Lecture 34: Designing Amplifiers, Biasing, Frequency Response Context
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EECS 105 Spring 2004, Lecture 34 Lecture 34: Designing amplifiers, biasing, frequency response Prof J. S. Smith Department of EECS University of California, Berkeley EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Context We will figure out more of the design parameters for the amplifier we looked at in the last lecture, and then we will do a review of the approximate frequency analysis of circuits which have a single dominant pole. Department of EECS University of California, Berkeley 1 EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Reading z Chapter 9, multi-stage amplifiers. The frequency analysis is in the first section of chapter 10, but we won’t go farther into chapter 10 for a while. z The Lectures on Wednesday and Friday will be given by Joe and Jason, respectively. They will be doing several example problems. Department of EECS University of California, Berkeley EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Lecture Outline z Example 1: Cascode Amp Design z Example 2; CS NMOS->CS PMOS z Review of frequency analysis (with a dominant pole) Department of EECS University of California, Berkeley 2 EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Amplifier Schematic Note that the backgate connection for M2 is not specified: ignore gmb Department of EECS University of California, Berkeley EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Complete Amplifier Schematic Bias voltages derived from Goals: gm1 = 1 mS, transistors under Rout =10 MΩ similar operating conditions to Cascode current source the transistors For high roc they supply CG output CS input, with low voltage gain Department of EECS University of California, Berkeley 3 EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Current Supply Design High impedance current source means all of the small signal current goes to the load resistance, giving more SS voltage gain Output resistance goal requires large roc for high gainÆ so we used a cascode current source Department of EECS University of California, Berkeley EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Totem Pole Voltage Supply DC voltages must be set for the cascode current supply transistors M3 and M4, as well as the gate of M2. M2B supplies the Bias quiescent voltage For the CG stage Department of EECS University of California, Berkeley 4 EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Miller Capacitance of Input Stage Find the Miller capacitance for Cgd1 Cgd Input resistance to common-gate second stage is low Æ gain across Cgd1 is small. Department of EECS University of California, Berkeley EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Two-Port Model with Capacitors Miller capacitance: C = (1− A )C M vCgd 1 gd1 g A ≅ − m1 vCdg1 gm2 Department of EECS University of California, Berkeley 5 EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Schematic Goals: gm1 = 1 mS, Rout =10 MΩ Department of EECS University of California, Berkeley EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Device Sizes M1: select (W/L)1 = 200/2 to meet specified gm1 = 1 mS Æ find VBIAS = 1.2 V Cascode current supply devices: select VSG = 1.5 V (W/L)4= (W/L)4B= (W/L)3= (W/L)3B = 64/2 Department of EECS University of California, Berkeley 6 EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Device Sizes M2: select (W/L)2 = 50/2 to meet specified Rout =10 MΩ Æ find VGS2 = 1.4 V Match M2 with diode-connected device M2B. Assuming perfect matching and zero input voltage, what is VOUT? Department of EECS University of California, Berkeley EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Output (Voltage) Swing Maximum VOUT Minimum VOUT Department of EECS University of California, Berkeley 7 EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Two-Port Model Find output resistance Rout -1 -1 λn = (1/20) V , λn = (1/50) V at L = 2 µm Æ -1 -1 ron = (100 µA / 20 V ) = 200 kΩ, rop = 500 kΩ 2I D2 2(100µA) gm2 = = = 500µS VGS 2 −VTn 1.4V −1V 2(−I D3 ) 2(100µA) gm3 = = = 400µS VSG3 +VTp 1.5V −1V Rout = roc || ro2 ()1+ gm2 RS 2 = ro3 (1+ gm3RS 3 )|| ro2 (1+ gm2ro1 ) Department of EECS University of California, Berkeley EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Voltage Transfer Curve Open-circuit voltage gain: Av = vout / vin = - gm1Rout 3 7 dv vOUT = −10 ×10 = out dv 4 in Q ≈ −10,000 3 2 1 0 1 2 34vIN Department of EECS University of California, Berkeley 8 EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Multistage Amplifier Design Example Start with basic two-stage transconductance amplifier: Why do this combination? Department of EECS University of California, Berkeley EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Quiescent level shifts NMOS PMOS CS ⇑ ⇓ (typical) (typical) CG ⇑ ⇓ CD ⇓ ⇑ (known shift) (known shift) Source follower Department of EECS University of California, Berkeley 9 EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith CS→CS Amplifier Direct DC connection: use NMOS then PMOS Department of EECS University of California, Berkeley EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Current Supply Design Assume that the reference is a “sink” set by a resistor Must mirror the reference current and generate a sink for iSUP 2 Department of EECS University of California, Berkeley 10 EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Use Basic Current Supplies Department of EECS University of California, Berkeley EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Complete Amplifier Topology What’s missing? The device dimensions, the bias voltage and reference resistor Department of EECS University of California, Berkeley 11 EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith DC Bias: Find Operating Points Find VBIAS such that VOUT = 0 V Device parameters: 2 2 µnCox = 50 µA/V µ pCox = 25 µA/V VTn = 1 V VTp = -1 V -1 -1 λn = 0.05 V λp = 0.05 V Device dimensions (for “lecture” design): (W/L)n = 50/2 (W/L)p = 80/2 Department of EECS University of California, Berkeley EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Finding RREF + V Require IREF = - ID3 = 50 µA M3 − 2I D3 VSG3 = −VTp + µ pCox (W / L)3 RREF − 2×50µA 4 VSG3 = −(−1)V + =1+ =1.32V - 25µA(80 / 2) 40 V + − [V −VSG3 ]− [V ] I REF = 50µA = Rref [2.5 −1.32]− [− 2.5] 50µA = ⇒ Rref = 74kΩ Rref Department of EECS University of California, Berkeley 12 EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith DC Operating Point IREF = 50 µA 2I D1 100µA 9 VBIAS = VGS1 = Vtn + =1+ −2 ≈ V µnCox (W / L) 50(µA/V )(50 / 2) 7 Department of EECS University of California, Berkeley EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Small-Signal Device Parameters Transistors M1 and M2 gm1 = 350 µS ro1 = 400 kΩ gm2 = 315 µS ro2 = 400 kΩ Current supplies iSUP1 and iSUP2 roc1 = ro4 =400 kΩ roc2 = ro6 =400 kΩ Department of EECS University of California, Berkeley 13 EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Two-Port Model Find Gm = iout / vin Department of EECS University of California, Berkeley EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Output Voltage Swing Transistors M2 and M6 will limit the output swing Department of EECS University of California, Berkeley 14 EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Limits to Output Voltage M6 will leave saturation when vOUT drops to: − 2I D6 vOUT ,MIN = V +VDS 6,sat = −2.5 + µnCox ()W / L 6 vOUT,MIN = -2.5 + 0.28 = - 2.22 V M2 will leave saturation when vOUT rises to: + 2(−I D2 ) vOUT ,MAX = V −VSD2,sat = 2.5 − µ pCox ()W / L 2 vOUT,MAX = 2.5 - 0.32 = 2.18 V What about M4? Department of EECS University of California, Berkeley EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Output Current Swing Load resistor: pick RL = 25 kΩ Output current: iOUT = −vOUT / RL iOUT = iD6 − (− iD2 ) iOUT Limits: asymmetrical M2: can increase - iD2 vOUT M6: can’t increase iD6 Department of EECS University of California, Berkeley 15 EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Output Current Limits • Positive output current (negative vOUT) iOUT ,MAX = iD6 − (0) = 50µA = −vOUT ,MIN / RL vOUT ,MIN = −(50µA)(25kΩ) = −1.25V (less negative than limit set by saturation of M6) • Negative output current (positive vOUT) No limit on current from M2, so voltage swing sets current limit iOUT ,MIN = −vOUT ,MAX / RL = − (2.18V / 25kΩ) = −87.2µA Department of EECS University of California, Berkeley EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Transfer Curves (for RL = 25 kΩ) Loaded voltage gain = vout/vin = (gm1Rout1)(gm2Rout||RL) = 490 Loaded transconductance = iout/vin = (-gm1Rout1)(gm2)(Rout/(Rout + RL) = -19.5 mS iOUT [µA] vOUT 2 100 1 50 1 1 -2 -1 0 2 vIN -2 -1 0 2 vIN -1 -50 -2 -100 Department of EECS University of California, Berkeley 16 EECS 105 Spring 2004, Lecture 34 Prof. J. S. Smith Review: Frequency Resp of Multistage Amplifiers • We have a systematic technique to study amplifier performance (derive transfer function, study poles/zeros/Bode pltos). • In most cases, the systematic approach is too cumbersome. • We have a good qualitative understanding of circuit performance (e.g., CS suffers from Miller effect, CD andd CG are wideband stages …) • Open Circuit Time Constants: Analytical technique is capable of estimating only the dominant (lowest) pole …for a restricted class of amplifiers.