# Exercise repeat the above example if the power budget

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Exercise Repeat the above example if the power budget is only 1 mW and the transconductance of is not given. The two rules depicted in Fig. 5.21 to lower sensitivities do impose some trade-offs. Specif- ically, an overly conservative design faces the following issues: (1) if we wish to be much much greater than , then and hence and are quite small, leading to a low input impedance ; (2) if we choose a very large , then ( ) must be high, thereby limiting the minimum value of the collector voltage to avoid saturation. Let us return to the above example and study these issues. Example 5.12 Repeat Example 5.11 but assuming mV and . Solution The collector current and base-emitter voltage remain unchanged. The value of is now given by . Also, V and (5.63) still holds. We rewrite (5.64) as (5.70) obtaining . It follows that (5.71) (5.72) Since the base voltage has risen to 1.278 V, the collector voltage must exceed this value to avoid saturation, leading to (5.73) (5.74) As seen in Section 5.3.1, the reduction in translates to a lower voltage gain. Also, the much smaller values of and here than in Example 5.11 introduce a low input impedance, loading the preceding stage. We compute the exact input impedance of this circuit in Section 5.3.1.

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 194 (1) 194 Chap. 5 Bipolar Amplifiers Exercise Repeat the above example if is limited to 100 mV. 5.2.4 Self-Biased Stage Another biasing scheme commonly used in discrete and integrated circuits is shown in Fig. 5.22. Called “self-biased” because the base current and voltage are provided from the collector, this stage exhibits many interesting and useful attributes. Q 1 V CC R I C X C R B Y I B Figure 5.22 Self-biased stage. Let us begin the analysis of the circuit with the observation that the base voltage is always lower than the collector voltage: . A result of self-biasing, this important property guarantees that operates in the active mode regardless of device and circuit pa- rameters. For example, if increases indefinitely, remains in the active region, a critical advantage over the circuit of Fig. 5.21. We now determine the collector bias current by assuming ; i.e., carries a current equal to , thereby yielding (5.75) Also, (5.76) (5.77) Equating the right hand sides of (5.75) and (5.77) gives (5.78) As usual, we begin with an initial guess for , compute , and utilize to improve the accuracy of our calculations. Example 5.13 Determine the collector current and voltage of in Fig. 5.22 if , , V, A, and . Repeat the calculations for .
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 195 (1) Sec. 5.2 Operating Point Analysis and Design 195 Solution Assuming V, we have from (5.78): (5.79) and hence mV, concluding that the initial guess for and the value of given by it are reasonably accurate. We also note that mV and V.

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