MadSci Network: Physics

Re: Is it easier to tune into a station approaching it from certain frequencies

Date: Fri Jan 24 18:49:57 2003
Posted By: Aurelio Ramos, Grad student, Computer Engineering
Area of science: Physics
ID: 1043080490.Ph

An FM radio detects the FM signal by using a band pass filter and "Phase 
Locked Loop" (PLL). The band pass filter is tuned to focus only on one 
station at a time (like a spotlight), and the PLL is employed to extract 
the music. the PLL is basically a voltage controlled oscilator and a 
comparator used as an error detector, linked in a control loop.

This control loop acts as a servo that constantly tries to keep the local 
oscillator synchronized (phase locked) to the incoming signal, by 
increasing or decreasing the frequency of the local oscillator as to 
minimize the error signal. Remember that the incoming signal is a varying 
frequency carier, and the actual music is encoded as the frequency 
variations (that's what Frequency Modulation means).

By amplifying the local oscillator's control voltage, the modulator is 
extracted (which is the signal of interest, the music). This is because 
the control loop supplying the control voltage is trying to make the 
oscillator mimic the incoming signal. And the control voltage is 
proportional to the frequency, which (if close enough to the incoming 
signal) is proportional to the music itself.

In order to scan, two things happen: the bandpass filter scans the 
spectrum, and at the same time, the characteristits of the PLL's control 
loop are changed as to make it capable of locking into the various 
frequencies being scanned.

However, the control circuit for the PLL and the PLL itself are not 
perfectly linear. As a result, chances are the control system as a whole 
has a step response that exhibits hysteresis. 

Hysteresis is what happens when a non-linear system behaves differently 
depending on the direction its being asked to go. For example, when you 
adjust the rear view mirror in your car, its sometimes very anoying that 
it does not stop where you leave it, and you have to push just a little 
further so it settles at the desired position (or jiggle it). When moving 
the mirror in a different direction, you also have to push a bit further 
so it stops at the desired position. Notice that the final position *of 
motion* is different depending on the direction you move it, even if the 
position it ends up is the same. This is a perfect example of hysteresis. 
Bycicle shifter cables, camera tripods, and many others are good examples 
as well.

The hysteresis of this step response would result in a scanning rate that 
is not always the same at all frequencies or in all directions. the 
scanner is probably moving linearly up or down the spectrum but the PLL 
control circuit does not just follow perfectly, it may lag behind and 
catch up, and it may even overshoot slightly after the catchup. And how 
it behaves in one direction does not need to match what happens in 
another because of nonlinearity.

I believe that in order for the circuit to work properly and avoid 
mistaking noise for a radio station, the scanner only stops if the PLL 
has seen a minimum amplitude signal for a minimum length of time. Because 
of the histeresys and nonlinearity of the PLL and its control loop, its 
quite possible that the scanning rate in one direction may prolong 
locking time barely longer than minimum for detection, and that in the 
opposite direction locking time may be well bellow the required minimum.

This would explain why a weak radio station may be easier to catch when 
going in one direction than the other. It is also possible that this 
phenomenon only occurs when the scan begins *near* the target station, 
and that there is no directional difference if the target station is far 
from the starting point. I have no reason to believe this would always 
work in the same direction in most radios, but that would be an 
interesting experiment.

Your mad scientist,

Aurelio R. Ramos

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