# Current mirror is a constant multiple of if and

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away. current mirror, is a constant multiple of if and remain at the same temperature. More accurately, we have for and : (13.49) (13.50) Similarly, for and : (13.51) (13.52) Equating (13.50) and (13.52) and assuming the same value of (i.e., the same temperature) for both expressions, we write (13.53) Since , , we observe that and “track” so long as the values (which are temperature-dependent) also track. 13.8 Efficiency Since power amplifiers draw large amounts of power from the supply voltage, their “efficiency” proves critical in most applications. In a cellphone, for example, a PA delivering 1 W to the antenna may pull several watts from the battery, a value comparable to the power dissipation of the rest of the circuits in the phone. The “power conversion efficiency” of a PA, , is defined as (13.54)

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 709 (1) Sec. 13.8 Efficiency 709 Thus, an efficiency of in the above cellphone translates to a power drain of 3.33 W from the battery. It is instructive to compute the efficiency of the two output stages studied in this chapter. The procedure consists of three steps: (1) calculate the power delivered to the load, ; (2) calculate the power dissipated in the circuit components (e.g., the output transistors), ; (3) determine . 13.8.1 Efficiency of Emitter Follower With the results obtained in Section 13.7.1, the efficiency of emitter followers can be readily calculated. Recall that the power dissipated by is equal to (13.55) or that consumed by is (13.56) If , the total power “wasted” in the circuit is given by (13.57) It follows that (13.58) (13.59) For proper operation, must be at least equal to , yielding (13.60) That is, the efficiency reaches a maximum of as approaches . Note that this result holds only if . Example 13.15 An emitter follower designed to deliver a peak swing of operates with an output swing of . Determine the efficiency of the circuit. Solution Since the circuit is originally designed for an output swing of , we have and . Replacing with and with in (13.59), we have (13.61) This is only an approximation because or the voltage across cannot go to zero.
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 710 (1) 710 Chap. 13 Output Stages and Power Amplifiers This low efficiency results because both the supply voltages and are “overdesigned.” Exercise At what peak swing does the efficiency reach 20%? The maximum efficiency of proves inadequate in many applications. For example, a stereo amplifier delivering 50 W to a speaker would consume 150 W in the output stage, neces- sitating very large (and expensive) heat sinks. 13.8.2 Efficiency of Push-Pull Stage In Section 13.7.2, we determined that each of and in Fig. 13.26 consumes a power of (13.62) Thus, (13.63) (13.64) The efficiency thus reaches a maximum of for , a much more attractive result than that of the emitter follower. For this reason, push-pull stages are very common in many applications, e.g., audio amplifiers.

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