EE354
1
EE354 Lab 4: Introduction to and Simulation of Analog Modulation
In this lab you will create and investigate the properties of a simple Amplitude Modulated and Frequency
Modulated (AM and FM) waveform. You will use Matlab to create and view these signals in the time and
frequency domain.
Part 1a: Amplitude Modulation Pre-Lab Theory
An amplitude modulation (AM) waveform can be represented mathematically by:
uDSBTC
= Ac 1 + amod m ( t )  cos ( 2π f c t ) ,
where m(t) is the message, and Ac cos ( 2π f c t ) is the carrier.
1. For a 1.450 MHz cosine carrier w/amplitude 1V, and a 5.0 kHz cosine message w/amplitude 0.75V,
fill out the Theoretical column of Table 1.
*** Note: Amplitudes should be in Volts, Powers in dBm (50Ω Load).
Table 1: Theoretical and Measured Characteristics of the AM Signal
Parameter
Theoretical
Value
Matlab
Simulated
Value
Min value of envelope, Amin
Max value of envelope, Amax
Amplitude of carrier, Ac
Modulation Index
AM Power Efficiency, η
Carrier Frequency, fC
Upper Sideband Frequency, fUSB
Lower Sideband Frequency, fLSB
RF Bandwidth
Overall power (50Ω load) (dBm), PAM
Power of carrier (50Ω load) (dBm), Pcarrier
Power of Upper Sideband (50Ω load) (dBm), PUSB
Power of Lower Sideband (50Ω load) (dBm), PLSB
1
EE354
2
2. Sketch the AM signal and the spectrum of the AM signal (positive frequencies only) The sketches do
not need to be to scale, however, all pertinent data needs to be labeled.
AM Signal – Time Domain
AM Signal – Frequency Spectrum
Instructor Verification:_____________
2
EE354
3
Part 1b: Frequency Modulation Pre-Lab Theory
A frequency modulation (FM) waveform can be represented mathematically by:
(
=
uFM ( t ) Ac cos 2π f c t + 2π k f ∫ m (t ) dt
t
−∞
)
where m(t) is the message, and Ac cos ( 2π f c t + 0 ) would be the unmodulated carrier.
1. For a 300 kHz cosine carrier w/amplitude 1V, a 20 kHz sinusoidal message and an FM modulator with
peak frequency deviation ∆f = 60 kHz, find the following:
Average power of FM signal (dBm)
FM modulation index (β)
Bandwidth (using Bessel Table, in Hz)
Bandwidth (using Carson’s Rule, in Hz)
2. Using the Bessel Function table (see back page of this lab), calculate the magnitude of the carrier and
the first four sidebands that appear in the FM Waveform, along with their associated frequencies.
Record these values in the first two columns of Table 1.
3. To fill in the third column of Table 1, normalize the sideband amplitudes by dividing each delta function
magnitude by the magnitude of the carrier.
4. Sketch the time domain and both the magnitude spectrum of the FM signal and the normalized
magnitude spectrum of the FM Signal (positive frequencies only).
Recall:
Each frequency component is associated with a Bessel function Jn(β ), where the subscript n is
negative for the lower sideband and n is positive for the upper sideband. J0 is associated with the
carrier.
3
EE354
4
Table 2: Theoretical FM Signal Sidebands
frequency
(kHz)
Magnitude
(volts)
Normalized
Magnitude
 magnitude 


 J0 ( β ) 


LSB (associated with J-4)
LSB (associated with J-3)
LSB (associated with J-2)
LSB (associated with J-1)
Carrier (associated with J0)
USB (associated with J1)
USB (associated with J2)
USB (associated with J3)
USB (associated with J4)
4
EE354
5
FM Signal – Time Domain
FM Signal – Frequency Spectrum
FM Signal – Normalized Frequency Spectrum
Instructor Verification:_____________
5
EE354
6
Part 2a: Simulation of the AM Signal
1.
In MATLAB, create the AM signal from part I (Hint: write an m-file – it will make your life easier!).
You will need to generate a sufficiently long time axis (the instructor prefers to use 200-300 cycles of the
message signal) to be able to resolve the upper and lower sideband frequencies.
Create a plot of the AM signal…zoom in as necessary to see approximately 0.5 msec of the signal.
Using Matlab, determine the following and record them in the Matlab Simulated column of Table 1:
Envelope minimum, Envelope maximum, Carrier amplitude, modulation index, power in the carrier,
and power in the sidebands.
Note: you can also use the frequency plot in step 2 to fill in the power portions of the table (that is, you
can use the plot to determine the amplitudes of the carrier and sidebands, then compute the power in
these sinusoids).
2.
Use MATLAB to create a plot of the frequency spectrum (positive frequencies only). Zoom in to clearly
see the sidebands and carrier. If you forgot how to generate the spectrum, review the sample code in earlier
labs, but realize that you are taking the FFT of the signal in this lab, using the sampling frequency from
this lab.
Part 2b: Simulation of the FM Signal
1.
In MATLAB, create the FM signal from the pre-lab (see the below example code). To avoid excessive
simulation run-times, recall that FM and PM signals are related – it is much easier and faster to generate a
PM signal in Matlab than an FM signal. You will need to generate a sufficiently long time axis (the
instructor prefers to use 200-300 cycles of the message signal) to be able to resolve the upper and lower
sideband frequencies.
Recall: Madhow provides a very simple formulation for generating a tone-modulated FM signal:
=
u p ( t ) Ac cos ( 2p f c t + β sin ( 2p f mt ) )
2.
Create a time-domain plot of the FM signal and zoom in as necessary to see the FM modulation of the
carrier. Using the datatip markers, verify the center frequency, max, and minimum frequency deviation.
3.
Create a plot of the magnitude (aka linear units) of the frequency spectrum (positive frequencies only).
Zoom in to clearly see the sidebands and carrier. Use the Matlab plot to determine the powers and
normalized powers in the FM sidebands and fill in Table 2.
Note 1: When filling in the Normalized Magnitude column of Table 2, recall that you cannot divide dB
values. You must first convert to linear magnitude values and then perform the normalization.
Note 2: When converting out of dB values, you will get power in Watts. To get Volts, you will need a
square root somewhere.
6
EE354
7
Table 3: Simulated FM Signal Sidebands
frequency
(kHz)
Magnitude
(volts)
Normalized
Magnitude
 magnitude 


 J0 ( β ) 


LSB (associated with J-4)
LSB (associated with J-3)
LSB (associated with J-2)
LSB (associated with J-1)
Carrier (associated with J0)
USB (associated with J1)
USB (associated with J2)
USB (associated with J3)
USB (associated with J4)
7
EE354
8
Table 4: Comparison of FM Spectra
Theoretical
Normalized
Magnitude
Simulated
Normalized
Magnitude
LSB (associated with J-4)
LSB (associated with J-3)
LSB (associated with J-2)
LSB (associated with J-1)
Carrier (associated with J0)
USB (associated with J1)
USB (associated with J2)
USB (associated with J3)
USB (associated with J4)
8
EE354
9
9