Physics 426 Homework 4: Amplitude Modulation and Demodulation - Prof. N. Duller, Assignments of Physics

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HW #4 Due Thursday, March 2 Physics 426

C:\TEACHING\PHYS426\SPRING00\HW4.DOC 1

1. Show that

K 1 m mt c t K ct Km c m t c mt

b +^ cos^ ω^ g cos^ ω^ =^ cos^ ω^ +^ cosb^ ω^ +^ ω^ g +^ cosb ω^ − ω g ,

as is claimed on page 2 of the handout, Concepts of Amplitude Modulation of a Carrier Frequency and “AM Demodulation”.

2. A very bright but misguided student is asked to build a circuit to demodulate a 1-MHz carrier which has been amplitude modulated sinusoidally at a rate of 1 kHz. To accomplish her task, she builds the following:

(a.) Explain why this student’s choice of values for R 1 and C 1 is a bad idea. What values of R 1 and C 1 might she use to fix the problem?

(b.) Explain why the choice of 20 k for R 2 and 5 pF for C 2 is bad.

(c.) What undesireable effect will the above choice of R 2 and C 2 have on the demodulator’s output signal?

3. Show that the time-varying voltage

v t ( ) = A cos ω t + B sin ωt

can be written as

v t ( ) = D cosb ω t − φ g

for some D and φ.

IN OUT

C 1

R 1

R 2

C 2

C 3

R 3

5 pF

1 k (^) 5 pF

2.2 uF

20 k