3.4 - BJT DIFFERENTIAL AMPLIFIERS

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1 BJT Differential Amplifiers (6/4/00) Page BJT DIFFERENTIAL AMPLIFIERS INTRODUCTION Objective The objective of this presentation is: 1.) Define and characterize the differential amplifier.) Show the largesignal and smallsignal performance 3.) Show alternate implementations of the differential amplifier Outline Characterization and definitions Largesignal transconductance Largesignal voltage transfer Smallsignal performance Other characteristics of the differential amplifier Summary ECE 4430 Analog Integrated Circuits and Systems P.E. Allen, 000

2 BJT Differential Amplifiers (6/4/00) Page CHARACTERIZATION AND DEFINITIONS What is a Differential Amplifier? A differential amplifier is an amplifier that amplifies the difference between two voltages and rejects the average or common mode value of the two voltages. Symbol for a differential amplifier: v 1 v v OUT Fig. 5.1A Differential and common mode voltages: v 1 and v are called singleended voltages. They are voltages referenced to ac ground. The differentialmode input voltage, v ID, is the voltage difference between v 1 and v. The commonmode input voltage, v IC, is the average value of v 1 and v. v ID = v 1 v and v IC = v 1 v v 1 = v IC 0.5v ID and v = v IC 0.5v ID v ID v OUT = A VD v ID ± A VC v IC = A VD (v 1 v ) ± A VC v 1 v v where v ID IC v OUT A VD = differentialmode voltage gain A VC = commonmode voltage gain Fig. 5.1B ECE 4430 Analog Integrated Circuits and Systems P.E. Allen, 000

3 BJT Differential Amplifiers (6/4/00) Page 3 Differential Amplifier Definitions Common mode rejection rato (CMRR) CMRR = A VD A VC CMRR is a measure of how well the differential amplifier rejects the commonmode input voltage in favor of the differentialinput voltage. Input commonmode range (ICMR) The input commonmode range is the range of commonmode voltages over which the differential amplifier continues to sense and amplify the difference signal with the same gain. Typically, the ICMR is defined by the commonmode voltage range over which all MOSFETs remain in the saturation region and all BJTs remain in the active region. Output offset voltage (V OS (out)) The output offset voltage is the voltage which appears at the output of the differential amplifier when the input terminals are connected together. Input offset voltage (V OS (in) = V OS ) The input offset voltage is equal to the output offset voltage divided by the differential voltage gain. V OS = V OS (out) A VD ECE 4430 Analog Integrated Circuits and Systems P.E. Allen, 000

4 BJT Differential Amplifiers (6/4/00) Page 4 LARGESIGNAL TRANSCONDUCTANCE Transconductance Characteristic of the Differential Amplifier Consider the following NPNBJT differential amplifier (sometimes called an emittercoupled pair): i C1 i C v I1 Q v BE1 v BE v I BJTDA01 LargeSignal Analysis: 1.) Input loop eq.: v I1 v BE1 v BE v I = v I1 v I v BE1 v BE = v ID v BE1 v BE = 0.) Fowardactive region: v BE1 = V t ln i C1 I and v BE = V t ln i C S1 I S 3.) If I S1 = I S then i C1 i = exp v I1 v I C V = exp v ID t V t 4.) Nodal current equation at the emitters: (i E1 i E ) = = 1 α F (i C1 i C ) 5.) Combining the above equations gives: i C1 = α F α F 1 exp and i v C = ID V 1 exp v ID t V t ECE 4430 Analog Integrated Circuits and Systems P.E. Allen, 000

5 BJT Differential Amplifiers (6/4/00) Page 5 Transconductance Characteristic of the Differential Amplifier Continued Plotting the collect current as a function of v ID : i C i C1 0.6 i C α Transconductance: g m1 = i C1 α F v ID Q = 1exp v ID V V t t g m = i C α F v ID Q = 1exp v ID V V t t v ID BJTDA00 V t = α F 4V t = α F 4V t = I C1 V t when V ID = 0 = I C V t when V ID = 0 ECE 4430 Analog Integrated Circuits and Systems P.E. Allen, 000

6 BJT Differential Amplifiers (6/4/00) Page 6 LargeSignal Voltage Transfer Function Assume load resistors as shown: VOLTAGE TRANSFEHARACTERISTICS v i1 v OD i C1 ic v O1 v O1 Q v BE1 v BE v i v OD = v O1 v O = i C1 i C = (i C i C1 ) Substituting in the previous expressions and using hyperbolic trig identities gives v OD = α F tanh v ID V t Illustration v OD α F BJTDA v ID V t BJTDA04 ECE 4430 Analog Integrated Circuits and Systems P.E. Allen, 000

7 BJT Differential Amplifiers (6/4/00) Page 7 Emitter Degeneration of the BJT Differential Amplifier Increases the range over which the emittercoupled pair behaves as a linear amplifier with lower gain at the cost of lower gain. v i1 i C1 v OD ic Q v BE1 v BE R E RE v i v OD α F Increasing R E R E =0 1 v ID V t BJTDA05 We know that, i D = i C1 i C = α F tanh v ID (R E i D /α F ) Vt α F v ID Solving for i D gives, i D = i C1 i C = V t R E g m (DC) = di D dv ID = (α F ) V t R E = (α F )/V t 1 R E /V t α F v ID (R E i D /α F ) Vt ECE 4430 Analog Integrated Circuits and Systems P.E. Allen, 000

8 BJT Differential Amplifiers (6/4/00) Page 8 SMALLSIGNAL PERFORMANCE Differential and Commonmode SmallSignal Performance The smallsignal performance of a differential amplifier can be separated into a differential mode and common mode analysis. This separation allows us to take advantage of the following simplifications. HalfCircuit Concept: v i1 v od i c1 ic v o1 v o Q v be1 v be R EE Differential Mode Analysis vi Common Mode Analysis v od i c1 ic v o1 v o Q v id v be1 vid v be v od i c1 ic v o1 v o Q v be1 v be R EE R EE BJTDA06 Note: The halfcircuit concept is valid as long as the resistance seen looking into each emitter is the same. ECE 4430 Analog Integrated Circuits and Systems P.E. Allen, 000

9 BJT Differential Amplifiers (6/4/00) Page 9 SMALLSIGNAL PERFORMANCE Differential and Commonmode SmallSignal Performance The smallsignal performance of a differential amplifier can be separated into a differential mode and common mode analysis. This separation allows us to take advantage of the following simplifications. HalfCircuit Concept: v i1 v od i c1 ic v o1 v o Q v be1 v be R EE Differential Mode Analysis vi Common Mode Analysis v od i c1 ic v o1 v o Q v id v be1 vid v be v od i c1 ic v o1 v o Q v be1 v be R EE R EE BJTDA06 Note: The halfcircuit concept is valid as long as the resistance seen looking into each emitter is the same. ECE 4430 Analog Integrated Circuits and Systems P.E. Allen, 000

10 BJT Differential Amplifiers (6/4/00) Page 10 SmallSignal, Common Mode Performance of the BJT Differential Amplifier Circuit and smallsignal model: R in Rout Halfcircuit performance: i c1 v o1 v be1 R EE R in1 = r π1 (1β o1 )R EE, R out1 = r o 1 β ο1 R EE R EE r π1 Common mode performance: r π v π gm v π r o R EE v out BJTDA08 R EE r π1, and v o1 = β o1 r π1 (1β o1 )R EE R ic = r π1 (1β o1 )R EE, R oc = r o 1 β ο1 R EE R EE r π1 R EE r π1, and v oc = β o1 r π1 (1β o1 )R EE where g m1 = g m, r π1 = r π and β o1 = β o. ECE 4430 Analog Integrated Circuits and Systems P.E. Allen, 000

11 BJT Differential Amplifiers (6/4/00) Page 11 Common Mode Rejection Ratio (CMRR) The common mode rejection ratio is a measure of the differential amplifier s ability to reject the common mode signal and amplify the differential mode signal. A dm CMRR = A = v o1 /v id cm v o1 /v = ic g m1 R EE β o1 R g m1 R EE = C V t r π1 (1β o1 )R EE Thus, the larger the input transconductance or R EE, the larger the common mode rejection ratio. ECE 4430 Analog Integrated Circuits and Systems P.E. Allen, 000

12 BJT Differential Amplifiers (6/4/00) Page 1 OTHEHARACTERISTICS OF THE DIFFERENTIAL AMPLIFIER Input Common Mode Voltage Range The input common mode voltage range (ICMR) is the range of common mode input voltages over which the differential amplifier amplifies the differential signal without significant change. Consider the following: (max) Q v CE (sat) V BE1 v BE (min) Q v CE (sat) V BE1 v BE V Bias Q3 Maximum Input Common Mode Voltage: (max) = 0.5 v CE1 (sat)v BE1 Q3 V Bias v CE (sat) BJTDA03 Minimum Input Common Mode Voltage: (min) = v CE3 (sat)v BE1 ECE 4430 Analog Integrated Circuits and Systems P.E. Allen, 000

13 BJT Differential Amplifiers (6/4/00) Page 13 Slew Rate of the BJT Differential Amplifier Slew rate is a voltage rate limit due to the fact that the current available to charge a capacitor is constant. Slew rate = SR = dv C dt = i C C where i C and v C are the current through and voltage across a capacitor C. A differential amplifier that has a capacitive load will experience slew rate which is seen as follows: R v C OD Situation at C s i C1 ic C C s v o OD 0 Q v i1 <<0 v BE1 v BE v i >>0 C s i Cs i C1 =0 v C1 v OD 0 vc C o i Co Q v i1 <<0 v BE1 v BE v i >>0 i Cs i C = C s BJTDA09A Note that the current in is 0 and Q is. Therefore, the initial value of i Co is i Co = 0.5 i Cs. If we define the slew rate across C o as SR = i Co C, then i Cs = 0.5SR C s = i Co o C C s, i.e. dv C1 o dt = 0.5 dv OD dt SR = C i Cs o C = o C SR C s o C SR 1 C s o C = o C SR = o 0.5 C o 0.5C s = C o C s ECE 4430 Analog Integrated Circuits and Systems P.E. Allen, 000

14 BJT Differential Amplifiers (6/4/00) Page 14 SUMMARY A differential amplifier amplifies the difference signal between two voltages and rejects the common mode signal The transconductance characteristics of the BJT differential amplifier switches from all of the current in one side to the other side within ±100mV The largesignal differential voltage transfer function has the form of hyperbolic tangent Emitter degeneration increases the range over which the differential amplifier behaves as a linear amplifier The half circuit concept is very useful for analyzing the smallsignal differential and common mode performance The maximum and minimum input common mode range is: (max) = 0.5 v CE1 (sat)v BE1 (min) = v CE3 (sat)v BE1 The differential amplifier has a slew rate limit of /C eq where C eq is the capacitance seen to ground from either collector. ECE 4430 Analog Integrated Circuits and Systems P.E. Allen, 000

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