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RF power terms

Fig1: An AM wave displayed on a CRO

The quick quiz

Try this quick quiz:

Q1. What is the PEP (ITU pX)?

Q2. What is the carrier power (ITU pZ)?

Q3. What is the modulation index?

Q4. What is the average power ("RMS power" as it is often termed) (you are free to make additional assumptions if necessary, but you must state them as part of your answer);

Q5. When power is calculated as you have done for Q4, is it meaningful for a single channel SSBSC transmitter under voice modulation?

Note that for the the purposes of the exercise, you should assume that all components etc are perfect unless stated otherwise. This means that for instance the oscilloscope is calibrated accurately, sampling port properly terminated, the modulation process is distortion free etc.

Answers

Q1

  where Vp-p is the peak to peak voltage at the crest of the modulation.

pX=(8*20E-3*10/(10^(-40/20)))^2/(8*50)W

pX=64W

Q2

where Vcp-p is the peak to peak voltage at the crest of the modulation and Vvp-p is the peak to peak voltage at the valley of the modulation.

pZ=((8+2)/2*20E-3*10/(10^(-40/20)))^2/(8*50)W

pZ=25W

Q3

For an AM wave  

m=(64/25)^0.5-1

m=0.6

Q4

Average power is a means of expressing the (DC) equivalent heating effect of an alternating voltage and current. It requires the averaging of the instantaneous power over a period of time. For a periodic waveform, a period of one complete cycle of the periodic waveform will yield the correct result.

For an AM wave   where m is the modulation index and Pc is the carrier power.

Since this sine wave modulated wave repeats with period of the inverse of the modulation frequency, it is necessary to calculate the average power over that period, and the answer is 29.5W. This also complies with  ITU pY in this case, but that equivalence is not general.

Q5

This metric is almost meaningless for an aperiodic waveform such as voice modulation of an SSBSC transmitter, unless you were specifically interested in the heating effect (eg in EMR context). It is a challenge to measure because it requires an instrument that integrates and averages instantaneous power values over a long (perhaps unspecified) period of time.

My previous measurements of the peak to average ratio of an SSB transmitter under normal voice modulation with normal ALC indicate a value of 11dB to 15dB depending on the individual speaker and compression options. So for example, a transmitter with an RMS power (measured over a transmitter on interval or "over") of 10W may be 125W PEP to 316W PEP

Definitions

The ITU Radio Regulations define the terms Peak Envelope Power, Mean Power and Carrier Power with regard to a radio transmitter. The terms are defined as:

Note: For use in formulae, the symbol p denotes power expressed in watts and the symbol P denotes power expressed in decibels relative to a reference level.


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