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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).
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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.
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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 hold-in range (delta fmas).
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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.
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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.
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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.
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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.
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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.
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Homework Solutions and Calculations

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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.

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