Lecture 5 Followers (1/11/4) Page 51 LECTURE 5 FOLLOWERS (READING: GHLM 344362, AH 221226) Objective The objective of this presentation is: Show how to design stages that 1.) Provide sufficient output power in the form of voltage or current. 2.) Avoid signal distortion. 3.) Be efficient 4.) Provide protection from abnormal conditions (short circuit, over temperature, etc.) Outline Source follower Emitter follower Common source stage Common emitter stage PushPull MOS (Class B) PushPull BJT (Class B) Summary Lecture 5 Followers (1/11/4) Page 52 SOURCE FOLLOWERS Maximum and Minimum Output Voltage of the Source Follower NChannel Source Follower Voltage transfer curve: with current sink bias: M3 M1 M2 Fig. 51 V ON1 V ON2 V GS1 Triode Maximum output voltage swings: (min) V ON2 (if is large) or (min) (if is small) (max) V ON1 (if > ) or (max) V GS1 V GS1 V ON2 V ON1 V GS1 < V ON2 Triode V GS1 Fig. 52
Lecture 5 Followers (1/11/4) Page 53 Output Voltage Swing of the Follower Continued The previous results do not include the bulk effect on V T1 of V GS1. Therefore, V T1 V T1 γ[ 2 φ F v BS 2 φ F ] V T1 γ v SB V T1 γ 1 (max) (max) V ON1 V T1 V ON1 V T1 γ 1 Define (max) (max) which gives the quadratic, (max) (max)γ 1 (max)( V ON1 V T1 ) Solving the quadratic gives, (max) γ 1 2 4 γ 1 2 γ 1 24( V ON1 V T1 ) γ 1 2 4( V ON1 V T1 ) 4 If 2.5V, γ N.4V 1/2, V TN1.7V, and V ON1.2V, then (max) 3.661V and (max) 3.6612.5.8661V Lecture 5 Followers (1/11/4) Page 54 Maximum Sourcing and Sinking Currents for the Source Follower Maximum Sourcing Current (into a short circuit): We assume that the transistors are in saturation and 2.5V, thus M1 I OUT (sourcing) K 1W 1 2L 1 [ V T1 ]2 where is assumed to be equal to. M3 M2 If W 1 /L 1 1 and if V, then V T1 1.8V I OUT equal to 1.11 ma. However, as increases above V, the current rapidly decreases. Maximum Sinking Current: For the current sink load, the sinking current is whatever the sink is biased to provide. I OUT (sinking) Fig. 51
Lecture 5 Followers (1/11/4) Page 55 Efficiency of the Source Follower Assume that the source follower can swing to power supply: Smaller i D1 Optimum for maximum swing IQ Larger v DS1 Fig. 53 (peak)2 (peak)2 P RL 2 2 v OUT (peak) 2 Efficiency P Supply ( ) (V DD ) ( ) 2 Maximum efficiency occurs when (peak) which gives 25%. Comments: Maximum efficiency occurs for the optimum value of which gives maximum swing. Other values of result in less efficiency (and smaller signal swings before clipping) We have ignored the fact that the dynamic Q point cannot travel along the full length of the load line because of minimum and maximum voltage limits. Lecture 5 Followers (1/11/4) Page 56 Small Signal Performance of the Source Follower Smallsignal model: v gs1 C 1 rds1 r ds2 g m1 v gs1 g mbs1 v bs1 C 2 vout v gs1 C 1 rds1 r ds2 g m1 g m1 v out g mbs1 v out C 2 vout Fig. 54 V out V in g m1 g ds1 g ds2 g m1 g mbs1 G L g m1 g m1 g mbs1 G L g m1 1 g m1 If 2.5V, V out V, W 1 /L 1 1µm/1 µm, W 2 /L 2 1µm/1 µm, and I D 5 µa, then For the current sink load follower ( ): V out V.869V/V, if the bulk effect were ignored, then V out in V.963V/V in For a finite load, 1Ω: V out V in.512v/v
Lecture 5 Followers (1/11/4) Page 57 Small Signal Performance of the Source Follower Continued The output resistance is: 1 R out g m1 g mbs1 g ds1 g ds2 G L For the current sink load follower: R out 83Ω The frequency response of the source follower: V out (s) V in (s) (g m1 sc 1 ) g ds1 g ds2 g m1 g mbs1 G L s(c 1 C 2 ) where C 1 capacitances connected between the input and output C GS1 C 2 C bs1 C bd2 C gd2 (or C gs2 ) C L z g m1 C 1 and p g m1g L C 1 C 2 The presence of a LHP zero leads to the possibility that in most cases the pole and zero will provide some degree of cancellation leading to a broadband response. Lecture 5 Followers (1/11/4) Page 58 EMITTER FOLLOWER Voltage Transfer Characteristic Q3 i IN R 1 V EE Q1 Q2 Maximum signal swings: (max) V CE1 (sat) Fig. 55 V CE1 (sat) V EE V CE2 (sat)v BE1 V BE1 <V EE V CE2 (sat) Q1 cutoff Q2 saturated Q1 Saturated V CE1 (sat)v BE1 V EE V CE2 (sat) or V BE1 if (max) Limited to V BE (on) if (The circuit driving the emitter follower must provide a current of V CE1 (sat) β F R ) L (min) V EE V CE2 (sat) or (min) (if < V EE V CE2 (sat) (source) β F i IN (sink)
Lecture 5 Followers (1/11/4) Page 59 Efficiency of the Emitter Follower Assume that the emitter follower can swing to power supply: Smaller i C1 V EE Optimum for maximum swing Larger V EE VCC v CE1 Fig. 56 (peak)2 (peak)2 P RL 2 2 v OUT (peak) 2 Efficiency P Supply ( V EE ) (V CC V EE ) V EE ( V EE ) 2 Maximum efficiency occurs when (peak) V EE which gives 25%. Comments: Maximum efficiency occurs for the optimum value of which gives maximum swing. Other values of will result in less efficiency (smaller signal swings before clipping) Lecture 5 Followers (1/11/4) Page 51 Power Considerations of the Emitter Follower Waveforms of the transistor variables for maximum efficiency ( V EE ). 2 v CE1 Quiescent Voltage V om 2 i C1 t Quiescent Current I om p C1 v CE1 i C1 t Quiescent Power t Fig. 57 p C1 v CE1 i C1 [ (1sinωt)][ [1sinωt)] (1sin 2 ωt) 2 (1cos2ωt)
Lecture 5 Followers (1/11/4) Page 511 Power Considerations of the Emitter Follower Continued Parabolas of constant power: 2 1.6 High Power Dissipation i C1 1.2.8.4 Low Power Dissipation Q for max. efficiency.4.8 v CE1 1.2 1.6 2 Fig. 58 Comments: Maximum power dissipation occurs at the Q point for the optimum corresponding to maximum efficiency. For smaller values of the power dissipation can become very large. Lecture 5 Followers (1/11/4) Page 512 Example Design of an Emitter Follower for Maximum Efficiency The emitter follower shown has V EE 5V, R 1 2.15kΩ, and V CE (sat).2v. Find the optimum value of for maximum efficiency and find the value of this efficiency. v Solution IN The optimum for maximum efficiency is found as, V CE (sat) Q3 V EEV BE R 5.7 1 2.15kΩ 2mA Fig. 59 5.2 2mA 2.4kΩ The efficiency can be found by calculating the power to the load and from the sources. P L (max) V CE (sat) 2 2.5(4.8V)(2mA) 4.8mW P supply 2 2(5)(2mA) 2mW η P L(max) P 4.8 supply 2.24 or 24% which is close to the theoretical maximum. i IN R 1 V EE Q1 Q2
Lecture 5 Followers (1/11/4) Page 513 Emitter Follower Small Signal Performance The small signal model of the emitter follower is: R in R S r π (1β F ) R out 1/gm (excluding ) v out (g m g π )v 1 (g m g π )(i in r π ) v out (g m g π ) r π R in (g m g π ) r π R S r π (1β F ) 1 g m R S β F If β F 1, g m 2mA/V, R S 1kΩ, C π 5pF and C L 1pF, we get R in 1kΩ5kΩ11kΩ 17kΩ, R out 5Ω, v out 1kΩ 1kΩ 5Ω 9.9Ω.943V/V The transfer function assuming R S, is given as, V out g m g π sc π V in g m g π G L sc π sc L Zero g m Cπ Zero 4x19 rads./sec. and Pole 1.4x19 rads./sec. R S C c C π r π v i CL g m v i and Pole g m G L C π C L v out Fig. 51 Lecture 5 Followers (1/11/4) Page 514 SUMMARY Requirements of Output Stages The objectives are to provide output power in form of voltage and/or current. In addition, the output amplifier should be linear and be efficient. Low output resistance is required to provide power efficiently to a small load resistance. High source/sink currents are required to provide sufficient output voltage rate due to large load capacitances. Types of output stages considered: Source and emitter follower (Class A) Did not consider the distortion analysis of GHLM, Sec. 5.3.2