3.5.2 Frequency modulation
FM also employs another method which is normally used for the transmission of radio broadcasts. FM radio again uses a high-frequency signal as the 'carrier' of the audio signal. The modulation of the carrier signal by the audio signal 'carries' the information by changing the frequency of the carrier.
The simplest case is where a sine wave audio signal is used to change (or modulate) the frequency of the carrier signal. The amount of frequency change is called the deviation, fc, and instead of producing just one pair of sideband frequencies, FM can produce many sidebands, where the extra sidebands are similar to the harmonics in the sawtooth AM case described in Section 3.5.1, and this is just for sine wave carrier and modulator frequencies.
The number of sidebands that are produced can be determined by using the modulation index which is a measure of the amount of modulation and is being applied to the carrier. The modulation index is given by dividing the deviation by the modulator frequency, fm:
Modulation index = δfc / fm
Note that the modulation index is dependent not only on how much the carrier frequency is changed but also on the modulator frequency. The resulting output signal contains not only the original carrier frequency, but also the sum and difference sidebands for each of the multiples of the modulator frequency.
For audio FM with two sine waves, the output consists of the carrier frequency and sidebands made up from the sum and difference frequencies of the carrier and multiples of the modulator frequency. The number of sidebands depends on the modulation index (Figure 3.5.4), and a rough approximation is that there are two more than the modulation index. The modulating frequency is not present in the output. The amplitudes of the sideband frequencies are determined by a set of curves called Bessel functions (Chowning and Bristow, 1986).
FIGURE 3.5.4 FM depends on the depth of modulation as well as the input frequencies. The number of sidebands that are produced depends on the modulation index.
For FM with waveforms other than sine waves, each component frequency is treated separately. So for a sawtooth carrier and a sine wave modulator, the
output is similar to the sawtooth AM case, but there are many more sidebands produced. FM is thus a very powerful technique for producing complex spectra, but in an analogue synthesizer it suffers from problems related to the frequency stability of the carrier and modulator VCOs, and the response of the carrier VCO to FM at audio frequencies.
In an analogue synthesizer, FM is produced by connecting one VCO to the frequency control input of another VCO. If the modulating frequency is lower than about 25 Hz, then FM is known as vibrato, and it is perceived as a cyclic change in pitch. FM is described in more detail in Section 5.1.
3.5.3 Ring modulation
Ring modulation takes two audio signals and combines them together in a way that produces additional harmonics. It uses a circuit known as a 'balanced modulator' to produce a single output from two inputs: the output consists of the sum of the two input frequencies and the difference between the two input frequencies. The original inputs are not present in the output signal (Figure 3.5.5).
FIGURE 3.5.5 Ring modulation produces only the sum and difference frequencies – neither the carrier nor the modulator frequencies are present at the output.
This is similar to AM, except that it is only the additional frequencies that are generated which are present at the output: only the sidebands are heard, not the carrier or the modulator. This means that ring modulation can be useful where the original pitch information needs to be lost, which makes it useful for pitch transposition, especially where one of the sets of extra frequencies can be filtered out. In an analogue synthesizer, ring modulation is produced by a special modifier circuit.
Table 3.5.1 Modulation Summary
Modulation summary is given in Table 3.5.1.