FM Modulation and Demodulation

Goal:
The goal of this experiment is to become familiar with FM modulation and demodulation.

Theory and background:

1. FM modulation:
Frequency modulation (FM) is a process in which the carrier frequency is varied by the amplitude
of the modulating signal (i.e., intelligence signal). The FM signal can be expressed by the
following equation:
𝑥𝐹𝑀 (𝑡) = 𝐴𝑐 cos(𝜃𝑡) = 𝐴𝑐 cos⁡(2𝜋𝑓𝑐 𝑡 + 2𝜋𝑓∆ ∫ 𝑥(𝜆)𝑑𝜆) (1)
If 𝑥(𝜆) = 𝐴𝑚 cos(2𝜋𝑓𝑚 𝜆), then:
𝑥𝐹𝑀 (𝑡) = 𝐴𝑐 cos⁡(2𝜋𝑓𝑐 𝑡 + 𝛽sin⁡(2𝜋𝑓𝑚 𝑡)) (2)
Where
θ (t) = instantaneous modulated frequency
𝑓𝑐 = carrier frequency
𝑓𝑚 = modulating frequency
β = modulation index = 𝐴𝑚 (𝑓∆ /𝑓𝑚 )
The frequency of FM signal 𝑥𝐹𝑀 (𝑡) may be expressed as
1 𝑑
𝑓= 𝜃(𝑡) = 𝑓𝑐 − 𝑓𝑚 𝛽 cos(2𝜋𝑓𝑚 𝑡) (3)
2𝜋 𝑑𝑡

From (3) we can find that the frequency of frequency modulated signal occurs frequency deviation
from the center frequency of the carrier when the intelligence amplitude is variation.
FM Generation with VCO
The VCO - voltage controlled oscillator - is available as a low-cost integrated circuit (IC), and its
performance is remarkable. The VCO IC is generally based on a bi-stable ‘flip-flop’, or ‘multi-
vibrator’ type of circuit. Thus its output waveform is a rectangular wave. However, ICs are
available with this converted to a sinusoid. The mean frequency of these oscillators is determined
by an RC circuit.
The controllable part of the VCO is its frequency, which may be varied about a mean by an external
control voltage.

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The variation of frequency is remarkably linear, with respect to the control voltage, over a large
percentage range of the mean frequency. This then suggests that it would be ideal as an FM
generator for communications purposes.
Unfortunately such is not the case.
The relative instability of the center frequency of these VCOs renders them unacceptable for
modern day communication purposes. The uncertainty of the center frequency does not give rise
to problems at the receiver, which may be taught to track the drifting carrier. The problem is that
spectrum regulatory authorities insist, and with good reason, that communication transmitters
maintain their (mean) carrier frequencies within close limits.
It is possible to stabilize the frequency of an oscillator, relative to some fixed reference, with
automatic frequency control circuitry. But in the case of a VCO which is being frequency
modulated there is a conflict, with the result that the control circuitry is complex, and consequently
expensive.
For applications where close frequency control is not mandatory, the VCO is used to good effect.
This experiment is an introduction to the FM signal and we use VCO for generating FM signals.
Varactor Diode is plays major rule in VCO. Therefore, we are going to describe it briefly.
Varactor Diode
The varactor diode, sometimes called tuning diode, is the diode whose capacitance is proportional
to the amount of the reverse bias voltage across p-n junction. Increasing the reverse bias voltage
applied across the diode decreases the capacitance due to the depletion region width becomes
wider.
Conversely, when the reverse bias voltage decreased, the depletion region width becomes narrower
and the capacitance increased. When an ac voltage is applied across the diode, the capacitance
varies with the change of the amplitude.
A relationship between a varactor diode and a conventional capacitor is shown in Figure 1. In fact,
a reverse-biased varactor diode is similar to a capacitor.
When a p and n semiconductors combined together, a small depletion region is formed because of
the diffusion of minority carriers. The positive and negative charges occupy n and p sides of
junction, respectively. This just likes a capacitor. The amount of internal junction capacitance can
be calculated by the capacitance formula
𝜀𝐴
𝑐= (4)
𝑑

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 Figure 1: Relationship between varactor diode and capacitor

From the formula above, we know that the varactor capacitance is inversely proportional to the
width of depletion region (or the distance between plates) if the area A is constant. Therefore, a
small reverse voltage will produce a small depletion region and a large capacitance. In other words,
an increase in reverse bias will result in a large depletion region and a small capacitance.
A varactor diode can be considered as a capacitor and resistor connected in series as shown in
Figure 2. The CJ is the junction capacitance between p and n junctions. The Rs is the sum of bulk
resistance and contact resistance, approximately several ohms, and it is an important parameter
determining the quality of varactor diode.

Figure 2: the equivalent circuit of varactor diode

2. FM Demodulation
a. The zero-crossing-counter demodulator
A simple yet effective FM demodulator is one which takes a time average of the zero crossings of
the FM signal. Figure 3 suggests the principle.

Figure 3: An FM signal, and a train of zero-crossing pulses

Each pulse in the pulse train is of fixed width, and is located at a zero crossing of the FM signal.
This is a pulse-repetition-rate modulated signal. If the pulse train is passed through a low pass

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filter, the filter will perform an averaging operation. The rate of change of this average value is
related to the message frequency, and the magnitude of the change to the depth of modulation at
the generator.
This zero-crossing-counter demodulator will be modeled in the latter part of the experiment and
used for demodulation low frequency FM. The phase locked loop (PLL) as a demodulator will be
studied in the next section.
b. FM Demodulation with the PLL
The phase locked loop is a non-linear feedback loop. To analyze its performance to any degree of
accuracy is a non-trivial exercise. To illustrate it in simplified block diagram form is a simple
matter. See Figure 4.

Figure 4: The basic PLL

This arrangement can be used for many purposes. For Carrier acquisition the output was taken
from
the VCO. As an FM demodulator, the output is taken from the LPF, as shown. It is a simple matter
to describe the principle of operation of the PLL as a demodulator, but another matter to carry out
a detailed analysis of its performance. It is complicated by the fact that its performance is described
by non-linear equations, the solution to which is generally a matter of approximation and
compromise.
The principle of operation is simple - or so it would appear. Consider the arrangement of Figure 4
in open loop form. That is, the connection between the filter output and VCO control voltage input
is broken.
Suppose there is an unmodulated carrier at the input.
The arrangement is reminiscent of a product, or multiplier-type, demodulator. If the VCO was
tuned precisely to the frequency of the incoming carrier, then the output would be a DC voltage,
of magnitude depending on the phase difference between itself and the incoming carrier.
For two angles within the 360 degrees range the output would be precisely zero volts DC.
Now suppose the VCO started to drift slowly off in frequency. Depending upon which way it
drifted, the output voltage would be a slowly varying AC, which if slow enough looks like a
varying amplitude DC. The sign of this DC voltage would depend upon the direction of drift.

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Suppose now that the loop of Figure 4 is closed. If the sign of the slowly varying DC voltage, now
a VCO control voltage, is so arranged that it is in the direction to urge the VCO back to the
incoming carrier frequency w0 , then the VCO would be encouraged to ‘lock on’ to the incoming
carrier. This is the principle of carrier acquisition.
Next suppose that the incoming carrier is frequency modulated. For a low frequency message, and
small deviation, you can imagine that the VCO will endeavor to follow the incoming carrier
frequency. What about wideband FM? With ‘appropriate design’ of the low pass filter and VCO
circuitry the VCO will follow the incoming carrier for this too.
The control voltage to the VCO will endeavor to keep the VCO frequency locked to the incoming
carrier, and thus will be an exact copy of the original message.
Analysis of PLL operation
The PLL is an electronic feedback control system, as illustrated by the block diagram in Figure 5,
of locking the output and input signals in good agreements in both frequency and phase. In radio
communication, if a carrier frequency drifts due to transmission, the PLL in receiver circuit will
track the carrier frequency automatically.

Figure 5. PLL block diagram

The PLL in the following experiments is used in two different ways: (1) as a demodulator, where
it is used to follow phase or frequency modulation and (2) to track a carrier signal which may vary
in frequency with time. In general, a PLL circuit includes the following sections:
1. Phase Detector (PD)
2. Low Pass Filter (LPF)
3. Voltage Controlled Oscillator (VCO)
The phase detector within the PLL locks at its two inputs and develops an output that is zero if
these two input frequencies are identical. If the two input frequencies are not identical, then the
output of detector, when passed through the low-pass filter removing the ac components, is a dc
level applied to the VCO input. This action closes the feedback loop since the dc level applied to
the VCO input changes the VCO output frequency in an attempt to make it exactly match the input
frequency. If the VCO output frequency equals the input frequency, the PLL has achieved lock,

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and the control voltage will be zero for as long as the PLL input frequency remains constant. The
parameters of PLL shown in Figure 5 are as follows:
Kd = phase detector gain in volts/radian
Ka = amplifier gain in volt/volt
Ko = VCO gain in kHz/volt
KL = KdKaKo =closed loop gain in kHz/volt

Figure 6: Phase detection

A better understanding of the operation of phase detector may be obtained by considering that the
simple EXCULSIVE-OR (XOR) gate is used as a phase detector. The XOR gate can be thought
of as an inequality detector which compares the inputs and produces a pulse output when these
inputs are unequal. The width of the output pulse is proportional to the phase error of the input
signals. As shown in Figure 6, the width of the output pulse of (b) is larger than that of (a) and is
smaller than that of (c). When the output of phase detector is applied to the input of low-pass filter,
the output of low-pass filter should be a dc level that is directly proportional to the pulse width. In
other words, the output dc level is proportional to the phase error of input signals. Figure 6 (d)
shows the relationship between the input phase error and the output dc level.

Figure 7: Operation of frequency locking

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For a further understanding of the operation of the PLL can be obtained by considering that initially
the PLL is not in lock. The VCO has an input voltage of 2V and is running at its free-running
frequency, say 1 kHz. Consider the signals shown in Figure 7. If the VCO frequency and the signal
A with the lower frequency 980Hz are applied to the inputs of the phase detector XOR, the
narrower width of output pulse will cause the low-pass filter obtaining the smaller output voltage
of 1V. This smaller voltage decreases the VCO frequency close to the input frequency. If the VCO
output frequency equals the input frequency, lock will result. On the contrary, the higher frequency
1.2 KHz of input signal B causes the larger filter output of 3V that increases the VCO frequency
output to lock at the input frequency.

PRELAB
Direct FM Using VCO
Perform a PSPICE simulation of a direct FM using a VCO. The VCO is located under anl_misc.olb
of the ORCAD library. Change the VCO parameter FCENTER to your carrier frequency and
FRANGE to your message frequency. Show your message wave, carrier wave, and the FM signal.
Submit your schematics and waveforms.