# Final RF envelope of FM and AM are the same

https://masi.vuse.vanderbilt.edu/images/0/0b/EECE_252_Final_Project2.pdf

Page 2 spectrum plots.

Effective RF electromagnetic power profile is effectively the same for baseband audio content modulated by AM or FM.

Question, Is this right?

**UPDATE

Based on this,

"a 1 kHz tone at maximum volume would make that frequency vary by plus or minus 75 kHz.  So 1,000 times per second, the carrier wave would sweep up to 97.175 and down to 97.025"

I would conclude that the RF power envelope should show something very different from FM to AM. In fact, the FM power plot should literally be flat, or spread spectrum power.

• On your update, I guess your are assuming an umodulated carrier of 97.1MHz, yep I think you are... BUT the power spectrum would not be flat unless the modulating waveform shape were a triangle wave causing the carrier to move linearly up and down in the spectrum. A sinewave modulation would congregate more energy at the frequency extremes because of its shape. BTW I wouldn't use the term spread-spectrum in this analogy because that tends to be exclusively used for modulation methods that either use multiple carrier frequencies or frequency hopping mechanisms. Aug 24 '13 at 22:32
• Wow,mind bender. Can't visualize that. The sine wave hits each point and moves on. So I guess the area under the curve closer to where it inflects is more than the area where it crosses zero. Aug 24 '13 at 22:48
• No wait, it crosses the middle point , the carrier freqeuncy twice each period, but hits the outlying extremes only once per period, once each side. Aug 24 '13 at 22:53
• So, you're saying then if we look at the FM plot , it is as peaked as it is, because that is such a narrowband FM signal, and a wideband FM signal is much more hump shaped at best. Aug 24 '13 at 22:54
• If the carrier (in an FM system) is moved up and down to a maximum of +deviation and a minimum of -deviation and this movement is linear (i.e. caused by triangle wave modulation), then the spectrum is flat across the extremes of maximum and minimum deviation. If it were "moved" by a sinewave, the spectrum would tend to have more energy closer to the max and min deviation points. The pictures you have linked are very poor at describing this and look more like the modulation is by data i.e. square waves. Aug 24 '13 at 23:57

Let me start by saying that the document you refer to compares AM with narrow-band FM and I would expect pretty similar results. Narrow-band FM is not used by music broadcast stations just in case you were wondering and my previous mentions of FM in other questions were based around conventional broadcast type FM.

Why is it narrow band -

Conventional broadcast modulators have a frequency deviation of 75kHz and generally limit the audio baseband to 15kHz. In other words the ratio of deviation to baseband width for broadcast is 5:1 whereas the document you are referring to has a ratio of 0.25 - that's a whopping difference of 20:1 and so you need to compare apples with apples.

I also note that in the linked document there is a discrepency in the amplitudes of the AM and FM signals. See below: -

Now this doesn't seem reasonable but it may be explained by someone!! With a mind to examining the total power in the AM and n-b FM cases, it seems to me that the AM signal with its double sidebands has much more power than the FM signal.

Hopefully someone might explain this discrepency in my thought process. I guess I'm looking at how much blue ink there are on both diagrams and there appears to be more blue (and hence power delivered to an antenna) in the AM case compared to the FM case.

In short I have doubts about this document with respect to what it is trying to demonstrate and its methods.

And now, to the OP's question (at long last)

Effective RF electromagnetic power profile is effectively the same for baseband audio content modulated by AM or FM. Question, Is this right?

According to the linked document it is not. However, there is no doubt that it should be and for narrow band FM versus AM I would expect about the same resiliance to broadband noise. I would also point out that resiliance to broadband noise is of academic interest but is not, by any means the whole story in determining system A against system B.

Neither of the modulated signals in this report correspond to real world radio signals. The AM signal is double sideband (DSB) which is why there is no signal at the carrier frequency (40 kHz) in the spectrum plot.

Indeed, according to the paper, the AM signal was generated by a direct multiplication of the modulation signal and the carrier which is the definition of DSB.

Broadcast AM radio uses normal AM modulation in which the carrier is multiplied by a constant plus the modulation signal resulting in a spectrum containing the sidebands with the modulation information and a spike at the carrier frequency. The FM signal is narrowband which can be seen by the spectrum of the signal.

In broadcast FM, as pointed out by Andy, the parameters for deviation and modulation bandwidth lead to a much wider bandwidth signal than the modulation. In fact, the advantage of FM over AM in terms of signal to noise ratio arise from this increase in bandwidth. For an explanation of this, look in any communications textbook.

I would also point out that the vertical scales in all of the plots are labeled a.u. which I am assuming stands for arbitrary units. That means you should not directly compare the amplitudes of the AM and FM spectras.

Also, Andy, the scale in the FM plot has a ${10}^4$ factor so the amplitude is actually $2.5 \times {10}^4$ or 25,000, not 2500.

• SO I can measure the frequency deviation of an AM signal? It seems looking at the referenced plots that doing so is a fait accompli. Aug 24 '13 at 21:37
• @Barry - well spotted about the $10^4$ - I guess this document is just as arbitrary as the units along it's y axis Aug 24 '13 at 22:28