While it is not possible to vary the frequency of a crystal oscillator directly, it is possible to vary its phase. The resulting PM signal can be used to create FM. This is the basis of the Armstrong modulator.
The mathematics required to analyze the Armstrong modulator completely are complex, so we will discuss only the basic circuit operation. An audio signal is passed through a preemphasis network and then an integrator, a special network whose output is the time integral of the input signal. The preemphasized integrated signal is used to phase modulate a crystal oscillator. Mathematically, it can be shown that PM using the integral of the audio signal is identical to FM using the audio signal itself. In this way an FM signal is generated.
The Armstrong modulator cannot produce much deviation, so combination of multipliers and mixers are used to raise the carrier frequency and the deviation. The multipliers are used to multiply the carrier and the deviation. The mixers are used to decrease the carrier, while keeping the deviation constant so that additional multiplier stages can be used to obtain more deviation. It is worth going through an example:
An FM station is authorized to operate at 90.9 MHz, with maximum deviation of 75 KHz. The FM signal is generated with an Armstrong modulator whose output is 500 KHz with a deviation of 15.432 Hz. The modulator output is applied to 3 triplers and a doubler to obtain a frequency of 81 MHz and a deviation of 2.5 KHz. The 81 MHz signal is mixed with a 77.97 MHz signal to produce a 3.03 MHz signal whose deviation is still 2.5 KHz. This signal is fed through a doubler, tripler and quintupler to multiply the carrier to 90.9 MHz and the deviation to 75 KHz.
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