This called piecewise linear analysis

206	C H A P T E R	F O U R		o f	n o n l i n e a r

Second, in contrast to all previous examples, the output waveform in this circuit is a gross distortion of the input waveform. Note in particular that the input voltage waveform has no average value, (no DC value), whereas the output has a significant DC component, roughly 0.3 Eo. The DC motors in most toys, for example, will run nicely if connected across the resistor in the circuit of Figure 4.21a, whereas they will not run if driven directly by the sinusoid vI(t). This circuit is called a half-wave rectifier, because it reproduces only half of the input wave. Rectifiers are present in power supplies of most electronic equipment to generate DC from the 60-Hz ‘‘sinusoidal’’ wave from 110-V AC power line.

4.4

10 pA	iD	10 mA	iD

different scales.	(a)	0.5 V		(b)	5 V

4.4 Piecewise Linear Analysis	C H A P T E R	F O U R	207
			207


			circuit
crudest approximation that preserves this dichotomy is the characteristic shown			circuit
			vD
			vD

	Open	(a)	+
The behavior of this piecewise linear model can be summarized in two	circuit


illustrate the piecewise linear analysis method applied to the circuit in Figure 4.16		iD
(also shown in Figure 4.24a). In particular, we will determine the voltage vR
			vD

vR		+	+	FIGURE 4.23 A piecewise
R		R
		R
	+
	vD
	-	(b) Short circuit segment	-	FIGURE 4.24 Piecewise linear
	vR			FIGURE 4.24 Piecewise linear
				analysis of a simple diode circuit.
		iD
	R	iD
		+
		vD