# Q 1 v be v ce i c q 1 v be v ce i c v ce i s exp v t

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Q 1 V BE V CE I C Q 1 V BE V CE I C V CE I S exp V T I C (a) (b) V I C BE V BE1 I S exp V T V BE2 V = BE V B1 V = BE V B2 Figure 4.15 Collector current as a function of (a) base-emitter voltage and (b) collector-emitter voltage. Next, we examine for a given but with varying. Illustrated in Fig. 4.15(b), the characteristic is a horizontal line because is constant if the device remains in the active mode ( ). On the other hand, if different values are chosen for , the characteristic moves up or down. A 500-mV change in leads to decades of change in .

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 138 (1) 138 Chap. 4 Physics of Bipolar Transistors The two plots of Fig. 4.15 constitute the principal characteristics of interest in most analysis and design tasks. Equations (4.24) and (4.25) suggest that the base and emitter currents follow the same behavior. Example 4.8 For a bipolar transistor, A and . Construct the - , - , - , and - characteristics. Solution We determine a few points along the - characteristics, e.g., (4.38) (4.39) (4.40) The characteristic is depicted in Fig. 4.16(a). V CE I C (a) (b) V I C BE V BE V BE V BE 1.153 mA 169 24.6 μ A μ A 700 750 800 (mV) 1.153 mA 169 24.6 μ A μ A = 700 mV = 750 mV = 800 mV V CE I V I BE V BE V BE V BE μ A μ A 700 750 800 (mV) = 700 mV = 750 mV = 800 mV (c) (d) B B μ A 11.5 0.169 0.025 μ A μ A μ A 11.5 0.169 0.025 Figure 4.16 (a) Collector current as a function of , (b) collector current as a function of , (c) base current as a function of , (b) base current as a function of . Using the values obtained above, we can also plot the - characteristic as shown in Fig. 4.16(b), concluding that the transistor operates as a constant current source of, e.g., 169 A if its base-emitter voltage is held at 750 mV. We also remark that, for equal increments in , jumps by increasingly greater steps: 24.6 A to 169 A to 1.153 mA. We return to this property in Section 4.4.3. For characteristics, we simply divide the values by 100 [Figs. 4.16(c) and (d)].
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 139 (1) Sec. 4.4 Bipolar Transistor Models and Characteristics 139 Exercise What change in doubles the base current? The reader may wonder what exactly we learn from the I/V characteristics. After all, com- pared to Eqs. (4.23)-(4.25), the plots impart no additional information. However, as we will see throughout this book, the visualization of equations by means of such plots greatly enhances our understanding of the devices and the circuits employing them. 4.4.3 Concept of Transconductance Our study thus far shows that the bipolar transistor acts as a voltage-dependent current source (when operating in the forward active region). An important question that arises here is, how is the performance of such a device quantified? In other words, what is the measure of the “good- ness” of a voltage-dependent current source? The example depicted in Fig. 4.1 suggests that the device becomes “stronger” as increases because a given input voltage yields a larger output current. We must therefore concentrate on the voltage-to-current conversion property of the transistor, particularly as it relates to amplification of signals. More specifically, we ask, if a signal changes the base-emitter voltage of a transistor

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