[AMRadio] Power Levels

[Bob Bruhns]

Oops, darn typo...  down near the bottom just before the PEP
equations, I wrote:
"An equation for PEP of an AM signal.: PEP = ((M+1)^2)C,
where M is the modulation factor.  100% modulation would be
M=1, 200% would be M+2, etc."

That last section should have read "200% would be M = 2,
etc."

  Bacon (the amateur typist), WA3WDR

----- Original Message -----
From: "Bob Bruhns" <bbruhns at erols.com>
To: <amradio at mailman.qth.net>
Sent: Sunday, June 30, 2002 4:19 PM
Subject: Re: [AMRadio] Power Levels


> Hi Dave,
>
> Classical AM has a carrier, an upper sideband and a lower
> sideband.  However, the power is not distributed 1:1:1
> (carrier/usb/lsb) unless supermodulation is used.
>
> I refer to classical or classic AM to distinguish it from
> compatible modes such as asymmetircal sideband used in
> analog television broadcasts, and similar techniques
> sometimes used in AM broadcasting to avoid adjacent
channel
> interference.
>
> If you had a classic 100% modulated AM signal on 1000 KHz,
> modulated by a 1 KHz sine wave, it would have a carrier at
> 1000 KHz, an upper sideband at 1001 KHz and a lower
sideband
> at 999 KHz.  The following would be true:
>
> 1) The energy in the upper sideband would be equal to the
> energy in the lower sideband.
>
> 2) The peak RMS sideband energy in both sidebands
combined,
> averaged over one RF carrier cycle, would be equal to the
> carrier level.  (This way, they cancel to zero at the
> negative peak.)
>
> 3) The RMS energy in each sideband would be 1/4 of the
> carrier level.
>
> #3 seems strange, after #2, but it is the case.  In this
> example, the upper sideband is a CW signal at 1001 KHz and
> the lower sideband is a CW signal at 999 KHz.  Take the
> carrier away, and you get a 2 KHz beat note.
>
> Remember, we said this was a 100% modulated classic AM
> signal.  In this example, if the carrier level is 1.0V
RMS,
> the upper sideband level will be 0.5V RMS, and the lower
> sideband level will be 0.5V RMS.
>
> The sidebands are on different frequencies, so one is
> cycling faster than the other, and it is alternately in
> phase, and out  of phase, with the other sideband.  As the
> upper and lower sideband add and subtract from each other
> (that 2 KHz beat note), the voltage adds to 1.0V RMS when
> the two sideband frequencies are in phase, then drop to 0
> when the two sideband frequencies are out of phase, then
add
> to 1.0V RMS when the two sideband frequencies are in phase
> again, and drop to zero when the two sideband frequencies
> are out of phase again, and so on.
>
> When we add the carrier, of course we get carrier level
when
> the sidebands cancel each other to zero, but we get either
> 2X carrier level when the sidebands add to 1.0V RMS, if
the
> combination at that point is in phase with the carrier, or
> we get 0 level when the sidebands add to 1.0V RMS, if the
> combination at that point is out of phase with the
carrier.
> In this example, the sidebands produce peaks of 1.0V RMS
> that are alternately in phase and out of phase with the
> carrier.  This results in 100% positive and negative
> modulation.
>
> The interesting thing is the power levels involved.  Since
> two 1.0V signals (the carrier, and the combination of the
> two sidebands), of equal power levels, are adding to
produce
> a 2.0V RMS positive peak, wouldn't you think the peak
power
> could only be 2X carrier level?  But it doesn't work that
> way.  The voltage is doubled, and the peak power is
> multiplied by 4X.
>
> Likewise, if there is 1/4C power in each sideband then
> wouldn't that add up to 0.5X power total, and wouldn't
that
> only modulate the carrier partially?  No, because that
> analysis is static, that is it does not allow for the 2
KHz
> beat, it just takes the average.
>
> In fact, the total signal energy increases exactly in that
> way, to 1.5X carrier power with 100% sinusoidal
modulation,
> if you take the composite signal RMS over a full cycle of
> modulation, or several full cycles of modulation, or over
a
> long period of time.  But the instantaneous power varies
> during this time, because of the beat note, and because
the
> combined sidebands are alternately in and out of phase
with
> the carrier.  The average power levels are squeezed into
the
> varying AM envelope, and this is how two sidebands of only
> 1/4C each add up with a carrier of 1C to produce positive
> peaks of 4X carrier (RMS taken over one carrier cycle),
and
> average power of 1.5C (RMS taken over one modulation
cycle,
> or an integer number of modulation cycles, or over a long
> period of time).
>
> So if I understand the example (classical AM at 100W PEP
> output, with sinusioidal modulation?), you would have 25W
> RMS carrier output, 6.25W RMS in each sideband, and 100W
RMS
> PEP.  (Remember that RMS in the context of PEP is taken
over
> one RF carrier cycle.)
>
> 33-1/3W carrier with 33-1/3 W in each sideband would add
up
> like this: 1.0C RMS carrier + 1.0C RMS USB + 1.0C RMS LSB
=
> 3.0C peak = 3 x 3 = 9X carrier level on peaks, so you
would
> have 33-1/3 x 9 = 300W PEP.  Modulation percentage would
be
> 1.0C +/- 2.0C SB, or 200% modulation.
>
> Note that compared to 100% modulation of a 33-1/3W carier,
> which would require only 16-2/3 W total from both
sideands,
> or 8-1/3W from each sideband, 200% modulation requires
> 33-1/3W per sideband, so you need 4X the modulator power
for
> a 2X increase in modulation.  That's why we like high
> modulation perentages; the sideband energy increases
> quickly.
>
> An equation for PEP of an AM signal.: PEP = ((M+1)^2)C,
> where M is the modulation factor.  100% modulation would
be
> M=1, 200% would be M+2, etc.  So with 100% modulation,
> M = 1,
> M + 1 = 2,
> 2^2 = 4 (2^2 means 2 squared),
> so PEP = 4C.
>
> With 200% modulation,
> M = 2,
> M + 1 = 2 + 1 = 3,
> 3^3 = 9,
> so PEP= 9C.
>
> A few good references:
>
> The older ARRL Handbook issues, maybe 1981 and back
>
> Radio Engineers Handbook, by Frederick Terman, McGraw-Hill
> 1943
>
> The Mechaics of Modulation" by Paul R. Huntsinger, October
> 1931 QST, with a missing figure or to appearing in
> Corrections, QST, November 1931 (page 34).
>
> "Lop Sided Speech and Modulation" by George Grammer,
> February, 1940 QST
>
> "A Course in Radio Fundamentals" by George Grammer (Part
6 -
> Modulation, QST November, 1942)
>
> Also look over anything you can find by John. R. Costas,
> W2CRR.  (I don't know whether he is still living, so his
> callsign may be reissued by now.)  Also look for Norgaard.
> These guys were pioneers in sideband, and they were
fooling
> with DSB with and without carrier.  Costas is also famous
> for the Costas-loop, used in Phase Locked Loops to this
day.
>
> Bacon, WA3WDR
>
>
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