CMOS. High-resistance device consisting of subthreshold-operated CMOS differential pair

Transcription

1 ECT991 CMOS High-resistance device consisting of subthreshold-operated CMOS differential pair Shin ichi Asai, Ken Ueno, Tetsuya Asai, and Yoshihito Amemiya, (Hokkaido University) Abstract We propose a CMOS circuit that can be used as an euivalent of resistors. This circuit uses a differential pair consisting of diode-connected MOSFETs and operates as a high-resistance resistor when driven in the subthreshold region. Its resistance can be controlled in a range of 1-1 MΩ by adjusting the driving current for the circuit. For example, we realized a 13 MΩ resistor with a tail current of 1 na. The results of the fabrication using a.35-µm P-4M CMOS process technology and measurement of the circuit are described. (integrated circuit, high resistance, differential circuit, subthreshold) 1. CMOS 1 M CMOS 1- kω/ 1 MΩ.5 mm CMOS (1) MOSFET - 1 MΩ () (3) (4) MOSFET ΔI V dd / 1 M1 M 1 Fig. 1 Outline of resistor circuit euivalent to a resistor with terminals 1 and. CR M1 M Ib Ib / ΔV / ΔI 16

2 1 V I I I V ( ) MOSFET ID MOSFET - VGS- VDS (5) I D = = W L I exp (V GS V th ) mkt I = μc ox (m 1) 1 exp V DS kt kt,... (1) W/L m k T Vth MOSFET µ Cox VDS >.1 V ID I D = = W L I exp (V GS V th )... () mkt 1- V M1 + ΔI = W L I exp (V GS V th + ΔV /) mkt = ΔV exp mkt... (3) ΔV/(mkT) << 1 (3) + ΔI = 1 + ΔV... (4) mkt R = ΔV ΔI = 4mkT... (5) Ib = 1nA 1MΩ mkt/ Ib M1-M5 MOSFET 1- V dd Biasing subcircuit Fig. Resistor circuit with biasing subcircuit. 3 Fig. 3 Offset currents of resistor circuit. Offset currents ΔI1 and ΔI consist of common-mode offset current ICM and differential offset current IDIFF. 3 I1 I i( ) ICMii IDIFF I1I ΔI 1 = I DIFF + I CM...(6) ΔI = I DIFF I CM...(7) ICM M5 M3-M4 1 IDIFF M1-M3 M-M µm P-4M CMOS MOSFET M3 M5 M4 1 M1 M ΔI 1 ΔI Resistor circuit ΔI 1 ΔI 1 I CM I DIFF V CM I CM 6

3 .4.3 V CM = 1.5 V.8.6 Current [na] ΔI (dashed line) ΔI 1 (solid line) Offset current [na] I DIFF I CM Voltage ΔV [mv] 4 - Fig. 4 Voltage-current characteristic of resistor circuit, measured for Ib = 1 na, Vdd = 3 V and VCM ( common-mode voltage for terminals 1 and ) = 1.5 V V CM [V] 5 -VCM Fig. 5 Offset currents as a function of common-mode voltage VCM for terminals 1 and, measured for Ib = 1nA and Vdd = 3 V. W/L = µm/4 µm 15 µm 11 µm 4 Vdd = 3 V ()VCM = 1.5 VIb = 1 na 1 - -(V-I ) 4 mv 4 mv - a -b 1 I1 () I () VCM 5 Vdd = 3 V Ib = 1 na VCM -3 V ICM () IDIFF () VCM.4-.8 V Ib 6 (5) Ib Ib Ib = 1 na 1 MΩIb = 1 na 13 MΩ 4. CR 41 CR 7 Resistance [MΩ] mkT Measured Tail current [na] 6 Ib - Fig. 6 Resistance of resistor circuit as a function of tail current Ib. Sold line shows measured data, and dashed line shows theoretical resistance. 3 G G = 1 5R ω C jrωc (R ω C 6)...(8) R C 1/jωC C (8) π RωC (R ω C 6) =...(9) 6 ω =...(1) CR 36

4 6 f =... (11) πcr R = 4mkT/(Ib) Ib f µm P-4M CMOS CR 35 µm 37 µm Rin = 5 kωrf = 17 kω 9 Vdd = 3 VE = 1.5 VC = 1 pf Ib = 1 na.7 khzib = 1 na 9 Hz PTAT 4mkT/(Ib) Ib PTAT (Proportional To Absolute Temperature current) Ib PTAT 1 PTAT M6M7M8M9 4 ß (CS CK CK ) PTAT Vdd M9 M6 M8 M9 IPTAT M6 - VGS6 M7 - VGS7 IPTATRS V GS6 = V GS 7 + I PTAT R S 1... (1) R S = C S f 7 CR Fig. 7 CR phase-shift oscillator. The elements circled by dashed lines represent resistor circuits. 35 μm 8 CR Fig. 8 Chip photograph of phase-shift oscillator. Chip size is 35 μm 37 μm. Parameters used for fabrication were Rin = 5 kω, Rf = 17 kω, C = 1pF, Vdd = 3 V, and E = 1.5 V. 14 mv 1 mv R in E R f Output V C C C Op Amps 1 ms (a) Ib = 1 na Resistor circuit High Resistance Resistors Capacitors 37 μm R in, R f μs (b) Ib = 1 na 9 Fig. 9 Output waveforms of phase-shift oscillator, measured for two values of tail current Ib for resistor circuit. 46

5 V dd M8 α : 1 M9 M1 M3 M4 8 stage I PTAT I PTAT α 1 M1 M Start up M6 1 : K M7 CK f C S CK M5 PTAT current source Resistor circuit 1 Fig. 1 Resistor circuit with temperature compensation. RS ( CS f )(1) I PTAT R S = V GS6 V GS 7 = mkt mkt = mkt ln I D L + V th 6 I W ln I D L... (13) V th 7 I WK ln K M6 M7 1K MOSFET PTAT IPTAT I PTAT = mktc S f ln K... (14) M9 M1 1 : α IPTAT 1/α 1- (5)(14) 4α R =... (15) C S f ln K 5.35-μm CMOS SPICE 11 () Resistance [MΩ] Temperature [K] =.9 na 14 (TC = 61 ppm/ C) = na 6 (66 ppm/ C) 4 = 6 na (66 ppm/ C) Temperature [ C] 11 Fig. 11 Temperature characteristic of resistor circuit for three tail currents..9 na - 6 na (TC) 61 ppm/ C - 66 ppm/ C 1 1 PTAT IPTAT CS =.55 pf f 91 khz MHz 13, PTAT 1 f MΩ - 14 MΩ 56

6 I PTAT [na] Temperature [K] switching freuency 6 f = 5.6 MHz (TC =.19 na/ C) f = MHz (.7 na/ C) 1 f = 91 khz (.3 na/ C) Temperature [ C] 1 PTAT Fig. 1 Temperature dependence of PTAT current for three switching freuencies. Temperature [K] switching freuency f = 91 khz 14 1 (TC = 69 ppm/ C) 1 w/o temperature compensation 8 f = MHz 6 (5 ppm/ C) 4 f = 5.6 MHz (33 ppm/ C) Temperature [ C] 13 Fig. 13 Temperature dependence of resistor with compensation. Parameters used for fabrication were Vdd = 3 V, α = 1, K =, CS =.55 pf. Resistance [MΩ] 33 ppm/ C - 69 ppm/ C ()PTAT ( 1 /(CS f )) CS f α K α = 1, K = 6 6. CMOS 1-1 MΩ CR PTAT PTAT 7. (VDEC) () A. Wang, B. H. Clhoun, and A. P. ChandracasanSub-Threshold Design for Ultra Low-Power Systems, Springer, New York (6) () K. Nagaraj : New CMOS Floating Voltage-Controlled Resistor, Electron. Lett., Vol., No.1 pp (1986) () S. P. Singh, J. V. Hanson, and J. Vlach : A New Floating Resistor for CMOS Technology, IEEE Trans. Circuits Syst., Vol.36, No.9 pp (1989) () S. Sakurai and M. Ismail : A CMOS Suare-Law Programmable Floating Resistor Independent of the Threshold Voltage, IEEE Trans. Circuits Syst. II, Vol.39, No.8 pp (199) () Y. Taur and T. H. Ning Fundamentals of Modern VLSI Devices,.Cambridge, Cambridge Univ. Press, U.K. () 66