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1.1 ELECTRICAL QUANTITIES AND SI UNITS The International System of Units (SI) will be used throughout this book. Four basic quantities and their SI units are listed in Table 1-1. The other three basic quantities and corresponding SI units, not shown in the table, are temperature in degrees kelvin (K), amount of substance in moles (mol), and luminous intensity in candelas (cd). All other units may be derived from the seven basic units. The electrical quantities and their symbols commonly used in electrical circuit analysis are listed in Table 1-2. Two supplementary quantities are plane angle (also called phase angle in electric circuit analysis) and solid angle. Their corresponding SI units are the radian (rad) and steradian (sr). Degrees are almost universally used for the phase angles in sinusoidal functions, for instance, sin !t 308 . Since !t is in radians, this is a case of mixed units. The decimal multiples or submultiples of SI units should be used whenever possible. The symbols given in Table 1-3 are pre xed to the unit symbols of Tables 1-1 and 1-2. For example, mV is used for millivolt, 10 3 V, and MW for megawatt, 106 W.

PRINCIPLE 4:

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The constant-base-current-biased ampli er of Fig. 5-7 contains a Si transistor. Let VCC 15 V; RC 2:5 k ; RE 500 ; Rb 500 k ; and 100. At 258C, ICBO 0:5 A and VBEQ 0:7 V. (a) Find the exact change in ICQ if the temperature changes to 1008C. (b) Use the stability factors developed in Problem 5.13 to predict ICQ for a temperature increase to 1008C. Ans: a ICQ ICQ2 ICQ1 10:864 2:645 8:219 mA; b ICQ 8:22 mA In the constant-base-current-biased ampli er of Fig. 5-7, the Si transistor is characterized by ICBO 0:5 A and VBEQ 0:7 V at 258C. (a) Find an expression for ICQ at any temperature T2 ! 258C. (b) Evaluate ICQ at 1008C if VCC 15 V; RC 2:5 k ; RE 500 ; Rb 500 k ; and 100. Ans: a ICQ b ICQ VCC 0:7 0:002 T2 25 0:5 10 6 Rb RE 2 T2 25 =10 ; Rb = RE 10:864 mA

The frequency scale of a lter may be changed by adjusting the values of its inductors and capacitors. Here we summarize the method (see also Section 8.10). Inductors and capacitors a ect the frequency behavior of circuits through L! and C!; that is, always as a product of element values and the frequency. Dividing inductor and capacitor values in a circuit by a factor k will scale-up the !-axis of the frequency response by a factor k. For example, a 1-mH inductor operating at 1 kHz has the same impedance as a 1-mH inductor operating at 1 MHz. Similarly, a 1-mF capacitor at 1 MHz behaves similar to a 1-nF capacitor at 1 GHz. This is called frequency scaling and is a useful property of linear circuits. The following two examples illustrate its application in lter design.

If a line slants upward from left to right, its inclination i is an acute angle and its slope is positive (Fig. 12-13).

EXAMPLE 12.17 The network function of the circuit of Fig. 8-42 with R 2 k , C 10 nF, and R2 R1 is H s V2 2 2 V1 s s 1 !0 !0

In the current-feedback-biased ampli er of Fig. 5-8, VCC 15 V; RC 1:5 k ; RF 150 k ; RE 500 ; and 100. ICBO 0:2 A and VBEQ 0:7 V at 258C for this Si transistor. (a) Find the exact change in ICQ when the temperature changes to 1258C. (b) Use the stability factors developed in Problem 5.14 to predict ICQ when the temperature is 1258C. Ans: a ICQ 8:943 mA; b ICQ 8:943 mA The shunt-feedback-biased ampli er of Fig. 5-8 uses a Si transistor for which ICBO 0:2 A and VBEQ 0:7 V at 258C. (a) Find an expression for ICQ at any temperature T2 ! 258C. (b) Evaluate ICQ at T2 1258C if VCC 15 V; RC 1:5 k ; RF 150 k ; RE 500 ; and 100. Ans: a ICQ b ICQ VCC 0:7 0:002 T2 25 0:2 10 6 RC RF RE 2 T2 25 =10 ; RF = RC RE 13:037 mA

Fig. 12-13

where !0 50, 000 rad/s (see Examples 8.14 and 8.15). This is a low-pass lter with the cuto frequency at !0 . By using a 1-nF capacitor, !0 500,000 and the frequency response is scaled up by a factor of 10. EXAMPLE 12.18 A voltage source is connected to the terminals of a series RLC circuit. The phasor current is I Y V, where Y s Cs LCs2 RCs 1

Fig. 12-14

CHAP. 5]

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