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By Robert W. Meister WA1MIK 		  Print this Page


Background:

In the early days of FM two-way radio, the modulation standard was +/- 15 kHz, which in the 1960s was converted to narrow-band at +/- 5 kHz. The old 15 kHz wide-band standard was retained for broadcast remote pickup service for many years, but most of those systems have converted to digital modulation modes. The modulation standard for current amateur FM systems on 10 meters, 6 meters, 2 meters, 220 MHz, and 450 MHz is +/- 5.0 kHz. Narrow-band, often used on the 902 MHz band, is half that, or 2.5 kHz. Most radios and systems in commercial service are adjusted for less than the maximum. There are circuits in all FM transmitters to limit the instantaneous frequency deviation to some maximum, adjustable value. CTCSS and DCS modulation is part of the transmitted signal and must be included when measuring deviation. There are EIA standards for audio deviation, CTCSS / DCS deviation, receiver modulation acceptance that most radios adhere to, but this still leaves room for adjustment when applied to the amateur equipment.

Frequency deviation due to audio modulation is usually measured and displayed as plus-or-minus (some number of) kiloHertz, as in +/- 5.0 kHz. The total bandwidth is the complete span of the frequency swing, which would be 10 kHz for a signal that is deviating +/- 5.0 kHz.

Receivers have band-pass filters that attempt to limit the selectivity so only signals on the assigned frequency are heard. Channel spacing between signals is set depending on the bandwidth of the receivers and modulation capability of the transmitters. On UHF, this is typically 25 kHz, but radios are often programmable in 6.25 or 12.5 kHz steps. The receiver's acceptance bandwidth is typically a lot less, on the order of +/- 7.0 kHz, however it is still sensitive to signals further away.

A transmitter on 460.00000 MHz that's deviating +/- 5.0 kHz can have its carrier swing from 459.99500 MHz up to 460.00500 MHz during any modulation peaks. This doesn't mean that the emitted signal only occupies this +/- 5.0 kHz band when modulation is present. The frequency modulation process creates sidebands that are on each side of the carrier, at lower power, and these extend much further than the expected +/- 5.0 kHz of deviation the radio has been set for. The sidebands actually extend out to infinity, but the level is so weak after the 3rd sideband, in a properly designed and functioning transmitter, that the rest can usually be ignored. The further away from the carrier, the weaker the sidebands, until they reach a level where they're undetectable. Under the right circumstances, this energy outside of the expected +/- 5.0 kHz can cause all sorts of problems to receivers that are only 25 kHz away.

Repeater channel spacing varies according to band and locale. In New England, two-meter repeaters are on 15 kHz and 20 kHz channels. A repeater that's deviating 5 kHz is very likely to create splatter for a mobile user trying to hear another repeater on an adjacent channel. UHF repeaters are typically on 50 kHz spacing, in-high, out-low, with other repeaters using in-low, out-high between these. One repeater transmitter's splatter can become a major headache for an adjacent repeater's receiver. Always follow the bandwidth guidelines set forth by the repeater coordinating body for your state or area.

This article shows the occupied bandwidth of various signals, in an attempt to show the reader why this problem exists, and what to do about it. There are about 60 small images that will be loaded and displayed as part of this article.

Measuring Instruments:

Oscilloscopes measure and display signal amplitude as a function of time. Spectrum analyzers measure and display signal amplitude as a function of frequency. Both have time bases to make the trace sweep across the screen, but in the case of a spectrum analyzer, a narrow filter is electronically tuned to one frequency as the sweep occurs, thus allowing only the energy present at that frequency to be displayed on the screen. A higher signal amplitude is represented by an increased trace height on the screen.

All of the traces came from an Agilent E4401B spectrum analyzer. On the spectrums, the span of the display is 100 kHz, so each horizontal box is 10 kHz. The carrier is always in the center of the screen. Vertical sensitivity is 10dB per division.

Basics of Frequency Modulation:

An FM transmitter's modulation circuitry takes the audio signal, runs it through some kind of filtering (to pass the normal 300-3000 Hz voice audio), applies pre-emphasis to raise the high frequency level, runs this through a soft limiter and possibly a splatter filter, and finally merges the CTCSS or DCS signal with it. The CTCSS or DCS signal, being low frequency, doesn't require limiting or filtering. It follows its own path and is merged with the modulating signal from the voice audio. The voice audio is filtered so it doesn't interfere with the low frequency CTCSS or DCS signal. The overall deviation is adjustable, but the ratio of voice audio to CTCSS or DCS level is usually not adjustable. The CTCSS or DCS deviation level is often a fixed percentage of the total deviation.

In all FM transmitters, the amplitude of the incoming audio controls the amount of frequency shift (deviation) of the carrier. The frequency of the incoming audio controls the speed (frequency) that the carrier shifts up and down.

Back in the beginning days of frequency modulation, the design of the modulation circuit actually changed the phase of the signal, rather than the frequency. Such transmitters created PM (phase modulation) and were prevalent up until recently. One characteristic of phase modulators is that the deviation doubles for each doubling of the input audio frequency. This is inherent and cannot be avoided. In a way, this is equivalent to the pre-emphasis circuit used in FM transmitters. The receivers were designed with de-emphasis to counteract this phenomenon. Thus the rise in transmitter deviation as the audio frequency increased was compensated for by circuitry in the receiver. This actually helped improve the fidelity of the signal. PM is fully compatible with FM.

Modern FM modulator circuits deviate the same regardless of the audio frequency (in other words, they are flat), but to be compatible with the receiver's de-emphasis, the transmitter incorporates pre-emphasis. For radio communications equipment, this occurs at 6dB per octave, in other words, for every doubling of the frequency, the audio is boosted to a level by a factor of two, and likewise the resulting peak deviation is also doubled Pre-emphasis does not normally affect anything below 300 Hz, but most transmitters have some sort of audio filtering that cuts off voice audio below 300 Hz and above 3000 Hz. These are not steep filters, so some voice energy below 300 Hz and above 3000 Hz will come through, but it will be severely attenuated. Here is the audio response of a commercial FM transmitter's audio circuitry:

The blue trace was done with an audio level that did not cause any limiting. Notice how the transmitter's deviation doubles for approximately twice the audio frequency, up to about 2800 Hz. At this point, the audio filter in the radio starts cutting back on the high frequencies.

The purple trace was done with an audio level that caused large amounts of limiting and distortion. Notice how the transmitter reaches its maximum deviation of just slightly over 4500 Hz at an audio frequency of 2200 Hz, then the audio filter starts cutting back, just as it did on the lower level audio. Notice how the extremely low frequencies, below 200 Hz, are attenuated; this reduces interference to the CTCSS and DCS signals by voice audio.

The green trace was created by injecting audio directly into the transmitter's VCO, bypassing all pre-emphasis, limiting, and filter circuits. The frequency synthesizer in the radio tends to cancel out any low-frequency modulation, so that's why the 100 Hz signal is so low. There's a strong peak at 200 Hz, but is fairly linear after that, falling off slightly, due to the interaction of the other parts of the circuit that remained connected. Theoretically, the modulation process should produce a constant output deviation level for a constant input audio level.

In telecommunications, Carson's Bandwidth Rule defines the approximate bandwidth requirements of communications system components for a carrier signal that is frequency modulated by a continuous or broad spectrum of frequencies rather than a single frequency. Carson's Rule does not apply well when the modulating signal contains discontinuities, such as a square wave. Carson's Rule originates from John R. Carson's 1922 paper. (Note: John Renshaw Carson was born in 1886. He worked at AT&T. He died in 1940. He had a twin brother, Joseph Robb Carson.)

Carson's Bandwidth Rule is expressed by the relation CBR = 2 * (Fd + Fm), where CBR is the bandwidth requirement, Fd is the peak frequency deviation, and Fm is the highest frequency in the modulating signal.

For example, an FM signal with 5 kHz peak deviation and a maximum audio frequency of 3 kHz, would require an approximate bandwidth 2 * (5 + 3) = 16 kHz. That means significant transmitter energy extends out from the carrier frequency by +/- 8.0 kHz.

Theoretically an FM signal has an infinite number of sidebands and hence an infinite bandwidth, but in practice all significant sideband energy (98% or more) is concentrated within the bandwidth defined by Carson's Rule. This is equivalent to everything less than 20dB below the carrier level. The remaining transmitted sidebands, however low they may be, can still wreak havoc with nearby receivers.

The unmodulated carrier amplitude is shown first in each section. Signal amplitude levels below that are often measured in dBc, dB below Carrier. Carson's Rule assumes the 98% energy level is -20dBc, so it really is concerned with everything above this.

Test Setup:

An Agilent E4430B signal generator was used as one signal source. It was connected to the spectrum analyzer directly through a coax jumper cable.

A 25-watt Motorola MaxTrac was used as the second signal source. It was connected to the spectrum analyzer through a 30dB 50-watt coaxial attenuator to reduce the signal level feeding the analyzer.

Modulating audio was generated by the E4430B and sent into the MaxTrac through a 470uF DC-blocking capacitor. Additional audio was provided by a portable FM radio. The drawing below shows the equipment setup:

Signal Generator Tests:

The equipment was set to 450 MHz. Here's the trace with no modulation. All you see is the carrier in the middle of the screen, at a signal level of -10dBm. All other noise is at least 60dB below this level.

Tests continued at audio modulation frequencies of 400 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz, 5 kHz, and 10 kHz. The deviation was set to 5 kHz for the images on the left and 10 kHz for the images on the right. They are paired so you can see the difference as the audio frequency and the deviation is changed.

400 Hz audio tone deviated at 5 kHz and 10 kHz:

1,000 Hz audio tone deviated at 5 kHz and 10 kHz:

2,000 Hz audio tone deviated at 5 kHz and 10 kHz:

3,000 Hz audio tone deviated at 5 kHz and 10 kHz:

4,000 Hz audio tone deviated at 5 kHz and 10 kHz:

5,000 Hz audio tone deviated at 5 kHz and 10 kHz:

10,000 Hz audio tone deviated at 5 kHz and 10 kHz:

Note that the 10 kHz deviation waveforms are about twice as wide as the 5 kHz waveforms. This is most noticeable at the lower audio frequencies. Each box represents 10 kHz of frequency, so 400 Hz at 5 kHz goes about +/- one half of a box, and 400 Hz at 10 kHz goes about +/- one box. As modulation frequency increases, you can begin to see the individual sidebands, which are repeated on multiples of the tone frequency. At the end, the 10 kHz modulation is clearly visible as each sideband is one box away from its neighbor.

As you notice on these last waveforms, there are three very visible sidebands on each side of the carrier, but anything after that is down in the noise, at least 60dB lower than the carrier. According to Carson's Rule, the bandwidth for the 10 kHz tone at 5 kHz deviation is 2 * (5 + 10) = 30 kHz; you can see that significant sidebands extend to +/- 30 kHz. Similarly, the bandwidth for the 10 kHz tone at 10 kHz deviation is 2 * (10 + 10) = 40 kHz; again the spectrum analyzer trace with sine-wave modulation shows that active sidebands exist out to +/- 40 kHz.

Carson's Rule measures bandwidth at the 20dB down point, but as you can see, there are significant sidebands extending out twice as far. However, the sidebands at 20 kHz are exactly 20dB lower than the carrier, giving a total bandwidth of 40 kHz, agreeing with Carson's Rule.

I modulated the signal generator with a wide-band random noise pattern at 5 kHz of deviation. There is no audio filtering, limiting, or pre-emphasis in the signal generator. There was so much sideband energy, I had to widen the display to 500 kHz, so each box on the trace represents 50 kHz. Notice that there is significant energy out to over 75 kHz on each side.

Radio Tests:

The MaxTrac radio was connected to the equipment. It had previously been set with test equipment for a maximum deviation of 4.5 kHz. The radio was programmed to 446.0000 MHz simplex, no CTCSS or DCS. Here's the trace of the carrier without modulation. All you see is the carrier in the middle of the screen, at a level of +24dBm. All other noise is at least 60dB below this level.

Tests continued at audio modulation frequencies of 400 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz, 5 kHz, and 10 kHz, just like the images above. The audio level at the MIC jack was adjusted to 35mVAC input for the images on the left and 350mVAC input for the images on the right. They are paired for easy comparison. The lower level was chosen because no limiting occurred at any test frequency. The higher level was chosen to insure limiting occurred at all test frequencies.

400 Hz audio tone at levels way below limiting and way above limiting:

1,000 Hz audio tone at levels way below limiting and way above limiting:

2,000 Hz audio tone at levels way below limiting and way above limiting:

3,000 Hz audio tone at levels way below limiting and way above limiting:

4,000 Hz audio tone at levels way below limiting and way above limiting:

5,000 Hz audio tone at levels way below limiting and way above limiting:

10,000 Hz audio tone at levels way below limiting and way above limiting:

As with the signal generator, note that the right-hand waveforms are about twice as wide as the left-hand waveforms, but only at the lower frequencies. As modulation frequency increases, you can begin to see the individual sidebands, which are repeated on multiples of the tone frequency. But due to pre-emphasis and audio filtering in the radio, no modulation is visible at 10 kHz except for a very slight blip one box away from the carrier frequency.

I modulated the radio with a wide-band random noise pattern at a level way above limiting (the same as in the tests above). Due to the audio filtering in the radio, very little energy is wasted in the sidebands. This is the kind of audio source that Carson's Rule would apply to, and as you can see, the occupied bandwidth is rather low.

I also fed audio directly into the VCO modulation point, bypassing any pre-emphasis, limiting, and filtering. As you can see, the radio is more than capable of deviating this amount, but the audio filters and other circuitry prevents the radio from developing significant sideband energy in this case. Here are two signals that were producing around 3 kHz of deviation:

5,000 Hz and 10,000 Hz audio tones at about 3 kHz of deviation directly into the VCO:

Deviation Measurements:

The spectrum analyzer also has the ability to display the demodulated signal, much like an oscilloscope. In these images, the vertical sensitivity is 1 kHz per division. Full screen is therefore +/- 5.0 kHz. Horizontal sweep time is 10 milliseconds, so each box represents 1 millisecond of time. Each cycle of a 1000 Hz tone takes 1 millisecond; this can be seen on two of the traces below.

The same modulating signals were used for this test as were used above: the audio frequencies were 400 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz, 5 kHz, and 10 kHz, just like the images above. The audio level was adjusted to 35mVAC input for the images on the left and 350mVAC input for the images on the right. They are paired for easy comparison. The lower level was chosen because no limiting occurred at any test frequency. The higher level was chosen to insure limiting occurred at all test frequencies.

400 Hz audio tone at levels way below limiting and way above limiting:

1,000 Hz audio tone at levels way below limiting and way above limiting:

2,000 Hz audio tone at levels way below limiting and way above limiting:

3,000 Hz audio tone at levels way below limiting and way above limiting:

4,000 Hz audio tone at levels way below limiting and way above limiting:

5,000 Hz audio tone at levels way below limiting and way above limiting:

10,000 Hz audio tone at levels way below limiting and way above limiting:

Below limiting, as the audio frequency increases, so does the deviation amplitude on the scope. This is due to pre-emphasis. But once 3000 Hz is reached, the deviation begins to drop off due to audio filtering in the radio. If a loud signal is fed into the radio, limiting occurs at all frequencies and the deviation reaches its maximum 4.6 kHz. But again, the audio filtering causes the higher frequencies to drop off.

The recovered audio, seen in these traces, is completely contained in the sidebands on the spectrum traces above. If the sidebands are very low, the audio will be very low. This relationship is the basis of FM. All of the waveforms and traces shown above agree with this basic premise.

I also fed audio directly into the VCO modulation point, bypassing any pre-emphasis, limiting, and filtering. Once again, the radio is more than capable of reproducing audio under these conditions. I adjusted the audio level for 5 kHz of deviation:

5,000 Hz and 10,000 Hz audio tones at 5 kHz of deviation directly into the VCO:

Here's the demodulated wideband random noise signal from the signal generator, and after being limited, filtered, and sent through the radio:

Due to the random-ness and wide frequency range, neither the signal generator nor the radio manages to even come close to hitting 4.5 kHz of deviation, even though both are capable of doing so under sine-wave modulation.

Real-World Signals:

Tones are nice because they're constant and last as long as you want them. But communications audio is mostly voice, and voice audio is constantly changing. This makes it hard to show the spectrum and the deviation waveform under the same conditions.

I connected an FM broadcast radio to the external modulation input of the signal generator and adjusted it for +/- 5.0 kHz of deviation as measured on the spectrum analyzer. I connected this same FM radio to the MaxTrac's microphone input, set the level for what appeared to be moderate limiting/clipping, and captured the deviation waveforms, shown below:

FM Radio audio feeding the signal generator and the communications radio (moderate limiting):

I then switched to the spectrum view and recorded both the signal generator and the output from the MaxTrac:

FM Radio audio feeding the signal generator and the communications radio (moderate limiting):

Conclusions:

What does all of this show or prove? It shows how the occupied bandwidth of an FM signal can far exceed the deviation setting, and that even though a transmitter is set for 5 kHz of deviation, the sidebands can extend out to 10 kHz or even further.

What sort of problems can over-deviation create? Primarily splatter on adjacent frequencies. For example, the normal communications bandwidth based on Carson's Rule is 16 kHz: 2 * (3 kHz maximum audio frequency + 5 kHz deviation). But if the audio is pushed up to 5 kHz and the deviation is adjusted for 7 kHz, the occupied bandwidth now increases to 24 kHz. Typical receivers have a modulation acceptance of at least 5 kHz of deviation, but the receiver filtering is not quite as sharp as it is in the transmitter audio section. A receiver just 25 kHz away will now hear the sidebands as they encroach on the receiver's bandwidth. It may not be enough to be heard, as there's very little energy at the carrier frequency 25 kHz away, but those sidebands will wreak havoc with a receiver trying to hear a weak on-frequency signal. In line-of-sight conditions, even the slightest splatter can have an effect 15-20 miles away. Excessively high audio frequencies will be just as much of a problem as over-deviation. The audio filtering in the transmitter is there for a very good reason and it must be used.

What can be done about it? First, make sure your total deviation INCLUDING CTCSS or DCS does not exceed +/- 5.0 kHz. In some areas, an even lower value is recommended, such as +/- 4.5 kHz. If you have defeated a repeater's internal de-emphasis and pre-emphasis because your external controller has that circuitry inside it, then you must make sure that there is adequate band-pass filtering in the controller and the transmitter to limit the energy outside the 300-3000 Hz audio frequency range. Most transmitters begin to roll off the higher frequencies - those above 3000 Hz - at 12dB per octave. This happens even with internal pre-emphasis. If you have a spectrum analyzer available, you should view the transmitted signal with varying input signals, including very loud audio and very noisy audio (the noise is very rich in high-frequency energy). Make sure the occupied bandwidth stays within the range specified by Carson's Rule and make adjustments so to minimize splatter. There's very little need for communications audio to exceed 4000 Hz; it conveys no significant information and can even fool some receivers into thinking the signal is noisy enough to close the squelch (most squelch systems look at the noise energy around 5000 Hz). Excessive energy at this audio frequency can do strange things. Amateur repeaters are not high-fidelity systems; the audio should be tailored for maximum intelligibility using the narrowest bandwidth possible.

Additional References:

The following files and articles may provide additional information about FM:

A rather dated article on FM standards from the 1970s can be found in this reprinted article from Ham Radio magazine titled FM Standards.

Primarily aimed at the Motorola MICOR radio, an article titled Why Pre-emphasis and De-emphasis is worth reading.

Information about repeater frequency spacing can be found in this reprinted article from Ham Radio magazine titled FM repeater separation - 20 kHz Yes, 15 kHz No.

Acknowledgements and Credits:

The MaxTrac (actually a Radius) radio used for these tests was sold to Will WB1DMK and used without his permission before he even knew about it.

Big thanks to Jeff WN3A, for his extremely detailed critiques of the article and his numerous suggestions for improving it.

Mike WA6ILQ provided additional changes and pointed out the references noted above.

Contact Information:

The author can be contacted at: his-callsign [ at ] comcast [ dot ] net.

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This page originally posted on Tuesday 26-Jun-2007


Photographs, article text, and hand-coded HTML © Copyright 2007 by Robert W. Meister WA1MIK.

This web page, this web site, the information presented in and on its pages and in these modifications and conversions is © Copyrighted 1995 and (date of last update) by Kevin Custer W3KKC and multiple originating authors. All Rights Reserved, including that of paper and web publication elsewhere.