Lecture 14 FET Current and Voltage Sources and Current Mirrors The Building Blocks of Analog Circuits - IV In this lecture you will learn: • Current and voltage sources using FETs • FET current mirrors • Cascode current mirror • Double Wilson current mirror • Active biasing schemes ECE 315 – Spring 2007 – Farhan Rana – Cornell University Motivation Questions: • Are there better ways to realize on-chip current sources to bias circuits? • Are there good ways to generate on-chip voltage levels to bias circuits? VDD VDD VB1 IBIAS Using large resistors too often is not a good idea VB2 in integrated chips ECE 315 – Spring 2007 – Farhan Rana – Cornell University 1 Characteristics of Ideal Current Sources and Sinks Ideal Current Sources: IOUT IOUT roc=∞ + I VOUT I I roc - VOUT One can have any voltage at the at the output terminals of an ideal current source and the current delivered will remain constant The output resistance of an ideal current source is infinity Ideal Current Sinks: IOUT IOUT roc=∞ + I VOUT I I roc - VOUT One can have any voltage at the at the output terminals of an ideal current sink and the current sinked will remain constant The output resistance of an ideal current sink is infinity ECE 315 – Spring 2007 – Farhan Rana – Cornell University Characteristics of Ideal Voltage Sources Ideal Voltage Sources: IOUT rov=0 IOUT + r V ov VOUT V V - V OUT One can draw any current from an ideal voltage source and the voltage at the output terminals will remain constant The output resistance of an ideal voltage source is zero Non-Ideal Voltage Sources: IOUT r ≠ 0 ov 1 slope = IOUT rov + r V ov VOUT V V - V OUT ECE 315 – Spring 2007 – Farhan Rana – Cornell University 2 A FET Voltage Source: Large Signal Analysis • Assume for the moment that we have a current source IREF VDD If VOUT > VTN : k I I I n V V 2 1 V I REF D OUT 2 OUT TN n OUT OUT I REF 2IREF IOUT VOUT VTN if nVOUT 1 kn Slope ID IOUT I dI OUT OUT g k V V dV m n OUT TN + IREF OUT VOUT - VTN VOUT Non-Ideal Voltage Source IOUT • The line can be made more vertical and the voltage 1 slope = source more ideal by increasing the value of gm rov V VOUT ECE 315 – Spring 2007 – Farhan Rana – Cornell University A FET Voltage Source: Large Signal Analysis VDD 2IREF IOUT VOUT VTN W L nCox IREF dIOUT W gm nCox VOUT VTN dVOUT L ID IOUT IOUT + V Increasing (W/L) OUT IREF - VOUT VTN • If the (W/L) ratio of the FET is made very large, the output voltage VOUT is fixed at approximately VTN for all values of the current IOUT drawn from the source (provided IOUT < IREF) ECE 315 – Spring 2007 – Farhan Rana – Cornell University 3 A FET Voltage Source: Small Signal Analysis VDD roc Small signal I REF roc roc (Ideal) + - Need to find the resistance rov looking into from the output terminals Small signal model rov ECE 315 – Spring 2007 – Farhan Rana – Cornell University A FET Voltage Source: Small Signal Analysis ig Gate Drain id 0 roc + v gs r r g v o oc - m gs gmbvbs Source + - - vbs Base + Small signal model Need to find the resistance rov looking into from the output terminals rov ECE 315 – Spring 2007 – Farhan Rana – Cornell University 4 A FET Voltage Source: Small Signal Analysis ig Gate Drain id roc gm ro roc Source + - - vbs Base Small signal resistance looking into the voltage + source is: 1 r 1 g || r || r Generally small ov m o oc g rov m if gm is large We have a voltage source that: • Gives a DC voltage VOUT adjustable by changing the value of IREF , and • Has an incremental or small signal resistance rov approximately equal to 1/gm (which can be pretty small) ECE 315 – Spring 2007 – Farhan Rana – Cornell University A FET Voltage Source: Simplest Implementation of IREF V DD If VOUT > VTN : V V k DD OUT I I n V V 2 I R D OUT 2 OUT TN OUT R 1 2V V R I 1 V V DD TN OUT OUT TN 2 2 knR kn knR ID I OUT Slope when R is much larger than 1/gm IOUT dIOUT gm kn VOUT VTN VOUT VDD dVOUT R Slope VOUT dIOUT 1 VTN dVOUT R • If the (W/L) ratio of the FET is made very large and R is much larger than 1/gm , the output voltage VOUT is fixed at approximately VTN for all values of the current IOUT drawn from the source - provided IOUT < (VDD - VTN)/R ECE 315 – Spring 2007 – Farhan Rana – Cornell University 5 FET Voltage Sources One can produce multiple voltage levels from the same structure using NMOS FETs, PMOS FETs, and combination of both NMOS and PMOS FETs VDD VDD VDD IREF V1 V1 I M1 1 V1 V2 V2 I2 M2 V2 IREF V3 IREF 2IREF I1 V1 V2 VTN1 kn1 2IREF I1 I2 But ………need to be careful about the small signal V2 VTN2 resistances associated with each voltage output! kn2 ECE 315 – Spring 2007 – Farhan Rana – Cornell University FET Voltage Sources: Small Signal Analysis Gate Drain id1 roc + v gs1 ro1 roc - gm1v gs1 Source rov1 Gate Drain id 2 rov 2 + vgs2 ro2 - gm2vgs2 Source Find the resistance looking into the first voltage source assuming the second one is incrementally open (why?) ECE 315 – Spring 2007 – Farhan Rana – Cornell University 6 FET Voltage Sources: Small Signal Analysis Gate Drain id1 r oc g m1 ro1 roc Source rov1 Gate Drain rov 2 gm2 ro2 Source Find the resistance looking into the first voltage source assuming the second one is incrementally open (why?) ECE 315 – Spring 2007 – Farhan Rana – Cornell University FET Voltage Sources: Small Signal Analysis Gate Drain id1 roc gm1 ro1 roc Source rov1 gm2 rov 2 1 1 rov1 Small gm1 gm2 Find the resistance looking into the first voltage source assuming the second one is incrementally open (why?) ECE 315 – Spring 2007 – Farhan Rana – Cornell University 7 FET Voltage Sources: Small Signal Analysis Gate Drain id1 roc + v gs1 ro1 roc - gm1v gs1 Source rov1 Gate Drain id 2 rov 2 + vgs2 ro2 - gm2vgs2 Source Then find the resistance looking into the second voltage source assuming the first one is incrementally open (why?) 1 rov 2 Small gm2 ECE 315 – Spring 2007 – Farhan Rana – Cornell University A FET Current Sink: Large Signal Analysis • Assume that we have a single current source IREF - but we want more……… VDD VGS2 VGS1 kn2 W L 2 Assuming ID2 ID1 ID1 I k W L M2 is in IREF OUT n1 1 saturation W L 2 + IOUT IREF W L 1 ID1 I D2 Slope V OUT dI 1 IOUT OUT dVOUT ro2 M1 M2 - W L 2 IREF W L 1 In saturation: k VOUT I n V V 2 1 V D 2 GS TN n DS W Small kn nCox • Not exactly the horizontal line of an ideal L current source but good enough for many practical applications ECE 315 – Spring 2007 – Farhan Rana – Cornell University 8 A FET Current Mirror • A ideal current mirror duplicates the current: IOUT IREF VGS2 VGS1 VDD Matched W L 2 W L 1 Transistors I IREF OUT IOUT IREF + I D1 ID2 Slope VOUT I dI 1 OUT OUT dVOUT ro2 M1 M2 - IREF A matched transistor pair VOUT VGS1 ECE 315 – Spring 2007 – Farhan Rana – Cornell University A FET Current Sink: Small Signal Analysis i rocref Gate Drain d 2 + + vgs2 ro2 - gm2vgs2 Source - Gate Drain id1 + r v oc gs1 ro1 rocref - gm1v gs1 1 Source roc ro2 go2 We have a current sink that: • Provides a DC current IOUT adjustable by changing the value of IREF , and • Has an incremental or small signal resistance roc approximately equal to ro2 (which can be pretty large) • The resistance roc will become small if M2 goes into the linear region ECE 315 – Spring 2007 – Farhan Rana – Cornell University 9 Multiple NFET Current Sinks VDD V VOUT 3 V V IREF OUT 2 OUT 4 OUT 5 I D1 ID2 ID3 ID4 ID5 M1 M2 M3 M4 M5 One can realize multiple current sinks for biasing applications from the same structure using NMOS devices with different (W/L) ratios: W L k IDk IREF W L 1 Note that VOUTk needs to be always large enough such that Mk remains in saturation ECE 315 – Spring 2007 – Farhan Rana – Cornell University A PFET Current Source and Current Mirror • A current mirror duplicates the current: IOUT IREF VGS2 VGS1 V V Matched DD DD W L 2 W L 1 Transistors M1 M2 IOUT IREF Slope ID1 ID2 VOUT + I dI 1 OUT OUT dVOUT ro2 IOUT IREF IREF A matched transistor pair VOUT VSG1 VGS1 VDD ECE 315 – Spring 2007 – Farhan Rana – Cornell University 10 Multiple PFET Current Sources VDD VDD VDD VDD VDD M1 M2 M3 M4 M5 ID1 ID2 ID3 ID4 ID5 I I OUT 2 OUT 3 IOUT 4 IOUT 5 IREF VOUT 2 VOUT 3 VOUT 4 VOUT 5 One can realize multiple current sources for biasing applications from the same structure using PMOS devices with different (W/L) ratios: W L k IOUTk IREF W L 1 Note that VOUTk needs to be always small enough such that Mk remains in saturation ECE 315 – Spring 2007 – Farhan Rana – Cornell University A Current Sink with Large Output Resistance: The Cascode Design VDD VDD I I IREF OUT IREF OUT + + I I D1 ID2 D1 ID3 VOUT V M1 M2 - M1 M3 OUT I D2 ID4 1 roc ro2 M2 M4 go2 - roc ro3 ro4 1 gm3ro3 gm3ro3ro4 ECE 315 – Spring 2007 – Farhan Rana – Cornell University 11 A Current Sink with Large Output Resistance: The Cascode Design VDD I Usually the substrate contact of all IREF OUT NFETs in the stack are tied to the ground in CMOS technologies in + which all NFETs share the same I D1 ID3 substrate Need to account for the body effect V (due to non-zero VSB) in M3 M1 M3 OUT I D2 ID4 M2 M4 - ECE 315 – Spring 2007 – Farhan Rana – Cornell University The Double Wilson Current Mirror VDD More immune to systemic errors in I IOUT the fabrication process than the REF cascode design + I D1 ID3 M1 M3 VOUT I D2 ID4 M2 M4 - ECE 315 – Spring 2007 – Farhan Rana – Cornell University 12 A PFET Current Source: The Cascode Design VDD VDD VDD VDD M1 M2 M2 M4 ID1 ID2 V OUT I I + D1 D4 M1 M3 IOUT IREF VOUT ID1 ID3 + 1 r r I oc o2 g OUT o2 IREF roc ro3 ro4 1 gm3ro3 gm3ro3ro4 ECE 315 – Spring 2007 – Farhan Rana – Cornell University A PFET