Chapter 6 Differential and Multistage Amplifiers1

# Input differential resistance of differential pair

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Input differential resistance of differential pair with emitter resistors. π β β r r r v v i v R e e d d b d id 2 2 ) 1 ( 1 2 = + = + = ) 2 2 ) 1 ( e e b id id R r i v R β + =

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Differential Voltage Gain Differential voltage gain Ø Output voltage taken single-ended Ø Output voltage taken differentially C m id o d R g v v A 2 1 1 1 - = C m id o d R g v v A 2 1 2 2 = C m id o o d R g v v v A = - 1 2
Differential Voltage Gain Differential voltage gain of the differential pair with resistances in the emitter loads Ø Output voltage taken single-ended Ø Output voltage taken differentially The voltage gain is equal to the ratio of the total resistance in the collector circuit to the total resistance in the emitter circuit. e e C id o d R r R v v A + - = 2 1 1 1 e e C id o o d R r R v v v A + = - 1 2 e e C id o d R r R v v A + = 2 1 2 2

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Differential Half-Circuit Analysis Ø Differential input signals. Ø Single voltage at joint emitters is zero. Ø The circuit is symmetric. Ø Equivalent common-emitter amplifiers in (b). D:\Ä£µç¿Î¼þ\ ·Ö·Å´óµçÂ·¶Ô¹²Ä£
Differential Half-Circuit Analysis Ø This equivalence applies only for differential input signals. Ø Either of the two common-emitter amplifiers can be used to find the differential gain, differential input resistance, frequency response, and so on Ø Half circuit is biased at I/2. Ø The voltage gain(with the output taken differentially) is equal to the voltage of half circuit.

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Differential Half-Circuit Analysis Ø The differential amplifier fed in a single-ended manner. Ø Signal voltage at the emitter is not zero. Ø Almost identical to the symmetric one.
Common-Mode Gain The differential amplifier fed by a common-mode voltage signal vicm .

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Common-Mode Gain Equivalent “half-circuits” for common-mode calculations. 2 1 1 2 2 c c EE C CM e EE C CM c v v R R v r R R v v = - + - = α α
Common-Mode Gain Common-mode voltage gain Ø Output voltage taken single-ended Ø Output voltage taken differentially EE C icm o cm R R v v A 2 1 1 - = 0 1 2 = - id o o cm v v v A EE C icm o cm R R v v A 2 2 2 - =

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Common-Mode Rejection Ratio
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• Fall '10
• ChengJianping
• Electronic amplifier, differential pair, CMRR

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