# By Bob Bruhns WA3WDR

Generally, FM does not perform as well as AM at frequencies below VHF, because selective fading really tears it up.  Still, many stations have run NBFM with reasonable results on AM receivers, because selective fading often causes a slope effect that gives the FM signal an AM component.  It sounds a little funny on an AM receiver.  It generally doesn't sound as loud as an AM signal, and unlike AM, you hear the station better while it is in a fade than you do when it peaks up.  That is because there is no slope effect when the signal peaks up, so there is no AM to demodulate.  With an FM receiver, the FM signal sounds OK when it peaks up, but it really tears up badly with interference, and when it is in a fade.  Probably advanced demodulation by DSP can improve this situation, and possibly this could make NBFM and PM roughly equivalent to AM.

Here's one of my famous Big Long Explanations.

AM, PM AND FM REVEALED!

I will try to explain FM and PM by explaining AM first.  Before I begin, let me state that FM and PM are almost equivalent, differing only in frequency response to the modulating signal.  You can simulate PM by passing the modulating signal through a 6 dB per octave rising filter response, from DC to daylight, and then applying that to a frequency modulator.  That will produce true PM.  Likewise you can produce FM with a PM modulator by passing the modulating signal through a 6dB per octave falling response, and applying that to a phase modulator.  That will produce true FM, although it has a well-known dynamic range limit at the lower frequencies.  But with enough frequency multiplication, you can get decent FM that way.  Well, it's not exactly 6 dB per octave, it's closer to 6.021dB per octave.  In fact, it is exactly 20dB per decade (10:1 frequency).  OK, on with the AM explanation.

AM

Imagine you have a clock with three hands.  One hand is long, the other two hands are of equal length, exactly half as long as the long hand.

I will use this diagram to represent AM with 100% modulated with 1 KHz sine wave audio.  The long hand represents the carrier.  The two short hands represent the sidebands.

The hands spin around at enormous speed.  In this example, the carrier hand spins at 3885000 times per second.  One short hand spins at 3884000 times per second (the lower sideband), and the other short hand spins 3886000 time per second (the upper sideband).  Mathematicians like to spin things counter-clockwise, but for this example, I will spin clockwise.

But these hands are spinning too fast to see.  So now, we make the spin relative.  Now the long hand is always pointing up at 12.  This means we are referencing to the carrier frequency and phase.  The two sidebands spin 1000 times per second in opposite directions.  Not only that, but they rotate such that they both point up at the same time, then one rotates back to the 9 o'clock position while the other rotates to the 3 o'clock position, then they rotate so that they both point down, then 3 and 9 o'clock, then straight up again, over and over.

These hands represent "trigonometric vectors" which represent the carrier and the two sidebands of a 100% modulated AM signal.  If you add these vectors to the carrier vector, you see the modulation: a positive peak of twice the carrier voltage when both short hands point straight up; a minimum of zero when both short hands point straight down, carrier level when both short hands point in opposite directions, and intermediate values between those instants.  The combined phase does not shift relative to the carrier phase, because phase differences between the sidebands cancel out, adding to and subtracting from the carrier, leaving only carrier amplitude variations.

We synthesize the sideband signals when we modulate an AM carrier.  It looks like we are raising and lowering the carrier level, and in one instantaneous sense we are, but we can also see the carrier level as constant, and the moment to moment level variations coming from heterodyning action from the sidebands.  We can work with whichever view is more convenient at the moment.

PHASE MODULATION

You can simulate phase modulation by moving the short hands a little differently.  Also, in FM and PM, we call the sidebands "sidecurrents" for some unknown reason.  It is easier to see PM this way if you use shorter hands.  So in the following example, imagine the short hands are 1/4 as long as the big hand.  If you have the big hand (carrier) at 12 o'clock, the small hands will rotate again in opposite directions, and again at 1000 times per second.  But this time, one short hand points toward 12 o'clock while the other short hand points toward 6 o'clock, then both short hands point toward 3 o'clock, then one short hand points toward 12 o'clock while the other short hand points toward 6 o'clock, then both short hands point toward 9 o'clock, then one short hand points toward 12 o'clock while the other short hand points toward 6 o'clock, over and over again.

This time, the amplitude is fairly constant.  When the two short hands are pointing at 12 and 6 o'clock, they cancel out, and you have the carrier level and phase.  When the two short hands point toward 3 o'clock, they add up to 1/2 the carrier length (remember they are extra short in this example), and they add to the carrier vector as a right triangle of carrier side = 1, sideband side = 0.5.  Total signal amplitude is the length of the diagonal or hypotenuse, which is the square root of 1 squared plus 1/2 squared, or the square root of 1.25, or about 1.118, and the phase angle relative to the unmodulated carrier is the angle whose "tangent" is 0.5 / 1, or arctan(0.5), which is about 27.6 degrees.  The same situation exists when both sideband vectors point toward 9 o'clock, but we have -27.6 degrees.  So we have a peak phase modulation of 27.6 degrees, and a little amplitude variation.

In real PM (and FM, too), we do not have any amplitude variation.  This is where the carrier level variations and the 2nd, 3rd, 4th, etc. order sidecurrents come from in PM and FM.   These "higher order" sidecurrents correspond to second, third, etc, harmonic distortion in AM sidebands, and they take up bandwidth.  Fortunately, the higher order sidecurrents have vanishingly low amplitude at low levels of phase modulation.  However, a particular carrier level and an infinite set of harmonically related sidecurrents are created by FM and PM, because the total angle-modulated signal amplitude is constant.

As you apply more phase modulation, a lot more high order sidecurrent energy is created.  This is why we go to narrow FM to reduce bandwidth.  At around a modulation index of 0.5, the 2nd and higher order sidecurrents are pretty low in amplitude, but you still have some reasonable length (amplitude) in the sidecurrents.  It is the energy in these sidecurrents that carries the sounds over the air in PM and FM, very much like AM.

More FM or PM deviation produces stronger sidecurrents, just like AM, corresponding to longer "short" hands in the example, but they also produce higher order sidecurrents that start spreading out in frequency.  This is not an overmodulation effect such as we sometimes see with AM, it is intrinsic to constant-amplitude angle-modulation (FM and PM) in general.  We can avoid it by adding some specific amplitude modulation, but that is complicated, and then we are again dealing with all of the technical difficulties of generating a varying-amplitude signal, as well as angle modulating it.

With narrowband PM and FM, we limit deviation to what we call a modulation index of about 0.5 to 1.  This corresponds to peak FM deviation of 1/2 to 1 times of the modulating frequency, or PM of 1/2 to 1 radian peak.  (A radian is about 57.3 degrees.)  In the example above, the sidebands were 0.25 carrier amplitude (1/16 carrier power) at +/- 27.6 degrees peak, which is about 1/2 radian.  With both of these sidecurrents together, the sidecurrents power is only 1/8 of unmodulated carrier power at that modulation index.  That's only 1/4 of the power in the sidebands of a 100% modulated AM signal of the same carrier power.  Each second order sidecurrent is about 33 dB below unmodulated carrier at a modulation index of 0.5.  Each third order sidecurrent is about -53dB below the unmodulated carrier level, and higher order sidecurrents are far below that.

At a modulation index of 1 (+/- 57.3 degrees peak phase modulation, and peak frequency deviation equals modulating frequency), you have slightly more total sidecurrent energy than 100% modulated AM of the same carrier strength, because the carrier level is dropping at this modulation index.  But now, some of that energy is in the second order sidecurrents.  The first-order sidecurrents are about 44% of the amplitude of the unmodulated carrier, which means they are about 1.1dB below the strength of the sidebands of a 100% modulated AM signal of the same unmodulated carrier power.  Each second order sidecurrent has about 11.5% of the amplitude of the unmodulated carrier.  This means each 2nd order sidecurrent is about 19 dB down from the unmodulated carrier level, corresponding to a 100% modulated AM signal of the same unmodulated carrier power with about 5% second harmonic distortion.  (This is not actual distortion in the angle-modulated signal, but it is "splatter" intrinsi!

c to the modulation mode.)  Each third order sidecurrent is pretty low at a modulation index of 1, around 34 dB below the unmodulated carrier level, and each fourth order sidecurrent is about 52 dB below unmodulated carrier level.  Narrowband angle modulation is not as clean as AM, although it comes close.

When multiple frequencies (such as speech) are combined to modulate an angle modulated transmitter, the bandwidth of the signal is not as wide as it would have been in the sine wave case, because the modulation index of each frequency component is less than the total.  However, sibilents will not benefit as much from this fact, because they are spectrally concentrated.

An interesting thing happens with sine-wave modulated FM and PM.  As deviation increases, at first the carrier level decreases as the sidecurrent level increases.  At certain modulation indexes, or indices, the carrier actually nulls out, and all of the signal energy is in the sidecurrents.  These points are called "Bessel nulls," and the first one happens at a modulation index of about 2.405.  This is called the "first Bessel null."  As deviation increases further, the carrier rises, peaks, and then decreases, finally reaching a second Bessel null around a modulation index of 5.52.  More Bessel nulls (the third, fourth, etc) appear around modulation indices of 8.65, 11.79, 14.93, and they go on forever.  When modulation is very linear, and a very clean sine wave is used for modulation, the Bessel nulls are very precise.  Bessel nulls are used to calibrate modulation metering equipment.

THE BANDWIDTH OF NBFM (NARROW-BAND FM)

I think it was Wayne Green who started that rumor that NBFM only takes up bandwidth equal to the deviation, and can drop to zero bandwidth at very low deviations. But that is not really true; with FM, bandwidth is very roughly equal to the modulation frequency times two plus the deviation times two. The modulation frequency multiplier factor in this equation varies from about 1.2 to 2.0 for different types of modulating signal.

There is a complicating factor, though: officially, bandwidth is considered equal to the measured bandwidth at some number of dB down from either the bulk of the spectral power (in the case of a continuously modulated signal), or from the unmodulated carrier (if it is available for comparison). I have found that different governing bodies define this differently in their radio regulations. In some cases bandwidth is defined as the width of the frequency band containing 99% of the signal energy. In other cases it is considered the width of the frequency band in which the sidecurrent strength equals or exceeds -26dB relative to the unmodulated carrier level. I believe that these definitions are approximately equivalent for a single sine-wave modulating signal, but the differences cause a great deal of confusion.

Here is the glitch: if the deviation is very low, the sidecurrent energy can fall below the official measurement limit, and bandwidth would officially be considered to be zero! However, the total sidecurrent energy in this case would have to be 20 dB or more below the unmodulated carrier level, which is not very strong. And if we completely remove the sidecurrents, which at such low deviations are almost exclusively the first order ones at +/- the modulating frequency from the carrier, then all deviation disappears, because there are no sidecurrents to cause it.

By the way, this would also hold true for an AM signal: if modulation percentage is below about 10%, the total sideband power is less than 1% of carrier power, and each sideband is below -26dB relative to the carrier level, so bandwidth would officially be zero according to those definitions. Of course, we know this is not an accurate picture of the real situation. And likewise, if we completely remove the sidebands, we lose all modulation.

SIGNAL TO NOISE IN DIRECT SPACE-WAVE, LINE-OF-SIGHT CONDITIONS (LOCAL, VHF/UHF, ETC)

FM has a capture effect that usually causes background noise to be lower than it would be for an AM signal of the same unmodulated carrier strength when envelope detection is used. For any amount of deviation above a modulation index of about one, there is a plateau of increase in S/N above that of equivalent-strength AM. In the case of FM with a modulation index of one, with strong signals, FM has a consistent 3dB advantage over AM. As signal level drops, both AM and FM get noisier, but the 3dB FM advantage holds down to the point where the AM signal has noise peaks equal to 79% modulation. Below this point, FM begins to lose its peak noise advantage. At the point where peak AM noise is equivalent to 100% modulation, FM peak noise is 1 dB worse than AM, although the FM 3dB RMS noise advantage holds for another 3dB below this. I think this advantage is due to limiting. Noise is a bunch of little vector lines ending to hang around a general length, but pointing in all ! phase directions. In FM, they sometimes point parallel to the carrier, so they are limited out. Only the vector components perpendicular to the carrier affect phase and demodulated output, and there goes 3dB of noise. In the case of AM with envelope detection, noise affects the received carrier amplitude at all phase angles.

Note that in the case of AM using synchronous detection with product detection, noise vectors perpendicular to the carrier can not produce noise output from the detector, pretty much removing removing the 3dB FM advantage at a modulation index of one.

At a modulation index of four, FM has a 15 dB advantage in S/N over envelope-detected AM at strong signal levels, but the FM peak-noise improvement falls apart very suddenly around 8dB above the point where the AM signal has peak noise equal to 100% modulation. The FM RMS advantage falls apart more gradually, dropping from 15dB at about 6dB above the point where the AM signal has peak noise equal to 100% modulation, down to a 3dB RMS noise advantage at the point where the AM signal has peak noise equal to 100% modulation, and continuing to drop rapidly below the RMS performance of narrower FM at signal levels below that. The FM RMS advantage falls 12 dB over this 6dB carrier level drop, and continues to fall at this rate as the signal continues to get weaker.

If deviation is high, as in FM broadcast, signal to noise gets very good at strong signal levels, but it falls apart at low to moderate signal levels. We experience this as crackling breakup as we drive through signal nulls and weak-signal areas. Also, signal bandwidth is much greater than AM. NBFM (modulation index of 1, or slightly less) is much better than wide FM for weak signal work.

AM is preferred over FM for aircraft communications at VHF. Partially this is because AM does not have the capture effect. A weak distress signal will be heard better under a strong signal from a nearby aircraft. Also, there is not as much of a noise burst at the end of a transmission, before the squelch closes, as there is in FM systems.

SIGNAL TO NOISE IN SELECTIVE FADING, SKYWAVE CONDITIONS (DISTANT, MF/HF, ETC)

Ordinary FM receivers using IF limiting and discriminators do not deal very well with MF and HF FM, because interference and selective fading cause intermittent complete signal cancellations that can produce relatively loud noise bursts from the receiver, similar to the crackling breakup in wide FM noted above. As FM deviation is reduced below the point where signal bandwidth becomes equivalent to AM, the amplitude of the received noise is not affected, but the signal volume drops. Really strong noise such as nearby lightning is limited in the IF and causes a limited amount of peak noise, unlike AM. But weaker noise such as weak lightning and interfering signals have a somewhatr worse effect on NBFM than on AM. Both modes benefit from some kind of audio peak clipping to limit the peak amplitude of noise blasts.

CONCLUSION

On MF and HF, I think performance is really a matter of the sideband energy and the detector technology. With current FCC Amateur rules, an NBFM transmitter can produce about the same or slightly more sideband energy as an AM transmitter, for a given official bandwidth. So NBFM has possibilities. For pure communications, SSB makes more sense.

On VHF and UHF, FM is by far the most popular mode, except in aircraft. Digital modes are becoming common, mostly for tactical security. Their performance is always inferior to a good FM system. Clean AM could be a bit more spectrally efficient than FM, but if badly set up it could be a disaster. FM tends to be cleaner if overmodulated, and overmodulation in FM systems tends to be self-correcting, because a severely overmodulated FM signal will break up badly in an FM receiver.

Overdriven SSB also splatters badly, yet this does not affect the functionality of the offending system. For this reason, and because of cost and frequency stability issues, VHF and UHF SSB is not commercially popular.

More on the subject...

BANDWIDTH OF NBFM VS. AM

Up until fairly recently, the standard for commercial NBFM was 5 KHz deviation and 25 kHz channel spacing in any given area. More recently, a 2.5 KHz deviation standard has been introduced for 12.5 KHz local area channel spacings. In both standards, 6 dB per octave rising pre-emphasis from 300 to 3000 Hz is applied at the transmitter. (This audio preemphasis essentially turns the FM signal into a PM signal.) Peak clipping is applied, so that deviation will not exceed the maximum for the standard used, and low pass filtering is applied after clipping so that the audio band harmonics generated by the clipping will be suppressed and not cause wideband sidecurrents. I will discuss the 5 KHz deviation system.

A 3 KHz audio signal at 5 KHz deviation has a modulation index of 5/3, or about 1.67. This results in second order sidecurrents at +/- 6 KHz from the carrier of about -12 dB each, referenced to the unmodulated carrier level. Third order sidecurrents at +/- 9 KHz from the carrier appear at about -23 dB each, referenced to the unmodulated carrier level.

A 2 KHz audio signal at 5 KHz deviation has a modulation index of 5/2 = 2.5. It has second order sidecurrents at +/- 4 KHz from the carrier, each at -7 dB relative to the unmodulated carrier; third order sidecurrents at +/- 6 KHz from the carrier, each at -13 dB relative to the unmodulated carrier; fourth order sidecurrents at +/- 8 KHz from the carrier, each at -22 dB relative to the unmodulated carrier.

A 1 KHz audio signal at 5 KHz deviation has a modulation index of 5. It has fourth order sidecurrents at +/- 4 KHz from the carrier, each at -8 dB relative to the unmodulated carrier; fifth order sidecurrents at +/- 5 KHz from the carrier, each at -12 dB relative to the unmodulated carrier; sixth order sidecurrents at +/- 6 KHz from the carrier, each at -18dB relative to the unmodulated carrier; seventh order sidecurrents at +/- 7 KHz from the carrier, each at -25.5dB relative to the unmodulated carrier.

The general consensus is that a 5 KHz deviation NBFM signal is about 12 to 15 KHz wide. (In comparison, an AM system would be 6 KHz wide.) But the FM receiver bandwidth has to be a little wider, because our IF filters are not perfect. In an AM system, the filter imperfection causes a little loss of higher frequencies, and a slight improvement in S/N. In an FM system, sloppy IF response causes degraded signal reception in weak signal conditions. A sharp IF filter tends to have response ripple and uneven delay times for frequencies across its passband, particularly near the edges of its passband. This upsets the phase relationship between the sidebands and the carrier, turning the FM into AM at some frequencies. This is in turn causes distortion and loss of high frequency audio. (In an AM system, it usually only causes loss of highs. It takes worse passband distortion to cause much distortion.) The resulting audio-rate variations in amplitude of the FM signal at the ! detector also increase the effects of noise bursts that come from atmospheric noise and other interference.

The usual solution to the above problem is to use a wider IF passband than actually needed for the transmitted bandwidth alone. This pushes the regions of high delay time distortion out to where there is not much transmitted energy, so it has less effect. However, this makes the receiver wider, and therefore more noise and interference can get into it, so weak signal performance suffers somewhat. It is a compromise solution, but it has worked for many years.

In an AM system, we can have a great deal of sideband trimming without distortion, if selectivity is symmetrical and the carrier is not in a response depression. We can even have seriously non-symmetrical response and deliberately use sideband diversity to avoid interference. This is not generally possible with FM using typical FM detectors (discriminators).

Advanced techniques improve the situation for FM and AM. Synchronous detection and digital filtering promise to reduce the issue to sideband energy, which will make NBFM and AM nearly equivalent in bandwidth and performance. NBFM will always be a little wider than AM, unless we really use QAM instead of NBFM to eliminate the higher order sidecurrents. This in turn requires power amplifiers with an amplification characteristic that is linear for small modulation percentages (10% or so).

Bacon, WA3WDR