AM Modulation calculator

[w1vtp]

This might come in handy for the Flexers or whomever has a reasonably calibrated frequency domain display (make that panadapter). The scale of the panadapter has to be in dB.

Input only in the yellow fields or you will lose the math.  You can do it either way: input % modulation and see what to expect for sideband level or input SBdBc and see what the APPROXIMATE % modulation is.  This might be especially handy if someone is asking if their modulation is high enough.  For the Flexers - this works best without the AVG or PEAK turned on.  You will have to use your calibrated eyeballs to see what the modulation SB peaks are in relation to the carrier.

Al

[WD5JKO]

Thanks Al,

  I just used that spreadsheet on my retro75 project.

Going from 50% modulation to 100% quadruples the sideband power
Going from an average of 60% modulation to 90% doubles the sideband power

Moving a rigs upper mod percentage limit from ~ 70% to 120% seems to give the headroom for at least doubling the sideband power. This is a big plus especially with QRP AM.

Jim
WD5JKO

[KF1Z]

Won't this only show you your peak modulation on one frequency?  ( AF )

It doesn't take into account the total audio power contained in the filter passband..

I hear  people, such as Steve QIX, who say their modulation peaks are "well above 100%", but never see any part of his sidebands come close to -6dbc


I mean, yes, if you could be mono sylabic ( or inject a sinewave ) and it shows on the panadapter as being -6dbc.
Sure, it does represent 100% modulation.

But now let's say you have injected say 6 tones, within a 3 khz passband. Spaced 500hz.

the level of all 6 ( well, 12 actually, 6 in each sideband) is -6dbc.

Is this STILL 100% modulation?

Or even better, inject a wide-band noise generator , so that the level of the noise is fairly flat from 0 to 3khz, at -6dbc...
Still 100% modulation?

[KA2QFX]

Bruce,
You make a good point. The breadth of frequencies used to modulate a typical AM carrier comprise a variety of phasor sums whose net resultant amplitude in the time domain, and resultant affect on carrier amplitude, bears little resemblance to the power/hertz representation in the frequency domain. 
Maybe that's why the FCC finally determined that legal limit for AM be the "same" as for SSB.  The math regarding bandwidth and power distribution was too hard for them  and couldn't be measured with a Bird.

[w1vtp]

Bruce

Using the frequency domain  as a % modulation does have its limitations.  However, it is a good way to observe low % modulation.  It is also good to check for distortion products (splatter).  I am less enamored with how high my % modulation is than the faithful reproduction of the modulation component.  Since the human voice is naturally assymetrical it is a good thing to have plenty of "headroom." 

[KA2QFX]

Just for fun, (I guess I have strange tastes) I put together a string of waveforms. First I used even harmonics, then odd harmonics and finally, as pictured below, 1, sgrt(2) sqrt(3) & 4 for the frequency relationships.
Note that each individual frequency has an amplitude of 1 and their combined peak is almost 4 (3.7).  On a spectral display if the peak were 100% modulating the carrier each individual modulating frequency would appear -17dBc. If my calculations are correct, but you get the idea.

But Al, you are certainly correct in that the spectral display will tell you more about your signal quality than any other method.

[KF1Z]

Mark,

Thanks for verifying my thoughts..
I almost deleted my post, because after I thought about it, it seemed ....... "off".

But what led me to the thought, other than as I stated, I very rarely see anyone's sidebands come up to -6dbc.
Usually, if they do, it's the energy below 100hz.
And almost always sound 'overmodulated", and grungy.
Though the SDR certainly does not minda very high level of modulation...
Steve's 150% or more is usually quite pleasing.. and I very rarely use Sync AM .


Also, These SDR's S meter is not based on the ALC as in most analog radios, so I'm told.
And it is the sum ( or possibly more complex than addition..as in your example) of the total power in the filter passband that the S-meter responds to.

So while you may see, for example, a SSB station's peaks at -73dbm ( S-9 ), the S-meter will likely read S9 +10... or some similar relationship., because of the total power in the filter passband, not just one instantaneous peak.


I thought about that, and couldn't help thinking that as in my previous example, if you have one sine wave tone, at -6dbc.... then add a second tone at a different frequency, also at -6dbc on the panadapter... and assuming the harmonics of each and their sum/difference were outside the filter cut-off.

Why is it that you would not have twice the audio energy modulating the carrier?

So I guess there is some validity after all! 

I was going to try it tomorrow with a tone generator  ( NCH ) that allows many tones at once.


And if we assume that it is voice modulation,  not a single sine-wave tone, and we DO see -6dbc peaks, then we can pretty safely assume ( I think ) that the actual modulation level would be MORE than 100%, right?

[KA2QFX]

Why is it that you would not have twice the audio energy modulating the carrier?

When the phase of the two signals coincide you would have 4 times the modulator power. When they subtract obviously less, including zero.  I saw somewhere on the web somebody had a nice posting showing the animated rotating vectors involved in modulating a carrier. It was very enlightening, but I have not yet located it.

So your intuition, from observed displays, is correct.   The math experiments I did with odd and even harmonics had a more predictable periodicity but never added up as high as the sqrt series. I don't know what the period of the resultant waveform might be. But interestingly enough I did an integration of sorts over the 720 degrees just to see what the time-averaged power might be; it was 0.94, slightly more than  any of the individual waves alone which would have been .707 of course. 

Neat stuff.

[k4kyv]

Maybe that's why the FCC finally determined that legal limit for AM be the "same" as for SSB.  The math regarding bandwidth and power distribution was too hard for them  and couldn't be measured with a Bird.

It was not too hard for the Canadians when they re-wrote their power limit rule. But we must remember, Canadians are smarter than United States-ese.

10.2 Amateur Radio Operator Certificate with Basic and Advanced Qualifications

The holder of an Amateur Radio Operator Certificate with Basic and Advanced Qualifications is limited to a maximum transmitting power of:

    * (a) where expressed as direct-current input power, 1,000 W to the anode or collector circuit of the transmitter stage that supplies radio frequency energy to the antenna; or
    * (b) where expressed as radio frequency output power measured across an impedance-matched load,
          o (i) 2,250 W peak envelope power for transmitters that produce any type of single sideband emission, or
          o (ii) 750 W carrier power for transmitters that produce any other type of emission.

http://www.ic.gc.ca/eic/site/smt-gst.nsf/eng/sf01226.html#fre

[KA2QFX]

750 watts of AM carrier output without a specified PEP. I could live with that.

[w1vtp]

This is a pretty good paper on AM modulation using frequency domain. 

http://cp.literature.agilent.com/litweb/pdf/5954-9130.pdf

I got my formula from HP Application note 150-1 which was published back in the 70s. The notes on AM have served me well since I am NOT an engineer - just a tinkerer who loves this RF business.

I have included the nomograph that I made from those notes along with some "hen scratching" that I used  for my TI-35 way back then.  Later on I actually programmed a TI-60 where I could store whatever value I wanted and then used that to perform my calibrations that were AM related.  The Excel spreadsheet was derived from the formula you see scratched on the borders of the nomograph.
It is correct that you cannot directly use this formula on a complex modulation component but it still works when you want to check your modulation on a spectrum analyzer.  It is especially useful for low lever AM modulation levels.  The time domain and other methods work better when you get into the higher levels – especially differentiating from positive modulation and negative modulation. I still think the spreadsheet will be useful when it is used correctly - using a single tone.

One word on looking at AM signals with a Flex.  It is true that I too have never seen modulation sidebands close to the carrier level with folks who have lots of positive modulation and a properly adjusted transmitter.  When looking at complex sideband components, it is well to keep in mind that the power is distributed across the modulation bandwidth. It makes sense to me that that that power will be displayed as lower than 6 dBc. I’m sure that a math type could come up with a way of transforming this power over bandwidth so that one could use frequency domain but why bother.  One advantage I have using the Flex and the second receiver is that I can actually monitor the transmitted component real time on the frequency domain and see any “splatter” – and that’s a good thing

Al

[w5omr]

Amplitude Modulation is the method of superimposing intelligence on a carrier wave by means of varying the amplitude with the wave shape of the intelligence. When one looks at an AM signal on a scope with a linear horizontal sweep and a wide band pass it appears as one signal varying in amplitude. This is known as viewing the envelope. But when the band pass is narrowed keeping the carrier frequency as the center, we begin to see that the higher frequency modulation disappears, and as we narrow the band pass further, more and more of the modulation disappears, until all that is left is a carrier of unvarying amplitude.

More at http://www.qsl.net/wa5bxo/amtech.html

[KB2WIG]

"  Amplitude Modulation is the method of superimposing intelligence on a carrier wave "

Is this an anti SSB thing??


klc

[Steve - K4HX]

The phasor animation at the link below may make it more clear. Use the slider control to change the display and stop at various instants in time. The carrier is red, one sideband is green, the other yellow. The display is referenced to the carrier, so only the sideband phasors are rotating. It's like using a strobe light to stop motion (like on a timing belt) and the strobe is synced to the carrier.

As you can see, the sidebands are rotating in opposite directions. This is because the angular velocity of the each of the sideband phasors is either greater and less than the angular velocity of carrier's phasor by the modulating signal’s angular velocity (rotation rate or angular velocity is related to frequency by v = 2*pi*freq) . This means they are just slightly different from the carrier's velocity because the modulating signal is such a low frequency compared to the carrier. You can think of the upper sideband as always slightly gaining on the carrier and the lower sideband as slightly losing angular velocity with respect to the carrier.

Their phases relative to the carrier are constantly changing. Each will add/subtract with the carrier to produce the familiar envelope pattern shown. The black bar in the envelope shows the portion of the envelope produced by the vector addition of the phasors at that particular time.

http://www.amwindow.org/misc/av/phwenvanim.mov

The display is for one modulating tone/frequency. For voice, there would be many, many rotating vectors, all rotating at slightly different rates, with different amplitudes.

Hope this helps.