Tetrode Modulator Negative Peak Limiter

[Jim KF2SY]

For those who like to experiment and use Tetrode/multi grid (sweep etc.) toobs in their PP modulator please read on.
 
This is an extremely easy circuit that provides a fairly clean semi-rounded negative peak.  Perhaps you may want to try it out and experiment as an alternative to the multi -diode schemes that have been debated to death recently on this board.  
 
Most of us are familiar with various variable RF power output reduction circuit methods: By varying the screen voltage.
As an experiment one day, and after being told by others who more or less poo-pooed the idea, I decided to try it on my very common and popular PP modulator stage in my DX100.  I simply identified by substitution with a known weak/gassy 807, the negative going part of the modulator as viewed on my scope.
I then looked up the max. screen current which follows the plate and grid in audio signal excitation/current.  I then simply calculated & put a large value series resistor
to the screen grid on the negative going tube socket only.  At least 10k is a fairly close starting point value for 100 watt class plate mod. boat-anchors.  This causes the modulator to behave like a dynamic VCA type action, where that series screen resistor will cause a large voltage drop with heavy modulation.  Getting it down to about 1/3 to 1/2 of the normal screen voltage or so, as measured (no signal) , will result in about 90-95 % limiting action with no audible (to my ears) artifacts.   I believe the "balance" of the PP scheme is preserved as you are not changing bias/conduction angle. No??  
Reports from some of the Northeast gang have been favorable, with some commenting that I sounded quite loud.  This is of course from the additional density of the audio with no base-lining the carrier.  Also, as most know the DX 100 can't do much above 100% pos. anyway, but if you have asymmetric voice characteristics it's nice to have a NPL'er anyway.  
 
I used to use the early version diode type NPL on the output ( no keep-alive supply, using 1 or 2 and 3 diodes) and would notice the mod xfmr would get warm after a long transmission.  With this modification, mod xfmr seems happy and runs cold; as it has that steady PA impedance to always work into.  Also, perhaps any "crud" generated by the negative going tube tube is filtered out by the mod tranny?  
 
 
There is virtually nothing written, or curves available in the data books for screen voltage or current, versus plate current.  I have seen articles that the screen voltage behavior is however, not a linear function.  Which in this negative peak limiting application is ok.  You only want it to starve the tube for gain on heavy peaks.  
 
Benefits are obvious; simplicity, 1 component (resistor).  Another is the natural soft clipping on a tube versus diodes.
One drawback is the variability of screen construction and behavior in all the different tetrode tube types.  
Experimentation is required with your tube type.  A scope of course --(a must in every AM amateur station).
 
On a related application and as a part of the inspiration for this experiment above, Bacon WA3WDR discusses in an old article the screen grid and amplifier lineraity, dropping resistors in PP modulators and RF apps. & some benefits, linearity, etc.  I simply just added a twist;  a ( larger value resistor) and for one tube only ( negative going) in the modulator for a  negative peak limiting application.
 
http://www.bruhns.us/T-P_Amp_Lin/T-P_Amp_Lin.html
 
 
This was all done in the noble amateur spirit of experimentation and curiosity......Anybody else try this
Lunacy??  Heresy?? Comments, drawbacks, ??  
 
Thanks,
Sincerely,
 
Jim KF2SY

[WA1GFZ]

how about this, Have the keep alive supply of the 3 diode NPL also feed the screen of the negative going tube so the screen voltage gets yanked down when the NPL starts to draw current. Anybody have any tetrodes in simulation?

[Steve - WB3HUZ]

Interesting Jim. You said you heard no artifacts. Was this one frequency or off. It can sound good on freq and still cause splatter off. Do some checking off to the side of your signal or have others who are receiving you well to check. If you get a clean report, it's probably a winner.

[WA1GFZ]

HUZ,
I was thinking you could build a nice mixer and reaally make some wideband crud if you were not careful. 

[Steve - WB3HUZ]

That is a fact.

HUZ,
I was thinking you could build a nice mixer and reaally make some wideband crud if you were not careful. 

[KA2DZT]

Jim,

Interesting idea,  I guess it could be made to work.  Probably an adjustable screen resistor would allow one to adjust the degree of limiting.

I use a regulated 300V PS on the screens of the 6550's I use in my xmtr.

Having one screen unregulated would create distortion, but limiting the negative peaks in anyway is a form of distortion.

Have to think about ur idea a bit.

Fred  KA2DZT

[Jim KF2SY]

Jim,

Interesting idea,  I guess it could be made to work.  Probably an adjustable screen resistor would allow one to adjust the degree of limiting.

I use a regulated 300V PS on the screens of the 6550's I use in my xmtr.

Having one screen unregulated would create distortion, but limiting the negative peaks in anyway is a form of distortion.

Have to think about ur idea a bit.

Fred  KA2DZT

The diode schemes are all distortion too.
Just add a dropping resistor that would give you about 1/3 to 1/2 the normal screen voltage at about 90% of the max signal screen current for that negative going tube.... (For 1 tube of course, I think IIRC screen current ratings are often given for 2 tubes for the AB1 and AB2 in the tube manuals, then divide by 2.)

[WD5JKO]

The diode schemes are all distortion too.

   Sorry, but that statement would do poorly on the "Truth-O-Meter" test. Why would I say that?

Well, whether were dealing with the classic QIX 3 diode circuit, the HRO 4 diode circuit, or the JKO 4 diode circuit, they all have one thing in common. That is before the diodes do their thing, usually around 90% negative modulation depending on bias voltage and circuit details, these circuits are transparent. This means they behave is if they are not there. What happens above the limiting threshold is another story, and that is where the three circuits mentioned tend to stand apart. I alone (on another thread) believe that a LPF following the diode circuit is a good idea, because yes distortion is generated. We did get consensus however that a soft clip was advantageous. So progress was made refining the diode limiter circuits..

I do like to see new approaches to this problem. If we can get 3db more talk power out of AM, then that is huge. Doing this without splatter is necessary however. Complaining that your S38 receiver diode detector overloads at > 70% modulation just means you need a better AM receiver.

Jim
WD5JKO

[k4kyv]

Anything that modifies the waveform, by definition, produces distortion.  Distortion inherently adds spurious products to the original signal. Spurious products inevitably increase the bandwidth of the signal, unless something between the source of distortion and the final amplifier filters the signal.  The modulation transformer, combined with the rf bypass capacitors, may form a crude low-pass filter and limit the spurious sideband products. In the late 40's or early 50's, a technique called "building out" the modulation transformer involved the use of specific values of by-pass capacitance to produce a desired low-pass cutoff.

A transformer cannot pass DC, so any asymmetrical peak limiting that occurs before the modulation transformer cannot modify the base-line of the waveform. Audio peaks of greater amplitude on one side of the base-line inevitably have a shorter dwell time than the lower amplitude peak at the opposite half-cycle on the opposite side of baseline, and vice versa.  On a graphic display, the area under the curve, between the audio wavefdorm and baseline, must be identical on both sides above and below the baseline.  This is the same kind of asymmetry that naturally occurs with the human voice.

[W1AEX]

I have worked Jim several times on 75 meters with a scope on the receiver running. I would add to the conversation here that the unique system he is using does appear to work quite well. His positive peaks regularly exceed 100% with no trace of baseline smacking in the negative direction. As I recall, after a few minutes of conversation and observation during our first contact, I asked him how he was able to attain such obvious asymmetry out of a DX-100 and he explained what he was doing.

The simplicity and effectiveness are very intriguing. His audio is very smooth, loud, and pleasant, whereas most DX-100's will get fairly gritty and quickly hit 100% in the negative direction when the audio is driven hard. During a second QSO at a later date, Jim asked me to tune above and below to see if I could detect artifacts/splatter. I did not hear anything going on 6 or 7 kc above and below his carrier. Next time I catch him on the air, I'll make a short video of the scope pattern and then make a few off frequency "air-check" excursions and stick it up on YouTube. At any rate, I'm glad he took the time to write this up for dissection by the engineer types here. From my perspective, as someone without much more than a hobby level of understanding, it looks like an interesting approach to negative peak limiting with tetrode modulators.

Rob W1AEX

[Steve - WB3HUZ]

In the purest sense of the word, that statement would peg the Truth-O-Meter. You are changing the shape of the waveform and that is distortion. That doesn't mean it's necessarily bad or unacceptable distortion, as you well know.

The diode schemes are all distortion too.

   Sorry, but that statement would do poorly on the "Truth-O-Meter" test. Why would I say that?

Well, whether were dealing with the classic QIX 3 diode circuit, the HRO 4 diode circuit, or the JKO 4 diode circuit, they all have one thing in common. That is before the diodes do their thing, usually around 90% negative modulation depending on bias voltage and circuit details, these circuits are transparent. This means they behave is if they are not there. What happens above the limiting threshold is another story, and that is where the three circuits mentioned tend to stand apart. I alone (on another thread) believe that a LPF following the diode circuit is a good idea, because yes distortion is generated. We did get consensus however that a soft clip was advantageous. So progress was made refining the diode limiter circuits..

I do like to see new approaches to this problem. If we can get 3db more talk power out of AM, then that is huge. Doing this without splatter is necessary however. Complaining that your S38 receiver diode detector overloads at > 70% modulation just means you need a better AM receiver.

Jim
WD5JKO

[Bacon, WA3WDR]

A dynamic low-level negative clip level can make up for the limit of transformer low frequency response, allowing the clip level to hold steady at the modulator output.  I accidentally discovered that if my low-level peak limiter detected audio that I ran through a separate amplifier and transformer (one of those Radio Shack 1000 CT to 8 ohm units backwards), the tilt out of that side chain pretty much matched the tilt on my mod transformer, and the result was that overall peak limit operation was just about perfect.  If the transformer output would begin to tilt, the gain reduction was reduced, thereby reversing the tilt. The throughput audio did not go through that little transformer, that circuit was only there to produce audio gain control voltage.  So any low frequency tilt, shuck and jive there would affect the dynamic of the audio gain system, and that would compensate for the low-frequency characteristics of the mod transformer.

If the peak limiter attack and delay were very fast, the peak limiting acted more like clipping.  So I added an adjustable degree of very fast action, along with slower acting stuff for the general speech compression effect.  Anyway, while experimenting one day, I happened to notice that the clipping was almost dead flat on the modulator output - there was just about no tilt.  Surprised, I looked into how that could be.  It turned out that it was caused by the dynamic that was accidentally built into the low-level side-chain audio design.
 
In fact the limiter put out reverse tilt, and then the modulator turned that into a flat clip line.  I imagine that the high frequency characteristics of the mod transformer were partially balanced out too.

Asymmetrical Peak Limiting
http://www.bruhns.us/APL/APL.html

I also had a low-pass filter, a simple 2-pole Sallen-Key thingie, after the limiter.  A little filtering, without hurting the mod transformer.  I can't find the schematic that I used, I'll have to look at the values, I still have it.  It was an equal-resistance Sallen-Key using an op-amp, cornering at 3.5 KHz, and I could switch it in or out. I was thinking of Bessel characteristics, but I think I wound up on the Butterworth side.  It seemed to work well, though.

Ha.  Once I got the RF out of the audio, it all sounded pretty good, when the clipping was not set very high.  In tough conditions, strong clipping wasn't too awful, though.  It wasn't just clipping, it was a little clipping on top of peak limiting.

The variable gain mechanism was a simple mosfet shunt.  It added some second-order distortion, which if polarized right pushed the positive peaks and squeezed the negative peaks a little.  Or it could be set up the other way, because natural asymmetry can be pretty high.

Some receivers have headroom, some do not.  The biggest complaint I got was from somebody who was using a solid-state receiver with a fast peak AGC.  He said I sounded really compressed.   But when he turned off the AGC and used manual RF gain, it sounded fine to him.  Fast peak AGC doesn't sound good on AM signals, especially if they have high positive asymmetry.  For AM, average AGC is better, and there should be 12 dB or more of headroom for positive peaks.  Certainly at least 6 dB for 100% positive modulation, but let's allow for some asymmetry and a little selective fading before the receiver makes things worse.

[Opcom]

In some older tube manuals there are curves for screen voltage vs plate current. For tetrodes and beam power tubes they are rather linear in most cases.
One thing about poo-pooers, they always make a smell!

[k4kyv]

A name comes to mind and that is James Marshall Hendrix

Without distortion he never would have been able to self generate the sounds he did using simple and very primitive audio amplifiers. It does have its benefits.

Hendrix started his career right in my backyard. But I never saw him perform here since I was halfway round the world at the time.

Hendrix got into trouble with the law twice for riding in stolen cars. He was given a choice between spending two years in prison or joining the Army. Hendrix chose the latter and enlisted on May 31, 1961. After completing boot camp, he was assigned to the 101st Airborne Division and stationed in Fort Campbell, Kentucky. His commanding officers and fellow soldiers considered him to be a subpar soldier: he slept while on duty, had little regard for regulations, required constant supervision, and showed no skill as a marksman. For these reasons, his commanding officers submitted a request that Hendrix be discharged from the military after he had served only one year. Hendrix did not object when the opportunity to leave arose.  He would later tell reporters that he received a medical discharge after breaking his ankle during his 26th parachute jump.

At the base recreation center, Hendrix met fellow soldier and bass player Billy Cox, and the two forged a loyal friendship that Hendrix would call upon from April 1969 until Billy's breakdown shortly before Hendrix' death. The two would often perform with other musicians at venues both on and off the base as a loosely organized band there named the Casuals. As a celebrity in the UK, Hendrix only mentioned his military service in three published interviews; One in 1967 for the film See My Music Talking (much later released under the title Experience), which was intended for TV to promote his recently released Axis: Bold as Love LP, in which he spoke very briefly of his first parachuting experience: "...once you get out there everything is so quiet, all you hear is the breezes-s-s-s..." This comment has later been used to claim that he was saying that this was one of the sources of his "spacy" guitar sound. The second and third mentions of his military experience were in interviews for Melody Maker in 1967 and 1969, where he spoke of his dislike of the army. In interviews in the US, Hendrix almost never mentioned it, and when Dick Cavett brought it up in his TV interview, Hendrix's only response was to verify that he had been based at Fort Campbell.

Early career

After his Army discharge, Hendrix and army friend Billy Cox moved to nearby Clarksville, Tennessee and undertook in earnest to earn a living with their existing band. Hendrix had already seen Butch Snipes play with his teeth in Seattle and now Alphonso 'Baby Boo' Young the other guitarist in the band, was featuring this gimmick. Not to be upstaged, it was then that Hendrix learned to play with his teeth properly, according to Hendrix himself: "... the idea of doing that came to me in a town in Tennessee. Down there you have to play with your teeth or else you get shot. There’s a trail of broken teeth all over the stage..."They played mainly in low-paying gigs at obscure venues. The band eventually moved to Nashville's Jefferson Street, the traditional heart of Nashville's black community and home to a lively rhythm and blues scene. After they moved to Nashville, upon learning there was already an established band by the name "The Casuals", they amended their name to the "King Kasuals". While in Nashville, according to Cox and Larry Lee—who replaced Alphonso Young on guitar—they were basically the house band at "Club del Morocco". Hendrix and Cox shared a flat above "Joyce's House Of Glamour". Hendrix's girlfriend at this time was Joyce Lucas. Bill 'Hoss' Allen's memory of Hendrix's supposed participation in a session with Billy Cox in November 1962, which he cut Hendrix's contribution due to his over the top playing, has now been called into question; a suggestion has been made that he may have confused this with a later 1965 session by Frank Howard And The Commanders that Hendrix participated in.

http://en.wikipedia.org/wiki/Jimi_Hendrix

[Bacon, WA3WDR]

The most elaborate work I did with screen resistors on audio power tetrodes was with 6L6GCs at about 300V or 350V plate and screen.  With no resistance in series with the screens, there was the usual upward curvature from cutoff on both sides.  The right value, about 5.1K to 5.6K, made the tubes remarkably linear.  Too high of a value caused a flattening of peaks.  It was a soft flattening.

Generally speaking, the screen current will rise as the plate voltage drops.  This makes sense because the electrons start to get less attracted to the lower voltage plate, and more of them find their way to the screen grid instead.  If there is a resistance in series with the screen, this will cause the screen voltage to drop when the instantaneous plate voltage is lower, and that will reduce the plate current - which will cause the instantaneous plate voltage not to fall as low as it would have otherwise.  A moderate amount of this effect compensates for the upward curvature that is normally seen with tetrodes and pentodes.  A larger resistor value will cause a soggy pull-down limit on the plate voltage.  Where that limit happens depends on the plate load, the screen supply voltage, the resistor value, etc.  The sogginess of the effect causes the resulting clipping to be rounded rather than hard, which is good because it causes less high order distortion to be generated.

So a larger resistor in series with the screen grid of the negative modulator tube will round down the negative peaks.  The inability of the transformer to pass DC will indeed cause this negative modulation limit to vary, depending on the amount of asymmetry and the amount of clipping.  But a reduction of negative peaks will reduce or eliminate overmodulation.  There will be distortion, but the rounding quality will reduce the splatter that will result.  Soft clipping is a compromise, but it can be simple to do.

A peak detector right on the modulated B+ line would be absolute.  If modulated B+ gets too close to zero, circuitry could start reducing gain somewhere.

[AB2EZ]

I heard Jim on the air yesterday... and his audio sounded excellent! I didn't have my wideband SDR on at the time... so I didn't check to see if distortion products were making his signal "wide"

Three comments:

1. It would be easy to check the audio spectrum of the voltage waveform at the output of Jim's modulator... as follows:

a. Use a voltage divider attached to the modulated B+ line to obtain an attenuated version of the modulated B+ (e.g. 1000:1)

b. Feed the attenuated, modulated B+ into any plain vanilla computer sound card

c. Use one of the free audio spectrum analysis programs (e.g. Spectrum Laboratory) in conjunction with the sound card + computer to observe the spectrum of the voltage waveform at the output of the modulation transformer (or, if you wish, the input to the modulation transformer)

2. On the subject of the blockage of: the DC (average value), and the low frequency components of the negative-peak-soft-limited waveform, by the modulation transformer:

a. Bacon and others have covered this in some detail, but I wanted to add an observation that is complementary to some of those prior comments

b. The negative peak soft limiting should be fairly infrequent on a percentage-of-time basis (unless you put a sine wave into the audio chain)... and the objective impact (i.e. what you could measure or see on a scope) of high-pass filtering the resulting waveform, after the soft limiting of the negative peaks,  (a.k.a "baseline wander") should be small. The subjective impact should be even smaller (probably imperceptible for most listeners).

3. If the push-pull modulator is operating in class AB2, you could get a similar soft limiting of the negative modulation peaks by putting some extra resistance in series with the grid of the associated tube (drops the grid voltage when the grid draws current). More generally, you could put a soft limiter... of one kind or another... on the grid of that tube.

Best regards
Stu

[w1vtp]

Sounded like this when I worked you Jim

Al

[Bacon, WA3WDR]

sounds ho-kay

[Jim KF2SY]

Thanks for all the responses so far, and for the nice reports (Rob, Stu, Al and Bacon).
(Checks are in the mail)  

Original point of the post was as a sanity check for viability as an option for NPL-- for those of us using tetrode modulators.  So far, seems like a promising & extremely simple approach we can all put in our "AM toolbox" to try out and experiment with, if desired.   Again, as per usual, the standard caveats: your mileage may vary with tube type, etc.  Wondering about though & as pointed out by ? Stu, Don & Bacon, etc. that the mod xfmr can't pass that DC clipping....does this harm/stress the mod xfmr  Effects & Saturation of the core  The mod xfmr on my little DX100 doesn't seem to be even getting warm under heavy modualtion or after a buzzard xmission.  

Thanks again,
Jim

[WA1GFZ]

The longer you sit at tube saturated the greater the temperature rise in the windings. Saturate the core and the current goes higher.  Pulling the screen down helps as long as you don't create a high level mixer. A limiter in th etransformer secondary does not limit current in the transformer primary.
4 diode circuit does nothing but add 1 diode drop to the B+

[AB2EZ]

Jim
et al.

In a push pull modulator: the tubes, the phase splitter that drives them, etc. are never perfectly matched... so even if you are using a Heising configuration, the effect of a small, unbalanced DC/low frequency component of the current... added to the existing unbalanced current in the primary of the transformer... should be negligible. It might even subtract from the existing unbalanced current.

In a non-Heising modulator configuration: the B-field produced, in the core of the transformer, by the plate current passing through the secondary winding of the transformer, will be two orders of magnitude larger than the B-field produced in the core of the transformer by unbalanced, DC/low frequency current passing through the primary of the transformer.

Therefore, unless the audio waveform is a sine wave, and you are removing a significant fraction of the negative portion in every cycle and you are using a Heising configuration... it seems to me that the effect of soft, negative peak clipping on the modulation transformer will be negligible.

Stu

[WBear2GCR]

I'm close in to Jim, maybe groundwave close.

I thought that I did not like his audio with the screen trick in there as much as i did before.
Dunno what else, if anything was changed.
It wasn't "bad".

Also Jim tends to be soft spoken and doesn't tend to hit his audio hard.

I'm skeptical of this method, because it will effect the gain and the linearity of the tube with the starved
screen all the time.

It is simple though.

dynamic negative modulation of the screen with a threshold as well might be very interesting, but not as simple.
(a negative only "soft knee limiter" anyone?)

personally, i'd do this sort of negative limiting in a low level stage and keep the mod tubes linear... but that's my
preference.

                    _-_-bear

[AB2EZ]

I did some simulations, using LTSpiceIV; and I obtained some interesting results that apply for the case where the input audio waveform is a sine wave.

Note: these results would not apply when the input audio waveform is a voice waveform... because the positive and negative peaks in a voice waveform occur a much smaller percentage of the time than they do in a sine wave. In that sense, the results obtained here, using a sine wave, represent a "worst case" scenario with regard to the effect of a high pass filter (i.e. a transformer) on a negative peak limited waveform.

In attachment 1, I show the circuit used for the simulation. The modulator (without negative peak limiting) is a 200 volt (amplitude) sine wave whose source resistance is 10000 ohms.

The modulator drives a 10000 ohm load, so, if there were no negative peak limiting, the voltage across the load would have a peak value of 100 volts

There is a diode, connected to a -85 volt DC supply added, in the circuit, to limit the negative peaks (before the coupling capacitor) to -85 volts (-85%).

The capacitor, in combination with the output load and the source impedance, produces a low frequency roll off that is 3dB down at approximately 30Hz (simulating the low frequency roll off of a modulation transformer)

Attachment 2 shows the case where the sine wave frequency is 1000Hz (much larger than the 30Hz low frequency roll off of the modulation transformer).

The green curve is the applied 200 volt (amplitude), 1000Hz sine wave. The blue curve is the negative-peak-limited voltage at the input of the capacitor (simulating the modulation transformer). The red curve is the voltage at the output of the modulation transformer.

Note that the high pass filtering resulting from the capacitor (simulating the modulation transformer) has some effect on the negative peak limited waveform, but the effect is small.

Attachment 3 shows the case where the sine wave frequency is 100Hz (not that much larger than the 30Hz low frequency roll off of the modulation transformer).

In that case, the high pass filtering resulting from the capacitor (simulating the modulation transformer) completely negates the intent of the negative peak limiter.

Again, this is a "worst case" result that is associated with a waveform that has negative peaks whose durations are relatively long (a 100 Hz sine wave), and where the time between negative peaks is only a small multiple of the duration of each negative peak.

Stu

[AB2EZ]

This simulation is simpler, and also closer to what Jim is actually doing.

Attachment 1 shows the circuit. There are two current sources. One current source generates a sequence of positive current pulses that are 1 millisecond long, 0.02 amperes in amplitude, and spaced 20 milliseconds apart. The other current source generates a sequence of negative current pulses that are 1 millisecond long, -0.015 amperes in amplitude, and spaced 20 milliseconds apart.

The modulator, in this case, has a source resistance of 5000 ohms.

The load is 5000 ohms

There is an inductor (representing the modulation transformer) that forms a high pass filter (in parallel with the source resistance and the load) whose 3dB roll off point is 20Hz

Attachment 2 shows the two current sources, interleaved in time. Since the current sources in attachment 1 point downward, you should read the red pulse as 20mA flowing into the load (positive modulation), and the blue pulse as 15mA flowing out of the load (negative modulation)

Attachment 3 shows the voltage across the load.

In my next post I will add an attachment that shows the voltage across the load when the positive and negative pulses both have amplitude .02A (20ma).

This illustrates that the negative peak limiting (before the modulation transformer), is, in fact, being carried through the transformer.

Stu  

[AB2EZ]

Refer to my post above...

The 1st attached slide shows the voltage across the load, when the positive and negative current pulses are equal (no negative peak limiting)

The 2nd attached slide shows the effect of more spacing between the pulses (no negative peak limiting)

As can be seen (independent of negative peak limiting): each pulse (positive or negative) in the modulating waveform experiences some "droop" (due to the magnetizing inductance of the modulation transformer that is in parallel with the load). When the pulse tries to return to zero, there is a "tail" of the opposite polarity.

As Don and others have pointed out, the area of one pulse (including the tail) is zero. This is another, more precise way of saying that "the transformer will not pass DC"

The 3rd attached slide shows the effect of putting the pulses very close together (relative to the width of each pulse) and having the positive pulse amplitude set to 0.02A and the negative pulse amplitude set to 0.15A (i.e. using negative peak limiting)

As was the case with sine wave modulation, if the spacing between the negative pulses is only a small multiple of the width of each negative pulse... then the modulation transformer erases some of the intended asymmetry (positive peaks bigger than negative peaks) associated with negative peak limiting.

Stu