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Author Topic: Downward Modulation?  (Read 35172 times)
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Ed/KB1HYS
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« on: September 07, 2007, 09:57:26 PM »

Say you have a transmitter that can put out 1500 watts carrier. Then you put in a modulation deck in such a way that instead of summing the modulation to the carrier for peaks, it reduces the carrier to zero. The reverse of what is normally done. opposite phase?? 

Wouldn you have a 1500 watt PEP transmission??

Why wouldn't it work??
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Bacon, WA3WDR
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« Reply #1 on: September 07, 2007, 10:07:20 PM »

It can be done and it can sound OK.  There are a few ways to do it.

http://www.qsl.net/wa5bxo/asyam/aam3.html
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Ian VK3KRI
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« Reply #2 on: September 08, 2007, 07:34:33 AM »

When you do this you will be pumping the AGC of the reciever. Whether or not this is objectionable depends on how far you take it and the quilities of the reiciver. 
I have a paper somewhere on tests the BBC did on this on AM BC stations. I think with the 6dB of carrier reduction on 100% modulation (same thing as your suggesting) the only noticable issues were in the presence of interference . They were varying the 'carrier level' at a sylaballic rate - same as controlled carrier.
                                                                  Ian VK3KRI
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Tom WA3KLR
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« Reply #3 on: September 08, 2007, 10:38:51 AM »

I guess if the Inverted Amplitude Modulation had a good advantage that it would be in service but it isn't. 

Bob you metioned in the article that a linear in this service would be operating at very close to maximum efficiency.  This is true and it would also be operating near maximum dissipation too!

With just a quick thought, it seems that this technique can only be done with low-level modulation (followed by a linear) or series modulation.  Plate modulation with a transformer is out.

One technique that comes to mind is having to put the audio to a clamp circuit also called a DC restorer, to get one peak of the audio waveform to hold to a dc reference level.

I heard Chuck K1KW on about a year ago with his highly modified FT-1000? and linear running inverted amplitude modulation.  He is the only one I have heard on running this.

I think that Chuck achieved the inverted AM by using the transmit system ALC action and over-driving the linear and having the negative swing modulation bring the output downward from full limiting output.  (Low-level modulation and linear amp., forced ALC action.)
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« Reply #4 on: September 08, 2007, 12:26:01 PM »

I agree with Tom's comments...

The only advantage I can think of, which would result from using "downward modulation"... and which could be implemented in a variety of different ways/flavors... would be that it would increase the "quieting" produced (at the receiver) by the carrier during periods between syllables, and also during times then one is transmitting, but not fully modulating (or not modulating at all).

The disadvantages I can think of are:

1. More wasted power, with the carrier moved up to full output (e.g. 1500 watts) during periods of time when it would normally be 25% of full output (e.g. 375 watts) or less. I agree with Tom that in the case of a linear amplifier the impact on electrical power consumption would be approximately 2:1. With a Class C plate modulated transmitter, the impact on electrical power consumption would be approximately 4:1. But whether using a linear amplifier or a plate modulated Class C transmitter, the electrical power consumption would be substantially higher using the downward modulation approach

2. The average plate dissipation that the output tube(s) would have to accommodate would, as in the case of the electrical power, be substantially higher for a plate modulated Class C transmitter: nominally 4 times higher. For a linear amplifier, the plate dissipation would be approximately the same. I.e., 375 watts output @ 33% efficiency => 750 watts plate dissipation; 1500 watts output at 66% efficiency => 750 watts plate dissipation.

3. Depending upon the time constant(s) with which the transmitted carrier level is adjusted (downward and upward) to accommodate the modulation, and depending upon whether the receiver's AGC circuitry is responding to the peak level or the average level of the received signal*, and depending upon the time constant(s) of the receiver's AGC circuitry, ... the AGC of the receiver might track the peak carrier level... resulting in reduced volume of the audio from the receiver compared to other signals in the same QSO; or the AGC might approximately track the changing carrier level... resulting in annoying variations in the volume of the audio coming out of the receiver.

*Most AGC circuits employ peak detectors... but in my 75A-4, I installed a precision rectifer + low pass filter circuit that tracks the carrier level of the received signal... which I use when receiving AM.

Best regards
Stu
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« Reply #5 on: September 08, 2007, 02:06:12 PM »

With just a quick thought, it seems that this technique can only be done with low-level modulation (followed by a linear) or series modulation.  Plate modulation with a transformer is out.

One technique that comes to mind is having to put the audio to a clamp circuit also called a DC restorer, to get one peak of the audio waveform to hold to a dc reference level.

I heard Chuck K1KW on about a year ago with his highly modified FT-1000? and linear running inverted amplitude modulation.  He is the only one I have heard on running this.

I think that Chuck achieved the inverted AM by using the transmit system ALC action and over-driving the linear and having the negative swing modulation bring the output downward from full limiting output.  (Low-level modulation and linear amp., forced ALC action.)

Most of the current Icom rigs, and maybe some of the current Yaesu's, use a similar form of low-level modulation for AM. I'm sure you've seen thread titles that "my Icom is downward modulating in the AM position" or something similar.

User key's down and looks at their forward power SWR meter in their antenna tuner or some external box and sees steady carrier. As they  modulate in the AM position, the forward carrier meter pointer moves down in sync with their modulation. If you're a "seasoned amateur" (i.e. been on the air since the dawn of mankind), your perception is that you are "downward modulating". Experience from using plate modulated rigs would indicate that's not a good thing. Actual on-the-air testing has proved that this perceived malady is not discernible to the "normal" ear listening on the inside or outside speaker. Plus, if you're using this rig to drive a linear, you could tune for maximum power carrier output at steady carrier, and then when modulating the driver, not fear you're going to exceed the maximum specs for the amplifier tubes.
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« Reply #6 on: September 09, 2007, 12:12:25 PM »

Tom - depending on the degree of modulation, dissipation actually may not be much higher.  For a 1.5 KW output linear, dissipation is about 1,000 watts at 1500 carrier output.  At the carrier level for 100% positive modulation (375 W carrier output), dissipation is about 875 watts, and at the carrier level for 150% positive modulation (240 W carrier output), dissipation is about 760 watts.  Dissipation in a linear amp reaches a broad peak at 50% efficiency, so if it is set up for 1500W peak output, dissipation will peak at about 1041 watts dissipation with about 1041 W carrier out.
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« Reply #7 on: September 09, 2007, 04:41:47 PM »

Hi Bacon,

My reference to increased dissipation refers to comparing the normal AM signal with modulation versus the "inverted modulation" signal with modulation, both passing out a linear amplifer with 1500 Watts PEP output.

Wouldn't the average dissipation in the linear with the normal AM signal be about 560 Watts, compared to the 1041 Watts for the inverted modulation signal?
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« Reply #8 on: September 09, 2007, 06:47:40 PM »

Tom
Bacon
et. al.

It would seem to me that, as a practical matter... we would want to make the comparison for the case where the operator is silent (between syllables or thinking about what to say next). Even for those of us (including me) who are old buzzards... most of the time, the audio level will be close to zero... and that is what will govern such things as average power consumption (using electricity/heating the room) and plate dissipation.

The exception might be people who spend their on-air time transmitting a 100% modulated sine wave tone.

Best regards
Stu
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« Reply #9 on: September 10, 2007, 01:27:11 AM »

Dissipation with a typical linear amp tuned for 1500W would be 540 watts at a carrier output level of about 97.5 watts.  Efficiency would be about 60 * ((1500/97.5) ^ 0.5) = 15.3%, so input power would have to be 97.5/.153 = 637.5 watts, and dissipation would be 637.5 - 97.5 = 540 watts.  This would permit positive modulation of ((1500/97.5) ^ 0.5) - 1 = 2.92 or 292%.  Alternatively, positive carrier control could be used, and positive modulation could be more like 200%, 150%, 100%, etc, or even 67% or 50%, etc, if the voice polarity was inverted.

Operation at 50% efficiency at 1041 watts output would allow 1500/1041) ^ 0.5) - 1 = 0.20 or 20% positive modulation, allowing a 5:1 asymmetry in the speech audio, or allowing whatever negative dynamic adjustment would be needed for the required modulation percentage.  Carrier input power would be about 2082 watts.  This might be best, so that the leading edge of an initial sound would not be clipped in the positive direction before the carrier control could act, although a slight delay in audio versus carrier control would allow these dynamic distortions to be avoided.

Figure we are using a class B linear amplifier tuned for 1500W PEP.  Figure six conditions: an unmodulated carrier of 1500W output, a carrier level of 666.667 watts for 50% positive modulation (for 2:1 asymmetry, negative pointing), a carrier of 540 watts for 66.667% positive modulation (for 1.5:1 asymmetry, negative pointing), a carrier of 375 watts for 100% positive modulation, a carrier of 240 watts for 150% positive modulation, and a carrier level of 167.667 watts for 200% positive modulation.

full pep output
carrier output power: 1500 watts
carrier efficiency: 60%
input power: 2500 watts
dissipation at carrier level: 1000 watts

50% positive modulation, 1500W pep output
carrier output power: 666.667 watts
carrier efficiency: 40%
input power: 1666.667 watts
dissipation at carrier level: 1000 watts

66.667% positive modulation, 1500W pep output
carrier output power: 540 watts
carrier efficiency: 36%
input power: 1500 watts
dissipation at carrier level: 960 watts

100% positive and negative modulation, 1500W pep
carrier output power: 375 watts
carrier efficiency: 30%
carrier input power: 1250 watts
carrier dissipation: 875 watts

150% positive modulation 1500 pep output
carrier output power: 240 watts
carrier efficiency: 24%
input power: 1000 watts
dissipation at carrier level: 760 watts

200% positive modulation, 1500W pep output
carrier output power: 166.667 watts
carrier efficiency: 20%
input power: 833.333 watts
dissipation at carrier level: 666.667 watts

Yes, dissipation is generally higher at the higher carrier levels, but not that much.  Is the extra few db of receiver quieting between syllables worth it?  Maybe.  Or, we could live with existing limitations, or we could switch to audio-derived AGC and use lower carrier levels.

If we use reverse carrier control, the receiver AGC time constant needs to be rapid for best performance.  But most of us use fairly fast AGC with envelope detectors, because we want the receiver to recover quickly after a strong signal.  And the audio processing and TX audio delay versus carrier control at the transmitter can compensate for the receive AGC tme constant.  In fact, the attack time of a transmit speech processor applies the right kind of compensation.

Positive carrier control emphasizes the noise between syllables, and it doesn't sound good.  Reverse carrier control sounds pretty good, and it reduces noise between syllables on an average-envelope derived AGC such as we have in classic AM receivers.  The the peak-envelope derived AGC of typical solid-state receivers stinks, because it compresses the receive audio, which messes up the received audio dynamics.

The issue is the extra power consumed during times of no transmit audio, and to a lesser extent the power dissipated in the transmitter during periods of no speech.  But this is very much like the argument about using a carrier at all.  We could keep our quality, and save a lot of power, by using DSB reduced carrier, and synchronous detection, and well-designed AGC.  And, we could get get useful noise reduction by using dbx or Dolby compansion with that (I think something like Dolby B would be best, so as not to blast us in the ears when interference overwhelms our signals).  But we prefer full-carrier AM.

It's just a thought.
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« Reply #10 on: September 16, 2007, 01:11:24 AM »

750 watts carrier (output), 100% modulated (in the positive and negative direction - sine wave) comes out to 1500 watts total, peak power on any spectrum analyzer.  Computations as follows:

A 750 watt (carrier) (RMS) 100% modulated (sine wave) signal breaks down like this ->  1/2 the (RMS) power is in the sidebands, or 375 watts of total sideband power (RMS).  The PEAK *power* in the sidebands is 749.7735 watts (750 watts), plus the carrier power of 750 watts comes out to 1500 watts.  This comes about because the peak *voltage* is 1.414 times the RMS voltage, which, when squared comes out to be 2 Power = (Voltage squared / Resistance), so the peak audio (sideband) *power* works out to be twice the RMS power.

You can think about it like this:  You have 750 watts of carrier.  That doesn't change.  You have a modulator that must supply 375 watts of RMS *power* into a known load (the RF ampflier).  Let's say you're using an RF amplifier that is 100% efficient, and has an impedance of 500 ohms (any numbers will work - I just chose these).  The RMS audio voltage required is 433 volts.  The peak audio voltage is 612 volts.  The peak audio *power* is (612 **2) / 500 = 749 watts.

For "real" RF amplifiers, with less than 100% efficiency, the output of all parts of the RF signal, sidebands and carrier, must be multiplied by the conversion efficiency of the RF amplifier, but everything still works out.  If the RF amplifier were, say, 75% efficient, you would then put 1kw of DC power into this RF amplifier to get 750 watts out.  The modulator power needed for 100% modulation would go from 375 watts to 500 watts (RMS).  The PEAK *power* from the modulator would go from 750 watts to 1kw.  The carrier RF output would be 750 watts (1000 * .75), and the PEAK sideband output power would be 750 watts (both sidebands added together) - 1KW of PEAK sideband *power* multiplied by the .75 efficiency factor.

No power was created or destroyed in this demonstration.
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« Reply #11 on: September 16, 2007, 01:44:09 AM »

There is no such thing as RMS power. Its average power and that's what you measure with most spectrum analyzers.
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« Reply #12 on: September 16, 2007, 08:07:51 AM »

HUZ Steve is right, Watts RMS is not a valid term. 

The peak power of a 750 Watt carrier with 100 % sine wave AM modulation is 6000 Watts.

Power terms can be confusing and the values are not intuitive - average power, peak power, peak envelope power. 

Since the power values of various rf modulated signals are not intuitive, therein lies some of the reason for the continuing "arguments" over what the "fair" power value is for AM versus SSB.   
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« Reply #13 on: September 16, 2007, 10:04:09 AM »

You can’t break down a modulated signal to its individual sidebands and then add the peak powers of the individual frequency components.  This is adding of time independent values.  The total peak power of the AM signal is time dependent on each of the modulation components.

The peak power of the 750 Watt carrier is 1500 Watts.  The power in each sideband is 187.5 Watts and the peak power of each sideband is 375 Watts, but I don’t see that you can pull the 2 sidebands out of the AM signal and just add them together (you can, but...).  This addition is 1500 pk +  375 pk + 375 pk = 2250 Pk., which is incorrect.  The composite signal’s peak power is 6000 Watts.

All of this discussion is completely moot if no one gets on the air with the Inverted Amplitude Modulation.  You’d think that Don K4KYV would be one of the first on with inverted modulation and would be doing it for many years now, because this would allow him to run 1500 Watts carrier output legally, essentially twice what was allowed BEFORE Johnny Johnston’s rule change!
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« Reply #14 on: September 16, 2007, 10:28:48 AM »

You can make it as complicated as you want.....

But right or wrong, when the little black vans pull up with their scope and dummy load,

They'll use a very simple equation....


Po=V(rms)/R


How they determine how you USUALLY operate your station...I have no clue.....

Dust on the knobs?

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« Reply #15 on: September 16, 2007, 11:02:56 AM »

Well if the men in black use that equation, every ham will come out o.k.

But if the one of the men (or women) in black is a degreed engineer, I expect he (or she) will use:

P = E2/R.
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« Reply #16 on: September 16, 2007, 11:37:35 AM »

You can make it as complicated as you want.....

But right or wrong, when the little black vans pull up with their scope and dummy load,

They'll use a very simple equation....


Po=V(rms)/R


How they determine how you USUALLY operate your station...I have no clue.....

Dust on the knobs?



Having dealt with the FCC before, I can tell you this:

Before they EVER come knocking on your door, they already know your effective Pout, off the front side of the antenna.  It doesn't take an idiot to see that it takes more than a 5 element beam to equate to a megawatt of ERP.  The FCC, contrary to what we all WANT to believe, doesn't hire idiots.

OTOH, 11 meter enforcement has picked WAY up, I've heard.  Three stations busted running high power this last month...  Very wide signals (running Johnson tube TXs, widebanded, etc).

The last station was allowed to keep his final PA.  They took his "driver" and his two export style radios. 

Yes, they have been to my house, no they didn't get any equipment.  Yes, I got into an argument about just the same kind of thing here:

1.  Legal output is 4 watts carrier at 100 percent modulation.

How can you have a 100 percent modulated carrier when your limited to 12 watts PEP?  That was a question that NONE of the people sitting in my radio room could answer...  And it really ticked off the local FCC Field Inspector, with a 15 yr old kid asking him a question he couldn't answer.


They came into my house with a termaline load.  I'm expecting since it was CB related, they didn't expect to find any ladder line or other such stuff.  The dusty old tram tube DSB transmitter did a whopping 4+ watts output.  He told me to retune the output network for 4 watts, as delivered into a dummy load.  I wasn't going to ask what happened when I hooked up a reactive antenna and the Pinput shot up.

Since I moved to the amateur radio category, no more neighbor problems, etc.  No more FCC at my door, either.

Shane
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« Reply #17 on: September 16, 2007, 01:19:49 PM »

From Part 95 on Personal radio services -

95.410 (CB Rule 10) How much power may I use?
(a) Your CB station transmitter power output must not exceed the following values under any conditions:
AM (A3) – 4 watts (carrier power) SSB – 12 watts (peak envelope power)

(b) If you need more information about the power rule, see the technical rules in subpart E of part 95.


In subpart E:
95.639 Maximum transmitter power. ( I didn’t see any further ramifications for voice phone.)

In 95.667, there is a 10 W dissipation limit on the final amplifier components, using the manufacturer’s component data.
- - - - - - - - - - - - - - - - - - - - -

The rule seems quite explicit to me.  They should have been able to answer the question.  Maybe the field people are idiots.

The 12 Watt PEP rule applies to SSB mode, not AM.  In AM with a 4 watts carrier out, the PEP is 16 watts, which is fine.
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« Reply #18 on: September 16, 2007, 01:56:43 PM »

From Part 95 on Personal radio services -

95.410 (CB Rule 10) How much power may I use?
(a) Your CB station transmitter power output must not exceed the following values under any conditions:
AM (A3) – 4 watts (carrier power) SSB – 12 watts (peak envelope power)

(b) If you need more information about the power rule, see the technical rules in subpart E of part 95.


In subpart E:
95.639 Maximum transmitter power. ( I didn’t see any further ramifications for voice phone.)

In 95.667, there is a 10 W dissipation limit on the final amplifier components, using the manufacturer’s component data.
- - - - - - - - - - - - - - - - - - - - -

The rule seems quite explicit to me.  They should have been able to answer the question.  Maybe the field people are idiots.

The 12 Watt PEP rule applies to SSB mode, not AM.  In AM with a 4 watts carrier out, the PEP is 16 watts, which is fine.

The problem arises with AMC / ALC (and in the earlier rigs, the generation method of SSB / DSB)  in the CB radio rigs.  When adjusted (the cheaper radios, or the old OLD radios) for 12 watts PEP, they won't DO 16 watts PEP linearly.

When adjusted (drive / mic / AMC / ALC levels) for 16 watts PEP, they don't DO 12 watts PEP.

Compound that with radios that didn't have amc / alc (before the rules effected them), and you have real problems.

I had a DSB, limiterless radio at the time.  Talk about having to "ride the mic gain" to keep legal... hahaha.  It was designed and marketed around the time of 5 watts DC input.  It did that, on output.

Later in life, to get around the ambiguity, manufacturers tried all sorts of things, including different output networks for SSB and AM. 

Of course, I come from the school that to do it PEP, an amplifier must also do it in carrier power.  That blows away ICAS, though. 

And another question, then.  If a 4 watt carrier equates to 16 watts PEP, then how do you arrive at 6Kw for a 750 watt carrier?  Wouldn't it be more like 32 watts PEP?  UGGGH more confusion.

Shane
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« Reply #19 on: September 16, 2007, 02:03:55 PM »

There is no such thing as RMS power. Its average power and that's what you measure with most spectrum analyzers.

Well, it could be that all of my college professors, when I was getting my EE were wrong :-)  But, we did in fact use RMS and peak (and average) for various calculations.

The whole discussion about measuring power on AM is very interesting, and has been going on for many years.  An AM signal is, in fact, a composite signal comprised of 3 individual, distinct components.

If I operate a double sideband transmitter with a total output of 375 watts - 1/2 of this power in each sideband, and operate another transmitter putting out a 750 watt carrier, and assuming everything is in phase and properly combined, or is transmitted into two different antenna systems, where can you prove to me that there is 3000 watts PEP?

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« Reply #20 on: September 16, 2007, 02:18:28 PM »

There is no such thing as RMS power. Its average power and that's what you measure with most spectrum analyzers.

I guess if we really want to get technical about it, my spectrum analyzer displays voltage :-), and it will measure peak, quasi-peak, average and RMS depending on how I set it.  Nice for this sort of thing!

Regards,

Steve
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« Reply #21 on: September 16, 2007, 02:28:35 PM »

You can make it as complicated as you want.....

But right or wrong, when the little black vans pull up with their scope and dummy load,

They'll use a very simple equation....


I've got it covered: I'm going to mount my final amp right at the antenna feedpoint.

When the black van shows up, I'll just point to the top of an eighty-foot tree ....

Bill
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« Reply #22 on: September 16, 2007, 02:30:28 PM »

Well if the men in black use that equation, every ham will come out o.k.

But if the one of the men (or women) in black is a degreed engineer, I expect he (or she) will use:

P = E2/R.


well, yes, I skipped that didn't I....?
oh well,
no ones prefect......
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« Reply #23 on: September 16, 2007, 02:42:55 PM »

Steve
et. al.

First, as a tongue-in-cheek comment... these analyses remind me of the analyses that "technical experts" put forward in legal proceedings... in which each side is trying to redefine whatever it is that needs to be proven... so that they can prove whatever it is they wish to prove.

An AM signal at the carrier frequency of 3.885 MHz has the form:

v(t) = A sin (3,885,000 x 2 x pi x t) x [ 1 + m(t)]

where m(t) is the modulating signal, and will be assumed to take on a peak positive value of 1... i.e., 100 positive peak modulation.

A is the amplitude of the unmodulated carrier

pi = 3.14159.....

t = time (seconds)

Furthermore, we will assume that m(t) has a bandwidth that is much, much less than 3.885 MHz.

If we observe v(t) on an oscilloscope, then it looks like a sine wave whose amplitude is slowly varying, and where the peak amplitude (for many, many cycles of the 3.885 MHz carrier) is 2A.

During those times when the amplitude of v(t) is close to 2A, the power associated with v(t) is 4 times (2 x 2) larger than when the amplitude of v(t) is "at a carrier" (i.e. =A)

So.... if we define peak envelope power as proportional to the maximum of the square of the amplitude of the slowly-varying (modulated) carrier... then we conclude that a 100% modulated carrier has a peak envelope power that is 4x the power of the unmodulated carrier.

Getting back to my comment about arguments that "technical experts" put forward in court rooms during litigation...

If you define peak envelope power in a totally different way... for example, the sum of the powers in the carrier and each of the two sidebands of an AM signal that is produced when a carrier is being AM modulated by a sine wave audio signal, then you get a different answer for what the peak envelope power is.

If you define peak envelope power in yet another way... e.g., the way that Steve is defining it... then you get yet another answer for what the peak envelope power of a 100% AM modulated (by a sine wave audio signal) carrier is.

The real question is: what objective (measurable/reproducible/unambiguous) definition does the FCC have in mind when they refer to the peak envelope power of a modulated carrier.

I believe that (for better or worse from the perspectives of those who wish it was something else), they meant the square of the amplitude of the waveform  v(t) = A sin (2 x pi x carrier frequency x t) x [1 + m(t)], where m(t) is a modulating signal whose bandwidth is much, much less than the carrier frequency, at a point in time where m(t) assumes its peak positive value.

Best regards
Stu
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Stewart ("Stu") Personick. Pictured: (from The New Yorker) "Season's Greetings" looks OK to me. Let's run it by the legal department
Bacon, WA3WDR
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« Reply #24 on: September 16, 2007, 03:16:26 PM »

Indeed it is possible to have some sort of isolated dual-feed antenna and put 750 W PEP DSB into one port, and 750W carrier into another port, and the peak measurable transmitter power, measured as the FCC prescribes, will be 1500 watts RMS, and yet a 3000W pep dBd erp output will be produced (minus any minor antenna losses).  And it's perfectly legal - because if that's illegal, then hams with beams had better drop their TX output!  The only problem might be neighborhood EM limits - just as with a beam.

Somewhere, the FCC defined peak power as the maximum RMS RF waveform value at the peak of modulation.  Because modulation is very slow compared to the RF waveform, and the RF is relatively narrowband, the RF waveform is essentially a sine wave (except for Ultra-Wideband, which we don't use below UHF), and there are plenty of cycles of RF to measure during a modulation peak whose level does not measurably change during the measurement.  When we have a sine wave like that, it is a simple matter to determine the power, whether we report it as instantaneous peak, RMS, etc.  I think that the FCC has that one covered pretty well.

It is true that the instantaneous peak level of a sine wave is 2X the RMS level, so a 1500W RMS sine wave would have an instantaneous peak power of 3000W.  But that does not mean that the sine wave power is 3000W RMS; clearly, 1500 does not equal 3000.  The FCC spec refers to the RMS RF level at the modulation peak.

It's a shame, because in reality the peak permissible AM PEP power was unlimited before June of 1990.  The FCC stooped to impossible splatter limits to bust W3PHL way back when; 100W PEP would have failed their infinite suppression requirement too.  They might have limited us to 125% positive like broadcasters, or maybe 150% or 200% positive, but what about SSB or DSB suppressed carrier, they must have a million percent positive.  So the FCC smirkingly went with PEP, costing us (typically) 3dB or more.

A 3dB loss isn't much when a station has good audio and a good antenna.  Even a 6dB loss isn't deadly with the rock-crushing signals even a 500W transmitter can produce with a good antenna system.  What's a shame is that it was done at all, and that it was presented deceptively by the FCC - 'level playing field' jive, and speciously citing K1MAN's supreme court challenge as coming from all AMers - but jive from the FCC was nothing new, as PHL Fred knew.
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Truth can be stranger than fiction.  But fiction can be pretty strange, too!
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