Lecture 11 ANNOUNCEMENTS • • • • Prob. 5 of Pre-Lab #5 has been clarified. (Download new version.) HW#6 has been posted. Review session: 3-5PM Friday (10/5) in 306 Soda (HP Auditorium) Midterm #1 (Thursday 10/11): • Material of Lectures 1-10 (HW# 2-6; Chapters 2, 4, 5) • 2 pgs of notes (double-sided, 8.5”×11”), calculator allowed OUTLINE • Review of BJT Amplifiers • Cascode Stage Reading: Chapter 9.1 EE105 Fall 2007 Lecture 11, Slide 1 Prof. Liu, UC Berkeley Review: BJT Amplifier Design • A BJT amplifier circuit should be designed to 1. ensure that the BJT operates in the active mode, 2. allow the desired level of DC current to flow, and 3. couple to a small-signal input source and to an output “load”. Proper “DC biasing” is required! (DC analysis using large-signal BJT model) • Key amplifier parameters: (AC analysis using small-signal BJT model) – Voltage gain Av vout/vin – Input resistance Rin resistance seen between the input node and ground (with output terminal floating) – Output resistance Rout resistance seen between the output node and ground (with input terminal grounded) EE105 Fall 2007 Lecture 11, Slide 2 Prof. Liu, UC Berkeley Large-Signal vs. Small-Signal Models • The large-signal model is used to determine the DC operating point (VBE, VCE, IB, IC) of the BJT. • The small-signal model is used to determine how the output responds to an input signal. EE105 Fall 2007 Lecture 11, Slide 3 Prof. Liu, UC Berkeley Small-Signal Models for Independent Sources • The voltage across an independent voltage source does not vary with time. (Its small-signal voltage is always zero.) It is regarded as a short circuit for small-signal analysis. Large-Signal Model Small-Signal Model • The current through an independent current source does not vary with time. (Its small-signal current is always zero.) It is regarded as an open circuit for small-signal analysis. EE105 Fall 2007 Lecture 11, Slide 4 Prof. Liu, UC Berkeley Comparison of Amplifier Topologies Common Emitter • Large Av < 0 - Degraded by RE - Degraded by RB/(b+1) • Moderate Rin - Increased by RB - Increased by RE(b+1) Common Base • Large Av > 0 -Degraded by RE and RS - Degraded by RB/(b+1) • Small Rin - Increased by RB/(b+1) - Decreased by RE • Rout RC • Rout RC • ro degrades Av, Rout • ro degrades Av, Rout but impedance seen looking into the collector can be “boosted” by emitter degeneration EE105 Fall 2007 Emitter Follower • 0 < Av ≤ 1 - Degraded by RB/(b+1) • Large Rin (due to RE(b+1)) • Small Rout - Effect of source impedance is reduced by b+1 - Decreased by RE but impedance seen looking into the collector • ro decreases Av, Rin, can be “boosted” by and Rout emitter degeneration Lecture 11, Slide 5 Prof. Liu, UC Berkeley Common Emitter Stage VA VA vout RC 1 RB vin RE gm b 1 Rin RB r ( b 1) RE Rout RC EE105 Fall 2007 Rout RC || rO 1 g m ( RE || r ) Lecture 11, Slide 6 Prof. Liu, UC Berkeley Common Base Stage VA vout RC RE 1 RB RS RE vin RS RE gm b 1 1 RB RE Rin gm b 1 Rout RC EE105 Fall 2007 VA Rout RC || rO 1 g m ( RE || r ) Lecture 11, Slide 7 Prof. Liu, UC Berkeley Emitter Follower VA VA vout RE vin R 1 RS E gm b 1 Rin r (1 b ) RE 1 Rs || RE Rout gm b 1 EE105 Fall 2007 vout RE || rO vin R || r 1 RS E O gm b 1 Rin r b 1RE || rO Rout Lecture 11, Slide 8 Rs 1 || RE || rO b 1 gm Prof. Liu, UC Berkeley Ideal Current Source Circuit Symbol I-V Characteristic Equivalent Circuit • An ideal current source has infinite output impedance. How can we increase the output impedance of a BJT that is used as a current source? EE105 Fall 2007 Lecture 11, Slide 9 Prof. Liu, UC Berkeley Boosting the Output Impedance • Recall that emitter degeneration boosts the impedance seen looking into the collector. – This improves the gain of the CE or CB amplifier. However, headroom is reduced. Rout 1 g m RE || r rO RE || r EE105 Fall 2007 Lecture 11, Slide 10 Prof. Liu, UC Berkeley Cascode Stage • In order to relax the trade-off between output impedance and voltage headroom, we can use a transistor instead of a degeneration resistor: Rout [1 g m (rO 2 || r 1 )]rO1 rO 2 || r 1 Rout g m1rO1 rO 2 || r 1 I C 2 I E1 I C 2 if b1 1 • VCE for Q2 can be as low as ~0.4V (“soft saturation”) EE105 Fall 2007 Lecture 11, Slide 11 Prof. Liu, UC Berkeley Maximum Cascode Output Impedance • The maximum output impedance of a cascode is limited by r1. If rO 2 r 1 : Rout,max g m1rO1r 1 b1rO1 EE105 Fall 2007 Lecture 11, Slide 12 Prof. Liu, UC Berkeley PNP Cascode Stage Rout [1 g m1 (rO 2 || r 1 )]rO1 rO 2 || r 1 Rout g m1rO1 rO 2 || r 1 EE105 Fall 2007 Lecture 11, Slide 13 Prof. Liu, UC Berkeley False Cascodes • When the emitter of Q1 is connected to the emitter of Q2, it’s not a cascode since Q2 is a diode-connected device instead of a current source. Rout 1 1 1 g m1 || rO 2 || r 1 rO1 || rO 2 || r 1 g m2 g m2 Rout g m1 1 rO1 1 2rO1 g m2 g m2 EE105 Fall 2007 Lecture 11, Slide 14 Prof. Liu, UC Berkeley Short-Circuit Transconductance • The short-circuit transconductance of a circuit is a measure of its strength in converting an input voltage signal into an output current signal. iout Gm vin EE105 Fall 2007 Lecture 11, Slide 15 vou t 0 Prof. Liu, UC Berkeley Voltage Gain of a Linear Circuit • By representing a linear circuit with its Norton equivalent, the relationship between Vout and Vin can be expressed by the product of Gm and Rout. Norton Equivalent Circuit Computation of short-circuit output current: EE105 Fall 2007 vout iout Rout Gm vin Rout vout vin Gm Rout Lecture 11, Slide 16 Prof. Liu, UC Berkeley Example: Determination of Voltage Gain Determination of Gm Gm iout vin g m1 vo ut 0 Determination of Rout Rout vx ro1 ix Av g m1rO1 EE105 Fall 2007 Lecture 11, Slide 17 Prof. Liu, UC Berkeley Comparison of CE and Cascode Stages • Since the output impedance of the cascode is higher than that of a CE stage, its voltage gain is also higher. vout g m1vinrO1 VA Av g m1rO1 VT EE105 Fall 2007 Av gm1rO 2 gm2 rO1 r 2 Lecture 11, Slide 18 Prof. Liu, UC Berkeley Voltage Gain of Cascode Amplifier • Since rO is much larger than 1/gm, most of IC,Q1 flows into diode-connected Q2. Using Rout as before, AV is easily calculated. iout g m1vin Gm g m1 Av Gm Rout g m1 1 g m 2 rO1 || r 2 rO 2 rO1 || r 2 g m1 g m 2 rO1 || r 2 rO 2 EE105 Fall 2007 Lecture 11, Slide 19 Prof. Liu, UC Berkeley Practical Cascode Stage • No current source is ideal; the output impedance is finite. Rout rO3 || g m2 rO 2 (rO1 || r 2 ) EE105 Fall 2007 Lecture 11, Slide 20 Prof. Liu, UC Berkeley Improved Cascode Stage • In order to preserve the high output impedance, a cascode PNP current source is used. Rout g m3rO 3 (rO 4 || r 3 ) || g m 2 rO 2 (rO1 || r 2 ) Av g m1Rout EE105 Fall 2007 Lecture 11, Slide 21 Prof. Liu, UC Berkeley