# 1- The following figure shows the block diagram of a commercial

```ES 442
HW # 7 - Chapter 4&amp;5 - PLL
1- The following figure shows the block diagram of a commercial broadcast-band transmitter, called Crosby
direct FM transmitter. This device includes an automatic frequency control (AFC). The output of the AFC is a
correction voltage which fed back to the carrier (master) oscillator (fc) to automatically compensate for any
drift that may have occurred. The transfer function of the discriminator has a gain of kd. For commercial
broadcast-band station the maximum frequency deviation allowed at the antenna is 75 KHz and the
maximum modulating signal frequency allowed will be fm=15KHz.
a- What does the value of the DC correction voltage depend on (what is the unit of kd)?
b- What is the maximum allowed frequency deviation a the output of the Frequency modulator (fc)?
c- What will be the modulation index at Frequency modulator block?
d- What will be the modulation index at antenna?
e- Calculate fd for the configuration below.
f- What is the transfer function of the discriminator, H(f)?
ES 442
HW # 7 - Chapter 4&amp;5 - PLL
2- In the lecture we discussed how to use frequency synthesizers in AM superheterodyne radio design. For
this problem you are asked to design a frequency synthesizer for use as the local oscillator in an AM
superheterodyne radio. The radio has a 455-kHz IF and can be tuned across the AM band from 530 kHz to
1,710 kHz in 10-kHz steps. The synthesizer uses a 1-MHz reference oscillator and generates a high-side LO
(local oscillator) injection signal. In this problem you should basically find M and N values for the frequency
synthesizer. Assume the frequency of the signal into the mixer of the synthesizer is 5KHz.
a- Complete the table below for the specified received signal frequencies (channel 1, channel 2, etc.).
b- A key component in this design is frequency multiplier. Referring to your textbook, draw the circuit
diagram for a frequency multiplier and briefly explain how it operates.
c- Mathematically, express the output of a general multiplier if the bandpass input signal is the following: