finding power of carrier signal using MATLAB changing phase frequency and amplitude

1. Lab Report 3:
Submitted By :
Syed Abuzar Hussain Shah
Reg # :
SP15-BEE-096
Submitted To:
Sir Ateeq-ul-Anaam
Class:
BEE-5A
Dated: 24/04/2017

2. Statement of Problem:
Generate a carrier wave and study its behavior as mentioned in the
procedure. What will happen to the power of carrier with the change of
carrier frequency, peak amplitude and phase?
Literature Background:
Carrier wave:
A High-Frequency Electromagnetic wave modulated in
Amplitude or Frequency to convey a Signal is called Carrier wave.
Figrure 1: Carrier wave representation.
Formula for Calculating power of Carrier wave:
Power =
∑
Where ‘S’ is the carrier wave vector and ‘t’ is the total time.
Colpitts oscillator:
It is an Electronic oscillators that use a combination of inductors and
capacitors to produce an oscillating signal at a certain frequency.

3. Formula for calculating frequency is:
√
(1)
Procedure:
Generating the carrier wave in time and Frequency domain using
MATLAB.
1. Plotting in time domain:
clc
clear all
close all
t=0:1:200;
fc=5000;
Vc=5; %Amplitude of Carier
Phase=0; %Phase of Carier
fs=10*fc; %Sampling Frequency
ts=t/fs; %Sampling time
y=Vc*cos(2*pi*fc*ts+Phase);
plot(ts*1000,y)
title('Carrier wave ')
xlabel('time (ms)')
ylabel('Amplitude')
grid on;

4. 2. Plotting in Frequency Domain:
z=fft(y);
z=abs(z(1:length(z)/2+1)); %Removing negative frequency
frq=(0:length(z)-1)*fs/length(z)/2;
plot(frq/1000,z);
figure
grid on;
title('Carrier Wave')
xlabel('Frequency(kHz)');
ylabel('Amplitude');
Figure 3: Frequency domain plot.
3. Calculating Power
Power=sum(y.^2)/length(t);
display(Power);
Output:
Power =
12.5622

5. Analysis:
1) Keeping Frequency and Phase constant, changing in Amplitude.
Figure 4: Amp = 7v, fc=5kHz, phase=pi/3
Figure 4: Amp = 1v, fc=5kHz, phase=pi/3

6. 2) Keeping Amplitude and Phase constant, changing in Frequency.
Figure 5: Amp = 5v, fc=1MHz, phase= pi/3
Figure 6: Amp = 5v, fc=10MHz, phase= pi/3

7. 3) Keeping Amplitude and Frequency constant, changing in Phase.
Figure 7: Amp = 5v, fc=5kHz, phase= pi/6
Figure 8: Amp = 5v, fc=5kHz, phase= pi/4

8. Table # 1:
S. No. Peak Amplitude Phase (radians) Frequency (Hz) Power (W)
1 7v π/3 5k 24.4391
2 1v π/3 5k 0.4988
3 5v π/3 1M 12.4689
4 5v π/3 10M 12.4689
5 5v π/6 5k 12.5311
6 5v π/4 5k 12.4689
Table # 2:
S. No. From Oscilloscope From Spectrum Analyzer From Formula
1 1MHz 1.0968MHz 1.0004MHz
Questions:
Q1): What will be the power of carrier wave when frequency of wave
is increasing?
Ans:
There is no effect on power of carrier wave when frequency of carrier wave
is changed, because depends only on amplitude of carrier wave.
Q2): In case of Collpitt’s oscillator, what can be the possible
capacitance and inductance for generating 6MHz carrier wave?
Ans:
From eq (1)
√
√

9. √
√
(2)
If we take C= = 1uF
Then L= 704uH
C1=2uF
C2=2uF
So putting values in eq(1) we get fc=600MHz.
Q3): What is the nature of the carrier wave? Is it energy signal or
power signal? Give mathematical reasoning.
Ans:
It is power signal because energy of the periodic signal is infinite.
Energy of Periodic Signal:
∫ .
Hence we can’t calculate energy of carrier signal.
Conclusion:-
 Power of the carrier signal depends upon amplitude of the signal. It
does not depend upon any other factor.
 If we change the phase , there will be negligible effect on power of
the signal so we can take sin or cosine both as a carrier.
 Energy of Periodic signal is Infinite.
 We deal with higher carrier frequencies to minimize the size of
components.