CHAP. 2]

13

CIRCUIT CONCEPTS

are shown as two ‘‘junctions’’ in (b). However, resistor R4 is bypassed by a short circuit and may be removed for purposes of analysis. Then, in Fig. 2-9(c) the single junction A is shown with its three meeting branches.

Fig. 2-9

2.8

NONLINEAR RESISTORS

The current-voltage relationship in an element may be instantaneous but not necessarily linear. The element is then modeled as a nonlinear resistor. An example is a ﬁlament lamp which at higher voltages draws proportionally less current. Another important electrical device modeled as a nonlinear resistor is a diode. A diode is a two-terminal device that, roughly speaking, conducts electric current in one direction (from anode to cathode, called forward-biased) much better than the opposite direction (reverse-biased). The circuit symbol for the diode and an example of its current-voltage characteristic are shown in Fig. 2-25. The arrow is from the anode to the cathode and indicates the forward direction ði > 0Þ. A small positive voltage at the diode’s terminal biases the diode in the forward direction and can produce a large current. A negative voltage biases the diode in the reverse direction and produces little current even at large voltage values. An ideal diode is a circuit model which works like a perfect switch. See Fig. 2-26. Its ði; vÞ characteristic is  v ¼ 0 when i  0 i ¼ 0 when v  0 The static resistance of a nonlinear resistor operating at ðI; VÞ is R ¼ V=I. Its dynamic resistance is r ¼ V=I which is the inverse of the slope of the current plotted versus voltage. Static and dynamic resistances both depend on the operating point. EXAMPLE 2.4. The current and voltage characteristic of a semiconductor diode in the forward direction is measured and recorded in the following table: v (V) i (mA)

0.5 2  10

4

0.6

0.65

0.66

0.67

0.68

0.69

0.70

0.71

0.11

0.78

1.2

1.7

2.6

3.9

5.8

8.6

0.72 12.9

0.73 19.2

0.74 28.7

0.75 42.7

In the reverse direction (i.e., when v < 0), i ¼ 4  1015 A. Using the values given in the table, calculate the static and dynamic resistances (R and r) of the diode when it operates at 30 mA, and ﬁnd its power consumption p. From the table

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Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An