A collector current waveformis shown. with the quiescent, minimum and maximum, signal levels, and the time they occur marked on the waveform. An equation which approximately describes the distorted signal waveform is

**i**_{c}** = ****I**_{CQ}** + I**_{0 }**+ I**_{1 }**Cos (****ωt****)**** + I**_{2}** Cos (2****ωt****)**

The given current waveform contains the original quiescent current I_{CQ}, that occurs with zero input signal, an additional dc current I_{0>} due to the non-zero average of the distorted signal, the fundamental component of trie distorted ac signal I_{1} and a second harmonic component 1_{2}, at twice_the fundamental frequency. Although other harmonics are present, only the second is considered here.

Equating the resultant current from equation at a few points in the cycle to that shown on the current wavefom we get

At point 1 *i.e. *when ωt = 0

i_{c} = Ic_{max} = I_{CQ} + I_{0 }+ I_{1 }Cos (0) + I_{2} Cos (0) = I_{CQ} + I_{0 }+ I_{1 }+ I_{2}

At point 2 i.e., when ωt * = *∏/2

*i _{c} = *I

_{CQ}+ I

_{0 }+ I

_{1 }Cos (∏/2 ) + I

_{2}Cos (2∏/2 ) = I

_{CQ}+ I

_{0 }+ I

_{2}

At point 3 i.e., when ωt * = *∏

*i _{c} = *I

_{C min }=I

_{CQ}+ I

_{0 }+ I

_{1 }Cos (∏ ) + I

_{2}Cos (2∏ ) = I

_{CQ}+ I

_{0 }– I

_{1 }+I

_{2}

After solving the equations we get

I_{0 }= (Ic_{max }+ Ic_{min } – 2I_{CQ})/4 and

I_{1 }= (Ic_{max }– Ic_{min})/2

By definition the percent of the second harmonic distortion is given as

**D**_{2 }**= I**_{2}**/I**_{1 }*** 100 % = {½( ****I**_{c}_{max }**+ I**_{c}_{min)}_{ – }**I**_{CQ}}**/( ****I**_{c}_{max }**– I**_{c}_{min}**) * 100**

The second harmonic distortion is the percent of the second harmonic componenl present in the output current waveform with respect to the amount of the fundamenta component. Obviously, 0% distortion is the ideal condition of no distortion.In a similar way, the percent of second harmonic distortion present in theoutpul voltage waveform w.r.t. the amount of the fundamental component can be jeterminec and is given as

**D**_{2 }**= V**_{2}**/V**_{1 }*** 100 % = {½( ****V**_{ce}_{max }**+ V**_{ce}_{min)}_{ – V}_{CEQ}}**/( ****V**_{CE}_{max }**– V**_{CE}_{min}**) * 100**