Homework 3, EEL 6509

**
Due Wednesday, March 1, 2000**

**Spring 2000**

- 1.
- Define
(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

- (a)
- Sketch
*m*(*t*) from*t*=0*s*to*t*=10*s*. - (b)
- Sketch the envelope of . Label relevant amplitudes and times.
- (c)
- 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 general idea.
- (d)
- Find the modulation index and percent modulation for .
- (e)
- Find the total average power for .
- (f)
- Find the carrier power.
- (g)
- Find the modulation efficiency.
- (h)
- 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).

- 2.
- 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.
- (a)
- What is the peak frequency deviation?
- (b)
- What is the modulation index?
- (c)
- Use Carson's rule to find upper and lower bounds for the 98% bandwidth,
*B*_{T}. - (d)
- Assume that
*B*_{T}is given by the upper bound. Find the frequency ranges for the upper and lower sidebands. - (e)
- Estimate the total transmitted power.