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Chapter 10 Differential Amplifiers

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Chapter 10 Differential Amplifiers 10.1 General Considerations 10.2 Bipolar Differential Pair 10.3 MOS Differential Pair 10.4 Cascode Differential Amplifiers 10.5 Common-Mode Rejection 10.6 Differential Pair with Active Load 1 Audio Amplifier Example An audio amplifier is constructed as above that takes a rectified AC voltage as its supply and amplifies an audio signal from a microphone. CH 10 Differential Amplifiers 2 “Humming” Noise in Audio Amplifier Example However, VCC contains a ripple from rectification that leaks to the output and is perceived as a “humming” noise by the user. CH 10 Differential Amplifiers 3 Supply Ripple Rejection vX Avvin vr vY vr vX vY Avvin Since both node X and Y contain the same ripple, their difference will be free of ripple. CH 10 Differential Amplifiers 4 Ripple-Free Differential Output Since the signal is taken as a difference between two nodes, an amplifier that senses differential signals is needed. CH 10 Differential Amplifiers 5 Common Inputs to Differential Amplifier vX Avvin vr vY Avvin vr vX vY 0 Signals cannot be applied in phase to the inputs of a differential amplifier, since the outputs will also be in phase, producing zero differential output. CH 10 Differential Amplifiers 6 Differential Inputs to Differential Amplifier vX Avvin vr vY Avvin vr vX vY 2Avvin When the inputs are applied differentially, the outputs are 180° out of phase; enhancing each other when sensed differentially. CH 10 Differential Amplifiers 7 Differential Signals A pair of differential signals can be generated, among other ways, by a transformer. Differential signals have the property that they share the same average value (DC) to ground and AC values are equal in magnitude but opposite in phase. CH 10 Differential Amplifiers 8 Single-ended vs. Differential Signals CH 10 Differential Amplifiers 9 Example 10.3 Determine the common-mode level at the output of the circuit shown in Fig. 10.3(b). In the absence of signals, VVVRIX Y CC C C and where RRRCCC1 2 IC denotes the bias current of Q1 and Q2 Thus, VVRICM CC C C Interestingly, the ripple affects VCM but not the differential output. CH 10 Differential Amplifiers 10 Differential Pair With the addition of a tail current, the circuits above operate as an elegant, yet robust differential pair. CH 10 Differential Amplifiers 11 Common-Mode Response VBE1 VBE 2 I I I EE C1 C 2 2 I V V V R EE X Y CC C 2 To avoid saturation, the collector voltages must not fall below the base voltages: I VRVEE CC C2 CM CH 10 Differential Amplifiers 12 Example 10.4 A bipolar differential pair employs a load resistance of 1 kΩ and a tail current of 1 mA. How close to VCC can VCM be chosen? I VVR EE CC CM C 2 0 5V That is, VCM must remain below VCC by at least 0.5 V. CH 10 Differential Amplifiers 13 Common-Mode Rejection Due to the fixed tail current source, the input common- mode value can vary without changing the output common- mode value. CH 10 Differential Amplifiers 14 Differential Response I IC1 I EE IC2 0 VX VCC RC I EE VY VCC CH 10 Differential Amplifiers 15 Differential Response II IC2 I EE IC1 0 VY VCC RC I EE VX VCC CH 10 Differential Amplifiers 16 Differential Pair Characteristics None-zero differential input produces variations in output currents and voltages, whereas common-mode input produces no variations. CH 10 Differential Amplifiers 17 Example 10.5 A bipolar differential pair employs a tail current of 0.5 mA and a collector resistance of 1 kΩ. What is the maximum allowable base voltage if the differential input is large enough to completely steer the tail current? Assume VCC=2.5V. Because IEE is completely steered, VRIVCC- C EE 2 at one collector. To avoid saturation, VVB 2 . CH 10 Differential Amplifiers 18 Small-Signal Analysis I I EE I C1 2 I I EE I C 2 2 Since the input to Q1 and Q2 rises and falls by the same amount, and their emitters are tied together, the rise in IC1 has the same magnitude as the fall in IC2. CH 10 Differential Amplifiers 19 Virtual Ground IC1 g m() V V P VP 0 IC2 g m() V V P I g V IICC2 1 0 C1 m gm()() V V P g m V V P IC 2 gmV For small changes at inputs, the gm’s are the same, and the respective increase and decrease of IC1 and IC2 are the same, node P must stay constant to accommodate these changes. Therefore, node P can be viewed as AC ground. CH 10 Differential Amplifiers 20 Small-Signal Differential Gain VX g m VR C V g VR 2g VR Y m C A m C g R v 2V m C VX V Y 2 g m VR C Since the output changes by -2gmVRC and input by 2V, the small signal gain is –gmRC, similar to that of the CE stage. However, to obtain same gain as the CE stage, power dissipation is doubled. CH 10 Differential Amplifiers 21 Example 10.6 Design a bipolar differential pair for a gain of 10 and a power budget of 1mW with a supply voltage of 2V. VCC 2 V 1 mW I 0.5 mA EE 2 V IC I EE / 2 0.25 mA 1 gm VVTT 26 mV 104 Av RC 1040 gm CH 10 Differential Amplifiers 22 Example 10.7 Compare the power dissipation of a bipolar differential pair with that of a CE stage if both circuits are designed for equal voltage gains, collector resistances, and supply voltages. Differential pair CE stage AVdiff g m 1 2 R C AV CE g m R C gm1 2 R C g m R C I I EE C 2VVTT IIEE 2 C PVIVID, diff C EE 2 C C PVID, CE C C CH 10 Differential Amplifiers 23 Large Signal Analysis VVVVin1 in 2 BE 1 BE 2 IICC1 2 VVTTln ln IISS1 2 and IIIC1 C 2 EE VVin1 in 2 IIIC2exp C 2 EE VT I I EE C2 VV 1 exp in1 in 2 VT VV I exp in1 in 2 EE V I T C1 VV 1 exp in1 in 2 VT CH 10 Differential Amplifiers 24 Example 10.8 Determine the differential input voltage that steers 98% of the tail current to one transistor. IIC1 0 02 EE VVin1 in 2 I EE exp VT VVVin1 in 2 3 91 T We often say a differential input of 4VT is sufficient to turn one side of the bipolar pair nearly off. CH 10 Differential Amplifiers 25 Input/Output Characteristics VVRIout1 CC C C 1 VV I exp in1 in 2 EE V VR T CC C VV 1 exp in1 in 2 VT VVRIout2 CC C C 2 I VR EE CC C VV 1 exp in1 in 2 VT VV 1 exp in1 in 2 V VVRI T out1 out 2 C EE VV 1 exp in1 in 2 VT VVin1 in 2 RIC EE tanh 2VT CH 10 Differential Amplifiers 26 Example 10.9 Sketch the output waveforms of the bipolar differential pair in Fig. 10.14(a) in response to the sinusoidal inputs shown in Figs. 10.14(b) and (c). Assume Q1 and Q2 remain in the forward active region. Figure10.14 (a) CH 10 Differential Amplifiers 27 Example 10.9 (cont’d) The left column operates in linear region (small-signal), whereas the right column operates in nonlinear region (large-signal). CH 10 Differential Amplifiers 28 Small-Signal Model vin1 v 1 v P v in 2 v 2 v1 v 2 gm1 v 1 g m 2 v 2 0 r1 r 2 With r1 r 2 and gm1 g m 2 v1 v 2 Since vin1 v in 2 , 2vin1 2 v 1 . vP v in1 v 1 0 CH 10 Differential Amplifiers 29 Half Circuits vout1 vout 2 g m RC vin1 vin2 Since VP is grounded, we can treat the differential pair as two CE “half circuits”, with its gain equal to one half circuit’s single-ended gain. CH 10 Differential Amplifiers 30 Example 10.10 Compute the differential gain of the circuit shown in Fig. 10.16(a), where ideal current sources are used as loads to maximize the gain. v v out1 out 2 g r Figure10.16 (a) m O vin1 vin 2 CH 10 Differential Amplifiers 31 Example 10.11 Figure 10.17(a) illustrates an implementation of the topology shown in Fig. 10.16(a). Calculate the differential voltage gain. vout1 v out 2 gm r ON r OP vin1 v in 2 Figure10.17 (a) CH 10 Differential Amplifiers 32 Extension of Virtual Ground VX 0 It can be shown that if R1 = R2, and points A and B go up and down by the same amount respectively, VX does not move. This property holds for any other node that appears on the axis of symmetry. CH 10 Differential Amplifiers 33 Half Circuit Example I Av gm1 rO1 || rO3 || R1 CH 10 Differential Amplifiers 34 Half Circuit Example II Av gm1 rO1 || rO3 || R1 CH 10 Differential Amplifiers 35 Half Circuit Example III R A C v 1 RE gm CH 10 Differential Amplifiers 36 Half Circuit Example IV R A C v R 1 E 2 gm CH 10 Differential Amplifiers 37 I/O Impedances v1 v 2 iX r1 r 2 i X vX v1 v 2 2r1 iX vX vX Rin 2 r1 iX iX iX In a similar manner, RRout 2 C v CH 10 Differential Amplifiers X 38 MOS Differential Pair’s Common-Mode Response I II SS DD1 2 2 I VVVR SS X Y DD D 2 Similar to its bipolar counterpart, MOS differential pair produces zero differential output as VCM changes.
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