Page 207 - Fundamentals of Communications Systems

Amplitude Modulation 6.29

since AM is not used much in practice) for a 1 kHz, 3 V peak amplitude test
tone, e.g.,

m(t) = 3 sin(2000πt) (6.30)
(a) She wants the transmitter to deliver a 5 W output power across a 1
resistor with MCPR = 8%. Provide the values of A c and a to achieve this
specification.
(b) What is the maximum MCPR that can be achieved in this problem and have
distortionless envelope detection still possible? Give the values of A c and a
to achieve this efficiency while maintaining a 5 W output power.
(c) Plot x I (t) and x Q (t) for the design in part (b).
Problem 6.5. A message signal of the form

m(t) = 2 cos(2π f m t)
is to be transmitted by LC-AM with a carrier frequency f c .

(a) Give the baseband and bandpass forms of the modulated signal for this mes-
= 8W(ina1 system) and MCPR = 1/8.
sage signal that has a power of P x z
(b) Assume f c = 10 f m give the baseband and bandpass spectral representa-
tion of this modulation. What is the transmission bandwidth, B T of such a
system?
(c) Give the simplest form of the modulator and a noncoherent demodulator
(d) How big can abe made in this system and still ensure distortionless envelope
detection?

Problem 6.6. A term often used to characterize LC-AM waveforms is the percent
modulation defined as
Maximum value of the envelope − Minimum value of the envelope
P LC =
Maximum value of the envelope
(6.31)
An example of this usage is seen on most microwave signal generators where
the LC-AM signal is characterized by percent modulation. For this problem
consider a sinusoidal message signal of unit amplitude and LC-AM. An example
LC-AM waveform is shown for P LC = 0.5 in Figure 6.32.

(a) What is the range for P LC ?
(b) Solve for the value of a to give a particular P LC .
(c) The bandpass frequency domain representation (Fourier series or Fourier
transform) of this signal will have three frequencies (the carrier and two
modulation sidebands). Plot the relative power ratio (in dB) between the
carrier and one of the modulation sidebands as a function of P LC .
(d) Plot the MCPR as a function of P LC .