2A5I:3EH> CMOS z x &)É
Transcript of 2A5I:3EH> CMOS z x &)É
ECT 09 091
1 6
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 equivalent 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 1-1000 MΩ by adjusting the driving current for the circuit. For example, we realized a 123 MΩ resistor with a tail current of 1 nA. The results of the fabrication using a 0.35-µm 2P-4M CMOS process technology and measurement of the circuit are described.
(integrated circuit, high resistance, differential circuit, subthreshold)
1.
CMOS10 M
CMOS
1-2 kΩ/100 MΩ 0.5 mm2
CMOS
(1) MOSFET-
100 MΩ
(2) (3) (4)
MOSFET
1
Fig. 1 Outline of resistor circuit equivalent to a resistor with terminals 1 and 2.
CR
M1 M2Ib
Ib /2
1 2M2M1
ΔI ΔI
ΔV
Ib
Ib /2Ib /2
Vdd
2 6
1 2 VI 2 I
IV 2
( )
MOSFET ID MOSFET -VGS - VDS
(5)
ID =I b2
=W
LI0 exp
q (VGS − Vth )
mkT
⎛ ⎝ ⎜ ⎞
⎠ ⎟
⋅ 1 − exp −qVDSkT
⎛ ⎝ ⎜ ⎞
⎠ ⎟
⎛ ⎝ ⎜
⎞ ⎠ ⎟ ,
I0 = μCox (m − 1) ⋅kT
q
⎛ ⎝ ⎜ ⎞
⎠ ⎟ 2
.................... (1)
W/L mk T q Vth
MOSFET µ CoxVDS > 0.1 V ID
ID =I b2
=W
LI0 exp
q (VGS − Vth )
mkT
⎛ ⎝ ⎜ ⎞
⎠ ⎟ ......................... (2)
1-2 VM1
I b2
+ ΔI =W
LI0 exp
q (VGS − Vth + ΔV / 2)
mkT
⎛ ⎝ ⎜ ⎞
⎠ ⎟
=I b2exp
qΔV
2mkT
⎛ ⎝ ⎜ ⎞
⎠ ⎟
........... (3)
qΔV/(2mkT) << 1 (3)
I b2
+ ΔI =I b2
1 +qΔV
2mkT
⎛ ⎝ ⎜ ⎞
⎠ ⎟ .......................................... (4)
R =ΔV
ΔI=4mkT
qIb......................................................... (5)
Ib = 1nA100MΩ
mkT/q
2Ib M1-M5
MOSFET1-2
2
Fig. 2 Resistor circuit with biasing subcircuit.
3 Fig. 3 Offset currents of resistor circuit. Offset currents ΔI1 and ΔI2 consist of common-mode offset current ICM and differential offset current IDIFF.
0 3I10 I20 2
i () ICM ii
IDIFFI10 I20
ΔI10 = IDIFF + ICM ...................................................(6) ΔI20 = IDIFF − ICM ...................................................(7)
ICM M5 M3-M42 1 IDIFF
M1-M3 M2-M4
3.
0.35-µm 2P-4M CMOSMOSFET
M3 M4
M5
M1 M2ΔI1 ΔI2
1 2
Vdd
Ib
Biasing subcircuit Resistor circuit
ΔI10 ΔI20
ICMICM
IDIFF
1 2
VCM
3 6
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 2 ) = 1.5 V. W/L = 20 µm/4 µm 105 µm × 110 µm
4 Vdd = 3 V( )VCM = 1.5 V Ib = 1 nA
1 - 2 - ( V- I ) 40 mV 40 mV
-a
- b 1I1 ( ) 2 I2
( )
VCM5 Vdd = 3 V Ib = 1 nA
VCM 0-3 VICM ( ) IDIFF ( )
VCM 0.4-2.8 V
Ib 6
(5)Ib Ib
Ib = 10 nA 12 MΩ Ib = 1 nA123 MΩ
4. CR
4 1
CR7
5 -VCM Fig. 5 Offset currents as a function of common-mode voltage VCM for terminals 1 and 2, measured for Ib = 1nA and Vdd = 3 V.
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 − 5R2ω 2C 2 − jRωC (R2ω 2C 2 − 6)...................(8)
R C 1/jωCC (8)
0 π RωC (R2ω 2C 2 − 6) = 0 ................................................(9)
ω =6
CR.......................................................................(10)
0
-40 -20 0 20 40-0.4
-0.3
-0.2
-0.1
0.1
0.2
0.3
0.4C
urre
nt [n
A]
ΔI1
ΔI2
(solid line)
(dashed line)
Voltage ΔV [mV]
VCM = 1.5 V
Res
ista
nce
[MΩ
]
Tail current Ib [nA]
Measured
1
10
100
1000
0.1 1 10 100
4mkTqIb
Offs
et c
urre
nt [n
A]
VCM [V]
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
0 0.5 1 1.5 2 2.5 3
ICM
IDIFF
4 6
f =6
2πCR.................................................................. (11)
R = 4mkT/(qIb)Ib f
4 2
8 0.35-µm 2P-4M CMOSCR350 µm × 370 µmRin = 5 kΩ Rf = 170 kΩ 9
Vdd = 3 V E0 = 1.5 V C = 10 pFIb = 10 nA 2.7 kHz Ib = 1 nA 290 Hz
5.
5 1 PTAT 4mkT/(qIb)
Ib
PTAT (Proportional To Absolute Temperature current) Ib
PTAT
10 PTATM6 M7 M8 M9 4
ß (CS CK CK )
PTATVdd M9
M6M8 M9
IPTAT M6 -VGS6 M7 - VGS7
IPTATRS
VGS6= VGS7 + IPTAT RS
RS =1
CS f
.............................................. (12)
7 CR Fig. 7 CR phase-shift oscillator. The elements circled by dashed lines represent resistor circuits.
8 CR Fig. 8 Chip photograph of phase-shift oscillator. Chip size is 350 μm × 370 μm. Parameters used for fabrication were Rin = 5 kΩ, Rf = 170 kΩ, C = 10pF, Vdd = 3 V, and E0 = 1.5 V.
(a) Ib = 1 nA
(b) Ib = 10 nA 9
Fig. 9 Output waveforms of phase-shift oscillator, measured for two values of tail current Ib for resistor circuit.
210
mV
200 μs
1 ms
140
mV
Rin
Rf
Output V0C C CE0
Resistor circuit
Op AmpsOp AmpsOp Amps
370 μm370 μm
350
μm35
0 μm High Resistance ResistorsHigh Resistance ResistorsHigh Resistance Resistors
CapacitorsCapacitorsCapacitors
Rin, RfRin, RfRin, Rf
5 6
10 Fig. 10 Resistor circuit with temperature compensation.
RS ( CS
f ) (12)
IPTAT RS = VGS6 − VGS7
=mkT
qln
IDI0
⋅L
W
⎛ ⎝ ⎜
⎞ ⎠ ⎟ + Vth6
−mkT
qln
IDI0
⋅L
WK
⎛ ⎝ ⎜
⎞ ⎠ ⎟ − Vth7
=mkT
qln K
................... (13)
M6 M7 1 KMOSFET
PTAT IPTAT
IPTAT =mkTCS f
qln K ............................................... (14)
M9 M10 1 : αIPTAT 1/α
1-2 (5) (14)
R =4α
CS f ln K............................................................ (15)
5 2 0.35-μm CMOS
SPICE 11( )
11 Fig. 11 Temperature characteristic of resistor circuit for three tail currents.
0.9 nA - 6 nA(TC) 2610 ppm/°C - 2660
ppm/°C 12 10 PTAT IPTAT
CS = 0.55 pFf 910 kHz - 5.6 MHz
13 , PTAT
10f 20 MΩ - 140 MΩ
CK
1 : K
CK
M6
M1
M9 M4M8
8 st
age
M3M10
M5
M7
M2
f
21
α
α : 1
Start up
PTAT current source Resistor circuit
Vdd
CS
IPTAT IPTAT
0
20
40
60
80
100
120
140
160
Res
ista
nce
[MΩ
]
Temperature [°C]
Ib = 0.9 nA
Ib = 2 nA
Ib = 6 nA
80 60 40 20 0 -20
(2660 ppm/°C)
(2660 ppm/°C)
(TC = 2610 ppm/°C)
353 333 313 293 273 253Temperature [K]
6 6
12 PTAT Fig. 12 Temperature dependence of PTAT current for three switching frequencies.
330 ppm/°C - 690 ppm/°C( ) PTAT
( 1 /(CS f ))CS f
α Kα = 10, K = 2
60
6.
CMOS
1-1000 MΩCR
PTAT
13
Fig. 13 Temperature dependence of resistor with compensation. Parameters used for fabrication were Vdd = 3 V, α = 10,K = 2, CS = 0.55 pF.
PTAT
7.
(VDEC)
( ) A. Wang, B. H. Clhoun, and A. P. Chandracasan Sub-Threshold Design for Ultra Low-Power Systems, Springer, New York (2006)
( ) K. Nagaraj : “New CMOS Floating Voltage-Controlled Resistor”, Electron. Lett., Vol.22, No.12 pp.667-668 (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.1217-1220 (1989)
( ) S. Sakurai and M. Ismail : “A CMOS Square-Law Programmable Floating Resistor Independent of the Threshold Voltage”, IEEE Trans. Circuits Syst. II, Vol.39, No.8 pp.565-574 (1992)
( ) Y. Taur and T. H. Ning Fundamentals of Modern VLSI Devices, .Cambridge, Cambridge Univ. Press, U.K. (2002)
353 333 313 293 273 253
f = 910 kHz
f = 2 MHz
f = 5.6 MHz
0
20
40
60
70
50
30
10
I PTA
T [n
A]
switching frequency
Temperature [K]
(0.07 nA/°C)
(0.03 nA/°C)
(TC = 0.19 nA/°C)
Temperature [°C] 80 60 40 20 0 -20
0
20
40
60
80
100
120
140
160
Res
ista
nce
[MΩ
]
Temperature [°C]
f = 910 kHz
f = 2 MHz
f = 5.6 MHz
80 60 40 20 0 -20
(500 ppm/°C)
(330 ppm/°C)
switching frequency
(TC = 690 ppm/°C)
w/o temperature compensation
353 333 313 293 273 253Temperature [K]