GM4ULS ham radio station

a QRM-free zone!

“You’re running HOW MUCH?”

Posted by gm4uls on November 27, 2011

As I never tire of saying, I got into this hobby because of my fascination with the medium not the technology. As a result of this I’m always learning something, even if it only sticks in my head for a short time. The other day an American operator was explaining to me how the change in FCC regulations some time ago regarding transmitter power for American hams had been good news for SSB and CW operators but bad news for enthusiasts of AM. He told me that when the upper limit was expressed as ‘1500W PEP’, CW and SSB operators effectively had their power levels increased whereas AM operators had them lowered, because the ‘PEP’ of an AM signal is equivalent to carrier power plus sideband power. He then asked me what the power limit was in the UK. I told him 400W, but that I didn’t know whether that was expressed in terms of PEP or what unless I looked it up. The reason why I didn’t know, by the way, is that I had been operating so far below this upper limit for so long that I hadn’t bothered to look into it.

“If it’s 400W PEP, you’ll be running about that with your Italian amplifier set to give you 100W,” he said.

Well, I know that the Zetagi B300P will give me 100W comfortably. In fact I cold get it to 120W I believe. So if what he was telling me was correct I was, for the first time in my amateur career, capable of operating at, close to, or over my permitted power level. Best I should find out. It took me a couple of minutes to find out that it was ‘26dBW PEP’ which is the equivalent of about 398.1W, and I communicated this to him.

Shortly after that I thought I might as well research a little more on the subject. A CB website had a handy definition of AM: ‘There are three parts that make up the composite AM signal: the carrier, the upper sideband, and the lower sideband. The information in an AM signal is contained in the sidebands. The carrier contains no information. Both sidebands are mirror images of each other and contain the same information.’ Okay so far, pretty basic stuff.

A Mcgraw-Hill textbook on line has some more information:

The output power of a transmitter that transmits an amplitude-modulated carrier is often specified in terms of its peak envelope power (PEP), which is the power that would be developed in a carrier whose amplitude is equal to the peak amplitude of the modulated carrier.

In radio transmission, the AM signal is amplified by a power amplifier and fed to the antenna with a characteristic impedance that is ideally, but not necessarily, almost pure resistance. The AM signal is really a composite of several signal voltages, namely, the carrier and the two sidebands, and each of these signals produces power in the antenna. The total transmitted power PT is simply the sum of the carrier power Pc and the power in the two sidebands PUSB and PLSB:

PT = Pc + PLSB +PUSB

Finally, we get a handy formula for computing the total power in an AM signal when the carrier power and the percentage of modulation are known:

PT = PC (1 + m2/2)

Where modulation is 100% m = 1. By that calculation if the total power of a 100% modulated AM signal is 400W, then the carrier power must be two thirds of that or about 267W, not 100W. Hmmm…

Okay, so is there more to it than that? W8JI, who seems to be an expert on Johnson Valiant transmitters and whom we can therefore trust to know something about AM has this to say about power:

One of the first things we must understand before discussing characteristics of AM is power measurement. First, there is no such thing as “RMS Power”. We find power by multiplying RMS voltage times RMS current, but there is really no such thing as “RMS power”. 

What does exist is equivalent or heating power. This is useful power over a defined period of time, even a very short time. It is power that does, or can do, some amount of actual work. Both PEP and average power are based on the heating or work power, even if that heating or work power is taken over a single RF cycle.

The old common method of quantifying RF power was average power. Average power is same as equivalent work power or heating power of each cycle averaged over a significant time compared to the time when power level changes. With an unchanging (during the measurement period) power level, such as a steady unmodulated carrier applied to a constant resistance load, average power and peak envelope power are the same. If we close and hold-closed a manual telegraph key on a good stable CW transmitter, we will see the average power displayed on a power meter. It will not be the “RMS power”.  It is also the peak envelope power, because it is the maximum stable heating power level over some period of time that we hold the key.

As for peak envelope power, peak envelope power is the very maximum short term peak reached of either steady or varying heating power levels!

Consider a sine wave with a peak voltage of 100 volts. The RMS voltage is 70.7107 volts, or 100 peak volts. If we placed that voltage across a 50 ohm resistance we would have 70.7107 / 50 = 1.414214 amperes. That would also be 100 watts average power in one complete cycle or any number of equal amplitude cycles that follow. The peak envelope power is also 100 watts because the peaks are the same cycle after cycle.

If we pulsed that power off and on rapidly with a 50% duty cycle the average power would be 50 watts. Half the time it would be 100 watts, and half the time zero watts. The peak envelope power would be 100 watts, because that would be the power at the crest of the envelope! The envelope can be as short as one cycle, although no meters ever respond to that.

Power cannot be “RMS power”. RMS is calculated by squaring the function’s value, taking the average (mean value) of the squared function, and finally converting that mean value back by finding the square root of that mean. If we had a peak power of 100 watts with a 50% duty cycle the RMS power, if there was such a thing, would be SQRT( (100^2 + 0)/2) = 70.71 watts. We see that 70.71 watts is not the average power, is not the heating or “work” power, and is not the peak power. It isn’t anything at all useful! We can have meters that read RMS voltage, and we can also have RMS current, but we don’t read RMS power with any of our power measuring instruments. We can’t even calculate “RMS power” to be anything useful or sensible at all…

Let’s consider the case of perfect undistorted sine wave modulation of an amplifier stage. The carrier, sidebands, and power levels of the various spectral components making up the signal have a certain ideal relationship. Consider the case below with symmetrical sine wave modulation.

Unmodulated carrier = 100 watts (PEP or) average carrier power (average is the same as PEP because, absent amplitude modulation, the carrier level is unchanging over time).

100% steady modulated 100 w carrier = 400 watts PEP or 150 watts average or “heating” power. Of this 150 watts average or “heating” power, 100 watts is in the carrier, and 25 watts average power is in each of the two AM signal’s sidebands.

Carrier average power = 2/3 of the total 100% modulated average power

Total of both sidebands, average power = 1/3 of total average power under 100% modulation

Average power one sideband = 1/6th average power with 100% modulation

Peak Envelope Power 100% symmetrical modulation = Four times carrier power.

Well, we get to the bottom line. By now anyone who is technically adept will be wondering why I couldn’t instantly understand something so basic. C’est la vie.

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