Questions about Optimum design parameters for a class E transmitter

[K9MB]

Since I have finally begun the process of building a Class E station, and having read all I can find on the Class E site, I have some questions about the recommended parameters and what happens if one diverges from them.

It seems to be a standard on the Class E site that one runs 45 volts DC for the carrier voltage and it also seems to be a common assumption that a modulation index of about 1.5 is desirable.

Question 1- Why is the 150% positive modulation peak a common assumption to be desirable?
I have read that the detectors in boat anchor radios that use diode arrangements have high audio distortion on modulation percentages that significantly exceed 100%.
Given- if one uses a synchronous detection system, the super positive peaks are no problem, but it seems to me that there must be a lot of old school radios out there being used for AM, so what use are those positive peaks if they just annoy an old geezer who still uses his 75A4, or Hammarlund receiver, or whatever?
Also, if one is trying to hear a weaker signal on these older receivers, would it not be better to raise the carrier power to help overcome selective fading, etc that further distorts the received audio. I realize that the dB scale might prove that adding 100 watts in carrier might not raise the S-meter much-if at all, but it seems to me that the end of the road for super modulation is to eliminate the carrier and just send out one sideband and use heterodyne detection. But we all know how good that sounds...😉

Next question-
If one were to increase carrier voltage up from 45 volts to-say 60 volts and limit modulation percentage to 120%, then the maximum voltage on the drains would be 132volts, which is close to the voltage seen at 45 volts at 150% modulation.

Which signal would provide the more readable and clear audio on a boat anchor receiver?

I know that this might have been discussed before, but I am unable to find clear answers for why the standard is super positives and not stronger carriers.

One more issue:
Jim Tonne’s article makes a compelling argument in favor of using All Filters to even out the spectral peaks in human speech to make it more symmetrical so that positive peaks will not need to be as high to give the power to the recovered audio spectrum for good intelligibility or to necessitate as much negative peak limiting or clipping.
I welcome opinions from those who favor or oppose the use of All Filters specially those who have tried them.
I apologize if there are clear answers elsewhere and I have failed to see them.
Any comments or help appreciated.

[N1BCG]

Question 1- Why is the 150% positive modulation peak a common assumption to be desirable?

Answer: It's not

Extreme positive peaks are popular with hamateurs who use peak reading watt meters, which are primarily meant for monitoring SSB power, not AM power. Watt-watching on these meters can be misleading and result in arc-overs, particularly in modulator, RF amplifier, and antenna circuits.

Professionally, positive peaks beyond +100% have been dismissed as unproductive by leading audio processor manufacturers such as Orban (see attachment from the Optimod 9200 AM manual). Their manuals discuss the advantages of running symmetrical modulation.

This video using an Optimod 9200 AM broadcast processor supports the claim that there's no discernable difference between positive peaks limited to +100% versus +150%:

https://www.youtube.com/watch?v=nVucVH0kNjc

It's also important to point out that while out voices are naturally asymmetric, particularly male voices, the polarity is not consistent over the entire vocal frequency range. Lower vocal frequencies are typically the opposite polarity of higher frequencies. Because of this, trying to run extreme positive modulation through negative clipping will result in distortion of the lower frequencies where the opposite peaks are severely clipped.

[K9MB]

Question 1- Why is the 150% positive modulation peak a common assumption to be desirable?

Answer: It's not

Extreme positive peaks are popular with hamateurs who use peak reading watt meters, which are primarily meant for monitoring SSB power, not AM power. Watt-watching on these meters can be misleading and result in arc-overs, particularly in modulator, RF amplifier, and antenna circuits.

Professionally, positive peaks beyond +100% have been dismissed as unproductive by leading audio processor manufacturers such as Orban. Their manuals discuss the advantages of running symmetrical modulation.

This video using an Optimod 9200 AM broadcast processor supports the claim that there's no discernable difference between positive peaks limited to +100% versus +150%:

https://www.youtube.com/watch?v=nVucVH0kNjc

It's also important to point out that while out voices are naturally asymmetric, particularly male voices, the polarity is not consistent over the entire vocal frequency range. Lower vocal frequencies are typically the opposite polarity of higher frequencies. Because of this, trying to run extreme positive modulation through negative clipping will result in distortion of the lower frequencies where the opposite peaks are severely clipped.

Thank you for the explanation. It makes sense to me, but I have little experience with AM.
In Jim Tonne’s article on the All Filter, he makes a similar point to the ine you made-that the asymmetry in a man’s voice will vary by frequency range and this is why he recommends the All Filter because, it ostensibly levels out the differences across the vocal spectrum so that one might see higher speech densities in areas that are weaker without  overmodulating in other spectral bands of the particular voice of the  operator.
Do you see value in the All Filter approach coupled with the idea that reaching but not exceeding 100% modulation gives good readability on weaker signals but less splatter and distortion caused by clipping negative peaks?

Edit: Here is Jim Tonne’s article on All Pass Filters for your reference.
http://tonnesoftware.com/downloads/AllpassNetworksInASpeechChain.pdf

[N1BCG]

Do you see value in the All Filter approach coupled with the idea that reaching but not exceeding 100% modulation gives good readability on weaker signals but less splatter and distortion caused by clipping negative peaks?

Absolutely. Every single broadcast processor made in the last 40 years includes an all-pass filter (aka "phase rotator") circuit because of the competitive nature of commercial radio. Success leaves clues and this is a wheel not to re-invent.

All-pass filters reduce asymmetry, and while that will appear as less modulation on a peak reading meter, it must be considered that peaks contain no useful energy. Average modulation is what determines perceived loudness. By reducing asymmetry, peaks that would otherwise cause unnecessary gain reduction in compression circuits are reduced. Reducing gain reduction is the same as increasing loudness, so the focus should be on maximizing average modulation and not letting positive peaks fly.

Also restricting positive peaks leaves more headroom for carrier power. You can fit a lot more carrier into a 1500W PEP limit with a signal limited to +100% than a 1500W PEP signal where much of the power is wasted in peaks.

[K9MB]

Do you see value in the All Filter approach coupled with the idea that reaching but not exceeding 100% modulation gives good readability on weaker signals but less splatter and distortion caused by clipping negative peaks?

Absolutely. Every single broadcast processor made in the last 40 years includes an all-pass filter (aka "phase rotator") circuit because of the competitive nature of commercial radio. Success leaves clues and this is a wheel not to re-invent.

All-pass filters reduce asymmetry, and while that will appear as less modulation on a peak reading meter, it must be considered that peaks contain no useful energy. Average modulation is what determines perceived loudness. By reducing asymmetry, peaks that would otherwise cause unnecessary gain reduction in compression circuits are reduced. Reducing gain reduction is the same as increasing loudness, so the focus should be on maximizing average modulation and not letting positive peaks fly.

Also restricting positive peaks leaves more headroom for carrier power. You can fit a lot more carrier into a 1500W PEP limit with a signal limited to +100% than a 1500W PEP signal where much of the power is wasted in peaks.

Ok- This is just what I suspected. One application would be to set the carrier voltage on s Class E transmitter up from 45 volts to say-60 volts allowing for a modulation factor just above 1, the peak voltage kn the FET drain bus will be about 120-125 volts.
The carrier- in the case of a 12 Amp carrier will approach 700 watts, given a 5 ohm PWM load, compare to 400 watts or so. When you start higher you can go lower- right?

Any other opinions on this?

[N1BCG]

In terms of a Class E transmitter, mine has a 43V carrier voltage and it does legal limit. I'm not aware of a benefit to running more carrier voltage and less current. Perhaps it will vary for different FETs but mine works well as-is.

[K9MB]

In terms of a Class E transmitter, mine has a 43V carrier voltage and it does legal limit. I'm not aware of a benefit to running more carrier voltage and less current. Perhaps it will vary for different FETs but mine works well as-is.

Putting the idea of legal limit aside, I am not at all sure that there is any advantage in a marginally higher drain voltage and there might be evidence that more current at a lower Drain voltage can yield a more thermally stabile amplifier that stays more safely in the SOA under full output loads.

My reason for asking the question is that- given that the idea of running at modulation factors closer to 1 rather than 1.5, and given that the pwm is capable of 130+ volts of output and is limited more, therefore by current capability rather than voltage due to copper losses, one is tempted to ask whether raising the power at dead carrier by increasing voltage and keeping current at about 1.0 amps per device, rather than 1.25 amps per device and a drain voltage of about 55 volts dc at carrier to give about the same 50 watts output per device as one gets at 45 volts, but at less current draw.
Of course, if increasing the voltage lowers the efficiency significantly, then it might be a bad idea because it could cause overheating of the wafer in the FETs and cause a meltdown. The block diagram of the 24 FET transmitter on Steve’s Class E site shows a wide range of voltages and currents that keep the load a 1.73 ohms. It shows input power for the carrier, but no output data is present to chart efficiency across the range shown from 22.5 volts to 45 volts. It would be interesting to measure input power and output power for each drain voltage to see if there is optimum voltage that gives highest efficiency, so that one might actually know the answer to the question.
I suppose than anyone with a class E transmitter with a carrier level control on the pwm could run this data by tuning to maximum efficiency at each drain voltage and calculating RF efficiency to see if it has a peak at some voltage, and it goes down on each side of the voltage input.
Of course, for a practical man, it would be useless because he already has a working design, but some of us have a sickness that makes us wonder... what if....😉

[steve_qix]

Ok, I should answer the original question (where did the 45 volts come from)?

45 volts DC came from:

1) The assumption that 900V MOSFETs are being used, and that there must be a minimum of 100% voltage headroom available for reliability.  This is VERY important.
2) That the power supply voltage is 135V or less
3) That the class E transmitter is properly designed with the correct shunt capacitors, and that it is tuned up.  This will result in peaks of approximately 3.5x the DC
4) The MOSFETs operate more efficiently at higher voltages given the same current

So, with this, the maximum repetitive peak voltage across the MOSFETs at 200% positive modulation (this could happen with a 135V supply and 45VDC at carrier) will be around 470V.

In actual practice, most of the transmitters I've seen are running a supply voltage somewhat less than 135V (for instance, I am running a 125V supply on one of my transmitters, and a 130V supply on the other).


---------------------- Topic Switch, Asymmetrical Modulation ----------------------

As far as asymmetrical modulation goes, there are widely differing opinions on this, and l have personally seen scant evidence to support the theory that high positive modulation causes distortion in old receivers.  I have seen evidence that high levels of negative modulation does cause problems !  Most stations with a lot of negative modulation have a lot of positive modulation also.  There are some real world examples available.

For instance, I run with a lot of asymmetry.  No one has ever told me my signal was distorted (unless something was wrong, and it really was distorted, which has certainly happened over the years)     Bob K1KBW, and Brent W1IA, Skip WT1H, and Mike K3FEF (as examples) are all running with "natural" asymmetry, meaning they have it, and the asymmetry exceeds 150% positive at times.  I have to say, I've never heard any of these guys told that they were distorted - Ever !  Always rather the opposite.

I am not at all convinced that it's the positive modulation that is the issue in these old boat anchor receivers with bad detectors and bad AGC (and these are likely the minority of receivers in use today anyway), and have actually never seen it in the field.

Real example:  Back in the '70s, there was an HRO-60 in the standards lab at the college I attended.  We used it to listen to A.M. broadcast stations (not to measure them).  Every station received on that thing was distorted, and the stations were not running highly asymmetrical modulation.   I fixed the problem, and it turned out that the distortion was occurring on the negative peaks.  The detector was the problem (I don't remember the particulars - it was 47 years ago), and as the negative modulation got close to 100%, the detector cut off.  The positive peaks were unmolested.

If a receiver generates distortion on positive peaks, it is highly likely that the same receiver generates distortion at ALL levels of modulation.  The I.F. chain and the detector typically must have headroom to avoid nonlinearity as saturation is reached.  It is unlikely there is a "hard" limit at 100% Positive modulation or even 150% positive modulation.

However, 100% negative has a finite limit.  Many diode detectors start becoming non-linear when there is a small amount of voltage applied to the diode (and this occurs at high levels of negative modulation).  And I have seen this in the field with many receivers that I've modified.

[K9MB]

Ok, I should answer the original question (where did the 45 volts come from)?

45 volts DC came from:

1) The assumption that 900V MOSFETs are being used, and that there must be a minimum of 100% voltage headroom available for reliability.  This is VERY important.
2) That the power supply voltage is 135V or less
3) That the class E transmitter is properly designed with the correct shunt capacitors, and that it is tuned up.  This will result in peaks of approximately 3.5x the DC
4) The MOSFETs operate more efficiently at higher voltages given the same current

So, with this, the maximum repetitive peak voltage across the MOSFETs at 200% positive modulation (this could happen with a 135V supply and 45VDC at carrier) will be around 470V.

In actual practice, most of the transmitters I've seen are running a supply voltage somewhat less than 135V (for instance, I am running a 125V supply on one of my transmitters, and a 130V supply on the other).


---------------------- Topic Switch, Asymmetrical Modulation ----------------------

As far as asymmetrical modulation goes, there are widely differing opinions on this, and l have personally seen scant evidence to support the theory that high positive modulation causes distortion in old receivers.  I have seen evidence that high levels of negative modulation does cause problems !  Most stations with a lot of negative modulation have a lot of positive modulation also.  There are some real world examples available.

For instance, I run with a lot of asymmetry.  No one has ever told me my signal was distorted (unless something was wrong, and it really was distorted, which has certainly happened over the years)     Bob K1KBW, and Brent W1IA, Skip WT1H, and Mike K3FEF (as examples) are all running with "natural" asymmetry, meaning they have it, and the asymmetry exceeds 150% positive at times.  I have to say, I've never heard any of these guys told that they were distorted - Ever !  Always rather the opposite.

I am not at all convinced that it's the positive modulation that is the issue in these old boat anchor receivers with bad detectors and bad AGC (and these are likely the minority of receivers in use today anyway), and have actually never seen it in the field.

Real example:  Back in the '70s, there was an HRO-60 in the standards lab at the college I attended.  We used it to listen to A.M. broadcast stations (not to measure them).  Every station received on that thing was distorted, and the stations were not running highly asymmetrical modulation.   I fixed the problem, and it turned out that the distortion was occurring on the negative peaks.  The detector was the problem (I don't remember the particulars - it was 47 years ago), and as the negative modulation got close to 100%, the detector cut off.  The positive peaks were unmolested.

If a receiver generates distortion on positive peaks, it is highly likely that the same receiver generates distortion at ALL levels of modulation.  The I.F. chain and the detector typically must have headroom to avoid nonlinearity as saturation is reached.  It is unlikely there is a "hard" limit at 100% Positive modulation or even 150% positive modulation.

However, 100% negative has a finite limit.  Many diode detectors start becoming non-linear when there is a small amount of voltage applied to the diode (and this occurs at high levels of negative modulation).  And I have seen this in the field with many receivers that I've modified.

Thank you Steve for the thorough answer. I was hoping that you might respond.
We all tend to paint with rather large brushes and often criticize something without understanding fully the causes for an observed problem.

Just a few more follow up questions:
1.You did not comment on the All Filter advocated by Jim Tonne and others, as a possible improvement in modulation density and with it, better intelligibility.
It obviously contributes to limiting the natural asymmetry of voice spectral content.
You say that asymmetry is not a bad thing as long as negative modulation is controlled. Do you consider All Filters a valuable tool in AM transmission, or an irrelevant option or perhaps even harmful? I do not mean to put words in your mouth here, but wish fir your ideas on it.

2. Given that efficiency improves with rising voltages- within parameters safe for given devices, please give me your opinion on increasing carrier voltage to-say 55 volts and then limit positive peaks to a modulation index of 1.2.
1.2 x 55 + 55 = 120 volts peak on the drains. This will give a 660 watts dc carrier input in a rig I am designing which will draw 12 amps from 12 fets and give an input and about 600 watts carrier output. The pwm filter will be designed for a 4.5 ohm load.
If I went with 45 volts, then the current would be nearly 15 amps to provide the about the same carrier output and into a 3 ohm pwm filter.

I had looked at this first, but since I want to use some nice Formvar coated #10 magnet wire for my 6 pole filter coils wound on some 3.5 OD lucite pipe, I wondered  if lowering the current a few amps might be a good idea.
I guess I am asking what would happen in an air wound solenoid wound with #10 carrying 15 amps of carrier current. Obviously- #10 is rated much higher than that for electrical applications, but peaks will be 2-3 times the carrier current on modulation peaks. Is voltage drop an issue in these filters when wire size is marginal? Heating likely is not, since it is a single layer air wound solenoid, so will the few tenths of a volt sag with peaks be an issue?
If it is not, them perhaps going with the standard 45 volts and the 15 amps carrier current is best. I do plan to use a 3kva isolation control transformer that weighs 77 lbs and it should handle the current.

I am relieved to hear that I will not offend Old Timers by running a rig with the positive peaks that you advocate.  I am still imclined to build an All filter using Jim Tonne’s design to check it out by comparison.
Thank you for your advice.

[steve_qix]

One more thing about asymmetry that must be stated:  Asymmetry occurs naturally.  I am not talking about "forced" asymmetry.  I am talking about the natural asymmetry that occurs in the human voice if it is properly reproduced and amplified by low phase shift systems that are linear in their amplitude response.

Removing this asymmetry is, by definition, distortion.

If I speak into my microphone, and observe the modulation on a modulation monitor, I will typically see 150% positive and 85% negative modulation occurring at the same time!  There is no clipping or negative peak limiting involved.  That is my natural waveform.  Do I really want to distort this ?  Personally, for me, since the system will easily pass this asymmetrical waveform, I see no particular reason for modifying the natural waveform.  Just sayin'  

[steve_qix]

Hmmmmm.  interesting question on modifying the class E parameters.

You should be able to safely do it within limits.  Running the voltage up to, say, 50V at carrier (maintaining the H.V. at 130V) shouldn't stress anything at all.  The designs have a lot of headroom built in.  However, you will generate more heat (because you are running more average power).  A transmitter designed to run 45V @ 10A, when run at 50V would then need to be run at 11A, so you'd be running about 550 watts.  Assuming the power supply is up to the task, and that the modulator components (number of MOSFETs in the modulator, heat sinks, etc.), and the RF amplifier heat sink is sufficient, it should work.

But, for that 450 Watt design, every component is spec'ed for 450 watts average power.

It's better to take a higher power design (say, 6 MOFETs per module instead of 4) and run that within parameters.  You are adding scant cost, but will have a conservative design rather than pushing a lower power design.

I have found that high reliability in these transmitters is best achieved with a conservative design, lower heat production, lower voltages and distributed power (modularized).

-------------------- All pass filters  ----------------------

Personally, I don't use them and I find the audio produced using them is not as pleasing (at least to me) as audio that has not been so filtered.  Everyone's ears are different of course.  I am speaking from personal experience only.  Your perception of audio so altered may vary  

[K9MB]

Hmmmmm.  interesting question on modifying the class E parameters.

You should be able to safely do it within limits.  Running the voltage up to, say, 50V at carrier (maintaining the H.V. at 130V) shouldn't stress anything at all.  The designs have a lot of headroom built in.  However, you will generate more heat (because you are running more average power).  A transmitter designed to run 45V @ 10A, when run at 50V would then need to be run at 11A, so you'd be running about 550 watts.  Assuming the power supply is up to the task, and that the modulator components (number of MOSFETs in the modulator, heat sinks, etc.), and the RF amplifier heat sink is sufficient, it should work.

But, for that 450 Watt design, every component is spec'ed for 450 watts average power.

It's better to take a higher power design (say, 6 MOFETs per module instead of 4) and run that within parameters.  You are adding scant cost, but will have a conservative design rather than pushing a lower power design.

I have found that high reliability in these transmitters is best achieved with a conservative design, lower heat production, lower voltages and distributed power (modularized).

-------------------- All pass filters  ----------------------

Personally, I don't use them and I find the audio produced using them is not as pleasing (at least to me) as audio that has not been so filtered.  Everyone's ears are different of course.  I am speaking from personal experience only.  Your perception of audio so altered may vary  

Ok on 50volts being ok. I will then plan to make a 12 FET rig, or half of the 24 FET rig, if you please, and load it to about 13 Amps on carrier. The PWM filter will be designed for 4 ohm load and I will use a 6 pole filter in it. It should give about 600 watts carrier and I  will try to run a maximum of 120 % positive and I believe that will give me more headroom on negative peaks also.
Thanks for your comments on the all filter. The op amp version is fairly simple if I get precision components do will likely try it when I get on anyhow.
Thank you for your advice.

[steve_qix]

Hmmmmm.  interesting question on modifying the class E parameters.

You should be able to safely do it within limits.  Running the voltage up to, say, 50V at carrier (maintaining the H.V. at 130V) shouldn't stress anything at all.  The designs have a lot of headroom built in.  However, you will generate more heat (because you are running more average power).  A transmitter designed to run 45V @ 10A, when run at 50V would then need to be run at 11A, so you'd be running about 550 watts.  Assuming the power supply is up to the task, and that the modulator components (number of MOSFETs in the modulator, heat sinks, etc.), and the RF amplifier heat sink is sufficient, it should work.

But, for that 450 Watt design, every component is spec'ed for 450 watts average power.

It's better to take a higher power design (say, 6 MOFETs per module instead of 4) and run that within parameters.  You are adding scant cost, but will have a conservative design rather than pushing a lower power design.

I have found that high reliability in these transmitters is best achieved with a conservative design, lower heat production, lower voltages and distributed power (modularized).

-------------------- All pass filters  ----------------------

Personally, I don't use them and I find the audio produced using them is not as pleasing (at least to me) as audio that has not been so filtered.  Everyone's ears are different of course.  I am speaking from personal experience only.  Your perception of audio so altered may vary  

Ok on 50volts being ok. I will then plan to make a 12 FET rig, or half of the 24 FET rig, if you please, and load it to about 13 Amps on carrier. The PWM filter will be designed for 4 ohm load and I will use a 6 pole filter in it. It should give about 600 watts carrier and I  will try to run a maximum of 120 % positive and I believe that will give me more headroom on negative peaks also.
Thanks for your comments on the all filter. The op amp version is fairly simple if I get precision components do will likely try it when I get on anyhow.
Thank you for your advice.

50V @ 13A = 3.846 ohms (3.85 rounded).  If you're using PWM, the filter should be built around that value, and not 4 ohms.

Your negative peak headroom is always 100%, regardless.  You are just limiting the positive peak headroom, but not adding anything to the negative peak headroom

Hmmm... what is the "op amp version".  Do you mean the low pass filter AHEAD of the PWM generator?  Yes, this is necessary to prevent aliasing.

You can probably use a 4 pole filter and it will be enough, if the switching frequency is high (like 160kHz or greater), and the filter corner is 12.5kHz or thereabouts.

I didn't hear anything about an overload shutdown.  For whatever reason, many builders seem to think this ultra-important component can be eliminated.  Please don't do this.  The reason why there are class E rigs in the field today that are 20 years old is due to the overload shutdown circuit.  EVERY higher power class E rig ever built without this has failed (usually catastrophically) at some point.  Note that some of the early analog modulators had overload "tolerance" built into them - in that those lower power modulators could tolerate a very short-term overload.  The PWM modulators do not have any "slop" built into them (which makes them very efficient).  Therefore an overload shutdown circuit, one which reacts in under 100 microseconds, is necessary.

[K9MB]

Hmmmmm.  interesting question on modifying the class E parameters.

You should be able to safely do it within limits.  Running the voltage up to, say, 50V at carrier (maintaining the H.V. at 130V) shouldn't stress anything at all.  The designs have a lot of headroom built in.  However, you will generate more heat (because you are running more average power).  A transmitter designed to run 45V @ 10A, when run at 50V would then need to be run at 11A, so you'd be running about 550 watts.  Assuming the power supply is up to the task, and that the modulator components (number of MOSFETs in the modulator, heat sinks, etc.), and the RF amplifier heat sink is sufficient, it should work.

But, for that 450 Watt design, every component is spec'ed for 450 watts average power.

It's better to take a higher power design (say, 6 MOFETs per module instead of 4) and run that within parameters.  You are adding scant cost, but will have a conservative design rather than pushing a lower power design.

I have found that high reliability in these transmitters is best achieved with a conservative design, lower heat production, lower voltages and distributed power (modularized).

-------------------- All pass filters  ----------------------

Personally, I don't use them and I find the audio produced using them is not as pleasing (at least to me) as audio that has not been so filtered.  Everyone's ears are different of course.  I am speaking from personal experience only.  Your perception of audio so altered may vary  

Ok on 50volts being ok. I will then plan to make a 12 FET rig, or half of the 24 FET rig, if you please, and load it to about 13 Amps on carrier. The PWM filter will be designed for 4 ohm load and I will use a 6 pole filter in it. It should give about 600 watts carrier and I  will try to run a maximum of 120 % positive and I believe that will give me more headroom on negative peaks also.
Thanks for your comments on the all filter. The op amp version is fairly simple if I get precision components do will likely try it when I get on anyhow.
Thank you for your advice.

50V @ 13A = 3.846 ohms (3.85 rounded).  If you're using PWM, the filter should be built around that value, and not 4 ohms.

Your negative peak headroom is always 100%, regardless.  You are just limiting the positive peak headroom, but not adding anything to the negative peak headroom

Hmmm... what is the "op amp version".  Do you mean the low pass filter AHEAD of the PWM generator?  Yes, this is necessary to prevent aliasing.

You can probably use a 4 pole filter and it will be enough, if the switching frequency is high (like 160kHz or greater), and the filter corner is 12.5kHz or thereabouts.

I didn't hear anything about an overload shutdown.  For whatever reason, many builders seem to think this ultra-important component can be eliminated.  Please don't do this.  The reason why there are class E rigs in the field today that are 20 years old is due to the overload shutdown circuit.  EVERY higher power class E rig ever built without this has failed (usually catastrophically) at some point.  Note that some of the early analog modulators had overload "tolerance" built into them - in that those lower power modulators could tolerate a very short-term overload.  The PWM modulators do not have any "slop" built into them (which makes them very efficient).  Therefore an overload shutdown circuit, one which reacts in under 100 microseconds, is necessary.

Sorry, I was not clear on the OP Amp version of the All Pass filter as published by Jim Tonne.
The circuit was actually designed by W3AM
See it in figure 8 in this article:
http://www.tonnesoftware.com/downloads/AllpassNetworksInASpeechChain.pdf

Regarding the actual exact impedance of the low pass filter for the pwm, please explain why the necessity for this level of precision in the load impedance. The difference between 4.0 and 3.85 seems small to an uninformed person like me. What happens when the load varies from the design impedance of the filter?
I actually did some experimentation using Jim Tonne’s ELSIE program. It is able to provide the exact values you spec on the Class E site for the operating parameters you specify in the designs, but it also has a tune feature that a.lows one to vary every component in turn and observe the response curve as a result of the changes in the  curve and the curves change slowly from optimum values. No doubt, I a,just looking at transmission and am missing some other factor, but I have not discovered that-at this point.
Also, given that I can make small changes in carrier voltage and by varying loading hold the current constant, I could match the amplifier to my 4 ohm filter easily by varying either voltage or current-right?  I mean, if I raised the voltage to 52 volts and loaded to 13 amps, that is 4 ohms and 50 volts loaded to 12.5 amps is also 4 ohms- right?
 If this assumption is false, then correct me here. I am reasoning with insufficient knowledge-no doubt.

This might seem pointless, except that I can see that the building of very highly accurate indicators that are thermally stabile over a wide temperature range seems impossible to me, so whether we mean to or not- we are going  to be operating filters that are sub-optimal across the spectrum of operating conditions and it seems to me that the control of voltage and load current allows ome to optimize the real world design on the fly  by optimizimg efficiency or minimizing distortion, etc, rather than splitting hairs over exact values of cold indictors or capacitors in these filters.
I know that you must have considered this- or have a good answer for it.
I do appreciate your patience and advice.

 Addendum:
Steve, Regarding your suggestion about running the pwm generator at 160khz. That is a great idea. However, I just checked the schematic on your Class E site for the PWM, the schematic has the Rt at 56k and the Ct at 220pF and using their formula fir the UCC25701-   F= 2/(Rt * Ct) , that calculates for me to 162kHz approximately.
I wonder how high one might go with that frequency on this device? I guess one must avoid harmonics that fall close to ham bands and the lower the better for that, so is 160 kHz the sweet spot?

[steve_qix]

The filter:  It is always best to be "right on" with respect to the terminating impedance.  Then if you vary a little one way or the other, the filter will still operate well.  I'm very much a design perfectionist whenever possible, you you must forgive that 

The PWM frequency - yes, 160kHz (more or less) is definitely a sweet spot.  The PWM modulator has to be able to properly resolve, and without integration, very small pulses as the far reaches of the PWM waveform are approached (high negative modulation and high positive modulation).  Stray capacitance (and inductance) will tend to cause an integration of the pulses to occur, along with "stretching" of the small pulses, resulting in non-linearity.  The switching frequency has to be low enough, such that these undesirable side effects are minimized.

With the system, as designed, 160kHz (more or less) was the highest frequency that would allow for good resolution of narrow pulses down to 99% negative modulation across the whole modulator system.  Various components are affected by increasing the switching frequency.  The damper diodes, charge pump diode, the MOSFET drivers, and even the modulator MOSFETs themselves work "harder" as the frequency is increased.

The old vacuum tube Gates MW series of PWM transmitters used a 70kHz switching frequency.  And even at that, small pulse integration was a problem (I built several tube PWM transmitters), to the point that analog compensation was necessary, where the modulator was essentially running as an analog series modulator as the modulation approached 100% negative.  That 70kHz waveform is a lot harder to filter, that's for sure.

[K9MB]

The filter:  It is always best to be "right on" with respect to the terminating impedance.  Then if you vary a little one way or the other, the filter will still operate well.  I'm very much a design perfectionist whenever possible, you you must forgive that 

The PWM frequency - yes, 160kHz (more or less) is definitely a sweet spot.  The PWM modulator has to be able to properly resolve, and without integration, very small pulses as the far reaches of the PWM waveform are approached (high negative modulation and high positive modulation).  Stray capacitance (and inductance) will tend to cause an integration of the pulses to occur, along with "stretching" of the small pulses, resulting in non-linearity.  The switching frequency has to be low enough, such that these undesirable side effects are minimized.

With the system, as designed, 160kHz (more or less) was the highest frequency that would allow for good resolution of narrow pulses down to 99% negative modulation across the whole modulator system.  Various components are affected by increasing the switching frequency.  The damper diodes, charge pump diode, the MOSFET drivers, and even the modulator MOSFETs themselves work "harder" as the frequency is increased.

The old vacuum tube Gates MW series of PWM transmitters used a 70kHz switching frequency.  And even at that, small pulse integration was a problem (I built several tube PWM transmitters), to the point that analog compensation was necessary, where the modulator was essentially running as an analog series modulator as the modulation approached 100% negative.  That 70kHz waveform is a lot harder to filter, that's for sure.

Hey- please do not apologize for being a perfectionist. I suffer from that disease- obviously 😬😉 from my inductance in knowing boundaries for good design. I do realize you know all these things snd I wish to know- as well, rather than just copying your obviously very good designs.
I will just stay with the 160 kHZ design you have and now understand better- why you have chosen these operating parameters.
Thank you.