The radiation efficiency of a monopole antenna system is related to the ratio of the radiation resistance of the unburied conductors of the antenna system at the operating frequency to all of the dissipative resistances in the antenna system [radiation resistance + the r-f resistance of the loading coil + the r-f resistance of the buried conductor(s) against which the monopole is driven].
If the r-f resistance of the loading coil and/or the r-f resistance of the buried conductor(s) against which the radiating conductors are driven are relatively low, then antenna system radiation efficiency is relatively high. But also the r-f bandwidth of the antenna system is relatively low. System tuning/matching is more difficult, not as stable with changing conditions, and even when optimized may reduce the high-frequency content of the original program audio that is present in the output audio of an AM receiver -- making it sound "muffled" or of "telephone quality."
For a given, unburied set of radiating conductors, an increase in the r-f resistance of the loading coil and/or the buried conductor(s) against which the monopole is driven will improve the audio quality that can be transmitted. But also this will reduce the distance that such a signal usefully can be received (other things equal).
This is the quandary.
Ermi,
You cited an IEEE paper that isn't available on the web if one is not an IEEE member, so readers here are not likely to view it.
AM modulation envelope distortion is a known phenomenon and can be a factor in some Class E implementations, particularly where the ratio of the carrier frequency to the modulation bandwidth is low and the Q is very high.
Even with a very low resistance ground connected to the AMT5000 (lower than anyone is likely to achieve in practice), the envelope distortion is negligible. The ground resistance is one component determining Q. There is always a fixed resistance due mainly to coil loss. The toroid has a fairly high Q, roughly equivalent to the Q of a 3.5 in. OD coil wound on PVC pipe using #16 wire. The real advantage is the toroid is inside the TX obviating the need to invest the effort into winding and fabricating an external coil and mounting hardware.
Following is are the results of a Fourier analysis of the AMT5000 with an antenna ground loss resistance of 5 ohms, operating at 1550k Hz and modulated at just under 100% by a 1 kHz sine wave. A simple diode detector was used in the model. The detector was implemented with ideal diodes to minimize detector distortion. The analysis spans one full cycle of the modulation signal. As shown below the THD is 1.25%. With the slight exception of the 3rd harmonic, the harmonic content declines with increasing harmonic number.
I have not done this analysis on a conventional class C or D output, and I have not tried to analyze how much my detector is contributing to the distortion figure, but I think it is reasonable to assume that 1.25% THD distortion on the detected signal is quite acceptable!.
Harmonic Frequency Fourier Normalized
Number [Hz] Component Component
1 1.000e+03 4.840e-03 1.000e+00
2 2.000e+03 3.410e-05 7.046e-03
3 3.000e+03 4.797e-05 9.913e-03
4 4.000e+03 1.093e-05 2.259e-03
5 5.000e+03 6.098e-06 1.260e-03
6 6.000e+03 4.812e-06 9.943e-04
7 7.000e+03 2.888e-06 5.968e-04
8 8.000e+03 1.978e-06 4.088e-04
9 9.000e+03 1.231e-06 2.544e-04
10 1.000e+04 5.893e-07 1.218e-04
11 1.100e+04 5.221e-07 1.079e-04
12 1.200e+04 5.018e-07 1.037e-04
13 1.300e+04 3.996e-07 8.258e-05
14 1.400e+04 3.352e-07 6.926e-05
15 1.500e+04 1.482e-07 3.063e-05
Total Harmonic Distortion: 1.249922%
There is an "aircheck" mp3 on the SSTRAN web site that demonstrates the audio quality of the AMT5000, http://www.sstran.com/pages/AMT5000/AMT5000_aircheck.html. This was done with the transmitter operating indoors with an AC wiring ground which turns out to be have a ground resistance of about 40 ohms so it doesn't substatiate the 5 ohm ground case, but it does at least demonstrate low distortion under ground resistance conditions more likely to be achieved in a typical part 15 installation.
It's too bad that 1580 has not described his antenna, because we cannot be sure if the antenna can have enough Q to even be a candidate for causing envelope distortion. In a previous thread, he said that he is trying to build as efficient an antenna as possible. It all depends on how well he has succeeded.
I want to point out that the phenomenon that an AM transmitter tuned off-resonance produces envelope distortion was known some decades before the class E amplifier was invented. However, before class E, it was customary to tune transmitters to resonance. Class E has the peculiarity that it has to be tuned below resonance in order to obtain the optimum efficiency. There is also the consideration that if the tuning is not exact, there is the possibility that the the amplifier is tuned more off-resonance than necessary, causing still more envelope distortion.
1580 had expressed concern that his tuning was not exact; and as I just noted, excessive off-resonant tuning can cause still more distortion.
The distortion increases with higher modulation frequency. In the analysis presented in the previous post, the harmonic distortion is (only) 1.25% at a modulation frequency of 1 kHz, but the distortion gets higher as the modulation frequency increases. Indeed, 1580 noticed the distortion he complained about at the higher audio frequencies.
The five ohm ground resistance that was mentioned, although remarkable, is within the realm of possibility, although not likely to be achieved for Part 15 AM. In fact, it is more difficult, at least in principle, to get very low loading coil RF loss resistance than very low ground resistance.
Would a bench test using a dummy load as previously suggested by Phil of 30 ohms in series with 30 pF (type CG0) and monitored with a receiver be a reasonable way to determine if the distortion originates inside the transmitter or is due to the antenna system parameters?
Could the audio signal at the modulator stage output be observed via a scope or an audio amplifier to check for distortion at this point in the system?
After checking components, this would be my approach.
Neil
Ermi posted between my post and Phil's so I didn't see his until after I posted so allow me to add that the loading coil I use with my transmitter (not a SSTRAN and probably not Class E) is wound on a 3" diameter acrylic form with #18 wire and presents a resistive component of 18 ohms at 1680 kHz. This is for a representative example of a typical coil resistance. Is there equivalent data for the internal toroid coil used in the SSTRAN AMT-5000?
Neil
Yes, bench testing should reveal envelope distortion. With a 30-ohm dummy load, however, loaded Q would not be particularly high--perhaps 75, or so, taking into account something like ten or more ohms loading coil loss resistance. To detect the distortion, higher modulation frequencies would have to be used. I believe that the AMT-5000 is rated for about 16 kHz maximun modulation frequency. Using the five ohms load resistance that was mentioned can increase the loaded Q to the vicinity of 200, but the maximum modulation frequency would have to be reduced compared to 16 kHz. Neil: Can you get access to a distortion meter to use for testing?
Until 1580 posted his compaint, I, too thought that, although envelope distortion definitely exists in Class E AM transmitters, it is minimal. In fact, the class E modulation waveforms I have personally observed looked pretty good; but 1580 caused me to look more closely into the matter. The symtoms he described do have the earmarks of envelope distortion.
The loaded Q of the tuning circuit of a normal AM transmitter is rarely greater than about 15, but Part 15 AM, because of the short antenna, and the high-inductance loading coil that must be used to tune it, can have considerably higher loaded tuning circuit Q, which increases the possibility of envelope distortion.
Ermi asked "Neil: Can you get access to a distortion meter to use for testing?"
I did such a test with my transmitter(not a SSTRAN) on the air as reported here:
http://www.part15.us/comment/25131
The "meter" was a NI LabView VI with the PC sound card as the input device.
Though the distortion could be from the interaction of the antenna and the transmitter a bench test would show if the problem was in the transmitter itself. If distorted during the bench test then the search is narrowed.
Neil
Neil,
Your test tone was only 800 Hz, and the asymmetry of the upper and lower sidebands caused by a non-resonant output tuning circuit would increase with audio frequency. It is the asymmetry of the sidebands that causes envelope distortion. Testing with higher-frequency audio signals would be in order.
I notice that 1580 is, unfortunately, now absent from these discussions. He had sent his transmitter back to the manufacturer, who was unable to help him with his audio distortion problem, and he then resorted to seeking help from this forum; but now he has gone under the radar. I think that the issue is actually bigger than his particular problem with his transmitter: He may have discovered an important phenomenon that is characteristic of any class E transmitter when used with a high-Q outout tuning circuit, such as is typical in Part 15 AM. He is actually contributing to the store of technical knowledge. He posted that some personal concern is keeping him away, and I wish him luck in getting his situation settled so that he can return to this thread, which he started.
I don't know if this will contribute anything to this discussion at this point, but for whatever it's worth, within days of reading PhilB's description of a proper dummy load for his part 15 transmitters I built a permanent such dummy load (30-ohm resistor, 30pF cap in series) and tested both my transmitters.
Both the AMT3000 and AMT5000 loaded into the dummy load with excellent audio modulation in as much the same way as the transmitters act when feeding antennas.
Carl,
This is precisely a bench test of the kind that Neil was talking about. Please tell us the details, like what kind of modulating signal was used, and how the modulated RF signal was monitored.
You might also try a dummy load resistor smaller than 30 ohms to see how higher Q affects the results, if at all.
Ermi,
You raise an interesting point about the frequency of the test tone but I follow it only to a point. As executed, my test was sensitive up to the sixth harmonic of the tone (4800 Hz). This was done to include a reasonable number of harmonics, if present, in the passband of the receivers. Raising the frequency would include fewer harmonics.
A better detector would be beneficial but is not being sought at present.
Neil
These results supersede my post above (post #17)
I reduced the capacitor value in the AM detector circuit to increase frequency response. It's now flat, and 1.5 dB down at 20 kHz. This gives a more accurate THD measurement without introducing effects of detector frequency response.
SUMMARY OF THESE MEASUREMENTS
THD was measured with an audio sine wave input at 1kHz, 5kHz, 10kHz and 15kHz. Output was taken from a simple AM diode detector circuit with an "ideal" diode model. Ground loss resistance = 5 ohms. Modulation just under 100% (approximately 95%). RF output stage tuned for maximum transistor efficiency.
THD at 1kHz = 1.019083%
THD at 5kHz = 0.680922%
THD at 10kHz = 3.840253%
THD at 15kHz = 4.495304%
3dB bandwidth with 5 ohm ground:
RF = 12017 Hz
Audio = 6009 Hz
CONCLUSIONS
The Class E amplifier "envelope distortion" phenomenon does not apply at all to the AMT5000. The important point to consider is that the low 5 ohm ground resistance increases the circuit Q, which decreases RF bandwidth. Even though distortion is higher at 10 kHz and 15 kHz, the higher distortion is meaningless because the reduced bandwidth will not pass those frequencies. When the ground loss resistance is higher, the Q will be lower. Frequency response will be higher, but the "envelope distortion" will be lower. In a sense, you can think of it as being "self regulating".
Again, to hear the AMT5000 running with a more typical ground loss resistance of about 40 ohms go to:
http://www.sstran.com/pages/AMT5000/AMT5000_aircheck.html
DETAILS (PROVIDED AS BACKUP FOR THE SUMMARY)
5 ohm ground
1kHz sine wave, 15 harmonics
Harmonic Frequency Fourier Normalized
Number [Hz] Component Component
1 1.000e+03 3.884e-03 1.000e+00
2 2.000e+03 2.881e-05 7.419e-03
3 3.000e+03 2.603e-05 6.702e-03
4 4.000e+03 6.300e-06 1.622e-03
5 5.000e+03 3.574e-06 9.201e-04
6 6.000e+03 1.746e-06 4.496e-04
7 7.000e+03 1.393e-06 3.587e-04
8 8.000e+03 6.269e-07 1.614e-04
9 9.000e+03 4.359e-07 1.122e-04
10 1.000e+04 5.556e-07 1.431e-04
11 1.100e+04 1.108e-07 2.852e-05
12 1.200e+04 2.464e-07 6.344e-05
13 1.300e+04 3.385e-07 8.715e-05
14 1.400e+04 4.180e-07 1.076e-04
15 1.500e+04 1.618e-07 4.166e-05
Total Harmonic Distortion: 1.019083%
5 ohm ground
5kHz sine wave, 6 harmonics
Harmonic Frequency Fourier Normalized
Number [Hz] Component Component
1 5.000e+03 3.458e-03 1.000e+00
2 1.000e+04 8.406e-06 2.431e-03
3 1.500e+04 2.053e-05 5.937e-03
4 2.000e+04 7.463e-06 2.158e-03
5 2.500e+04 2.417e-06 6.989e-04
6 3.000e+04 8.660e-07 2.505e-04
Total Harmonic Distortion: 0.680922%
5 ohm ground
10kHz sine wave, 3 harmonics
Harmonic Frequency Fourier Normalized
Number [Hz] Component Component
1 1.000e+04 2.417e-03 1.000e+00
2 2.000e+04 8.823e-05 3.650e-02
3 3.000e+04 2.883e-05 1.193e-02
Total Harmonic Distortion: 3.840253%
5 ohm ground
15kHz sine wave, 3 harmonics
Harmonic Frequency Fourier Normalized
Number [Hz] Component Component
1 1.500e+04 1.580e-03 1.000e+00
2 3.000e+04 6.965e-05 4.407e-02
3 4.500e+04 1.399e-05 8.854e-03
Total Harmonic Distortion: 4.495304%
The envelope distortion analysis was done using a modulation frequency of 1 kHz, but this time higher modulation frequencies were included. It has been well-established since at least 1984 that increased modulation frequency causes increased AM envelope distortion in a class E amplifier. This is because, when the output tuned circuit is adjusted below resonance, which it is for class E operation, the upper sideband has lower amplitude than the lower sideband, and the phase shift of the upper sideband is more negative than the phase shift of the lower sideband. Increasing the modulation frequency causes the difference between the amplitudes and phase shifts of the upper and lower sidebands to increase. The difference between the amplitude and phase shifts of the upper and lower sidebands is what causes envelope distortion, and higher modulation frequency causes greater difference between amplitude and phase shift of the sidebands, and therefore greater envelope distortion
It is now also well established that envelope distortion is NOT a problem in the AMT5000.
I think this discussion about envelope distortion as relates to the AMT5000 can be closed. It is clear that it cannot be a cause for the severe distortion described by the original poster in this thread.
The modified analysis that was presented had at least agreed with the assertion that higher modulation frequencies cause greater envelope distortion. It has been defensively argued, but not proved, that envelope distortion is not the cause of the complaint by 1580. The data presented does not agree with analysis using the equations in Kazimierczuk's 1984 paper. Thus, further work is in order; especially since the actual cause of the problem reported by 1580 has not been found, even though his transmitter was returned to the factory for evaluation.
Nevertheless, Mr. Bolyn should be commended for his efforts to evaluate envelope distortion; but the problem presented by 1580 is not yet solved, and still requires more work.