

Homework 10  VCO and PLL Calculations
Problem 6.
For a Voltage Controlled Oscillator (VCO) input versus output characteristic curve shown in
Figure 1 below, determine (a) the frequency of operation for a negative 2V input signal, (b)
the frequency deviation of a plus or minus 2Vp input signal, and (c) the transfer function Ko
for the linear partition of the curve (3V to +3V).
{ Solution }
Problem 7.
For the output voltage versus phase difference characteristic curve provided in Figure 2
below, calculate the (a) output voltage for a negative 45 degree phase difference, (b) the
output voltage for a positive 60 degree phase difference, (c) the maximum peak output
voltage, and (d) the transfer function Kd.
{ Solution }
Problem 8.
For the Phase Lock Loop (PLL) provided in Figure 3 below, a voltage controlled oscillator
(VCO) natural frequency of fn = 150KHz, an input frequency of fi = 160KHz, and the circuit
gains are Kd = 0.2V/rad, Kf = 1, Ka = 4, and Ko = 15KHz/V. Determine the following, (a) the
open loop gain Kv, (b) the change in frequency (delta f), (c) Vo, (d) Vd, (e) phase
difference (theta e), and (f) the holdin range (delta f_{mas}).
{ Solution }
Problem 9.
Plot the frequency response for a PLL with an open loop gain of Kv = 20KHz/rad. On the
same log paper, plot the response with a single pole loop filter with a cutoff
frequency of Wc = 100 rad/s and a two pole filter with the same cutoff frequency.
{ Solution }
Problem 10.
Determine the change in frequency for a voltage controlled oscillator (VCO) with a transfer
function of Ko = 2.5KHz/V and a DC input voltage change of delta V = 0.8V.
{ Solution }
Problem 11.
Calculate the voltage at the output of a phase comparator with a transfer function of
Kd = 0.5V/rad and a phase error of theta e = 0.75 rads.
{ Solution }
Problem 12.
Determine the hold in range, (i.e. the maximum change in frequency) for a phase
lock loop with an open loop gain of Kv = 20kHz/rad.
{ Solution }
Problem 13.
Find the phase error necessary to produce a VCO frequency shift of delta f = 10KHz for an open loop gain of Kv = 40KHz/rad.
{ Solution }
Engineering key words: RF devices, calculations and homework solutions, PLL, VCO, oscillators, phase
comparator, frequency shift, open loop gain, filters, error, peak voltage, transfer function.
