Fatih University
Electrical and Electronics Engineering Department
EEE 316 - Communications I
EXPERIMENT 5
FM MODULATORS
5.1 OBJECTIVES
1. Studying the operation and characteristics of a varactor diode.
2. Understanding the operation of voltage-controlled oscillator in frequency modulators.
3. Implementing a frequency modulator with a varactor diode and a voltage-controlled
oscillator (MC1648).
5.2 PRELIMINARY WORK
Read chapter 5 in the textbook.
5.3 EQUIPMENT AND MATERIALS
The equipment list that will be used in this experiment is shown in Table 5.1. Before
starting the experiment, record the model, serial number and office stock number of the
equipment that will be used throughout the experiment. Also, record any damages.
Table 5.1 Equipment list for experiment 5.
Item
Equipment
No
Digital Oscilloscope (DO)
1
Function Generator (1)
2
Function Generator (2)
3
DC Power Supply
4
Connecting Probes and Cables
5
MC1648 FM Modulator Unit
6
Record of damages or other comments:
Model
Serial No
Office Stock
No
5.4 THEORY
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 ωc t + K ∫ x(t )dt
EEE 316 - Communications I
]
Experiment 5
(5.1)
Page 1 of 8
where,
xc (t ) = Ac cos ω c t
(5.2)
is the unmodulated carrier, and x(t ) is the modulating signal. The instantaneous frequency of the FM
signal can be obtained by taking the derivative of the angle of cos function in Eq. (5.1). The result is
ω (t ) =
[
]
d
ω c t + K ∫ x(t )dt = ω c + Kx(t ) .
dt
(5.3)
Hence, the instantaneous frequency of the FM signal is changing in proportional with the modulating
signal x(t ) , K being the proportionality constant.
When the modulating signal is a pure sinusoid with the peak value Am and frequency ω m , i.e.,
x(t ) = Am cos ω m t ,
(5.4)
the FM signal and the instantaneous frequency can be found by using Eqs. (5.1), (5.3), and (5.4).
as follows:


KAm
x FM (t ) = Ac cos ω c t +
sin ω m t ,
ωm


ω (t ) = ω c + KAm cos ω m t
(5.5)
(5.6)
The frequency deviation ω D is obtained from Eq. (5.6) to be
ω D = KAm
(5.7)
Hence, the instantaneous frequency varies in [ω c − ω D , ω c + ω D ] since cos ω m t varies between [-1,
+1].
The deviation ratio β of an FM signal is defined as
β=
ωB
ωm
(5.8)
where, ω D is the frequency deviation and ω m is the highest frequency component of the intelligence.
Using Eqs. (5.7) and (5.8), the relation between the modulation constant K and the deviation ratio β
is found to be
β=
KAm
ωm
or K =
βω m
Am
,
(5.9)
5.4.1 Varactor Diode
The varactor diode sometimes called the tuning diode is the diode whose capacitance
is proportional to the amount of the reverse bias voltage across the p-n junction. Increasing the
reverse bias voltage applied across the diode decreases the capacitance since the depletion
EEE 316 - Communications I
Experiment 5
Page 2 of 8
region width becomes wider. Conversely, when the reverse bias voltage is decreased, the
depletion region width becomes narrower and the capacitance is increased. When an AC
voltage is applied across the diode, the capacitance varies with the change of the AC voltage.
A
d
Figure 5.1 Relationship between a varactor diode and a parallel plate capacitor.
A relationship between a varactor and a conventional capacitor is shown in Figure 5.1.
In fact, a reverse-biased varactor diode is similar to a capacitor. When p and n junctions are
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 the junction, respectively.
This is just like a capacitor. The amount of the internal capacitance of the diode can be
calculated by the capacitance formula
CD =
εA
d
,
(5.10)
where,
ε =11.8 ε 0 = dielectric constant,
ε 0 = 8.85 x 10 −12 F/m,
A = Cross sectional area of the capacitor,
d = The width of the depletion region.
According to the above formula, the varactor capacitance is inversely proportional to
the width of the depletion region (or the distance between plates) if the area A is constant.
Therefore, a small reverse voltage will produce a small depletion and a large capacitance.
Conversely, an increase in reverse bias will result in a large depletion region and a small
capacitance.
CD
RD
Figure 5.2 Equivalent circuit of a varactor diode.
EEE 316 - Communications I
Experiment 5
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A varactor diode can be considered as a capacitor and resistor connected in series as
shown in Figure 5.2. C D is the junction capacitance between p and n junctions. R D is the
sum of bulk resistance and contact resistance, approximately several ohms, which is an
important parameter determining the quality of a varactor diode.
Tuning ratio (TR) is defined as the ratio of the capacitance of varactor diode at the
reverse voltage V2 to another reverse voltage V1 , and can be expressed as
TR =
C D ,V 2
(5.11)
C D ,V 1
where TR = Tuning ratio, C D ,V 1 = Capacitance of varactor diode at V1 , C D ,V 2 = Capacitance of
varactor diode at V2 .
TR is usually expressed as a number greater than 1, hence C D ,V 2 > C D ,V 1 which
implies that V2 < V1 . 1SV55 varactor diode is used in our experiment and its major
characteristics are C D ,3V = 42 pF (capacitance of varactor diode at 3V), TR = 2.65 (at
3V~30V).
5.4.2 Frequency Modulator Based on MC1648 VCO
In this experiment the frequency modulator is implemented with MC1648 VCO chip
as shown in Figure 5.3. Basically, this circuit is an oscillator, and the tuning circuit at the
input end determines its oscillating frequency. In this circuit, capacitors C 2 and C 3 are the
bypass capacitors for filtering noise. When operating at a high frequency (for example 2.4
MHz), the capacitance reactance of these two capacitors are very small and can be neglected
in the LC loop formed by C 3 , L1 , D1 , C 2 for practical purposes. This makes possible to assume
D be in parallel with L1 . Therefore, the AC equivalent circuit is a tuning tank which consists
of a parallel LC resonant circuit as shown in Figure 5.4. C can be considered as the sum of
the capacitance of 1SV55 ( C D ) and the input capacitance of MC1648 ( C in ) connected in
parallel, i.e., C = C D + C in . The value of C in is approximately 6 pF. If the stray capacitance is
neglected, the oscillating frequency can be calculated by the formula
f0 =
1
2π LC
EEE 316 - Communications I
=
(
1
2π L C D + 6 x10 −12
)
(Hz)
Experiment 5
(5.12)
Page 4 of 8
Figure 5.3 MC1648 FM modulator circuit.
As mentioned above, the capacitance C D of the varactor diode D varies with the
amount of its reverse voltage. It is known that the change of C D will cause the change of
oscillating frequency. In the circuit of Figure 5.3, a small DC bias will produce a large C D
and a low frequency output. On the other hand, an increase in DC bias will result in a small
C D and a high frequency output. Therefore, if the DC bias is fixed and an audio signal is
applied to the audio input to change the bias voltage around the fixed value, the VCO output
signal will be a frequency-modulated signal of the audio input.
Figure 5.4 AC equivalent circuit of the tuning tank.
5.5 EXPERIMENTAL PROCEDURE AND RESULTS
Note: When using digital oscilloscope (DO), record the critical data related with any
observation on DO, for example DC level, peak values, period and frequency for different
regions; then draw the waveform based on this data on scale. The critical data should appear
just below the associated figure. You can take the DO display by holding and taking it in
storage.
EEE 316 - Communications I
Experiment 5
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5.5.1 Characteristic Measurements on MC1648
1.
Take MC1648 FM Modulator Unit supplied at your experiment table and connect +5
V supply voltage to it. Use the switch SW1 to set the inductor L1 to 100 µH .
2. Connect 2 V DC bias input and observe the output waveform by using the
oscilloscope. Adjust Rv until a sine wave appears at the output. Record the frequency
in Table 5.2.
3. Repeat the above step for all the DC bias input voltages shown in Table 5.2.
Table 5.2 Change of the free oscillation frequency of MC1648 VCO with the bias
voltage.
DC Bias input
(V)
Output
frequency f 0
MHz.
(experimental)
2
3
4
5
6
7
8
9
10
5.5.2 Frequency Modulation by MC1648 FM Modulator Unit
1. Repeat the first step of section 5.5.1.
2. Connect a 5 V DC bias input and observe the output waveform using the second
channel of DO. Adjust Rv until a sine wave appears at the output. Record the
unmodulated carrier frequency f 0 and the pp value of the output on the legend of
Table 5.3.
3. Connect 3 kHz. sine wave to the audio input and adjust its amplitude to 2 Vpp by using
the first channel of DO. Plot this input on Table 5.3 at the appropriate place on scale.
Indicate the frequency and the peak value explicitly.
4. With the above input still connected, observe and plot the FM output signal observed
on channel-II. Plot this waveform on Table 5.3 at the appropriate place on scale.
Measure and record the pp value and the maximum and minimum frequencies of the
FM output signal. Use the hold and memory control of DO.
5. Observe the spectrum of the FM signal output on the spectrum analyzer. Record the
frequency and amplitude of each component in Table 5.3.
6. Repeat steps 3-5 for 5 kHz and 8 kHz audio frequencies.
EEE 316 - Communications I
Experiment 5
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Table 5.3 The input intelligence and FM Output signals of the MC1648 FM Modulator
Audio input: 0.5 Vpp ; Unmodulated carrier:………Vpp, f 0 = ….….kHz.
Audio
input
Audio waveform
FM output signal
Spectrum of
frequency
(Intelligence or message signal)
(FM modulated carrier)
FM signal
f m (kHz)
Freq. Amp.
3
peak value:
f 0 min =
, f o max =
Freq. Amp.
5
peak value:
f 0 min =
, f o max =
Freq. Amp.
8
peak value:
f 0 min =
, f o max =
EEE 316 - Communications I
Experiment 5
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5.6 RESULTS AND DISCUSSIONS
1. Using the experimental results in Table 5.2, plot the frequency versus voltage curve in
Figure 5.6.
f0
DC bias voltage
(V)
Figure 5.6 Variation of the oscillation frequency of the VCO MC 1648 shown in Fig. 5.3
with the DC bias voltage; L1 = 100µH .
2. For each of the input signal frequencies f m = 3, 5, 8 kHz. appearing in Table 5.3,
compute the approximate frequency deviations by the formula
fD =
f 0 max − f 0 min
2
(5.13)
and find the deviation ratio using Eq. (5.8). Enter the results in Table 5.4. Comment on
the results.
Table 5.4 Change of the deviation ratio in FM by MC1648.
Audio input
frequency f m (kHz.)
3
5
8
EEE 316 - Communications I
Frequency deviation
f D (kHz.)
Experiment 5
Deviation ratio
β = fD / fm
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