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]

Hi, Tom.

With coaxial cable's velocity factor of approximately 2/3, the speed of signal propogation would be 200 million meters per second. That velocity amounts to 5 nSec of delay per meter so 10 nSec would take 2 meters of cable or approximately 6.56 feet, not an impossible number.

Some FM demodulation circuits that come to mind are phase-locked loops, the Foster-Seely discrminator and the ratio detector.

John

[John Dunn]

Oops! I left one out. FM singals can also be demodulated using a slope detector.

[William Ketel]

This is certainly a way to detect frequency modulation, much the same as most modern IC detectors do, with an external delay element. BUT it does not match the frequency discriminator description given in the explanations of Armstrong's original frequency discriminator.
So YES, it is an FM detector, but NO, it is not really a "Frequency discriminator" in the common understanding of the term.

[Jerry Meyerhoff]

Fun with FM demodulators . Names like Foster-Seely , Quadurature, Ratio detector & RCA's CA3089 (over-used) IC come rushing back to me from working on Motorola Two-way radios & entertainment automotive receivers of the 70's & 80's. Today its "quadrature detection" done in software at base-band.
Perhaps some application notes and textbooks survive to show "how it was done in the day". e.g. for 230 kHz bandwidth FM broadcast in stereo, tuning up (phasing in factory language) the CA3089's phase-shift coil (tuned circuit) was a snap. For Motorola 2-way radios, all's you did was tune the coil to "zero the discriminator" (meter 5) on the serviceman's test set.
## But the real trick was getting a 100 dB gain 10.7 MHz IF strip to NOT self-oscillate. Till that was achieved by applying all the black-arts of EMC control, the detected audio output at minimum sensitivity was often quite distorted. Thanks John for another opportunity to walk down memory lane. jdm 2/1/2012