Question

Assume that an AM transmitter is modulated with a video testing signal given
by em(t) = =20 + 60 sin (2πf1t), where f1 = 3.57 MHz. Let the carrier signal
c(t) = Ac cos(2πfct), where Ac = 100 and fc = 100 MHz. The AM signal is fed into
a 50-Ω load.
(a) Derive an expression for the AM DSB-FC signal in time domain.
(b) Construct the AM waveform, giving numerical values of the maximum amplitude, Amax and the minimum amplitude, Amin of the envelope.
(c) Determine the percentages of positive and negative modulation.
(d) Derive an expression for the spectrum of the AM waveform.
(e) Construct the spectrum of the AM waveform for f > 0, clearly labelling the
frequencies and amplitudes of the components.
(e) Evaluate the peak envelope power (PEP) of the AM signal.

Answer 1

Given that the modulating signal is

                                                                  

and the carrier signal is

                                             

Where f1 = 3.57MHz and fc = 100MHz. Since modulation index is not given, we will assume it is 1.

(a) For DSB-FC signal, modulated signal is given by

                                                  

Or

                                 

Or

                  

Or

(b) The output is the modulated cosine wave with zero crossings of the waveform seperated by the time interval = 1/fc.

From Eq. (1),

Amax = 120+60 = 180, Amin = 120-60 = 60.

s(t) is plotted using MATLAB using following code:

fc = 1e8;
f1 = 3.75*1e6;
tres = 1/(100*fc);
ttot = 2/f1;
t = (0:tres:ttot);
emt = 20 + 60*sin(2*pi*f1*t);
ct = 100*cos(2*pi*fc*t);
st = (100+emt).*ct/100;
plot(t/1e-9/1,st);
grid on;
xlabel('time(ns)');
ylabel('modulated signal s(t)');

(c)

Similarly

        

(d) Time domain modulated signal is

         

So the double sided spectrum of the modulated signal is