# frequency modulation

## Transcription

frequency modulation
```EXPERIMENT #4
FREQUENCY MODULATION
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Purpose:
The objectives of this laboratory are:
1. To investigate frequency modulation characteristics in the frequency domain.
2. To implement a classical double-tuned FM demodulator and measure its characteristics.
3. To implement a modern PLL FM demodulator and measure its characteristics.
4. To investigate the effect of FM signal bandwidth on the detected signal-to-noise ratio.
Equipment List
1. PC with Matlab and Simulink
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Frequency Modulation
FM results when the time derivative of the phase of the carrier is varied linearly with the
message signal m(t). The frequency deviation is proportional to the derivative of the phase
deviation. Thus, the instantaneous frequency of the output of the FM modulator is maximum
when the message signal m(t) is maximum and minimum when m(t) is minimum.
Carson’s Rule:
Carson’s Rule is used to determine the bandwidth of the FM wave. According to Carson’s
Rule, the bandwidth is given by:
BW = 2(+1)fm
Hertz.
Laboratory Procedure
Determining Constants:
Before proceeding to perform the experiment, the following steps were performed:
1. Calibrate the multiplier and determine the multiplier constant.
2. Determine the VCO conversion constant Ko
3. Set the VCO’s frequency for 5 kHz.
4. Verify the outputs of the 1st order Low Pass Filter.
1. Multiplier Constant, Km
With a 1V p-p sinusoidal voltage at both inputs of the multiplier, the output was observed and
the multiplier constant was calculated to be 0.206.
2. VCO Conversion Constant, Ko
An external voltage may control the output frequency of the VCO. The change in the output
frequency per change in the dc input voltage was measured.
Ko = f / v
Ko = 1 / 0.5 = 2 kHz/sec/volt
Ko = 4103 = 12566 rad/sec/volt
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FM Transmission:
The following schematic was implemented.
Figure 4 A (a) FM detector
Figure 4 A (b) FM Input signal
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Figure 4 A (c) PSD of message signal
Figure 4 A (d) Limter - Unmasked
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The output of the function generator is set to 1 kHz (modulation frequency fm = 1kHz) and
no output level.
Figure 4 A (e)Band pass block parameters
Figure 4 A (f)Output of Limiter
A 5kHz carrier “delta” function was observed on the signal analyzer. We increased the output
level of the function generator by pressing the Delta Level key on the generator and selecting
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delta of 0.1 volt. Setting the Vpp to 0 volts and incrementing the Vpp by 0.1 V increments,
we increased the level until a of  = 0.5 was achieved.
Figure 4 A (g)Output of 4k Band pass filter
Figure 4 A (h)Output of 8k Band pass filter
Figure 4 A (i)Block parameters of envelope detector
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Figure 4 A (j)Output of difference block
Figure 4 A (k)Output of Cheby filter
 = Ko A./ (2fm);
A = Vpp /2
The above procedure is repeated for  = 1 and  = 2.
We observed that the carrier disappears at A = 1.05 V.
Setting the frequency axis on the spectrum analyzer to a linear scale, the approximate
bandwidth for different values of  was observed. The results are tabulated below:
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Figure 4 A (l) Received signal
Figure 4 A (m) Recovered signal
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Figure 4 A (n) Recovered signal
Figure 4 A (o) Input signal
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The output is read from the frequency counter. By varying the frequency, and observing the
output, we see that the discriminator output follows the following characteristic. The signal is
also monitored on the oscilloscope.
PLL Detection
In this part of the experiment, we detect the Fm signal using a PLL. Using VCO #1, we made
an FM signal by setting the center frequency of the VCO in open loop to 5 kHz and putting
the function generator’s signal (1kHz 0 Vpp) and putting the function generator’s signal
(1kHz 0Vpp) into the input of the VCO #1.
figure 4 B (a) FM PLL
The PLL circuit is built according to the schematic shown below. The LPF with 1kHz cutoff
frequency is to remove high frequency components from the detected signal. It is not a part of
the PLL. In the open loop, the VCO#2 is set for 5kHz.
figure 4 B (b) Block parameters of carrier VCO – 5kHz
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VCO#1 is part of the FM transmitter, VCO #2 is part of the PLL detector. With the function
generator putting out no signal, the VCO #1’s output frequency is varied. We note the dc
voltages for the corresponding input frequencies. We observe that the discriminator curve
generated using the PLL is more linear than the Double Tuned Detector.
figure 4 B (c) PSD of message signal
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figure 4 B (d) Input signal
figure 4 B (e) vco output
figure 4 B (f) Limiter
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figure 4 B (g)VCO spectrum
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figure 4 B (h) Recovered Signal spectrum
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Appendix
Pre – Lab
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Prelab Questions
Consider a carrier signal (cos ct) being frequency modulated by a sinusoidal signal (A cos mt).
The result can be expressed as a series of Bessel functions:
S(t) 

J
n  -
n
( β ) cos(ωc  nωm )t 
where
Jn() are Bessel functions of nth order
 = 2koA / m = koA / fm = modulation index
ko = frequency deviation constant
1. for  = .5, 2, and 2, sketch the positive frequency domain representation (magnitude only).
For = 0.5
J0() = 0.9385
J1() = 0.2423
J2() = 0.0306
J3() = 0.0026
Magnitude spectrum of s(t) for beta = 0.5
1
0.9
0.8
Magnitude
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-3
-2
-1
0
1
2
Deviation of frequency from fc in multiple of fm
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3
For = 1
J0() = 0.7652
J1() = 0.4401
J2() = 0.1149
J3() = 0.0196
J4() = 0.0025
Magnitude spectrum of s(t) for beta = 1
0.8
0.7
0.6
Magnitude
0.5
0.4
0.3
0.2
0.1
0
-4
For = 2
J0() = 0.2239
J1() = 0.5767
J2() = 0.3528
J3() = 0.1289
J4() = 0.0340
J5() = 0.0070
J6() = 0.0012
-3
-2
-1
0
1
2
Deviation of frequency from fc in multiple of fm
3
4
Magnitude spectrum of s(t) for beta = 2
0.7
0.6
Magnitude
0.5
0.4
0.3
0.2
0.1
0
-6
-4
-2
0
2
4
Deviation of frequency from fc in multiple of fm
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6
2. If fc = 5,000 Hz, fm = 1,000 Hz and ko = 2,000 Hz/V, find RMS value of the modulating
signal for  = 0.5, 1, and 2
 P
 1
2
A2
J
(

)
 n
2
n   (  1)
2πk 
Ak
ω
m
f
Forβ= 0.5o 
o  A  2000  2 A  modulation index
1000
m
Then A = /2
For  = 0.5
A=
P = (0.24232 + 0.93852 + 0.24232 )*A2 /2 = 0.0312 J
RMS value = P1/2 = 0.02441/2 = 0.1766 V
For  = 1
A = 
P = ( 0.76522 + 0.44012 + 0.44012 + 0.11492 + 0.11492 )*A2 /2 = 0.1249 J
RMS value = P1/2 = 0.12491/2 = 0.3534 V
For  = 2
A = 
P = ( 0.22392 + 0.57672 + 0.57672 + 0.35282 + 0.35282 + 0.12892 + 0.12892 )*A2 /2
= 0.4987 J
RMS value = P1/2 = 0.49871/2 = 0.7062
3. Using Carson’s rule, what is the approximate bandwidth occupied by s(t) for  = 1 and 2
For  = 1
Bandwidth = 2( + 1)fm = 2(1 + 1)*1000 = 4000 Hz
For  = 2
Bandwidth = 2( + 1)fm = 2(2 + 1)*1000 = 6000 Hz
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```