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N.E.D. University of Engineering and Technology
Department of Electronic Engineering
Lecture Notes: Communication Systems II
Detection or Demodulation of FM Signals:
FM detector or demodulator is a device which produces an output voltage that varies
linearly with the instantaneous frequency of input signal. A frequency detector is also
known as Discriminator.
Based on the principle of operation, FM demodulators are categorized as follows:
1. FM to AM converters
2. Phase Shift Discriminators
3. Zero Crossing Detectors
 FM to AM Converters:
Consider the equation of a frequency modulated carrier signal:
xc (t) = Ac Cos {2πfct + 2πfΔ∫ m(t)dt}
Differentiating with respect to “t”
d/dt {xc (t)} = - Ac Sin {2πfct + 2πfΔ∫ m(t)dt} d/dt {2πfct + 2πfΔ∫ m(t)dt}
d/dt {xc (t)} = - Ac Sin {2πfct + 2πfΔ∫ m(t)dt} x {2πfc + 2πfΔm(t)}
d/dt {xc (t)} = - 2πAc {fc + fΔ m(t)} Sin {2πfct + 2πfΔ∫ m(t)dt}
In the above equation the factor fc + fΔ m(t) represents the instantaneous frequency of the
modulated signal i.e.
f(t) = fc + fΔ m(t)
So,
d/dt {xc (t)} = - 2πAc f(t) Sin {2πfct + 2πfΔ∫ m(t)dt}
This equation shows that the derivative of FM signal is an amplitude and frequency
modulated signal. But, a most significant property of the above equation is that the
amplitude of the signal is proportional to the instantaneous frequency of input signal.
Hence, if the derivative of the FM signal is fed to an envelope detector then the actual
signal can be extracted. Therefore a conceptual block diagram of FM to AM converter
can be given as:
Since FM signal has a constant amplitude, therefore it is first fed to an amplitude limiter
to remove any amplitude variations due to noise. Following two blocks perform the
functions described above. Finally a dc block removes any dc offset from the
demodulated signal.
 Practical Circuits:
FM to AM converters are actually implemented using tuned circuits. Consider an LC
circuit tuned at frequency fo. Output voltage characteristics of this circuit versus
frequency can be given as:
N.E.D. University of Engineering and Technology
Department of Electronic Engineering
Lecture Notes: Communication Systems II
This graph shows that at frequencies below fo the slope of the curve can be approximated
to a straight line. Hence, in this region output voltage Vo of the LC circuit varies linearly
with the frequency. This method is also known as Slope Detection.
The only problem in this circuit is that the linear region is very small. Frequency
deviations beyond this region suffer considerable distortion. It is obvious from the above
graph that fo must be higher than carrier frequency fc and fc should lie somewhere in the
middle of the linear region. The circuit diagram of a slope detector is as follows:
To expand the linear operating region and accommodate larger frequency deviations
balanced configuration is used.
 Balanced Slope Detector:
This circuit is also known as Travis Detector. This circuit consists of two slope detectors,
connected back to back to the opposite ends of a centre tapped transformer. So, when
modulated signal is applied to the primary side of the circuit, both circuits are fed 180o
out of phase. The circuit configuration is given below.
The upper circuit is tuned above fc by an amount more than fΔ. Similarly, the lower circuit
is tuned below fc by an amount fΔ. The output is taken across a series combination which
represents the sum of individual outputs.
N.E.D. University of Engineering and Technology
Department of Electronic Engineering
Lecture Notes: Communication Systems II
This scheme expands the linear operating range as shown in the following graph:
This circuit does not require a dc block, as dc offset is cancelled.
 Phase Shift Discriminator:
Phase shift discriminators exploit the fact that in a frequency modulated carrier phase
varies linearly with integral of the message signal. Hence, FM signal can be demodulated
by observing the varying phase of the carrier signal.
Consider the mathematical expression of a FM carrier signal.
xc (t) = Ac Cos {2πfct + 2πfΔ∫ m(t)dt}
In the above equation, the instantaneous phase is:
φ(t) = 2πfΔ∫ m(t)dt …………(i)
Differentiating with respect to “t”
d/dt {φ(t)} = 2πfΔ m(t)
We know that time derivative of any function f(t) is given by:
d/dt {f(t)} = limit {f(t) – f(t – Δt)}/ Δt
Δt → 0
If Δt is assumed to be a very small quantity, then:
d/dt {f(t)} ≈ {f(t) – f(t – Δt)}/ Δt………(ii)
Using above equation, we can rewrite equation (i).
d/dt {φ(t)}= {φ(t) – φ(t – Δt)}/ Δt ≈ 2πfΔ m(t)
or φ(t) – φ(t – Δt) ≈ 2πfΔ Δt m(t) ……….……(iii)
This equation shows that the phase shift is proportional to the message signal. Now
consider the frequency modulated signal again.
xc (t) = Ac Cos {2πfct + φ(t)}……..…..(iv)
This signal is passed through a circuit which produces a Carrier Delay of 90o and Group
Delay of Δt. So, after passing through this circuit the signal acquires following
mathematical form.
x’c (t) = Ac Sin {2πfct + φ(t - Δt)}…………..(v)
Now, the actual FM signal xc (t) and delayed signal x’c (t) are fed to a multiplier to
produce the following output:
xc (t) x’c (t) = A2c Cos {2πfct + φ(t)} Sin {2πfct + φ(t - Δt)}
’
xc (t) x c (t) = ½A2c [Sin {4πfct + φ(t) + φ(t – Δt)} + Sin {φ(t – Δt) - φ(t)}]
xc (t) x’c (t) = ½A2c [Sin {4πfct + φ(t) + φ(t – Δt)} - Sin {φ(t) - φ(t – Δt)}]
N.E.D. University of Engineering and Technology
Department of Electronic Engineering
Lecture Notes: Communication Systems II
The higher frequency sine term can be filtered out using a low pass filter. Hence the final
output comes out to be:
YD(t) = - ½A2c Sin {φ(t) - φ(t – Δt)}
If
│φ(t) - φ(t – Δt)│<< π
then
Sin {φ(t) - φ(t – Δt)}≈ φ(t) - φ(t – Δt)
Therefore
YD(t) = - ½A2c {φ(t) - φ(t – Δt)}
Using equation (iii)
YD(t) = - ½A2c 2πfΔ Δt m(t)
YD(t) = KDfΔm(t) …………...(vi)
where KD = - A2c πΔt called Detection Constant. Equation (vi) represents that YD(t) to the
message signal. A conceptual block diagram of the phase shift discriminator can be given
as:
 Practical Circuit:
Phase shift discriminators are implemented using modified form of balanced slope
detectors or Travis detectors. This modified form uses a single resonant circuit tuned at
carrier frequency fc. This design avoids the problems of tuning two resonant circuits at
different frequencies to achieve a larger linear region. This circuit is known as FosterSeeley Discriminator.
In Foster-Seeley Discriminator, primary winding of the transformer is connected to the
centre of secondary winding through a capacitor. An inductor is attached between centres
of the secondary winding and output load. A capacitor is used across the secondary to
tune it at carrier frequency.
If a voltage Vp is applied at the primary side then it induces a voltage Vs in the secondary
side which has two components that are 180o apart. If the applied signal has a frequency
fc then the secondary circuit resonates and behaves as a pure resistive circuit because at
resonant frequency, XL = Xc. Thus the secondary voltage Vs and current Is are in phase.
N.E.D. University of Engineering and Technology
Department of Electronic Engineering
Lecture Notes: Communication Systems II
The primary voltage Vp also appears directly across the inductor through the capacitor C1.
This voltage is 90o out of phase from both components of Vs. Hence a phasor diagram of
the voltages in the above circuit can be drawn as follows:
Now the voltages across the diodes D1 and D2, which are represented by VD1 and VD2, are
the vector sums of Vp and Vs/2 as shown in the above figure. It is also obvious from the
figure that these voltages are equal and thus the voltage at output terminals is zero.
When frequency of the signal on primary side increases from fc, the secondary circuit
becomes inductive, i.e.
XL > Xc
jωL > 1/(jωC)
In this situation Is and Vs are no more in phase. Thus, one component of the Vs lags Vp by
more than 90o and other one leads it by less than 90o, maintaining their 180o separation.
Now VD1 exceeds VD2 and a positive voltage appears across the output terminals as
depicted in the following figure.
Similarly, when the frequency of the signal applied at the primary side decreases from fc,
the secondary circuit becomes capacitive, i.e.
XL < Xc
jωL < 1/(jωC)
The phasor diagram of the voltages is now as follows which shows that V D2 is more than
VD1 and output voltage becomes negative.
Hence, the output voltage is varying in accordance with the message signal.
 Zero Crossing Detector:
It is true to say that the information is hidden in the zero crossings of a frequency
modulated signal. Therefore, it is possible to demodulate FM signal by observing its zero
N.E.D. University of Engineering and Technology
Department of Electronic Engineering
Lecture Notes: Communication Systems II
crossings. A zero crossing detector circuit is also known as Pulse Averaging
Discriminator.
 Practical Circuit:
A zero crossing detector comprises of following operational blocks whose connectivity
and performance is described as follows:
First of all, the frequency modulated signal is fed to a hard limiter whose output is a
square wave FM signal. A hard limiter basically chops off the sinusoidal carrier at a very
small amplitude and thus generates an approximated square wave preserving the zero
crossings of the FM signal. Limiter output is used to trigger a mono-stable multi-vibrator,
which produces a short pulse v(t) of fixed amplitude A and duration τ. This pulse is
produced at every upward or downward zero crossing of the limiter output wave. It is
obvious that more pulses are generated as the frequency of the FM signal increases.
These pulses are further fed to an integrator which evaluates the integral or average area
under these pulses over a certain period of time T. This interval T is chosen so that the
pulses’ frequency f(t) remains nearly constant during this period. Thus, the total number
of pulses during this interval can be given as:
n = T f(t)
Since, the area of a single pulse is:
Area = Aτ
Hence;
(1/ T) ∫ v(t) dt = (1/ T) nAτ = Aτ f(t)
T
The above equation shows that the output of the integrator is proportional to the
instantaneous frequency of the FM signal. The block diagram of a zero crossing detector
can be given as:
Actual FM signal, hard limiter output, MVB pulses and integrator’s output which is
proportional to the message signal are as follows:
N.E.D. University of Engineering and Technology
Department of Electronic Engineering
Lecture Notes: Communication Systems II
Interference in FM Signals:
 Definition:
“The undesirable mixing of external signals from other sources and transmitters is
defined as interference.”
 Common Causes:
Most commonly it occurs in radio communications. A receiving antenna picks up some
other information bearing signals in the same frequency range. At some other occasions,
the desired signal is received after a delay due to reflections from the neighboring
objects. This phenomenon is known as Multi-path Propagation. The received signal, in
this situation, behaves as another information bearing signal in the same frequency range
and thus causes interference. It is also possible that the transmission cable catches
electromagnetic radiations from other machinery or nearly laid cables. But in any case,
message signal is partly or completely destroyed.
 Vulnerable Frequency Ranges:
Since there are no amplitude variations in FM signals, therefore they are more immune to
noise as compared to AM signals. But any noise or undesirable information signal whose
frequency falls within the message bandwidth can damage the actual information as
stated above.
Consider an interfering signal with amplitude Ai having same frequency as message
signal with amplitude Ac. Here we define a parameter “ρ” as follows:
ρ = Ai / Ac
If ρ << 1 then the interfering signal does not cause severe damage to the message and an
intelligible signal is received. But, in case ρ exceeds 0.7, the interfering signal takes over
and displaces the message signal. This phenomenon is known as Capture Effect, i.e. the
interfering signal captures the channel and received instead of message signal. This is the
most undesirable situation.
We know that the high frequency components of signal possess relatively smaller
amplitudes as compared to those near the center frequency. We also know that the
impulses or short bursts of noise are limited in time but occupy large frequency ranges, a
phenomenon known as Reciprocal Spreading. Therefore, in noise impulses high
frequency components have larger amplitudes. Thus, if signal catches impulse like noise
then its high frequency components are more vulnerable due to smaller amplitudes.
 Remedy:
To prevent high frequency components from noise, a technique known as Pre-emphasis
Filtering is used at transmitter side, whereas its inverse procedure called De-emphasis
Filtering is done at the receiver.
 Pre-emphasis Filtering:
A pre-emphasis filter is used prior to modulation where noise is theoretically absent. It
amplifies the high frequency components of the message signal above noise level. On the
N.E.D. University of Engineering and Technology
Department of Electronic Engineering
Lecture Notes: Communication Systems II
other hand low frequency components pass through it without any amplification. Its
circuit diagram is given below.
The frequency f1 at which this circuits starts amplification is given by:
f1 = 1 / (2R1C)
For normal voice applications:
R1C  75  sec
Thus
f1  2.1 kHz
Similarly, the upper break frequency f2, to which amplification is done, can be given as:
f2 = (R1 + R2) / (2R1R2C)
Usually f2 comes out to be:
f2  30 kHz
The transfer function Hpe of the pre-emphasis filter is given below in dB scale.
 De-emphasis Filtering:
De-emphasis filter is used after demodulator and performs the reverse function of preemphasis filtering. It attenuates the high frequency components of the message signal and
produces an output proportional to the message signal. Lower frequency components pass
through it without any attenuation. A typical de-emphasis filter circuit is given below:
Its transfer function Hde is mathematically reciprocal of pre-emphasis filter.
Hde = 1 / Hpe
A Bode plot of Hde is given below.