FM Discriminator, First Principle - John Dunn, Consultant, Ambertec, P.E., P.C.

We examine frequency modulation (FM) demodulation or detection from a first principle standpoint using differentiation and subtraction:  

 

The constant delay of the delay line shown above translates to varying phase angles as the input frequency is varied which alters the amplitude of the vector subtraction of signals e1 and e2.

Note in this sketch that vertical scaling is arbitrary, just for the sake of visual convenience.

Although this envelope result looks linear, it is really a small part of a sinuoidal envelope. If we increase the delay from 0.01 µSec as above to 0.1 µSec, that sinosoidal envelope becomes visually obvious.

 

 

If you'd care to play around with the equations of this, the followng GWBASIC code is provided.

 

10 CLS:SCREEN 9:COLOR 15,1:YSTART=250:XSTART=50:PI=3.14159265#:DT=.05

20 PRINT "save "+CHR$(34)+"fmdiscr1.bas"+CHR$(34):PRINT:XS=1:YS=1

30 PRINT "save "+CHR$(34)+"a:\fmdiscr1.bas"+CHR$(34):LOCATE 12,1

40 C$="#.## MHz to ##.## MHz Delay = #.## uSec":GOTO 110

50 X=TUSEC*200:Y=E1*20:GOTO 90

60 X=TUSEC*200:Y=E2*20-50:GOTO 90

70 X=TUSEC*200:Y=(E1-E2)*40-130:GOTO 90

80 X=TUSEC*200:Y=(E2-E1)*40-220:GOTO 90

90 CC=XSTART+1.33*X*XS:DD=(320-Y*YS-YSTART):IF KK<>0 THEN LINE (AA,BB)-(CC,DD)

100 AA=CC:BB=DD:KK=1:RETURN

110 FCTR=1E+07:DEV=.7:F=FCTR*(1-DEV):TD=.1/FCTR

120 FOR TUSEC=0 TO 2.00001 STEP .0001:T=TUSEC/1000000!:IF TUSEC=0 THEN FLOW=F

130 E1=SIN(2*PI*F*T):E2=SIN(2*PI*F*(T-TD))

140 F=F+.0001*DEV*FCTR:KK=0:GOSUB 50:GOSUB 50:KK=0:GOSUB 60:GOSUB 60

150 KK=0:GOSUB 70:GOSUB 70:KK=0:GOSUB 80:GOSUB 80:NEXT TUSEC:FHI=F

160 PRINT USING C$;FLOW/1000000!,FHI/1000000!,TD*1000000!

Comments

[John Dunn]

Typo! That middle line should read "....just for the sake of visual convenience."

Sorry about that.

[george storm]

This is a method that works in principle, but the described requirement for small delay would appear to present a conflict between linearity and circuit noise.
On which subject: with a delay of 10-ns, the signal at the 17 MHz end of the range would already be reduced below half that expected from the initial slope.
Things are somewhat better if we shift the 14-MHz range to sit symmetrically around 100-MHz (i.e. from 93 and 107 MHz). The signal reduction relative to peak slope is "only" 10%.
Nevertheless, linear FM systems typically reduce the mudulation range to below 5% and use resonant detectors - both for practicality and to reduce the noise

[John Dunn]

Actually, this item, like all of the others I've posted, was put to practical use. In this case, I needed to make an FM demodulator that was as idiot-resistant as possible and as easily constructed as possible. This was it.

[Tom Christian]

John,
That's interesting. I'm interested in radio receiver
design, but I've found that many books give little
information on practical circuits for demodulation.
Frequently the demodulator is simply depicted as a
block.
But now what about the 10 nS time delay depicted in your
diagram. How might that be implemented in circuitry?
What other types of FM demodulators are there?