Input DifferentialResistance: Input differential resistance is finitedVdA=(1+β)2r。= 2r元iL2rβ+1Theresistanceseen betweenthetwo basesisegual tothetotal resistance intheemittercircuit multipliedby(1+β).Inputdifferential resistance ofdifferential pairwithemitterresistorsVid-=(1+ β)(2r+2R.)R3Microelectronic Circuits
Microelectronic Circuits Input Differential Resistance • Input differential resistance is finite. The resistance seen between the two bases is equal to the total resistance in the emitter circuit multiplied by (1+β). • Input differential resistance of differential pair with emitter resistors. r r r v v i v R e e d d b d i d (1 )2 2 1 2 = + = + = (1 ) 2 2 ) e e b i d i d r R i v R = + （ ＋
Differential Voltage Gain. Differential voltage gain> Output voltage taken single-ended2oV02-1gmRc一A=gmRcd2VidVid> Output voltage taken differentiallyDol02= gmRVidMicroelectronic Circuits
Microelectronic Circuits Differential Voltage Gain • Differential voltage gain ➢ Output voltage taken single-ended ➢ Output voltage taken differentially m C i d o d g R v v A 2 1 1 1 = − m C i d o d g R v v A 2 2 1 2 = m C i d o o d g R v v v A = − 2 1
Differential VoltageGain.Differential voltage gain of the differential pair withresistances intheemitterloads> Output voltage taken single-ended1 RcR.V2022 r. +R2 r.+ RVidVidOutput voltage taken differentiallyRcVV02-nre+R.VidThe voltage gain is equal to the ratio of the totalresistanceinthecollectorcircuittothetotalresistanceintheemittercircuitMicroelectronic Circuits
Microelectronic Circuits Differential Voltage Gain • Differential voltage gain of the differential pair with resistances in the emitter loads ➢ Output voltage taken single-ended ➢ 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 i d o d r R R v v A + = − 2 1 1 1 e e C i d o o d r R R v v v A + = − 2 1 e e C i d o d r R R v v A + = 2 2 1 2
Differential Half-Circuit Analysis>Differential input signalsU-2>Single voltage at jointemitters is zero.VidVid22>The circuit is symmetricOV>Equivalent common-emitter amplifiers in (b)D:\模电话件！差分放大电路对共-(a)Microelectronic Circuits
Microelectronic Circuits Differential Half-Circuit Analysis ➢Differential input signals. ➢Single voltage at joint emitters is zero. ➢The circuit is symmetric. ➢Equivalent commonemitter amplifiers in (b)
Differential Half-Circuit Analysis>This equivalence applies only for-differential input signals>Either of the two common-emitter amplifiers can be used tofind the differential gain,1002differential input resistance,Vidfrequency response, and so on2>Half circuit is biased at I/2>The voltage gain(with the outputaken differentially) is equal to theBiasedatvoltage of half circuit(b)Microelectronic Circuits
Microelectronic Circuits Differential Half-Circuit Analysis ➢This equivalence applies only for differential input signals. ➢Either of the two commonemitter amplifiers can be used to find the differential gain, differential input resistance, frequency response, and so on ➢Half circuit is biased at I/2. ➢The voltage gain(with the output taken differentially) is equal to the voltage of half circuit