The first diagram shows the usual method to null the undistorted component and extract the distortion D for an inverting amplifier. The input Vx and the undistorted part of the output -20Vx cancel, and the small variable resistor compensates for component tolerances and the finite gain of the power amplifier, and in practice a trimmer capacitor will also be needed to compensate for high frequency gain and phase variations. An output D/21 is obtained here from a unity gain buffer stage. The adjustment involves setting resistor and capacitor values very accurately, and this takes considerable time and patience. The use of a speaker load and a music signal make adjustment even more difficult. For an example of how this can be done and a more detailed treatment of the null method see Distortion Measurement, but there follows an alternative method which avoids much of the difficulty.
With a high open-loop gain, over 200,000 at 1kHz, and an input stage with a unity gain output available at the input transistor emitter, the mosfet amplifier already includes everything needed to extract the distortion by this method, apart from the trimmers. An approximate equivalent circuit is shown next.
The 200k and 10k resistors are already in effect included in the amplifier, and connect to the input stage which can now be used as a unity gain buffer. Because of the heavy overall feedback used the input stage handles a very small signal, and contributes little to the distortion. Almost all of the distortion comes from the output stage non-linearities.
The lack of trimmers in the basic version of this circuit means that there is no way to compensate for the finite gain of the amplifier, and good results will only be obtained if the open-loop gain is very high. Fortunately the gain is over 200,000 at 1kHz, and so the undistorted component at the input is the output voltage -20Vx divided by 200,000. The distortion component D is only reduced by a factor of 21 by the feedback network, so the undistorted component is reduced relative to the distortion by over 10,000, i.e 80dB.This diagram shows where the 'distortion' output is obtained. A 47R resistor is included to prevent test equipment input capacitance affecting amplifier stability. The input cfp stage finite input impedance and less than unity gain will add a small error, but the results are accurate enough to assess amplifier performance at the design stage. Note the 220p input base to earth capacitor, this gives more accurate results than the 390p in later versions which will attenuate distortion components well above 20kHz. The 1n input filter capacitor should also be left out if high frequency measurement accuracy is important, but it is usually just the audio frequency components we need to observe.
One advantage of this method is that the noise added by the 10k input resistor is in effect part of the input voltage Vx, and is rejected along with all other input signal components. When distortion is found to be below the noise level in some of the tests this refers to the extracted noise rather than the actual output noise of the amplifier, so the distortion is even further below the real noise level.
There is one small problem with this approach. Increasing the open-loop gain reduces the undistorted signal at the test output, but it also reduces the output distortion in the same proportion. As a result of this the test output always has about the same distortion percentage as the open-loop distortion of the amplifier. For the 10% open-loop distortion at 20kHz in the present design the test output also includes 10% distortion, the other 90% being undistorted test signal, so we have not extracted the distortion alone. A typical output is shown next:
This looks like a slightly rounded triangular wave, and consulting a 'mathematical handbook' the Fourier series analysis of this sort of wave shows that there is about 11% 3rd harmonic, 4% 5th harmonic, 2% 7th harmonic, and so on. The The test frequency is 20kHz, and for this test the emitter resistor used was 1ohm. The input signal was 740mV pk-pk and the test output was 0.4mV pk-pk. The test output 3rd harmonic distortion voltage was therefore 11% of 0.4mV = 0.044mV. The distortion at the output is attenuated by the feedback network by a factor of 21, so to give 0.044mV at the test output the amplifier output distortion is 21 x 0.044mV = 0.924mV (pk-pk). The amplifier output was then about 15V pk-pk, i.e. 15000mV pk-pk, so the distortion was 0.924mV / 15000mV x100% = 0.006%. Including other harmonics there will be 0.006% 3rd, 0.002% 5th, 0.001% 7th etc. The slight rounding of the triangular wave suggests that in fact the harmonics will be lower than these figures, and it seems safe to conclude that the 20kHz distortion is close to the design aim of under 0.01%. Increasing the signal level to 3dB below clipping made little change to the shape of the triangular wave, although the points became sharper, showing that high harmonics increase faster than low harmonics, which is normal. Reducing the signal level the rounding increased to the point where the test output looked more like an undistorted sinewave, showing that distortion falls at low signal levels, with no sign of crossover effects.
Using a 22ohm emitter resistor instead of 1 ohm the feedback loop gain was about 20 times lower, but the shape again remained about the same, while the level was about 20 times greater, showing that reducing the feedback loop gain by a factor of 20 increases distortion by the same factor. In other words 20 times the feedback gives a 20th of the distortion percentage, with no obvious change in the nature of the distortion at a given output signal level. The idea that high feedback can make distortion worse is based on results at low feedback levels, where high order harmonics can be increased by the feedback, but it is known that at sufficiently high feedback levels high order harmonics are also reduced.
A test output of under 1mV is not easy to observe or measure, and to carry out further tests an op-amp was used to amplify this level to the point where a PC based spectrum analyser could be used, so that intermodulation and lower frequency tests become possible. Test results obtained by the methods described here are shown in the 'Test results' page.
This test method may not detect distortion from incorrect earthing. If the output earth differs from the input earth by a distorted signal voltage this can escape detection, so this needs to be checked also. I have not found this to be a problem with my recent designs, all of which use a similar layout with low, high and non-linear current earth connections all taken via different heavy gauge wires to a common earth point. Also not detected by this test method is any distortion from the input filtering capacitors, here 1n and 2.2uF, which should be known low distortion types. The output inductor also is excluded, and this should be air-cored, with no other components near its ends, and well away from high non-linear current loops, which should anyway be minimised.
It is possible to improve the nulling by adding more components, as shown here, to add a further small fraction of the -20Vx output to the output end of the 47R resistor. The input stage is again shown as a separate unity gain stage in this diagram. The adjustments for nulling are far easier than in the top diagram because we are only nulling the very small remaining undistorted signal, already reduced by up to 80dB, rather than the entire output. Results from this arrangement are shown HERE.