Oscillator Design and Computer Simulation, Second Edition

Chapter 1: Analysis Fundamentals

For this section, we assume that networks are linear and time invariant. Time invariant signifies that the network is constant with time. Linear signifies the output is a linear function of the input. Doubling the input driving function doubles the resultant output. The network may be uniquely defined by a set of linear equations relating port voltages and currents.

1.1 Voltage Transfer Functions

Consider the network in Figure 1-1A terminated at the generator with R g, terminated at the load with R l, and driven from a voltage source E g [1]. E l is the voltage across the load.


Figure 1-1: A linear, time-invariant network defined in terms of terminal voltages (A) and in terms of port incident and reflected waves (B).

The quantity E avail is the voltage across the load when all of the available power from the generator is transferred to the load.

(1.1)

For the case of a null network with R l = Rg,

(1.2)

since one-half of E g is dropped across R g and one-half is dropped across R l. For the case of a non-null network, dividing both sides of the equation 1.1 by E l gives

(1.3)

We can then define the voltage transmission coefficient as the voltage across the load, E l, divided by the maximum available voltage across the load E avail, or

(1.4)

This voltage transmission coefficient is the "voltage gain" ratio. For the...

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