The ‘classic’ two-beam optical interferometer is the Michelson Interferometer. At microwave and THz frequencies a different type of system, the Martin Puplett Polarising Interferometer (MPI) tends to be used because it has a number of practical advantages over a conventional Michelson. Here we will use the MPI as an example of how an interferometer can be use for FM signal demodulation. The quasi-optical circuit diagram for an MPI and its use as a Frequency Discriminator or demodulator is illustrated in figure 13.4.
For the sake of simplicity we can assume that the signal passing through the system is essentially a ‘plane wave’. (In practice we'd have to take diffraction, etc, into account, but we can ignore this as it doesn't change the points we're interested in here.) An input beam of power, P, and frequency, f, will pass through the MPI and produce power levels on the two output detectors of
where and are the distances of each roof mirror from the central ‘beamsplitting’ polariser. Each detector has a responsivity, (i.e., they produce an output voltage when illuminated with a power level, P). A pair of ‘sum and difference’ amplifiers are used to combine the outputs from the detector and generate the levels
where and are the voltage gains of the two amplifiers. These two voltages are then fed to a circuit which takes their ratio to produce an output
By combining expressions 13.30 - 13.34 we can therefore say that
Consider what happens when the input signal is a beam whose (unmodulated) carrier frequency is and whose modulated frequency at any instant is . To use the system as an FM demodulator/discriminator we adjust the roof mirror positions so that the Path Difference, , is such that
where is the beam's carrier wavelength, , and N is any integer. The output from the system at any instant will therefore be
We can now say that the FM signal's frequency deviation (how much its frequency differs from the carrier frequency) at any instant will be
Combining 13.37 & 13.38 we get
which, by looking in a good maths book on trig relationships, we can rewrite as
where or depending on whether N is odd or even. In most cases of practical interest we can arrange that so expression 13.40 can be approximated by
i.e. we get an output voltage proportional to the frequency deviation where
is the Conversion Gain of the system.
From the above arguments we can see that, by setting an appropriate path difference and using sum & difference amplifiers, we can employ the MPI system as an FM demodulator. A similar analysis can be performed for other types of interferometer such as the Michelson and we get a comparable result. Being optical, these systems can be used at much higher frequencies than conventional optics. Their main practical drawback is that a high conversion gain requires a large N value — i.e. a large path difference.
You should now understand how a Double Balanced Mixer (DBM) works and how we can use it as a form of Phase Detector. That the phase detector can be combined with a voltage controlled oscillator to make a Phase Lock Loop. That the PLL, when Locked, makes the VCO follow the frequency variations of an input FM/PM wave and provides us with an output voltage which represents the demodulated FM information. You should also understand why the PLL won't lock onto a wave unless it's frequency comes within its Lock in range, but — once locked — the loop will track frequency variations over its Tracking range, and that these two ranges can have quite different values.
You should now also understand how a Martin Puplett Interferometer (MPI), or any other type of two-beam interferometer, can be used as an FM Discriminator to recover FM/PM modulation information. That these optical systems can be used at frequencies too high for conventional electronic PLL's.
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University of St. Andrews, St Andrews, Fife KY16 9SS, Scotland.