## Tuesday, December 16, 2008

### Amplitude Modulation

December 17, 2008 Educational Radio Net, PSRG 30th session, Lee Bond N7KC

The subject of tonight’s discussion material is amplitude modulation and the fundamentals thereof. This is the first of a three part series dealing with the process of transmitting voice band frequencies via radio. My next session will focus on single sideband processes and the third session will focus on frequency modulation.

If one looks at the bandwidth required to transmit various signals it is immediately apparent that three designations will suffice to describe the bandwidth required to do the job. The first segment is very narrow bandwidth and this includes CW and several of the popular digital modes. The second definable segment would be moderate bandwidth and this includes voice transmissions, facsimile, and slow scan television. The third segment is the very wide bandwidth signals such as fast scan television.

For this session we are interested in moderate bandwidth voice transmissions and, in particular, the amplitude modulation approach to transmitting voice using radio techniques. As a practical matter we are interested in somehow shifting voice range frequencies to a range more suitable to fit our antennas since the antenna is really where the ‘rubber hits the road’. We will assume that our antennas are cut to fit whatever amateur band we choose to use.

Lets define voice range frequencies for radio purposes as those starting at 20 hertz and extending to 2500 hertz. The, so called, high fidelity range extends to 20,000 hertz but most of the important voice energy required for communications is contained in the region under 3000 hertz. The ratio of the high voice frequency to the low frequency is about 125:1. In principle one can transmit audio frequencies in the same manner as ‘radio’ frequencies but the antenna dimensions would be enormous. For example, assuming standard propagation velocity, a half wavelength at 20 hertz is about 4600 miles and a half wavelength at 2500 hertz is about 37 miles. If you were to cut the antenna for midrange then it would be seriously de-tuned at either end frequency. So what to do?

Mathematics to the rescue. Everyone has heard the rule that two frequencies, if mixed, will produce sum and difference frequency spectra and this spectra will include the original two frequencies as well. This ‘mixing’ behavior is predicted using trig product identities and the mathematics is valid for audio frequencies right up through radio frequencies. Let’s play with some numbers to get a feel for how this mixing business works.

First however, we want to appreciate a couple of terms often used to describe the behavior of circuits. Linear and non linear. A linear circuit processes signals in a straight line fashion. For example, if you double the signal feeding a linear amplifier circuit then the output signal will precisely double. There is no perfectly linear active electrical circuit but it is possible to come very close to perfectly linear. A perfectly linear amplifier will process multiple signals without any interaction between signals. One simple measure of linearity is harmonic distortion. If you drive an amplifier with a single perfect sine wave signal then you would expect a perfectly linear amplifier circuit to present only a single output frequency. If a spectrum analyzer shows any energy at multiples of the driving frequency then these added frequencies are a result of harmonic distortion caused by the amplifier and harmonic distortion is an artifact of non linear performance.

On the other hand, there are circuits which have been deliberately designed to be non linear. If a non linear circuit is used as a ‘mixer’ then you can assume that at least two frequencies are being processed by this circuit. Mixing, in actuality, is really multiplication or the product of at least two frequencies as defined by the product identities in trigonometry.

Now, with that aside, let’s get back to playing with our numbers. Assume that we are feeding two audio frequencies into a non linear ‘mixer’. One frequency is 1000 hertz and the other is just twice the first or 2000 hertz. The sum output is 3000 hertz and the difference is 1000 hertz which is the same as one of the driving frequencies.

Now let’s mix another pair, this time 1000 hertz and 3000 hertz. This time the sum is 4000 hertz and the difference is 2000 hertz. A look at the spectra would show four frequencies namely 1 Khz, 2 Khz, 3 Khz, and 4 Khz.

In like manner let’s mix 1000 hertz and 100,000 hertz. The sum is 101,000 hertz and the difference is 99,000 hertz. The spectra shows our original ‘mixing’ frequencies, 1 Khz and 100 Khz, and the product frequencies of 101 Khz and 99 Khz. The maximum difference between upper sideband frequency and lower sideband frequency is just 5000 hertz so the percentage of bandwidth compared to carrier is just 5%.

Finally, let’s mix 1000 hertz and 10,000,000 hertz or 10 Mhz. This time the sum frequency is 10001000 hertz and the difference is 9999000 hertz. The spectra shows our mixing frequencies of 1 Khz and 10 Mhz plus the product frequencies of 10.001 Mhz and 9.999 Mhz. The audio range frequency, 1000 hertz, could be any frequency between 20 hertz and 2500 hertz and would produce mixing products with the ‘carrier’ frequency (10 Mhz) that extend from 9.9975 Mhz to 9.99998 Mhz and from 10.00002 Mhz to 10.0025 Mhz. The, so called, carrier frequency has energy below it called the lower sideband energy and energy above it called the upper sideband energy. The maximum difference between upper sideband frequency and lower sideband frequency is just 5000 hertz so the percentage of bandwidth compared to carrier is just 0.05%. This indicates that both the carrier frequency and sideband frequencies will ‘fit’ our antennas nicely in the band we choose to transmit within. Voice modulating frequencies in the range of 20 to 2500 hertz are so far removed from the carrier energy that they are filtered out of the final product.

Voice modulation is the process of imprinting intelligent baseband information upon a signal suitable for radio transmission. In the case of amplitude modulation the baseband voice information causes the instantaneous carrier amplitude to change and this change can be detected at great distance to reconstruct the original baseband voice information.

Nothing is free and so it is with amplitude modulation. To 100% modulate a 1000 watt carrier using AM it is necessary to provide 500 watts of audio power. The 500 watts ends up being split between the upper sideband and the lower sideband and, spectrally, the carrier amplitude remains constant. Amplitude modulation is inefficient from the power standpoint since the full carrier power is transmitted but this power contributes nothing to the impressed intelligence. Amplitude modulation is also inefficient from the bandwidth standpoint since identical upper and lower sideband information is transmitted requiring a bandwidth twice as large as the modulating signal.

Recovering the impressed information from an AM signal can be as simple as detecting the, so called, envelope of the signal. This amounts to rectifying the signal and filtering out the carrier. What remains is just the analog of the original modulating signal. This is the precise method used by simple ‘crystal’ sets which are still popular with experimenters. One particularly nasty artifact of operating AM is the heterodyning of adjacent carriers. Radio operators put up with this howling until improved techniques made AM obsolete.

In summary, amplitude modulation or AM is a very simple but inefficient means of impressing information on a ‘carrier’ signal. The AM process is very straight forward and easy to understand but lacks the elegance of improved methods of communication.

This concludes the set up for the discussion of AM. Are there any questions or comments?

This is N7KC for the Educational Radio Net