# The ratio of collector current and the base current

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some others recombine in the base region. The ratio of collector current and the base current is denoted by . In the forward active region, the bipolar transistor exhibits an exponential relationship be- tween its collector current and base-emitter voltage. In the forward active region, a bipolar transistor behaves as constant current source. The large-signal model of the bipolar transistor consists of an exponential voltage-dependent current source tied between the collector and emitter, and a diode (accounting for the base current) tied between the base and emitter. The transconductance of a bipolar transistor is given by and remains indepen- dent of the device dimensions. The small-signal model of bipolar transistors consists of a linear voltage-dependent current source, a resistance tied between the base and emitter, and an output resistance. If the base-collector junction is forward-biased, the bipolar transistor enters saturation and its performance degrades. The small-signal models of and transistors are identical. Problems In the following problems, unless otherwise stated, assume the bipolar transistors operate in the active mode. 1. Suppose the voltage-dependent current source of Fig. 4.1(a) is constructed with mA/V. What value of load resistance in Fig. 4.1(b) is necessary to achieve a voltage gain of 15? 2. A resistance of is placed in series with the input voltage source in Fig. 4.2. Determine . 3. Repeat Problem 2 but assuming that and are related: and . Plot the voltage gain as a function of . 4. Due to a manufacturing error, the base width of a bipolar transistor has increased by a factor of two. How does the collector current change? 5. In the circuit of Fig. 4.48, it is observed that the collector currents of and are equal V Q 1 I C1 BE1 V Q I BE2 C2 2 Figure 4.48 if mV. Determine the ratio of transistor cross section areas if the other device parameters are identical. 6. In the circuit of Fig. 4.49, A. (a) Calculate such that mA. (b) With the value of found in (a), choose such that mA. 7. Consider the circuit shown in Fig. 4.50. (a) If A, determine such that mA.

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 163 (1) Sec. 4.7 Chapter Summary 163 V Q 1 I X Q I Q 2 3 Y B Figure 4.49 V Q 1 I X Q 2 B V CC R C = 2.5 V Figure 4.50 (b) What value of places the transistors at the edge of the active mode? 8. Repeat Problem 7 if is lowered to 1.5 V. 9. Consider the circuit shown in Fig. 4.51. Calculate the value of that places at the edge Q 1 V CC R C = 2 V 500 V B Figure 4.51 of the active region. Assume A. 10. In the circuit of Fig. 4.52, determine the maximum value of that places at the edge of saturation. Assume A. Q 1 V CC R C 1 k 10 k R 1 = 2 V Figure 4.52 11. Calculate in Fig. 4.53 if A. 12. An integrated circuit requires two current sources: mA and mA. Assuming that only integer multiples of a unit bipolar transistor having A can be placed in parallel, and only a single voltage source, , is available (Fig. 4.54), construct
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 164 (1) 164 Chap. 4 Physics of Bipolar Transistors Q 1 V CC = 2 V 1 k X 1.5 V Figure 4.53 V I B 1 I

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