Communication Systems/Frequency Modulation

Frequency Modulation

If we make the frequency of our carrier wave a function of time, we can get a generalized function that looks like this:

$s_{FM}=A\cos (2\pi [f_c+ks(t)]t+\varphi )$

We still have a carrier wave, but now we have the value ks(t) that we add to that carrier wave, to send our data.

As an important result, ks(t) must be less then the carrier frequency always, to avoid ambiguity and distortion.

FM Transmission Power

Since the value of the amplitude of the sine wave in FM does not change, the transmitted power is a constant. As a general rule, for a sinusoid with a constant amplitude, the transmitted power can be found as follows:

$P(t)=\frac{A^2}{2R_L}$

Where A is the amplitude of the sine wave, and R_L is the resistance of the load. In a normalized system, we set R_L to 1.

FM Transmitters

FM Transmitters can be easily implemented using a VCO (see why we discussed Voltage Controlled Oscillators, in the first section?), because a VCO converts an input voltage (our input signal) to a frequency (our modulated output).

Signal ----->|VCO|-----> FM Signal

FM Receivers

Any angle modulation receiver needs to have several components:

1. A limiter, to remove abnormal amplitude values
2. bandpass filter, to separate the out-of-band noise.
3. A Discriminator, to change a frequency back to a voltage
4. A lowpass filter, to remove noise added by the discriminator.

A discriminator is essentially a differentiator in line with an envelope detector:

FM ---->|Differentiator|---->|Envelope Filter|----> Signal

Also, you can add in a blocking capacitor to remove any DC components of the signal, if needed.