University of Akron
Department of Electrical and Computer Engineering
4400 341: Introduction to Communication Systems - Spring 2015
Assignment – 5
5.1-5
A periodic message signal m(t) as shown in Figure 1 is to be transmitted by using angle
modulation. Its bandwidth is approximated by 200 Hz. The modulation system has
𝜔! = 4𝜋10! 𝑟𝑎𝑑 𝑠.
a) If an FM signal with kf = 500π is generated, sketch the FM signal in time domain.
b) If a PM signal with kf = 0.25π is to be generated, sketch the PM signal waveform in
the time domain.
Figure 1
Solution:
5.2-3 For a message signal
𝑚 𝑡 = 2 cos(1000𝑡) + 9 cos(2000𝜋𝑡)
a) Write expressions (do not sketch) for φPM(t) and φFM(t) when A = 10, 𝜔! = 10! ,
𝑘! = 1000𝜋, and 𝑘! = 1. For determining φFM(t), use the indefinite integral of m(t);
that is, take the value of the integral at 𝑡 = − ∞ to be 0.
b) Estimate the bandwidth of φPM(t) and φFM(t).
Solution:
5.2-4 An angle-modulated signal with carrier frequency 𝜔! = 2𝜋10! is described by the
equation
𝜑!" 𝑡 = 10 cos(𝜔! 𝑡 + 0.1 sin(2000𝜋𝑡))
a)
b)
c)
d)
Find the power of the modulated signal.
Find the frequency deviation Δf.
Find the phase deviation Δφ.
Estimate the bandwidth of φEM(t)
Solution:
5.3-1 Design (the block diagram of) an Armstrong indirect FM modulator to generate an FM
carrier with a carrier frequency of 96 MHz and Δf = 20 kHz. A narrowband FM generator
with fc = 200 kHz and adjustable Δf in the range of 9 to 19 Hz is available. The
stockroom also has an oscillator with adjustable frequency in the range of 9 to 10 MHz.
There are bandpass filters with any center frequency, and only frequency doublers are
available.
Solution:
5.3-3 Design an Armstrong indirect FM modulator in block diagram to generate an FM signal
with carrier 96.3 MHz and Δf = 20.48 kHz. A narrowband FM generator with fc = 150
kHz and Δf = 10 Hz is available. Only a limited number of frequency doublers are
available as frequency multipliers. In addition, an oscillator with adjustable frequency
from 13 to 14 MHz is also available for mixing, along with bandpass filters of any
specification.
Solution: