THD+N is the abbreviation for a measurement technique, used mainly in audio performance testing. It is short for "Total harmonic distortion plus Noise". Total harmonic distortion measurement in general has it's vocal detractors, mainly via the popular audio press, who in summary would claim that the technique has no value, single sine-waves are 'too simple' and that the results obtained bear little resemblance to subjective audibility of distortion. By my observations over many years, I conjecture that most of these critical commentators are neither trained in electronic theory, nor experienced through working in a test laboratory. Audio performance measurement, like no other field of engineering, appears to generate discourse by non-experts in their thousands offering dubious analysis and pseudo-science to support their questionable theories. This short article is to discuss the usefulness of THD+N, while noting the limitations of the method.
Distortion of signals through an electronic device is inevitable. It takes many forms. Designers of all such devices must ensure that the level of distortions created are acceptably low. That statement is meant to be open because acceptability is very application-dependent, especially in these modern times where digital processing creates an endless panorama of trade-offs.
The THD+N test is, in principle uncomplicated. A single sine wave tone is fed to the input of the device being tested. A sample of the output of the device is fed into the analyser, which uses a notch filter to reject the original tone, then a measurement is made of all that remains, presenting the result as a percentage of the level of the original tone. Simple and elegant. THD+N is a proxy method of measuring device non-linear distortion, which additionally includes all unwanted artefacts that are produced within the device, both related to and unrelated to the incident tone. This makes a THD+N result a very useful single figure-of-merit of non-linear distortion and overall performance. Of course, there is a requirement for precision in the test equipment, for it must exceed the performance of the device under test by at least 10x. The tone generator must be pure so that no harmonics are built-in. The analyser must be able to completely reject the test tone but pass all harmonics of that tone without loss. In fact, the narrower the fundamental notch, the better. It is always good practice when testing to initially connect the tone generator directly to the analyser in order to establish baseline test equipment performance. The older test instruments like the AWA F240 (pictured) required the operator to manually tune the notch filter; in effect adjusting until the lowest THD+N reading is obtained. Later instruments did this automatically. The Audio Precision System One generator/analyser for example is a professional instrument for audio testing. It has a tone generator with a THD of only 0.0005% (-106 dB) and a THD analyser capable of measuring down to below 0.001%. Latest versions of the instrument better even these specifications.
Objectors to the method say that one does not know the ratio of harmonics present to non-harmonics or noise, and this is true, but in many cases this does not matter and an experienced operator will be able to tell if the result is predominately harmonics or is noise by making a swept frequency plot of THD+N or a set of measurements at differing levels.
A primary need in broadcast transmission is to periodically test transmitters or links for performance to ensure they do not worsen over time and exceed their performance specification. How often things were tested depended on what it was. Modern equipment, especially that with digital processing is fairly stable over time and requires only infrequent verification.
During the 1970's, I helped look after a number of AM stations, which used valve transmitters. Transmitters ranged in power from 2000 watts to 20,000 watts. Transmission hours then were less than 24 hours as is the case today, so either before, or after every days' transmission, we ran a set of quick frequency response and THD+N tests. For the latter, we fed in tones and adjusted the level until 90% modulation of the transmitter was reached. A typical set of THD+N results with new valves would look like this:
40Hz: 0.9%, 150Hz: 0.7%, 800Hz: 0.7%, 3000Hz: 1.2%, 5000Hz: 1.6%, 8000Hz: 1.8%
These figures would vary a little while the modulator valves were new, and worsen slowly with time, but it became clear when they were nearing their end of life because the THD+N at 5000Hz and up would climb rapidly, exceeding 3% at 8,000Hz. You might argue that these figures are rather poor, but remember, this is AM radio and the transmitters at that time used high level anode modulation, which means the modulator for a 10kW transmitter is essentially a 5kW audio amplifier, which used two large type 892R tubes (pictured) in push-pull. Some might also note that harmonics of 8kHz exceed AM channel bandwidth, however, the test point for us was a probe directly on the transmitter output producing 10 volts of RF into a diode detector, making the demodulation process quite linear and not bandwidth limited.
Of course, modern AM transmitters are all modular solid-state types using PWM techniques. They produce much better THD+N results and neither do the results vary much over time, so testing is less frequent. The biggest problem for modern AM transmitters is that they are usually loaded into electrically short antennas, making the bandwidth poor and causing high reflected power under conditions of high frequency audio modulation. There is little need for vanishingly low THD+N in AM transmitters, since the vast majority of AM receivers are very poor in performance, making them the limiting factor.
The first TV transmitter I was associated with was the 10kW Marconi BD371 type. The sound, of course was FM, which was produced in a modulator called the FMQ unit. It is short for 'frequency-modulated quartz'. In this system the audio modulates a crystal oscillator directly, producing a small frequency deviation. A series of frequency multipliers follow, multiplying the crystal frequency up to the final on-air value. The method also multiplies the crystal deviation in order to produce the required deviation at the output. In this way a small, perhaps 2kHz deviation of the crystal becomes 50kHz deviation at the transmitter output. When doing THD+N testing for these, the tones were input at a level to produce full 50kHz deviation. Due to pre-emphasis in the modulator, the tone level had to be decreased as the tone frequency was increased in order to stay at 50kHz deviation. The THD+N results were under 1% for frequencies 150Hz to 7500Hz, but could worsen for lower audio frequencies, down to 30Hz.
Later TV sound modulators were much better; for those and for FM stereo transmitters, our specification for THD+N was to achieve less than 0.3% over the frequency range 30Hz to 7500Hz. Stability of performance over time became a lot better allowing an increase of testing period to 6-monthly intervals.
THD+N is a valuable tool within a suite of tests for comparing and rating products. Our laboratory frequently tested professional equipment prior to being placed into service for a broadcaster, and also domestic products like stereo amplifiers, tape cassette units, CD players, home-theatre units, FM tuners plus TV sets, VCR's, DVD players and set-top boxes. All were subjected to appropriate audio performance measurements. The domestic items we were involved in testing tended to be the consumer grade products that would be the volume sales from appliance stores. We rarely tested high-end "audiophile" products. In many ways, the lower spec products were more interesting and challenging to test in a meaningful and comparable way. Sometimes we would test one sample from a higher price range to try and establish what performance improvement was gained by paying more.
Here are some examples highlighting the usefulness of the THD+N test.
First a table from a 1987 test of five professional audio line amplifiers: Here, three discrete frequencies are checked; 80Hz, 1kHz and 10kHz. The System One measuring bandwidth is 80kHz for this measurement. From the results, although model E is clearly a little worse than the others, all results are well below distortion audibility, and yes, this means intermodulation is low too. Hum and other non-related products are also acceptably low. No further checks for non-linearity are needed. The test takes 30 seconds to run on each unit, once the test setup is initially verified. Of course, we always did checks of frequency response first, since in order to get meaningful THD+N figures, the response of the device has to be flat to the highest harmonic frequency you want to include. In this case, the 3rd harmonic of 10kHz (30kHz) is as high as the amplifier needs to be flat to. For devices in Class A, like these amplifiers, there is no need to do perform runs at low power to determine if crossover distortion might exist.
Now an interesting example of a test of seven 29 inch TV sets in 2002. These are taken at the line output of the TV set. The following table has THD results at 80Hz, 1kHz and 5kHz from a spectrum analyser, showing calculated sum of harmonics to the 5th for the first two frequencies but only to the 3rd harmonic of 5kHz. (TV modulators have a response only to 15kHz.) The fourth row shows an THD+N result for the 1kHz test tone. Well, what is going on here. The harmonics of 1kHz are very low, but the THD+N figures of 1kHz are worse and much worse for sets A and G especially. Below is an analyser plot for set A:
Here you see the 1kHz tone at 0dB; a second harmonic at just under -80dB. Higher harmonics are not visible. If you had measured just the harmonics, you get 0.01%, but a THD+N test resulted in a figure of 4.3%. The THD+N result captured not only the harmonic of 1kHz, but included the mains hum at 50Hz, all the noise and the nasty unrelated product on the right which is only around 29dB below the 1kHz test tone. The product is of course the TV line frequency of 15625Hz (PAL). All analogue TV's produce this on the audio outputs to some extent but you can see from the table that set B did a much better job than set A. The THD+N test was valuable in capturing non-harmonic problems.
In a similar vein to the TV tests, the following table is of FM receiver tests done in 2001. As before, the 1kHz THD+N check is done first, revealing two receivers with sub-standard results. A spectrum analyser is then used to measure the harmonic components at three test frequencies, with the THD sum of each of these shown in the following table.
Below is the spectrum of the 1kHz test for RX3: Note the presence of the 19kHz pilot in the audio output. This receiver is not the worst I have seen for pilot rejection. On poorly designed FM receivers, the pilot tone may be only 30dB down with respect to a 1kHz tone at maximum deviation.
In fact, FM receivers can be so poorly designed that an aliasing effect can be produced in the demodulator leading to the example spectrum shown below. This receiver is part of an inexpensive but well known brand of mini-stereo. In this case the test tone is 5kHz. A 'perfect' receiver would have only the 5kHz tone in the spectrum. In this non-perfect case, the 2nd harmonic (at 10kHz) is -39dB and the 3rd harmonic (at 15kHz) is -44dB, leading to a calculated THD of 1.3%. Furthermore, the 19kHz pilot is only 36dB down and there are two other mysterious non-harmonic components present, due to poor linearity of the stereo decoder. One unwanted component occurs at 13kHz; 52dB down and another is at 8kHz which is -50dB. The THD+N meter returned a result of 2.7% for the same test.
Even products that operate with digitised audio can create alias and other unwanted products in the output, which are not related to the original test tones and therefore would not show in straight harmonic distortion measurements. For example, NICAM 728 is an early digital audio for analogue TV technology, which provided stereo sound plus very good performance generally. This technology will disappear once analogue TV is finally closed down. THD+N tests of the NICAM sound from TV receivers, VCR's and also DVD/HDD recorders would inevitably include 15625Hz components and hum related products. Because the audio sampling frequency for NICAM was just 32kHz (c.f CD of 44.1kHz), the audio frequency response was limited to 15kHz, however, if one injected a 15kHz tone to the NICAM test modulator, some receivers would produce an unwanted 17kHz product as well as the 15kHz wanted signal.
Similarly, CD players and DVD players can produced alias signals and other unwanteds such as power supply hash, which are unrelated to any incident tone. Modern AV devices such as set-top boxes, MP3 players and similar are quite prone to noise and hash appearing in the audio output from their switch-mode power supplies. THD+N testing is an relatively simple way of 'screening' such appliances for their performance once appropriate thresholds have been set.
THD+N tests are not primarily useful for diagnostic or analysis of sources of distortion. However, some limited analysis is possible. For example, a swept THD+N test of a cheap mini-system amplifier showed a near constant THD+N result of 1.1% across the audio spectrum from 20Hz to 10kHz, except near 50Hz, where it reduced to 0.18%. This is shown on the plot below:
In this case, the harmonic distortion components are masked by 50Hz hum which is only around 40dB below the power output used for the test (50% of rated power in this case). As the analyser sweeps the test frequency from 10Hz to 10kHz, it passes through 50Hz where the analyser notch rejects all 50Hz components, including any hum present. The residual result (0.18%) is the THD of 50Hz and it is reasonable to assume that harmonic distortion for all frequencies is of that same order, although a slight rise of distortion is indicated from 5kHz up.
As a further example of THD+N analysis, the following stereo amplifier, quoted to be 80 watt output power, is swept in level, using a fixed frequency of 1kHz. In this plot, the THD+N is the vertical axis and power output is the horizontal. To assume the harmonic distortion is poor at low power is incorrect; instead, the noise is predominant until the point where the curve flattens out. In this case the residual harmonics of 1kHz total around 0.14%, which will be the order of harmonic distortion for all power levels until it starts to rise again above about 40 watts. The onset of clipping is rapid from that point; the amplifier produces about 74 watts at the point where THD+N is 10%. So, from the one THD+N power sweep, we have the approximate harmonic distortion, the signal to noise ratio and the maximum power output. A more than useful data set from a singular measurement.
One problem with THD+N is making the choice of measurement bandwidth. An THD+N result will include all unwanted products, whether harmonics, noise or aliasing. Any noise or non-harmonic tones that fall above human audibility are irrelevant, so a measuring bandwidth up to 22kHz only is indicated. However, to obtain an accurate picture of the harmonic distortion part, one needs to include a meaningful number of harmonics, depending on what is being tested. For example, an audio amplifier ideally needs to be tested up to 20kHz, but that means harmonic products might extend to 60kHz and beyond. First, the amplifier itself has to reproduce frequencies of 60kHz and more and preferably be no more than 3dB down in response at that frequency, in order to permit a meaningful harmonic distortion measurement. That itself is often an issue, but in any case, the analyser should have a response out to much higher than 60kHz. (The AP System One analyser is flat to over 200kHz but has an switchable 80kHz low pass filter for this purpose). Despite a human being unable to hear such high frequencies, the point is that unless the analyser can measure the harmonics of 20kHz, then the measurement result of THD+N at that frequency will be incorrect. When doing amplifier tests using the System One, I made THD+N readings first with the 80kHz low pass filter, then with the 22kHz low pass filter. In this way I could estimate how much of the result related to something above audibility. That works well except that when testing amps above say 10kHz, one still does not know the ratio of harmonics to non-harmonics. Not much of this matters for band-limited products such as FM receivers. Since FM modulators and demodulators do not pass audio above 15kHz, there is no value in trying to capture harmonics of tones higher than 7.5kHz because none will exist. For these kinds of products, linearity measurements above 7.5kHz require 2-tone tests. The subject of a future article.
The THD+N measurement is a very useful tool for pre-screening and for producing a single figure-of-merit when comparing like products. It is also invaluable for logging changes of performance of any particular device over time. While modern techniques like FFT analysis would appear to have overtaken the humble THD+N analyser, the actual measurement is still useful. When using FFT techniques, much care is needed to avoid aliasing (and therefore false results), more so when attempting to use domestic quality sound cards fitted to ordinary pc's. For the serious professional lab, the Audio Precision APx525 analyser, for example, can sample at up to 1248ksamples/sec at a bit depth of 24 bits, with a residual THD+N of -110dB, or 0.00032%.
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