Modulation question

[Steve - K4HX]

But they are phase coherent and that is all that matters when measuring the power of a signal. Otherwise, you could claim a harmonic is not part of the fundamental but a separate signal. Or that a SSB signal has zero power since none of the components are in phase. Try either of those with the FCC. Good luck.

Further, most (all?) wattmeters/power meters are phase insensitive. So if the FCC hooks one to the output of your TX, all arguments about phase are irrelevant.

Finally, let's look at Part 97. The definition of PEP is:

(6) PEP (peak envelope power). The
average power supplied to the antenna
transmission line by a transmitter during one RF cycle at the crest of the
modulation envelope taken under normal operating conditions

Note the section 'power supplied by a transmitter.' It does not say multiple transmitters at one station to separate antennas. It's one transmitter and one antenna.


phase coherence: The state in which two signals maintain a fixed phase relationship with each other or with a third signal that can serve as a reference for each.

Steve

Minor comment (for clarification):

RF signals at different frequencies cannot be phase locked. They can, however, be forced to maintain a fixed frequency separation. If the frequency separation is fixed at B Hz, then they will move in and out of phase and back in phase again every (1/B) seconds.

Yes, good clarification!  I should have said the sideband transmitters are derived from the carrier signal, but of course they are on their own frequencies, so cannot [by definition] be phase locked.

This is a good discussion, even if it is a deviation from the original thread  

[AB2EZ]

Fred

Yes... I should correct/clarify (although this doesn't impact on the main results quoted regarding the required audio power to modulate a carrier):

The peak instantaneous power of a waveform that is the sum of two sine waves... whose frequency difference is a small fraction of either of their two frequencies... is: [(A+B) x (A+B)] /R.

The peak envelope power is (by definition): [(A+B) x (A+B)]/ 2R. I.e. PEP is the average power, averaged over 1 RF cycle of a sine wave whose peak instantaneous voltage (amplitude) is the same as the peak instantaneous voltage (peak amplitude) of the composite/modulated signal.

Note that the above is the defiinition that the FCC uses for peak envelope power: "Finally, let's look at Part 97. The definition of PEP is:

(6) PEP (peak envelope power). The
average power supplied to the antenna
transmission line by a transmitter during one RF cycle at the crest of the
modulation envelope taken under normal operating conditions"

The minimum instantaneous power is [(A-B) x (A-B)] /R.

The minimum envelope power is [(A-B) x (A-B)] / 2R

The time averaged power of the composite signal [the instantaneous power averaged over a time that is greater than 1/(the difference of the two frequencies)] is: [(A x A) / 2R] + [(B x B) / 2R].

Example: if a(t)= 200V sin (2 x pi x 3,800,000t) and b(t)=100V sin (2 x pi x 3,801,000t), and R = 50 ohms... then

The peak instantaneous power is 300V x 300V /50 ohms = 1800 watts
The peak envelope power is 300V x 300V / 100 ohms = 900 watts

The minimum instantaneous power is 100V x 100V / 50 ohms = 200 watts
The minimum envelope power is 100V x 100V / 100 ohms = 100 watts

The time averaged power (as would be measured with a non-peak-reading Bird wattmeter) is [200V x 200V / 100 ohms]  + [100V x 100V / 100 ohms] = 500 watts

[AB2EZ]

Steve (K4HX)

Signals at different frequencies, by definition, cannot be phase coherent. For example, a sine wave at frequency 2f will incur 2 cycles (720 degrees) of phase change for every cycle (360 degrees) of phase change incurred by a signal at frequency f. By definition, phase coherent signals are (for example) phase modulated sinousoids at the same nominal frequency, whose phases a locked.  

When sine waves at different frequencies add.. their time averaged powers (i.e. when the composite signal's power is averaged over a time greater than 1/(smallest difference in the frequencies) add.

Thus the tiime averaged power in a modulated signal is equal to the sum of the time averaged power in each of the components of the modulated signal (or, for random modulation, the time averaged power in the composite signal is the integral of the power spectral density over the band of frequencies occupied by the modulated signal).

Stu

[Steve - K4HX]

Thus the time averaged power in a modulated signal is equal to the sum of the time averaged power in each of the components of the modulated signal (or, for random modulation, the tiime averaged power in the composite signal is the integral of the power spectral density over the band of frequencies occupied by the modulated signal).

Thanks for the clarification. You are correct. The point I was trying to make was that it is not proper to decompose a signal into some subset of spectral components and claim each of these is separate and distinct in terms of power and do not add to the total power.

I'm still a little confused with the definition though.

phase coherence: The state in which two signals maintain a fixed phase relationship with each other or with a third signal that can serve as a reference for each.

Wouldn't a signal at 2x f maintain a fixed phase relationship (a 2:1 relationship) to the fundamental?

[AB2EZ]

Steve (K4HX)

I guess that one could create a different/extended definition of phase coherence, which would nevertheless be quite useful for some practical engineering purposes. For example, one could create an extended definition in which two sine waves are phase coherent if the phase change of one sine wave... in time T... is exactly N x the phase change of the other sine wave, in time T... where N is an integer.

However, to the best of my knowledge, the standard definition of phase coherence would not extend to the case you mentioned.

Stu

[KA2DZT]

Stu,

Thanks for your reply.

I've studied your comments and see the difference in the math between the instantaneous power and the PEP.  I just noticed in that first equation you were dividing by R* (a number of posts back) which I think was just an oversight.

No wonder most hams, including myself, would have so much trouble trying to understand all this correctly.

Fred

[steve_qix]

The point I was trying to make was that it is not proper to decompose a signal into some subset of spectral components and claim each of these is separate and distinct in terms of power and do not add to the total power.

The point I am making is that a power measurement that might be suitable for a relatively simple signal (such as ssb) is not suitable for a complex signal that is indeed made up of 3 distinct and frequency disparate components (signals) such as AM.  

The field day example works very well here.  I'm betting that if one were to "inspect" a field day operation, that only one component (the most powerful generated signal) would be considered when measuring the power of the operation, and the resultant combination of every signal simultaneously generated would in fact not be used.

[Steve - K4HX]

I'd bet not. The power from each transmitter would be measured and nothing else. Read the section of Part 97. It's one transmitter and one antenna.

The field day example works very well here.  I'm betting that if one were to "inspect" a field day operation, that only one component (the most powerful generated signal) would be considered when measuring the power of the operation, and the resultant combination of every signal simultaneously generated would in fact not be used.

This doesn't square with Part 97. Once again, it's one transmitter and by extension the total power output from that transmitter. Parsing the signal is not legitimate. Further, SSB is made up of distinct frequency components. So is FSK, SSTV and even CW.

The point I am making is that a power measurement that might be suitable for a relatively simple signal (such as ssb) is not suitable for a complex signal that is indeed made up of 3 distinct and frequency disparate components (signals) such as AM. 

[KA2DZT]

Steve,

If we're talking about staying below radiation limits at any given spot near many xmtrs, it is the sum of all signals hitting that spot.  How exactly all the signals would be summed up is another story.

Fred

[Steve - K4HX]

Yes, if you are talking about RF exposure, it's a different story. I thought we were talking about measuring the power supplied to an antenna.

[steve_qix]

I'd bet not. The power from each transmitter would be measured and nothing else. Read the section of Part 97. It's one transmitter and one antenna.

Ok, I bet so    But seriously,  In the case of the discussion about a field day operation, the term "component" that I used (not quoted in the above example, but it was there elsewhere in the text) means a signal as part of the field day operation, and not a sub-part of a signal.  I should have used a different word.  We are, in fact, in agreement about that.

Using PEP measurements of AM signals "constructs" a single signal out of otherwise discrete signal components, and the result is not a true measurement of the actual power.  This is not the case with CW, SSB, SSTV, and many others where PEP is, in fact, a valid measurement of the actual power.  I am not "deconstructing" a signal, I am in fact stating that I do not want to "construct" a signal that is not "really" there and then make measurements against that result.

[Steve - K4HX]

If I arranged for a visit to your station by the FCC, you'd bet your license? It's easy to bet when there are no stakes.

Using PEP measurements of AM signals "constructs" a single signal out of otherwise discrete signal components, and the result is not a true measurement of the actual power.

How so?

It is not constructing anything. It's the measurement of the total power output of the transmitter. And I don't see how it's any different for CW, SSB or any other mode. They all have "discrete signal components." The easiest example is 2-FSK. There are two easily discerned components. Should we throw away one of these when measuring the power? And what should we do with the discrete components of a CW signal?

[KM1H]

I'd bet not. The power from each transmitter would be measured and nothing else. Read the section of Part 97. It's one transmitter and one antenna.

I asked Riley Hollingsworth this some years ago at Dayton. The question was if I was in a contest or a DX pileup and controlling 2 transmitters on the same frequency into 2 amps and 2 antennas how much total power could I run?

His answer was 1500W.

Another FCC engineer might have a different answer since Ive not seen it posted in writing.

Carl

[steve_qix]

If I arranged for a visit to your station by the FCC, you'd bet your license? It's easy to bet when there are no stakes.

Hey, you try it first and let me know how you make out! 

[w1vtp]

This is how I measure W1VTP for 1500 PEP operation.

Al

PS: Couple of typos corrected

[KA2DZT]

If I arranged for a visit to your station by the FCC, you'd bet your license? It's easy to bet when there are no stakes.

Hey, you try it first and let me know how you make out! 

Hey, can Steve really do that

[Steve - K4HX]

Are you lonely Fred?   

The point is that trying to come up with technically incorrect explanations for why one can run more power on AM than as prescribed by Part 97 doesn't stand up to reality (aka a visit from the FCC), let alone technical analysis. If those who think their method of measuing power is correct, let them run it by the FCC. Or let them petition not only the FCC but the ITU and the IEEE to have the power measurement system corrected (since they claim that the current system is wrong).

To claim that AM is some how different from other modes like SSB and CW when it comes to power measurement is incorrect. First, all these modes are AM and all will show an envelope when observed in the time domain. All will show multiple spectral components when observed in the frequency domain.

[Opcom]

It's possible that the only thing that will matter is what the FCC employee sees on their meter.

Calibration ought to be simple for those without a peak meter - set the carrier to 375W, and set the scope to 2 divisions. Then when it hits 4 divisions, that is 1500W. This does not mean a 375W carrier is required for operation. It means only that twice the voltage, or 1500W, is a known position on the scope screen.

Unless the black helicopters are circling overhead, the scope ought to agree with the peak meter.

Reducing things to the lowest common denominator is a good way to get as the core. If a simple and transparent measurement shows operation is legal, then there ought never be a problem.

It's not a good bet to guess the FCC employee will give up and go away just because there is no 50-Ohm connector to be seen. There is probably a set of instructions for that situation. I'd like to see their measurement manual.

[R. Fry SWL]

Calibration ought to be simple for those without a peak meter - set the carrier to 375W, and set the scope to 2 divisions. Then when it hits 4 divisions, that is 1500W. This does not mean a 375W carrier is required for operation. It means only that twice the voltage, or 1500W, is a known position on the scope screen.

Should these measurements be made using the forward power sample of a good r-f directional coupler at the tx output connector, so as to ~eliminate the effect of load reflections on the measured values?

Or should the r-f sample source be a non-directional probe so as to include reflections in the measurements?  Of course, this would make the measurements more dependent on the load impedance and line length.

[AB2EZ]

Al (W1VTP)

In my experience, peak reading wattmeters (including very expensive models, and models like the Bird that include a peak adapter board) have too slow a response speed to capture voice peaks... and therefore, are not accurate in measuring the PEP of voice modulated signals. It is typical for these meters to produce a reading that is only around 70%-80% of PEP when used with AM transmitters.

I once had a telephone discussion with a fellow who sells a popular power meter that uses sampling/digital technology. I asked him why he intentionally designed it to be too slow to capture actual voice peaks. He told me that he had to do that so that his meter wouldn't read a higher PEP than competing products (which don't capture voice peaks). If he made his meter fast enough to capture true voice peaks... his sales would drop, because the people who buy his meters want to run higher PEP, and they don't want a meter that discloses their true PEP. I once designed my own peak detecting adapter to work with an expensive digital wattmeter... and it produced a reading that matched the scope measurement. It wasn't easy to make the peak detector fast enough, using analog components, but I was able to do it. The key limitation is the skew rate of the op-amp that drives the integrating capacitor of the peak detector circuit. That op-amp has to deliver enough current to charge the capacitor to as close as possible to the actual voice peak voltage... while the RC time constant of the integrator must be long enough to allow the meter to respond to the voice peaks.

Steve (WA1QIX) might want to comment on the challenges he encountered in designiing the analog peak detectors in his first generation modulation monitor product.  

Using a digital oscilloscope, observing the RF sample... and triggered by the modulating audio... is the best way to measure actual PEP

R. Fry SWL

You raise a very good point. If the antenna is not resonant, I suspect that the FCC would define the power limit in terms of the forward power - the reflected power (i.e. the power that is actually leaving the antenna, neglecting any resistive losses in the antenna itself).

Stu

[flintstone mop]

Stu brings up a good point about accurate peak reading monitors.
The Ham op is not impressed to see those little instantaneous 6 microsecond peaks, indicating that MAX PEP has been attained. They would like to see more of an "averaged" (peak) reading displaying the munkey swinging steady at the so called PEP.
Steve's (QIX) mod monitor showed me that I was way out in left field with my settings, for what I thought was a well adjusted AM TX.

This is slightly off-topic, but pertains to max peaks as seen on a broadcast FM monitor. (1977). College Radio 7KW ERP. And I understand that FM max modulation is bandwidth, but same consideration to FCC rules.
The Belar FM mod monitor, and that special design in the metering, would indicate 80% peaks, and the PEAK light (Real 100% FM modulation) would start flashing. The station engineer, at that time, would count how many flashes in a 5 minute period would occur.
He claimed that was the ABSOLUTE max the FCC would accept, if they came to the station for a visit. And you hope your mod monitor was recently calibrated. (Have the DJ play a song with little high-end audio).
The pre-emphasis for high freq audio would make the peak light flash more. That was the downfall of audio processing back in the 70's. The Audimax / Volumax were about the best in those dayz. The college bought an Orban processor and we could bring the modulation up to 95% looking at the meter, and the same count on the peak light.
Today FM broadcasters can take the entire modulation envelope right up to 100%.
I'm purposely not getting into any RDS or other uses of sub-carriers that would complicate adjusting the main stereo audio on the assigned freq.
Boring story over
Fred

[R. Fry SWL]

This is slightly off-topic, but pertains to max peaks as seen on a broadcast FM monitor. (1977). College Radio 7KW ERP. And I understand that FM max modulation is bandwidth, but same consideration to FCC rules.

Just to note that the total power output of an FM transmitter into a load Z having sufficient VSWR bandwidth is not a function of modulation, as it is in transmitters using some form of amplitude modulation.

[w1vtp]

Stu and others:

As far as I know this is the current accepted approach among amateur radio circles who care to measure peak envelope power (PEP).  A refinement might be to use Steve's mod monitor and backward calculate a correction factor or to use more expensive peak reading power meters that cost in the thousands (this expense will be unacceptable among most amateur radio stations and is, in my view, unnecessary).

I have had a lot of contact in my professional life with Agilent, Weinschel and others and this approach is, in my view preferred, to no effort to monitor one's PEP.  After performing the calibration procedure as outlined in my document, I have seen reasonable correlation between the scope and the 43 in the peak reading.  I understand the principle; it's a matter of accepted practice by the FCC in the amateur community.  I prefer my technique over no monitoring of PEP.  My scope shows no discernable flat-topping and reasonable correlation between the scope which I run concurrently with the 43. The degree of accuracy is another topic of discussion and probably does not fit in amateur radio circles.   My next step would be to do some calculation based on the mod monitor that Steve made that I am using or employ yet another crosscheck as outlined below regarding adjusting the duty cycle of a CW keyed transmission.

The point is to do SOMETHING if one is running enough power that might produce more PEP than is allowed in part 97.  To do nothing based on some argument of peak reading equipment inadequacy without checking the degree of that inadequacy is not, in my view, good practice.  It is not preferred to at least to have some idea what is happening with one's AM PEP.

One thing I might do is change the duty cycle of the keyed CW emission to see how the peak reading 43 performs as the duty cycle is decreased - all the while monitoring the scope to see that at least some of the RF output touches the pre-calibrated 1500 PEP point.  I think I will see the same result on the 43 as I am now seeing with a 50% duty cycle of the keyed output.  My concern is that many AMers will hide behind the argument that required equipment is too expensive or would hide behind some undefined inadequacies of currently accepted peak reading modifications of amateur grade power meters.  I prefer making the measurement based on a properly calibrated scope and if I can include a peak reading Bird all the more convenient.  But do SOMETHING!

Al

[R. Fry SWL]

...I suspect that the FCC would define the power limit in terms of the forward power - the reflected power (i.e. the power that is actually leaving the antenna, neglecting any resistive losses in the antenna itself).

If so, the only accurate means of doing that is to measure the power delivered to, and accepted by the feedpoint of the radiator.

AM broadcast stations measure power using an r.m.s. r-f ammeter in series with the lead from the matching network to/at the base of the tower.  The unmodulated r-f current into the impedance measured at the feedpoint is set so that it results in the power authorized for that station by the FCC.

When that transmitter is modulated +/-100% by a sine wave, the current reading on the r-f ammeter increases by a factor of SQRT(1.5), i.e., 1.225.

[flintstone mop]

...I suspect that the FCC would define the power limit in terms of the forward power - the reflected power (i.e. the power that is actually leaving the antenna, neglecting any resistive losses in the antenna itself).

If so, the only accurate means of doing that is to measure the power delivered to, and accepted by the feedpoint of the radiator.

AM broadcast stations measure power using an r.m.s. r-f ammeter in series with the lead from the matching network to/at the base of the tower.  The unmodulated r-f current into the impedance measured at the feedpoint is set so that it results in the power authorized for that station by the FCC.

When that transmitter is modulated +/-100% by a sine wave, the current reading on the r-f ammeter increases by a factor of SQRT(1.5), i.e., 1.225.

Your post is petty close to correct for AM B'cast. The FCC allows B'cast 125% pos peaks MAX. They are not concerned about PEP ratings for b'cast.
It's us poor AM Ham ops who got screwed into the 1500 W PEP crap. The SSB folks felt we had an "unfair" advantage over them and the 1500 W PEP regulation.
Canada is even more confusing in their rules lately.

And R. Fry, the RF power output of an FM transmitter is constant no matter if it's 10% modulated or 100% modulated. It's interesting to see the modulation of a B'cast FM transmitter on a real spectrum analyzer. The louder the audio, the fatter the bandwidth. And there are times the carrier actually disappears.
link to Bessel Null before ya'll think I'm blabbering:
http://www.fmsystems-inc.com/manuals/BESSELart.pdf
Fred