# Frequency demodulation with a spectrum analyzer

In my university lectures I have generated an FM signal (for instance with carrier frequency of 2GHz, frequency deviation equal to 100kHz, and modulating frequency equal to 100kHz.)

In order to perform the demodulation, my teacher has followed these steps:

1. Choosing a high resolution bandwidth in order to incorporate all the side bands inside one single peak (obviously it is not good if we want to analyze the spectrum properties.)
2. Choosing as center frequency a point in the transition between the peak and the "null" part of the spectrum.
3. Switching to time domain and visualizing the modulating signal.

I have some questions about step 1 and 2:

• about 1: Why do we have to choose a so large RBW (for instance 3MHz?)
• about 2: Why do we have to choose a point of demodulation which is not the peak of the spectrum?

My professor has said that choosing the peak frequency will lead to a demodulated signal with 0 voltage dynamic. Why?

• The following picture...... Commented Feb 28, 2020 at 15:54
• Sorry, I thought I have the picture, but not:( Commented Feb 28, 2020 at 16:00

The trick here is that the RBW filter is placed so that its transition band (on one side) spans the frequency range that the modulated signal covers, so the attenuation of the filter is dependent on the modulation signal.

The RBW must be selected so that the transition band is wide enough that the entire signal fits into one half of the filter, but typical RBW filters fall off quickly beyond their design 3dB bandwidth.

If you were to demodulate the center of the signal for the time domain view, you wouldn't see much of an amplitude change, since it's a frequency modulated signal, and what you see as a change in amplitude in the time domain view is really the shape of the RBW filter.

• This is called slope detection. Commented Feb 28, 2020 at 19:22

1 is to view outside the normal bandwidth to look for intermeodulated distortion (IMD) or other spurious emissions. PIM and such.

1. Choosing a high resolution bandwidth in order to incorporate all the side bands inside one single peak (obviously it is not good if we want to analyze the spectrum properties.)

This is in order to get the entire signal energy into one bandpass filter. An FM signal will nominally have constant amplitude.

1. Choosing as center frequency a point in the transition between the peak and the "null" part of the spectrum.

This is setting up for what is called 'slope demodulation'. The slope of a typical spectrum analyser IF filter is 'linear in dBs' for quite a wide range about a point halfway down the skirt.

1. Switching to time domain and visualizing the modulating signal.

As the frequency varies, the signal will move up and down the side of the filter, due to the slope. This turns changes of frequency into changes of amplitude, that is FM into AM. Putting the analyser in time domain mode means it then plots the modulation against time, like an oscilloscope.

This sort of demodulator is handy to use on spectrum analysers, as it comes for free. It's OK for visualisation, and identifying what the modulation is carrying, but it's by no means HiFi. Analogue FM receivers use a far more linear arrangement with two filters, one above and one below, and use their outputs differentially.