2.1

Solve y ?( t) = y( t) ? at.

2.2

Solve y ?( t) = b y( t) ? at ².

2.3

Solve y ??( t) = y( t) ? a.

2.4

Solve y ??( t) = y ?( t) ? a y( t).

2.5

Find the inverse Laplace Transform for .

2.6

Find the inverse Laplace Transform for .

2.7

Find the Laplace Transform for f( t) = at ² sin (2 ? f t).

2.8

For a first order phase-locked loop with:

VCO: K _o = 100 Hz/Volt, Phase Detector: Kd = 1/2 Volt/Radian

Input Power: P=0.01 W, Loop Filter K _f = 0.1

Input Phase Step = 1.0 Volts

Find how long it takes for the phase-locked loop error voltage to be less than 20 ?Volts.

2.9

Power supply noise is often a problem for phase-locked loops. For the PLL of Problem 2.8, what is the error response of the phase-locked loop to a sinusoidal input of 30 mV at 60 Hz?

2.10

Derive the error response functions for the second order phase-locked loop with the passive loop filter.

2.11

For a second order active filter phase-locked loop with:

VCO: K _o = 100 Hz/Volt, Phase Detector: Kd = 1/2 Volt/Radian

Input Power: P=0.001 W,...