ࡱ> %'$l'` =bjbjLULU 6.?.? ,ZZZ^3^3^383L3,"Vp46LP6P6P6NNNUUUUUUU$WhYUZN7NNNNUP6P6UPPPNF"P6ZP6UPNUPPvTrZvUP64 ^35OBUUU0V\UZPZ4vUZZvU(NNPNNNNNUUPNNNVNNNN"""^3"""^3nd@ Differential and Common-Mode Gain Recall that in a previous handout, we analyzed this circuit:  and found that the output is related to the inputs as:  EMBED Equation.DSMT4  This circuit is a weighted difference amplifier, and typically, it is expressed in terms of its differential gain Ad and common-mode gain Acm. To understand what these gains mean, we must first define the difference signal  EMBED Equation.DSMT4  and common-mode signal  EMBED Equation.DSMT4  of two inputs  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4 . The difference, as we might expect, is defined as:   EMBED Equation.DSMT4  whereas the common-mode signal is simply the average of the two inputs:   EMBED Equation.DSMT4  Using these definitions, we can express the two input signals as:   EMBED Equation.DSMT4  Thus, the differential signal  EMBED Equation.DSMT4  and the common-mode signal  EMBED Equation.DSMT4  provide another way to completely specify input signals  EMBED Equation.DSMT4 if you know  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4 , you know  EMBED Equation.DSMT4 and  EMBED Equation.DSMT4 . Moreover, we can express the behavior of our differential amplifier in terms of  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4 . Inserting these functions into the expression of the amplifier output  EMBED Equation.DSMT4 , we find:  EMBED Equation.DSMT4  Thus, we now have an expression for the open-circuit output in the form:  EMBED Equation.DSMT4  where:   EMBED Equation.DSMT4  Note that each of these gains are open-circuit voltage gains. * An ideal differential amplifier has zero common-mode gain (i.e., Acm =0)! * In other words, the output of an ideal differential amplifier is independent of the common-mode (i.e., average) of the two input signals. * We refer to this characteristic as common-mode suppression. Typically, real differential amplifiers exhibit small, but non-zero common mode gain. The Common-Mode Rejection Ratio (CMRR) is therefore used to indicate the quality of a differential amplifier:  EMBED Equation.DSMT4  Note the CMRR of a good differential amplifier is very large (e.g., > 40 dB). For our example circuit, we find that the differential and common-mode gain are:  EMBED Equation.DSMT4  The ratio of these two gains is thus:  EMBED Equation.DSMT4  and therefore CMRR is:  EMBED Equation.DSMT4  It is evident that for this example, the common-mode gain Acm is minimized, and thus the CMRR is maximized, when:  EMBED Equation.DSMT4  so that  EMBED Equation.DSMT4 .      DATE \@ "M/d/yyyy" 2/17/2011  FILENAME Differential and Common Mode Gain.doc  PAGE 4/ NUMPAGES 6 R4 R3 v2 v1 ideal vout - + R1 R2 RV`a' 4 9 : ; < @ K Q R T    ʽ{njhWhWEHU%jQ hWCJOJQJUVaJjhWhWEHU%jQ hWCJOJQJUVaJhW6H*] hW6]jhWhWEHU%jQ hWCJOJQJUVaJjhWUjhWCJUmHnHu hW5\hW*"#`bcdefghijklmnopqrV W B u $a$$a$<    $ % < = > ? F P v w x y A B C D [ ӬӜӉ|ӬӬӜi\ӜjhWhWEHU%jgQ hWCJOJQJUVaJj.hWhWEHU%jwQ hWCJOJQJUVaJjhWCJUmHnHu hW5\j hWhWEHU%jQ hWCJOJQJUVaJhWjhWUj hWhWEHU%jQ hWCJOJQJUVaJ$u v x @ A C _ 2:;=YZ$a$$a$[ \ ] ^ } ~  ! 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