Week 12: Output Stages, Frequency Response

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1 ELE 2110A Electronic Circuits Week 12: Output Stages, Frequency esponse (2 hours only) Lecture 12-1

2 Output Stages Topics to cover Amplifier Frequency esponse eading Assignment: Chap 15.3, 16.1 of Jaeger and Blalock or Chap of Sedra & Smith Lecture 12-2

3 Multistage Amplifiers Practical amplifiers usually consist of a number of stages connected in cascade. The first (input) stage is usually required to provide a high input resistance a high common-mode rejection for a differential amplifier Middle stages are to provide majority of voltage gain conversion of the signal from differential mode to single-end mode shifting of the dc level of the signal The last (output) stage is to provide a low output resistance in order to avoid loss of gain and provide the current required by the load (power amplifiers) Lecture 12-3

4 Example The input stage (Q 1, Q 2 ) is differential-in and differentialout biased by current source Q 3 (Q 4, Q 5 ) is a differential-in and single-ended-out stage biased by current source Q 6 Q 7 provides additional gain shifting the dc level of the signal The output stage Q 8 is an emitter follower Lecture 12-4

5 Output Stages Function of an output stage is To provide a low output resistance so that it can deliver the output signal to the load without loss of gain equirements of an output stage: Large input signal range b/c it is the final stage of the amplifier, and usually deals with relatively large signals. Small-signal approximations and models either are not applicable or must be used with care. Low distortion High power efficiency Lecture 12-5

6 Classification of Output Stages Class A Class AB Class B Class C Class A: the transistor conducts for the entire cycle of the input signal Class B: the transistor conducts for only half the cycle Class AB: conduction cycle is greater than 180 o and less than 360 o Used for opamp output stage and audio power amplifiers Class C: conduction cycle is less than 180 o Collector or Drain current waveforms of different output stages Used for radio-frequency (F) power amplifications (mobile phones, radio and TV) Lecture 12-6

7 Class-A Amplifier: Source/Emitter Follower For a source follower biased by an ideal current source, v GS is fixed and v O v I V GS1 v I V TN + 2I K SS n Input range: V + V v V + V SS GS I DD TN Output range: V SS v O V DD The largest output voltage is vo V DD sinωt (if V SS V DD ) Lecture 12-7

8 Source Emitter with Load To maintain class A operation, i s > 0 at all times: v i I + o 0 S SS L v I o For largest output amplitude: SS L vo V DD sinωt We have: V DD sinωt I SS L for all t The lowest value for the LHS occurs when sin ωt -1, V DD I SS V I SS DD L L Lecture 12-8

9 Power Efficiency Average power supplied to the source follower: P av 1 T I SS 0 T I SS ( V + V ) DD SS V + ( V ) DD + VSS 2I SSVDD DD sinωt V L DD dt (if V SS V DD ) The largest output voltage is vo V sinωt DD Average power delivered to the load: 2 V DD 2 2 VDD P ac 2 Efficiency of amplifier is: 2 P V /(2 ) ζ ac DD L P 2I V av SS DD V 2 /(2 ) DD L 25% 2V / V DD L DD L L I SS V DD - Low efficiency L Lecture 12-9

Push-Pull Operation: Class B When a push-pull amplifier is operated in Class B, all of the output current comes either from the current-sourcing transistor or

10 Push-Pull Operation: Class B When a push-pull amplifier is operated in Class B, all of the output current comes either from the current-sourcing transistor or from the currentsinking device but never from both at the same time. Source: B. Putzeys, Digital Audio s final frontier, IEEE Spectrum, Mar Lecture 12-10

11 Class-B Amplifier A complementary pair of source followers biased at zero source current When V TP v I V TN neither transistor conducts No quiescent (DC) current consumption! Lecture 12-11

12 Class-B Amplifier When V I > V TN, M 1 turns on and acts as an source follower, v o v I -V TN M 2 off When V I < V TP, M 2 turns on and acts as an source follower, v o v I V TP M 1 off Power efficiency is high, can be up to about 80% Disadv.: Output waveform suffers from a dead-zone Large distortion Lecture 12-12

13 Class AB Class AB exhibits less distortion by allowing the transistors to work together when the output signal is near zero, in what is called the crossover region. Source: B. Putzeys, Digital Audio s final frontier, IEEE Spectrum, Mar Lecture 12-13

14 Class-AB Amplifiers emove dead zone by biasing transistors into conduction but at a low quiescent current level Distortion less than Class-B but worse than Class-A amplifier For each transistor, <conduction angle<360 0 Class AB amplifier Power efficiency lower than Class-B but higher than Class-A amplifier Lecture 12-14

15 Lecture Class-AB Amplifiers Biasing examples: TN V GG V n K D I T V B B I S I C I 2 exp DC currents:

16 Output Stages Topics to cover Amplifier Frequency esponse Lecture 12-16

17 Frequency esponse of Amplifiers A typical amplifier: Block DC and low frequency signals Amplifier s gain is frequency dependent! By-pass high frequency currents Lecture 12-17

18 Typical Amplifier Transfer Function Mid-band gain Lower cut-off frequency Upper cut-off frequency In low frequency side, drop in gain is caused by coupling and bypass capacitors In high frequency side, drop in gain is caused by transistor s parasitic capacitors More on this topic later In the mid-band range, no capacitors are in effect: Coupling and bypass capacitors are short circuits Transistor parasitic capacitors are open circuits Lecture 12-18

19 Estimate f L : Short-Circuit Time Constant Method Lower cutoff frequency for a network with n coupling and bypass capacitors can be estimated by: n 1 ω L i 1 C is i f ω /2π L L is resistance at terminals of i th capacitor C i with all other capacitors replaced by short circuits. Product is C i is short-circuit time constant associated with C i. Lecture 12-19

20 SCTC: Example β 100 and V A 75V Q-point: (1.73mA, 2.32V) AC equivalent with finite coupling capacitances BJT small signal parameters: r π VT 25mV 1. 45kΩ I 1.73mA/100 B r VA + VCE 75V V 44. kω I 1.73mA o 7 C Lecture 12-20

21 Time Constant Associated with C 1 To find the time constant associated with C 1 : + ( ) ( ) 1 I B CE in + S I B r π (C 2 and C 3 are short-circuited and set v i 0) 1s 1000Ω + (7500Ω 1450Ω) 2220Ω 1 1 s C 2.22kΩ 2µ F rad/s Lecture 12-21

22 Time Constant Associated with C 2 To find the time constant associated with C 2 : (C 1 and C 3 are short-circuited and set v i 0) + ( CE out ) + ( r o ) + 2S 3 C 3 C 3 s 100kΩ + (4.3kΩ 44.7kΩ) 104kΩ s C 104kΩ 0.1µ F rad/s C Lecture 12-22

23 Time Constant Associated with C 3 3S E CC out E r π + th β + 1 E r π + ( ) I B β + 1 To find the time constant associated with C 3 : 3 s 1450V 1300kΩ 22.7Ω Ω 7500Ω s C 22.7kΩ 10µ F rad/s (C 1 and C 2 are short-circuited and set v i 0) Lecture 12-23

24 Lower Cutoff Frequency The lower cutoff frequency is: 3 1 ω L i 1 C is i rad/s and f L ω L 753 Hz 2 π In this example the time constant associated with the bypass capacitor C 3 is dominant. Lecture 12-24

25 High Frequency esponse Mid-band gain Lower cut-off frequency Upper cut-off frequency At high frequency side, drop in gain is caused by transistor s parasitic capacitors Lecture 12-25

26 High Frequency Small Signal Model for BJT B Model for active mode BJT C π : diffusion capacitance of the forward-biased base-emitter junction. C µ : depletion capacitance of the reverse-biased base-collector junction. r x : the resistance of the silicon material of the base region between the base terminal and the intrinsic base terminal B that is right under the emitter region. Lecture 12-26

27 High-frequency Small Signal Model for MOSFET 2 C gs WLC ox 3 L ov Model for saturation mode MOSFET the capacitance between the Gate and the conducting channel. C C WL C the overlap capacitance (very small). gd ov ov ox Lecture 12-27

28 Open-Circuit Time Constant Method to Determine f H f H can be estimated by open-circuit time constant method: 1 ω m, f ω / 2π H H H C io i i 1 where io is resistance at terminals of i th capacitor C i with all other capacitors open-circuited. Lecture 12-28

29 High Frequency Analysis of C-E Amplifier B 30kΩ10kΩ 1 2 β 100 and V A 75V Let Q-point be (1.6mA, 3V) L 3 C 100kΩ 4.3kΩ C 9 pf 19. π C µ r x 0.5pF 250Ω v th v i I + B B th I B 882Ω + I B Lecture 12-29

30 High Frequency Small Signal Equivalent Norton source transformation v i th s + r th x r π o r π ( r x ) th + Lecture 12-30

31 Determine A mid v v v ) 2 gm( isrπ 0 v i th s + r r ( r ) th x π o r π th + x r 2 π 0 π gml gml th th + rx th + rx + L r r π A mid th βol + r + r x π 100(4120) Lecture 12-31

32 OCTC: Time Constant Associated with C π To find the time constant associated with C π : (C µ is open-circuited and set i s 0) π o rπ o rπ ( + r x ) 1.56kΩ (882Ω+ 250Ω) 656Ω th C 9 pf 19. π C π π Lecture 12-32

33 Lecture OCTC: Time Constant Associated with C µ L m x x L L x x v g i r i i r i v ) ( π π Ω + + Ω k o (4120) µ C µ µ + + o r L L m g o r o π π µ 1 x i x v To find the time constant associated with C µ : (C π is open-circuited and set i s 0) r π 0 i v x

34 Upper Cutoff Frequency Upper cutoff frequency: ω H πo C π µ o C µ rad/s f H ω H 2 π 1.56 MHz Lecture 12-34

BJT Circuits (MCQs of Moderate Complexity)

BJT Circuits (MCQs of Moderate Complexity) 1. The current ib through base of a silicon npn transistor is 1+0.1 cos (1000πt) ma. At 300K, the rπ in the small signal model of the transistor is i b B C r