Lecture 070 Stage Frequency esponse I (/0/0) Page 070 LECTUE 070 SINGLESTAGE FEQUENCY ESPONSE I (EADING: GHLM 488504) Objective The objective of this presentation is:.) Illustrate the frequency analysis of single stage amplifiers.) Introduce the Miller technique and the approximate method of solving for two poles Outline Differential and Common Frequency esponse of the Differential Amplifier Emitter/Source Follower Frequency esponse Common Base/Gate Frequency esponse Summary ECE 64 Analog Integrated Circuits and Systems II P.E. Allen 00 Lecture 070 Stage Frequency esponse I (/0/0) Page 070 FEQUENCY ESPONSE OF THE DIFFEENTIAL AMPLIFIE Differential Mode Differential Amplifiers: Q Q I EE M M I SS HalfCircuit Concept: V EE V SS Fig. 0700 Q M Fig. 0700 Note that the following analysis is applicable to the CE and CS configurations. ECE 64 Analog Integrated Circuits and Systems II P.E. Allen 00
Lecture 070 Stage Frequency esponse I (/0/0) Page 0703 Differential Mode Analysis Miller Approach Small Signal Model: Miller Approach: rb v C i C f For MOS: r b 0 and g m v L Fig. 07003 Assume that < (/ωc f ), then g m v Therefore, the smallsignal model can be approximated as, where C m C f (g m ) rb Ci C m v g m v L For MOS: r b 0 and Fig. 07004 ECE 64 Analog Integrated Circuits and Systems II P.E. Allen 00 Lecture 070 Stage Frequency esponse I (/0/0) Page 0704 Differential Mode Analysis Continued The smallsignal analysis of the previous circuit defining C t C i C m is, v v (g m ) C t s g m C t s r π r b I r b sc t ( r b ) r π r b Therefore we see that the gain (K), pole (p ), and 3dB frequency (ω 3dB ) is given as, K p ω 3dB BJT g m r π r r b r b b C t ( r b ) C t ( r b ) MOS g m C t C t ECE 64 Analog Integrated Circuits and Systems II P.E. Allen 00
Lecture 070 Stage Frequency esponse I (/0/0) Page 0705 Example If kω, r b 00Ω, I C I D ma, β o 00, K N 00µA/V, f T 400MHz (I C I D ma), C µ 0.5pF, C gd 0.5pF, W/L 000, 5kΩ, find the gain and 3dB frequency of the BJT and MOS differential amplifier. Solution BJT: β o g m 00(6).6kΩ, τ T πf 398ps C π g m τ T C µ 5.3pF0.5pF 4.8pF T K 5000.6 0..6 3.6V/V 6 C t C π C µ (g m ) 4.8pF 0.5pF 5000 6 4.8pF 96.7pF.5pF ω 3dB r b C t ( r b ) 60000000 600(00000).5pF 0.9x06 f 3dB.74MHz MOS: g m 000 00 000 4.mS and C gd C gs g m /ω T 4.x0 3 /800πMHz 5.6pF C gs 5.6pF0.5pF 5.pF, C t 5.pF0.5pF(4. 5) 5.pf35.7pF 40.8pF K 4. 570.5V/V and ω 3dB 40.8pF(000) 4.5x06 f 3dB 3.90MHz ECE 64 Analog Integrated Circuits and Systems II P.E. Allen 00 Lecture 070 Stage Frequency esponse I (/0/0) Page 0706 Differential Amplifier Exact Frequency esponse The second method solves for the poles without using the Miller approximation. Smallsignal model: rb C f v Ci g m v L For MOS: r b 0 and I in V C i C f g m V V out where I in V in r and b ( r b ) Nodal Equations: I in [G s(c i C f )]V [sc f ]V out and 0 [g m sc f ]V [G L sc f ]V out Solving using Cramer s rule gives, V out (s) I in (s) (g m sc f ) G G L s [G C f G L C i G L C f g m C f ]s [C f C i ] V out (s) or V in (s) g m [ s (C f /g m )] r b s [ C f C i C f g m C f ]s ( C i C f ) V out (0) Note that the gain is V in (0) g m I r b Fig. 07003 ECE 64 Analog Integrated Circuits and Systems II P.E. Allen 00
Lecture 070 Stage Frequency esponse I (/0/0) Page 0707 Differential Amplifer Exact Frequency esponse In general, D(s) s p s p s p p s p p p C f C i C f g m C f p [C f C i C f g m C f ] C i C f The Miller approximation gave, p (BJT) r b C t ( r b ) which verifies the two methods. g m C f g mc f C i C f D(s) s p s p p, if p >> p r b g m C f ( r b ), g m C i where g m > r b g m C f ( r b ) and p (MOS) C t z g m C c g m C f ECE 64 Analog Integrated Circuits and Systems II P.E. Allen 00 Lecture 070 Stage Frequency esponse I (/0/0) Page 0708 CommonMode Analysis of the Differential Amplifier Assumptions: Tail capacitance is dominant and selfresistance is negligible. Q v oc For MOS: r b 0 and r C b f v C i g m v L v oc M v oc Fig. 07006 C T T vic C T T C T T A cm v oc T Z T where Z T s T C T A cm v oc T (s T C T ) This zero at ω / T C T causes the CM gain increases, resulting in a CM decrease. g m T r π r b CM A dm sc t ( r b ) r π r b A cm (s T C T ) g m T r π r b (s/ω T )(s/p ) ECE 64 Analog Integrated Circuits and Systems II P.E. Allen 00
Lecture 070 Stage Frequency esponse I (/0/0) Page 0709 CM Frequency esponse Acm db 6dB/octave High Frequency Common Mode Poles Adm db Log 0 f 6dB/octave CM db 6dB/octave Log 0 f π T C T p π db/octave Log 0 f Fig. 07007 ECE 64 Analog Integrated Circuits and Systems II P.E. Allen 00 Lecture 070 Stage Frequency esponse I (/0/0) Page 0700 Voltage Buffers Fig. 07008 Q V in I For MOS: r b 0 and i r b V C i g m V ECE 64 Analog Integrated Circuits and Systems II P.E. Allen 00 M v in V out L Define I r b and write, V in I i I V V out, I i V z π, and I i g m V V out where z π sc i Combining the last three terms gives, V (sc i ) g m V V out V V out g m r (sc π i ) Finally, V in I z π V out g m (sc i ) where z g m(/ ) C, p i C i V out and I g m V out V in g m g m I s z s p
Lecture 070 Stage Frequency esponse I (/0/0) Page 070 Frequency esponse of the Emitter Follower Assume that g m >> and g m >> ( I )/, then z g m(/ ) C g m i Cπ and p C π Example Calculate the transfer function for an emitter follower with C π 0pF, C µ 0, kω, 50Ω, r b 50Ω, β 00, and I C ma. From the data, g m /6S 38.5mS,.6kΩ, and I r b 00Ω. z g m C π 38.5x03 0 3.85x0 9 rad/s ω T I.k g m.6k L 76.9 7.9Ω p C π 7.9 0 3.58x0 9 rad/s (570MHz) Note the pole and zero are closely spaced. Should consider the influence of C µ for ω 3dB. g m g m I 76.9 000 600 76.9 00 0.986 600 ECE 64 Analog Integrated Circuits and Systems II P.E. Allen 00 Lecture 070 Stage Frequency esponse I (/0/0) Page 070 Emitter Follower Frequency esponsecontinued Include the influence of C µ. r b v C g i m v v L out C µ ωc i << Fig. 07008 ECE 64 Analog Integrated Circuits and Systems II P.E. Allen 00 ' I C µ The pole due to C µ is approximately, p / I C µ. For C µ pf, p π(795mhz) 5 4 Fig. 0700 3 splane x09 jω σ 0dB 3dB 6dB 9dB MHz 0MHz 00MHz GHz f C µ Cgd 0 795MHz C µ pf The emitter follower bandwidth is still quite good even considering C µ. Next, we will consider the input and output impedances of the emitter follower in the next lecture.