The Distortion Analyser, THD and SINAD

The distortion analyser allows the measurement of desired signal power and noise power content of a composite audio signal containing both noise/distortion and a desired signal. The result of the measurements is the ratio of noise plus distortion power to signal plus noise plus distortion, or percent distortion. This is accomplished by injecting a single tone, usually 1 Khz, as the desired signal. The instrument takes two measurements: one of total RMS input level, and the second of total RMS input level with the desired tone "notched out". The meter reading, labeled THD (total harmonic distortion), represents the ratio of these two measurements:

"THD" = RMS{input - test tone}/RMS{input} = RMS{noise}/(RMS{signal + noise})

Quotation marks are used above because the only time the measurement can be accurately called THD is when the noise component consists only of harmonics of the test tone. However, the dB scale on the distortion analyser can be used to measure SINAD, the most commonly used measure of signal quality in noise (from which SNR or signal to noise ratio may be extracted if desired).

SINAD is defined as:

SINAD(dB) = 10 log {(signal power plus noise power)/(noise power)}

= 10 log { SNR_p + 1 }

(p subscript denotes power ratio as opposed to voltage ratio)

To demonstrate this, let

V_n = the RMS noise voltage,

V_s = the RMS signal voltage,

V_t = the RMS voltage of the combined signal and noise waveform

P_n = noise power, P_s = signal power,

P_t = total power in the combined signal plus noise waveform.

Using Parseval's Theorem, we may write :

V_t² = V_s² + V_n² and P_t = P_s + P_n

Now, "THD" = V_n/V_t or, "THD"(dB) = 20 log{V_n/V_t}, therefore,

P_t/P_n = V_t² / V_n² = ( V_t/V_n)² = ("THD")^-2

Thus SINAD = ("THD")^-2, and we can write

SINAD(dB) = 10 log{P_t/P_n} = 10 log{("THD")^-2} = -20 log{"THD"}, or

SINAD(dB) = -"THD"(dB)

Thus the instrument can be used to measure both THD in the case of a single tone passing through an amplifier, or signal to noise ratio (actually SINAD in dB) in the case of a noisy signal.

It is important to note the advantage of using the dB unit of ratio measurement. Whereas "THD" represents a voltage ratio and SINAD represents a power ratio, our convention of calculating dB using a factor of 20 for voltage ratios and 10 for power ratios allows us to read SINAD in dB (a power ratio) directly off of the scale measuring "THD" in dB (a voltage ratio), even though, as we have shown, SINAD is a squared function of "THD" in an algebraic sense.

Procedure:

1. Measure power level and frequency of DS and US Channels. Based on the percent modulation values set on the generators, compute actual signal (sideband) powers for each channel. For the US channel (narrowband noise), assume 100% modulation.

 
2. Connect a step attenuator to each of DS and US channels, and combine the step attenuator outputs using a ZSC2-1. Connect the output of the combiner to a third step attenuator, thence to the input of a ZHL-1-A amplifier. Connect the output of the amp to a ZSC2-1 splitter. Connect one output of the splitter to a 10 dB fixed attenuator attached to the power meter probe. The other splitter output should be connected to a detector, and the detector output to the AUX input of the audio amplifier.

 
3. Connect the loose wires dangling from the audio monitor to the input binding posts of the distortion analyser. VERIFY THAT THE INPUT REFERENCE SWITCH FOR THE INPUT BINDING POSTS IS IN THE ISOLATED/UNGROUNDED POSITION.

 
4. Determine reference detector power levels for DS and US channels alone by setting one channel's attenuation to zero while the other is at max. Adjust the third step attenuator for approximately 0 dBm into the detector (-10 dBm reading on the power meter). Record power meter reading and attenuator setting on all three attenuators.

 
5. Set the attenuator for the DS channel to 0 dB, and measure SINAD for attenuations of 0 to 30 dB on the US channel using 2 dB steps. When making SINAD readings, adjust the third step attenuator to maintain approzimately 0 dBm into the detector. Repeat for DS attenuations of 6 and 12 dB. (You may wish to adjust the volume control on the audio monitor.) Record power meter reading, SINAD, and attenuator setting on all three attenuators for each measurement.

THE LAB WRITE UP SHOULD CONFORM TO DEPARTMENTAL STANDARDS AS DESCRIBED IN THE GUIDELINES FOR LABORATORY REPORTS. INCLUDE THE FOLLOWING :