Homework 3, EEL 6509
Due Wednesday, March 1, 2000
(read ``triangle of t'') by
Suppose m(t) is the waveform given by
and m(t) is used to amplitude modulate a carrier such that the
output signal is given by
- Sketch m(t) from t=0 s to t=10 s.
- Sketch the envelope of
amplitudes and times.
- Sketch roughly
You may overlay this
sketch with that in part (b) if you label each part clearly. Do not
try to show every cycle of the carrier waveform - just give the
- Find the modulation index and percent modulation for
- Find the total average power for
- Find the carrier power.
- Find the modulation efficiency.
- Suppose you did not know m(t) but knew the percent modulation
was the value you found in part (d). Calculate the efficiency under
the assumption that m(t) is a sinusoid. Compare your answer to
your answer for part (f).
- Suppose a sinusoid of amplitude 4 V and frequency 1 kHz is used
to modulate a carrier of frequency 100 kHz and amplitude 40 V. The
FM modulator has a modulator gain (i.e., frequency deviation
constant) of 50 Hz/V.
- What is the peak frequency deviation?
- What is the modulation index?
- Use Carson's rule to find upper and lower bounds for the 98% bandwidth, BT.
- Assume that BT is given by the upper bound. Find the
frequency ranges for the upper and lower sidebands.
- Estimate the total transmitted power.