k0k0 v m (s)f out (s) f0f0 + + A VCO has a free-running frequency of 120 Mhz and sensitivity (gain) of 20 kHz/v. Assume linear operation over an input range of +/- 5 volts. a. Draw plot of the VCO operating characteristic. b. The input is v i (t) = 2.5 cos(w m t), where w m = 10 4 r/s. What is the output v o (t) = ? c. What is the modulation index for part b? d. Indicate the operating region on your plot from part a. e. Draw a block diagram for the device suitable for use in system analysis.

A frequency discriminator has a crossover frequency of 80 Mhz and sensitivity (gain) of 5.0 v/Mhz. a. Draw plot of the discriminator operating characteristic. b. The input is v i (t) = 2.5 cos(w m t), where w m = 0.5 x 10 9 r/s. What is v o (t) = ? c. Indicate the operating region on your plot from part a. (You choose, > +/- 2.1 v) d. Draw a block diagram for the device suitable for use in system analysis. kdkd fdfd f in (s) v out (s) _ +

Phase Locked Loops VCO Input Loop Filter + _ + + kk Phase Detector VCO k   : v/rad k v : rad/s/v + _ -

Phase ErrorFrequency Error + _ + - F(s) is forward gain from input to point of interest. Simple example: uncompensated loop H(s) = 5 = k A k  = 0.1 v/rad k o = 60  x 10 3 rad/s/v  I = -10 khz = -20,000  rad/s Frequency Error: F(s) = 1 Steady State Response = 0 Surprise! Phase Error: F(s) = 1/s VCO Voltage: F(s) = 0.5/s

Dynamic response: Hold in Range: Phase error For step change in input frequency    X(s) =   /s Frequency Error: F(s) = 1 Phase Error: F(s) = 1/s

FM Application + _ + - V out (s)

FSK Application f FR = 3.5 khz f MARK = 2 kHz f SPACE = 4 kHz BR = 1333 Bit/s t BIT = 0.75 ms