This document discusses FM demodulation techniques. It describes the slope detection or discriminator method, which converts an FM signal to an AM signal that can then be demodulated using an envelope detector. It provides the mathematical analysis and diagrams of the discriminator circuit. It also discusses direct demodulation methods like the phase-locked loop, which tracks and extracts the modulating signal from an FM carrier. Key circuits discussed include the balanced slope detector, Foster-Seeley discriminator, and ratio detector for improved linearity and noise performance.

1. Fundamental of
Communication
System
Abdirahim Khalif Ali
M.Eng (Electrical-Electronics and Telcommunications)
Universiti Teknologi Malaysia (UTM)
B.Sc. (Honors), Electronic and Electrical Engineering.
International University of Africa (2009)
Email: abdirahim.kh@gmail.com

2. Ch 3– Angle
Modulation
FM Demodulation

3. Demodulation of FM signal
• Demodulation process is done in order to recover/get back the
information signal transmitted.
• Basic concepts of demodulation circuit is to detect the frequency
variation.
• Two techniques can be used:
FM Demodulation
Indirect
Direct
Discriminator Phase Lock Loop(PLL)
3

4. Conversion circuit - FM to
AM (Discriminator)
• This technique is required to convert FM signal to AM signal and then by using
AM demodulation circuit is to get back the information signal.
• This technique is called slope detection or discriminator.
• Block diagram of the detection circuit is as shown below:
t t
t
y(t)
Envelope
Detector
dt
d
vFM(t) y(t)
 
t
vFM

 
t
vFM

vFM(t)
4

5. )
)
(
cos(
)
(
0



t
m
f
c
c
FM dt
t
v
k
t
E
t
v 
)]
(
[ t
v
k
E m
f
c
c 

Mathematical analysis :
Differentiate; yields :
FM equation :
   
   
 




 dt
t
v
k
t
t
v
k
E
dt
t
dv
m
f
c
m
f
c
c
FM

 sin
• From the above equation it can be seen that the amplitude of the signal
contains the information signal.
• The amplitude of the signal is an envelope of the signal and the equation is
given by :
5

6. • For envelope detector to be used the frequency deviation, Δω required
must be smaller than the carrier frequency, ωc or otherwise an envelope
detector cannot be used.
0
]
[ 

 
c
c
E
)
(
)
( t
v
k
E
t
y m
f
c

c
m
f t
v
k 
 

 )
(
for all t
• In practice a limiter circuit (litar penghad amplitude) can be used.
• It is due to the FM signal received at the antenna was influenced by the
noise and therefore the amplitudes of the signal were varied and not
constant.
• Hence the output equation of the envelope detector :
• Therefore the envelope equation can be written as:
6

7. 7
• For effective detection the constant amplitude of the FM signal is required.
Therefore an amplitude limiter is used.
• Below is a block diagram of FM detection circuit with limiter circuits.
)]
(
cos[
)
( t
t
t
E c
c
c 
 





1
1
)
(
o
v
cos(θ) > 0
cos(θ) < 0 vi(θ)
vo(θ)
1
-1
Penghad BPF )]
(
cos[
4
t
t c
c 



(Limiter)
Amplitude
limiter
Pengesan
Sampul
dt
d
vFM(t) y(t)
Discriminator
• A limiter will limits the output to +1 or -1 depends on the positive or negative
cycles of the FM signal and Ec(t) ≥ 0.

8. • Output of the limiter is a square wave signal as
shown below.
]
)
(
[
)]
(
[
0



t
m
f
c
o
o dt
t
v
k
t
v
t
v 










 ...
)
5
cos(
5
1
)
3
cos(
3
1
)
cos(
4
)
( 




o
v
vo(θ)
θ
2

2
3
2
5
-1
1
Fourier series equation for square
wave:



t
m
f
c dt
t
v
k
t
t
0
)
(
)
( 

t
vo[θ(t)]
• Therefore the limiter output is a
function of θ(t) and the equation can
be written as :
For FM signal the angle varied in
accordance to the amplitude of the
information signal.
8

9. • Output of
limiter :
]
)
(
cos[
4
)
(
0



t
m
f
c
o dt
t
v
k
t
t
e 

eo(t)

4
t

4




















...
]
)
(
5
5
cos[
5
1
]
)
(
3
3
cos[
3
1
]
)
(
cos[
4
]
)
(
[
)]
(
[
0
0
0
0
t
m
f
c
t
m
f
c
t
m
f
c
t
m
f
c
o
o
dt
t
v
k
t
dt
t
v
k
t
dt
t
v
k
t
dt
t
v
k
t
v
t
v






• Output of BPF :
9

10. Analysis (continued) :Slope detection
Bandpass
limiter
Pengesan
Sampul
dt
d
vFM(t) y(t)
v2(t)
v1(t)
Limiter output :
 ]
cos[
4
)
(
1 t
t
V
t
v c
L 




Differentiator output :    ]
sin[
4
)
(
2 t
t
dt
t
d
V
t
v c
c
L 














)]
(
cos[
)
(
)
( t
t
t
E
t
v c
c
FM 
 
 

t
m
f dt
t
v
k
t
0
)
(
)
(

where
FM signal :
Output of the envelope detector :  









dt
t
d
V
t
y c
L



4
)
(
Since
dt
d
c

 
 








dt
t
d
V
t
y c
L



4
)
(
;
10

11.  
t
v
k
V
V
t
y m
f
L
c
L



4
4
)
( 

which indicates that the output consists
of a dc voltage plus the ac voltage, which
is proportional to the modulation on the
FM signal.
Therefore :
dc ac
Slope detector circuit
The slope detector is essentially a tank
circuit which is tuned to a frequency
either slightly above or below the FM
carrier frequency. It is not widely used
because of the characteristics
of LC tuned circuit which is
nonlinear especially for FM
signal with large f .
11

12. Is addressed by using - Balanced Slope Detector– Using two
tuned circuit.
To create wider linear region for signal with large f – achieved by
using two diodes and tuned at two different tuning frequency.
12

13. Foster – Seeley Discriminator
D1
D2
C2
C
C3
C4
R1
R2
V12
Vo
I1
I2
C1
L
Ip
1
2
6
7
3
4
5
The Foster-Seeley discriminator is a widely used FM detector. The detector
consists of a special center-tapped transformer feeding two diodes in a full wave
DC rectifier circuit. When the input transformer is tuned to the signal frequency, the
output of the discriminator is zero when there is no deviation of the carrier; both
halves of the center tapped transformer are balanced. As the FM signal swings in
frequency above and below the carrier frequency, the balance between the two
halves of the center-tapped secondary are destroyed and there is an output voltage
proportional to the frequency deviation.
13

14. Ratio Detector Circuit
Pemodulatan Sudut
L1
L2
D1
D2
C
CR
R1
R2
V12
Vo
C1
L
Ip
1
2
3
4
5
VDC
+
-
The ratio detector is a variant of the Foster-Seely discriminator, but, the diodes
conduct in opposite directions. The output in this case is taken between the sum of
the diode voltages and the center tap. The output across the diodes is connected
to a large value capacitor, which eliminates AM noise in the ratio detector output.
While unlike the Foster-Seely discriminator, the ratio detector will not respond to
AM signals, however the output is only 50% of the output of a discriminator for the
same input signal. 14

15. Phase-Locked Loop (PLL) –
Indirect Method
• Above is a block diagram of FM detector using Phase-Locked Loop
(PLL).
• The input is FM signal:
LPF
Voltage-Controlled
Oscillator (VCO)
X
vin(t)
ve(t)
vvco(t)
vo(t)
)
)
(
cos(
)]
(
cos[
)
(
0





t
m
f
c
c
c
c
c
in
dt
t
v
k
t
E
t
t
E
t
v



)]
(
sin[
)
( t
t
E
t
v o
c
o
vco 
 

15

16. )
(
)]
(
)
(
[ t
t
t e
o
in 

 

)
(
)]
(
sin[ t
t e
e 
 
Then
1
)
( 
t
e

If
)]
(
)
(
sin[
2
)]
(
)
(
2
sin[
2
)]
(
sin[
)]
(
cos[
)
(
)
(
)
(
t
t
E
E
t
t
t
E
E
t
t
t
t
E
E
t
v
t
v
t
v
o
in
o
c
o
in
c
o
c
o
c
in
c
o
c
vco
in
e


















)]
(
sin[
)
( t
t
E
t
v o
c
o
vco 
 
 

t
o
o
o dt
t
v
k
t
0
)
(
)
(

• VCO output:
• Multiplier in the circuit will function as a phase variation
detector:
• LPF will pass all the lower frequency components and
filtered all the higher frequency components:
Phase-Locked Loop
)
(
2
)
(
sin
2
)]
(
)
(
sin[
2
)
(
t
E
E
t
E
E
t
t
E
E
t
v
e
o
c
e
o
c
o
in
o
c
o








where
16

17. e
e
a
vo
vo
Figure shows the plot of vo vs e . Using this plot we
can explain the tracking mechanism.
17

18. 18
• Frequency generated at the VCO output is proportional to
the input voltage of the VCO.
• Therefore
• Output of the PLL is given by:
• Given:
• Hence:
)
(
)
( t
v
k
t o
o
o 

dt
t
v
k
dt
t
t
t
o
o
t
o
o )
(
)
(
)
(
0
0

 
 

dt
t
d
k
t
v o
o
o
)
(
1
)
(


1
)
(
)
(
)
( 

 t
t
t o
in
e 


)
(
)
( t
t o
in 
 
)
(
)
(
)
(
1
)
(
1
)
( t
kv
t
v
k
k
dt
t
d
k
dt
t
d
k
t
v m
m
o
f
in
o
o
o
o 




