modulation percentage

[KF1Z]

There's been some discussion lately here on the air about how moduation percentage is figured.

There is a chart at AM Window....

http://www.amwindow.org/tech/htm/modulation1.htm

But the math found in manuals and internet, don't seem to correspond with that chart.


So, the question is ...  what is the correct way to measure/calculate modulation percentage of an AM signal?

[w3jn]

What about the chart doesn't correspond?  Looks correct to me.

The chart's sidband power table is for ONE sideband, as indicated by the footnote.

The chart makes it easy, when using a scope, to view your instantaneous modulation percentage.  Key the rig with no modulation, adjust the scope so the pattern fills two divisions vertically, then modulate the rig and see where the positive peaks are.   Of course you can also see negative percentage as well.

[AB2EZ]

There may be people who have personal definitions of modulation percentage... and who will therefore disagree with respect to how modulation percentage should be measured.

The standard (engineering) definition is as follows.

An AM signal can be represented as A [1 + m(t)] sin [2pi x f x t)

Where A is the amplitude of the carrier
m(t) is the modulation (as function of time), and is assumed to have zero average value
f is the frequency (Hz)
t is the time (seconds)

The modulation index (in percent) is defined as 100 x the peak value of m(t)

For example, if m(t) has a positive peak value of 1.25 and a negative peak value of 0.9, the the modulation index is 125% positive and 90% negative.

Stu

[KF1Z]

Modulation Percentage = (Vpp – Vc)/Vc X 100

I'm told by people ( 5 so far) that have been into AM a LOT longer than myself, that the above equation is the way to calculate modulation percentage.

So, according to that, the chart at AM Window, is incorrect for everything above 100%.  100% and below appear correct.

Does anyone know what formula that chart wast calculated with? and/or reasoning behind the calculations?

Was there a different formula applied for percentages above 100?

[AB2EZ]

Any definition of modulation index could have been selected to be the standard definition... but the standard definition was selected based on the usual criteria: a) it has to be something that can be measured, independently, by different people, using a specified measurement methodology... to produce the same result, b) it has to provide a result that people find useful for some purpose, and c) it should be convenient for most people to interpret.


The standard definition is

100 x [V(max) -V(carrier)]/V(carrier) = positive modulation index (as a percentage)

100 x [V(carrier) - V(min)]/V(carrier) = negative modulation index (as a percentage)

Stu

[k4kyv]

Modulation percentage may be defined not to apply specifically to either positive or negative peaks, but as the mean percentage of modulation.  At one time this was how it was defined by the FCC: ratio of half the difference between the maximum and the minimum amplitudes of the amplitude modulated wave to the average amplitude, expressed in percentage (RADIO, December 1939, p. 12).

This allowed a transmitter to legally be modulated beyond 100% on positive modulation peaks, even though the regulations clearly stated "...in no case shall the emitted carrier be amplitude modulated in excess of 100 per cent".  Due to the natural asymmetry of the human voice, 100% positive peak modulation may be exceeded well before 100% negative peak modulation occurs.  For example, if the ratio of the amplitude of the positive half to that of the negative half of a particular voice waveform averages 2:1, the transmitter could be modulated to 133% positive while the modulation would go only to 67% negative, and this would not exceed 100% modulation as defined by the FCC, assuming no carrier shift is present.

This is now a moot point because the FCC subsequently removed all references to percentage of modulation in the amateur rules.  Also, the prohibition of simultaneous amplitude and frequency modulation was deleted, thus making Timtron's "SBE" rig perfectly legal.  I  suspect these changes were inadvertent, as it didn't occur to those who formulated the revised rules that amateurs were still using AM.  Ironically, at least one of these deletions occurred with the R&O of Docket 20777, which had originally proposed regulation by bandwidth in similar fashion to the recently defunct ARRL petition, but worded in such a manner that it would have effectively eliminated amateur AM below 28 mHz.

[KA2QFX]

This summarizes a discussion we had earlier this week regarding the erroneous ‘chart’ (http://www.amwindow.org/tech/htm/modulation1.htm) that is posted here for calculating percent modulation.  I hope some find it informative.

The calculated examples given were to determine “Percent Modulation” without regard to peak, average, RMS or any other definitive description.   I believe however that the information offered was intended to focus on PEAK modulation percentage. Further, it seems that the equation used was likely one found in several (a)vocational texts on the subject.

Namely:    % Modulation = 100  x Vpk-Vmin/2 x Vcarrier

This equation works for any values within 100% modulation and is derived as follows.

Modulation index is the modulating waveform amplitude divided by the carrier amplitude. The above equation effectively separates the carrier from the modulating waveform in Vpk-Vmin, yielding the pk-pk modulating waveform, or TWICE the value of the modulating waveform.  To determine the ratio of this waveform to the carrier (=  m or modulation index), the carrier must also be multiplied by 2, hence the above equation.

However, once 100% modulation is achieved the negative portion of the modulating waveform, as viewed on an oscilloscope, is removed below the baseline, and it’s (-) value no longer contributes to the proper value of the numerator in determining the pk-pk modulating waveform.  Hence, the chart was wrong for any values above 100%.

A correct methodology for determining peak % modulation is as follows;


As stated earlier in this thread by AB2EZ, and for the record, can be found in the “ITT Reference Data for Radio Engineers” handbook, and elsewhere;

The AM waveform =  A(1 + m(t))sin(2*pi*f(t))  where A is the Amplitude of the carrier and m is the modulation index such that m = amplitude of the modulating waveform/A.

For 100% modulation m would equal 1.0.  This equation represents a continuous function and may be manipulated easily to express peak, RMS, minimum or any other instantaneous value by substituting the appropriate value for m.  It is suffice to say that this is a very linear function that returns a constant ratio of peak % modulation for any given value of peak modulating waveform/A.

By the above methodology a valid method for determining peak % modulation would be;

measure the peak modulated signal amplitude, Vpeak
subtract from this the carrier amplitude leaving only the peak value of modulating signal, Vpk-Vc
Compare their ratio to determine m = Vpk-Vc/Vc
Multiply by 100

         Peak % modulation = 100 x Vpk-Vc/Vc

BTW, K4KYV's comments regarding legal definitions and limitiations lends a fascinating insight into the technical prowess, or lack thereof, of the administrative body governing such matters. 
Regards,
Mark KA2QFX

[Steve - WB3HUZ]

What was subsequently removed?

[KA2QFX]

Steve,

This chart

http://www.amwindow.org/tech/htm/modulation1.htm

appears to have been removed from the the General Technical Info page

http://www.amwindow.org/tech/htm/gen.htm

I am told that this same chart appears in several places on the internet, sometimes crediting AMfone, sometimes not.  Either way, it is incorrect.

When I get around to it....  I will be posting a nice interactive spreadsheet to my website that calculates several parameters of voltage, current, dB, sideband energy etc, for a given power and load impedance.   It's too big to attach here unfortunately.


Mark

[KA2QFX]

Steve,

My mistake. The chart is still there under "Working Aids". And it's still wrong.

Mark

[Steve - WB3HUZ]

Please supply the correct numbers and it will be changed. Many thanks.

[Steve - WB3HUZ]

http://www.amwindow.org/tech/htm/modulation1.htm


That is an old page. The current one is at

http://www.amwindow.org/tech/htm/modulation.htm


Which one is incorrect? Or are both?

[KF1Z]

I see, there's 2 different ( but similar) pages, accessed through 2 different sections.

This one appears to be the incorrect one.
http://www.amwindow.org/tech/htm/modulation1.htm
http://www.amwindow.org/tech/htm/gen.htm


This appears correct
http://www.amwindow.org/tech/htm/modulation.htm
http://www.amwindow.org/tech/htm/tutor.htm

[KA2QFX]

Steve,

The latter (later) one appears quite correct.

http://www.amwindow.org/tech/htm/modulation.htm

As Bruce said there are two pages accessible which can be corrected here but the others propagated elsewhere on the internet... oh well.   I suspect we've put this issue to bed for a few more years at least.

Thanks,
Mark

[Steve - WB3HUZ]

Good catch. I didn't realize there was still al link to the old one. It will be gone tonight!!

I greatly appreciate the help.

[flintstone mop]

Whew! I was afraid that I was illegal exceeding the modulation peaks from my TX.
Everything is good now

Fred

[k4kyv]

Whew! I was afraid that I was illegal exceeding the modulation peaks from my TX.
Everything is good now

Fred

Not to worry.  The FeeCees deleted the 100% modulation limit years ago.

The No FM with AM rule was on the books for many years, and so was the rule that in no case shall the modulation percentage exceed 100%. When the FCC "simplified" the rules and regs governing amateur radio they left out, perhaps inadvertently, the clauses "Thou Shalt Not Amplitude and Frequency Modulate simultaneously" and "Thou  Shalt Not Exceed 100% Modulation".  Perhaps they just assumed that all amateurs had  changed over to slopbucket and there was no longer any need for those references.

The standard now is "good engineering and amateur practice".