# V b m m v dd 18 v in v out v 1 2 m 3 m 4 m 5 1 ma

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V b M M V DD = 1.8 V in V out V 1 2 M 3 M 4 M 5 1 mA Figure 9.88 References 1. B. Razavi, Design of Analog CMOS Integrated Circuits McGraw-Hill, 2001.

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 466 (1) 10 Differential Amplifiers The elegant concept of “differential” signals and amplifiers was invented in the 1940s and first utilized in vacuum-tube circuits. Since then, differential circuits have found increasingly wider usage in microelectronics and serve as a robust, high-performance design paradigm in many of today’s systems. This chapter describes bipolar and MOS differential amplifiers and formulates their large-signal and small-signal properties. The concepts are outlined below. General Considerations Differential Signals Differential Pair Bipolar Differential pair Qualitative Analysis Large Signal Analysis Small Signal Analysis Differential pair Qualitative Analysis Large Signal Analysis Small Signal Analysis MOS Other Concepts Cascode Pair Common Mode Rejection Pair with Active Load 10.1 General Considerations 10.1.1 Initial Thoughts In order to understand the need for differential circuits, let us first consider an example. Example 10.1 Having learned the design of rectifiers and basic amplifier stages, an electrical engineering student constructs the circuit shown in Fig. 10.1(a) to amplify the signal produced by a microphone. Unfortunately, upon applying the result to a speaker, the student observes that the amplifier output contains a strong “humming” noise, i.e., a steady low-frequency component. Explain what happens. Solution Recall from Chapter 3 that the current drawn from the rectified output creates a ripple waveform at twice the ac line frequency (50 or 60 Hz) [Fig. 10.1(b)]. Examining the output of the common- emitter stage, we can identify two components: (1) the amplified version of the microphone signal and (2) the ripple waveform present on . For the latter, we can write (10.1) noting that simply “tracks” and hence contains the ripple in its entirety. The “hum” originates from the ripple. Figure 10.1(c) depicts the overall output in the presence of both the signal and the ripple. Illustrated in Fig. 10.1(d), this phenomenon is summarized as the “supply 466
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 467 (1) Sec. 10.1 General Considerations 467 110 V 60 Hz R out V V CC C Q 1 C 1 To Bias t V CC t out V (c) (a) (b) V CC Ripple Signal (d) Voice Signal Figure 10.1 (a) CE stage powered by a rectifier, (b) ripple on supply voltage, (c) effect at output, (d) ripple and signal paths to output. noise goes to the output with a gain of unity.” (A MOS implementation would suffer from the same problem.) Exercise What is the hum frequency for a full-wave rectifier or a half-wave rectifier?

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