# Zero-Crossing Demodulation of FM signals

## Main Question or Discussion Point

Hey guys,

For school I have to study the zero-crossing demodulation method of reconstructing an FM signal.

So far what I've been reading has been confusing me a bit and I have a few questions to ask:

1) How does a LP-filter act as a "time averager" for a train of impulses?
2) Does the resultant signal after LP-filtering resemble the original message signal? Is it DC shifted or amplified at all? If it is DC shifted how can you get rid of that?

thanks guys.

## Answers and Replies

Related Electrical Engineering News on Phys.org
Zero Crossing FM detector:

Hi bumclouds:
1) A LPF can be characterized in the frequency or time domain. The fact that it is called a 'Lowpass Filter' shows that most people are most comfortable in the frequency domain. Of course, in the freq domain a low pass filter passes low frequencies and attenuates high frequencies. The math that describes a LPF can be represented either as a transfer function in the freq domain (where we just multiply it by the input to get the output) or as an impulse response function in the time domain (where we employ the convolution integral to transform the input to the output). Convolution integrals scare a lot of people, and many forget them once they leave school, but they are useful. For a LPF, the impulse response is a smooth function of time. The simplest form is a decaying exponential for a singel pole RC LPF. The convolution integral uses this impulse repsonse to compute a weighted moving average of all past inputs to the filter. For an exponential function, the most recent inputs are weighted most heavily, and later inputs are less so. This is generally true of many LPFs. A single pole low pass filter will average inputs over approximately one time constant. It is this averaging (which is what the circuit is really doing) that causes it to attenuate high frequencies in the frequency domain (which is where most people like to analyze it).

2)I imagine your 'zero crossing' FM detector goes something like this: construct a circuit that detects zero crossings and outputs a pulse of given amplitude , say 1 volt, for a given time, say 500ns, at every positive zero crossing. This pulse train is applied to a lowpass filter to generate the output. Make the FM signal 1MHz. The pulse train will be 1 volt high for 500ns out of every 1us cycle. The DC content is 0.5volts. Do the same for 800kHz and 1.2Mhz and you'll find the DC output varying from .4v to .6v. Now imagine that your FM signal is modulated by a 100Hz signal such that its frequency varies from 800kHz to 1.2MHz. The output of your LPF will now vary from .4 v to .6v at 100hz rate: you get a 100Hz sine wave with .1v amplitude and 0.5v DC offset. This is typical of demodulators: they have a scale factor and a DC offset. For audio, the DC can be removed by a series capacitor. The capacitance must be large enough to pass the lowest frequecy of interest. For audio that would be 20Hz or so. SInce most FM singals don't vary this much, your signal may be a lot smaller, so you will need an amplifier. In any case, you need to figure out what the scale factor is based on the original signal characteristics and the choices you make in your detector.

3) the questions you didn't ask: FM is a tricky signal. In it's simplest form its easy to understand, we just vary the frequency with a signal at the transmitter and then detect the changes at the receiver. But FM actually has infinite bandwidth for a finite signal. This means that you can't ever transmit and demodulate an FM signal perfectly. AM, on the had, has limited bandwidth for a limited bandwidth input and can, in principle, yield perfect results. The trouble is that the engineering reality is quite different. It turns out that the unavoidable FM distortions can be kept very small by good engineering, and FM has a really nice reaction to noise. It almost completely ignores noise until it gets up to a certain point, and then it caves in and you lose the signal completely. AM on the other hand, is always susceptable noise so we tend to keep the bandwidth down to keep the hiss down. So FM is a great engineering example of how to interprete mathematical results, and how a seeming flaw may actually be an advantge.