## Wednesday, February 11, 2009

### Total Harmonic Distortion & SINAD

Harmonic Distortion & SINAD by Lee Bond, N7KC

February 11, 2009 Educational Radio Net, PSRG

For the 38th session of the Educational Radio Net, I have chosen to continue a review of basic and important concepts that cannot be avoided when dealing with radio equipment. Earlier sessions dealt with the relationship of energy, power, time, voltage, current, and resistance. The 13 parts of the Impedance series is a good starting point for individual review. This week I will delve into harmonic distortion, total harmonic distortion, and SINAD.

Lets get started. I have talked previously about 'linear' amplifiers. Imagine some 'box' which has gain properties. This box simply makes whatever goes into it on one side come out the other side larger. For example, if the box is 'linear', a man entering the box would emerge looking larger and retain whatever proportions he had before entering the box. This means that all parts of the man's body have been scaled by the same number. If the man's arm were scaled by 2 then so goes the foot or nose.

On the other hand, if the man emerged with one arm scaled by 2 and the other by 3, or if he were 3 times as tall but only 2 times as wide then we would know that the properties of the box were nonlinear.

Extending this idea to an electronic amplifier goes as follows. We need to consider 3 situations. Situation 1 considers a small signal, situation 2 considers a medium signal, and situation 3 considers a large signal. From situation 1 we plot a point on graph paper which represents the gain for small signals. Then, from situation 3, we plot another point on the paper which represents the gain for large signals. Now draw a straight line between the two points. If results from situation 2 plot on this straight line then we can say, with some assurance, that the amplifier is 'linear' over the operating region tested. All test points plot on a straight line so the amplifier is 'linear'.

Clearly there must be a signal which will not plot on the line so we are right to assume that some limits exist on linearity. Very large signals which are compressed or clipped certainly will not plot on a straight line so the amplifier is nonlinear in the over driving region defined by very large input signals.

A 'perfect' amplifier should only make a signal larger and not distort proportionality. We can come close to perfection but, alas, the completely perfect amplifier does not exist. We do have, however, instrumentation which will tell us how close our amplifier comes to perfection. Enter the spectrum analyzer and total harmonic analyzer.

Now it is time to talk about various signals. Everyone knows that square waves or triangle waves can be synthesized by carefully selecting sine waves of various frequencies and adding them together properly. If you were to look at a square wave on a spectrum analyzer... in the frequency domain... you could see the various frequency components associated with the input waveform. Now understand that the same waveform viewed on an oscilloscope in the 'time' domain looks like a square wave. The spectrum analyzer shifts the point of view from the oscilloscopic amplitude vs time to amplitude vs frequency. The various frequency components are completely exposed and can be easily measured. The central idea that I want to impart is that only one waveform, the sine wave, has no side spectra. A perfect sine wave produces only one line on a spectrum analyzer. Of course there is no such thing as a 'perfect' sine wave but carefully engineered circuits can come very close to the perfect waveform.

Now, back to our amplifier driven with an input signal which is a near perfect single frequency sine wave. We would expect our linear amplifier to only make this single frequency sine wave signal larger but the spectrum analyzer shows a different situation. There is a 'bump' or 'spike' on the analyzer which is harmonically related to the input signal. With the amplifier out of the test circuit there is no harmonic bump on the analyzer but, with the amplifier in place, the bump is clearly there. Harmonic means integer multiples so if the input frequency is f then the 'second' harmonic is 2f and the third would be 3f, etc. So, we fed our amplifier with a near perfect signal and the output is a larger signal but which includes some trash in the form of harmonic energy. The height or amplitude of the second harmonic component compared to the amplitude of the input signal is a measure of how linear the circuit under test is. By using a spectrum analyzer we can easily determine individual amplitudes of what might be called trash frequency components.

Historically, before the spectrum analyzer became widespread, there was an instrument called a Total Harmonic Distortion Analyzer or THD Analyzer for short. This instrument had a generator which produced a near perfect sine wave for test purposes. The instrument also had a very good tunable 'notch' filter circuit aboard. In use, the THD analyzer supplied near perfect, very clean, sine waves to the amplifier under test. The amplifier output went back into the analyzer and the notch filter removed the input signal. Anything left over was considered to be produced by nonlinear circuit performance in the amplifier under test. By comparing total left over energy to the original signal energy one could compute total harmonic distortion. This is important in both high performance high fidelity audio amplifiers and radio SSB linear amplifiers where one desires distortion free output signals.

Closely allied with THD measurements is the SINAD or Signal plus Noise and Distortion specification which you may have noticed listed in your radio manual. This is a common test performed on FM receivers. SINAD is the ratio of signal plus thermal noise plus distortion to thermal noise plus distortion expressed as decibels. A perfect radio receiver would produce no thermal noise or distortion but, alas, the perfect radio receiver does not exist. Assuming that we have a receiver with some inherent thermal noise and distortion the question becomes one of determining just how weak a signal must be before losing intelligibility. Careful testing has shown that the signal must be at the least 4 times the inherent thermal noise plus distortion to be easily tolerated by the ear and for ease of understanding. The common log of 4 times 20 is 12 so a 12 db ratio indicates the point of maximum thermal noise and distortion that can be tolerated in voice communications.

Simply measuring the 20 db quieting sensitivity of an FM receiver is not the full story since distortion products certainly will interfere with voice intelligibility. Both SINAD and quieting sensitivity are useful performance parameters to check when looking for a new FM transceiver. One point to note is that the testing audio frequency is a standard 1 Khz note. Since the audio passband seldom exceeds 2.5 Khz the 1 Khz fundamental and the 2 Khz second harmonic fit in the expected linear region of the receiver audio chain. Since the 3rd and higher harmonic energy is outside the passband it is pointless to attempt any measurement of components beyond the 2nd harmonic.

In summary, thermal noise and harmonic distortion are very likely present in any electrical system including radio frequency equipment. The relationship of signal energy to thermal noise energy plus distortion products sets the performance standard for a particular radio.

This concludes the set up discussion of Total Harmonic Distortion & SINAD. Are there any questions with regard to tonight's discussion?

This is N7KC for the Wednesday night Educational Radio Net

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