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Allen&Holberg - Analog CMOS Circuit Design

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Allen and Holberg - CMOS Analog Circuit Design							Page V.2-5
NMOS Parallel Transistor Realization :
			+				+
			D1	i	D2		i
-			D1		D2		i
-		i			i2
VC		i	1		i2
VC			1
+						G2 +	r ac
G1						G2 +	r ac
G1	M1					VC	v
	M1		v VSS		M2	VC
			v VSS		M2	-
						-

S1	S2
	S2
-	_
-
Voltage-Current Characteristic :

2mA

1mA

I(VSENSE)	0

-1mA

-2mA

-2

Vc=7V 6V

W=15u	4V
W=15u
L=3u	3V
VBS= 5.0V

-1

VDS

NMOS parallel transistor realization M1 2 1 0 5 MNMOS W=15U L=3U M2 2 4 0 5 MNMOS W=15U L=3U

.MODEL MNMOS NMOS VTO=0.75, KP=25U, LAMBDA=0.01, GAMMA=0.8 PHI=0.6

VC 1 2

E1 4 0 1 2 1.0 VSENSE 10 2 DC 0 VDS 10 0

VSS 5 0 DC -5

.DC VDS -2.0 2.0 .2 VC 3 7 1

.PRINT DC I(VSENSE)

.PROBE

.END

Allen and Holberg - CMOS Analog Circuit Design

Page V.2-6

P-Channel Extended Range Active Resistor Circuit

	vAB
	iAB		VDD
			VDD
M2A			M2B
	+	M1A	+
	V	M1A
	V		VC
	-C		VC
			M1B
			-
M3A	+		M3B
	+	V
	-	C

VSS

Voltage Current Characteristics

100uA 4V

60uA

20uA		Vc=2V
i AB
- 20uA
- 60uA
-100uA
-4 -3 -2 -1	0 1	2	3
	VAB

P-Channel Extended Range Active Resistor M1A 3 4 5 10 MPMOS W=3U L=3U

M1B 3 6 5 10 MPMOS W=3U L=3U

M2A 10 3 4 4 MNMOS W=3U L=3U

M2B 10 5 6 6 MNMOS W=3U L=3U M3A 4 7 0 0 MNMOS W=3U L=3U

M3B 6 7 0 0 MNMOS W=3U L=3U

VSENSE 1 3 DC 0V

VC 7 0 VAB 1 5

VDD 10 0 DC 5V

.MODEL MNMOS NMOS VTO=0.75, KP=25U

+ LAMBDA=0.01, GAMMA=0.8 PHI=0.6

.MODEL MPMOS PMOS VTO=-0.75 KP=8U +LAMBDA=0.02 GAMMA=0.4 PHI=0.6

.DC VAB -4.0 4.0 0.2 VC 2 5 1

.PRINT DC I(VSENSE)

.PROBE 4 .END

Allen and Holberg - CMOS Analog Circuit Design																																																								Page V.2-7
THE SINGLE MOSFET DIFFERENTIAL RESISTOR
																																															VC
	v1			i1				R									+															v1					i1																			+
	v1													v2			+															v1																					v2			+
														v2																																							v2
- v1														v2			-														- v1																						v2			-
														v2			-														- v1						i2																			-
				i2
								R
								R																																								VC
																																																VC
Assume the MOSFET's are in the non-saturation region
				i									- v				-V			)(v					- v						1			(v						- v
				i	1		= β (V				C		- v			2	-V	T		)(v		1			- v		2		) -			2		(v		1				- v		2		)2
					1						C					2		T				1					2					2				1						2
				i									- v				-V			)(-v					- v					) -		1			(-v						- v
				i	2		= β (V				C		- v			2	-V	T		)(-v			1		- v			2		) -		2			(-v					1	- v				2		)2
					2						C					2		T					1					2				2								1					2
Rewrite as
				i									- v				-V			)(v					- v						1			(v				2			- 2v						v				+ v
				i	1		= β (V				C		- v			2	-V	T		)(v		1			- v		2		) -			2		(v		1		2			- 2v					1	v		2		+ v			2	2)
					1						C					2		T				1					2					2				1										1			2					2
				i									- v				-V			)(-v					- v					) -		1			(v					2	+ 2v								v			+ v
				i	2		= β (V				C		- v			2	-V	T		)(-v			1		- v			2		) -		2			(v		1			2	+ 2v							1	v		2	+ v			2	2)
					2						C					2		T					1					2				2					1											1			2				2
i		- i							-v				-V				)(2v			) -		1		(v		2-2v						v			+v				2-v				2-2v								v		-v
i	1	- i	2	= β (V				C	-v			2	-V		T		)(2v		1	) -		2		(v		2-2v					1	v	2		+v				2-v				2-2v							1	v	2	-v		2)
	1		2					C				2			T				1			2			1						1		2			2				1										1		2		2
i1 - i2 = 2β [ (VC - VT)v1 - 2v1v2 + 2v1v2 ]
							v1-(-v1) 2v1																		2v1																	1
				2R =				i1-i2						= i1-i2 = 2β(VC-VT)v1 = β(VC-VT)
or
																					R =									1
																					R =						W
																											W
							≤ V																		2K L					(VC-VT)
				v		1	≤ V	C		- V				T
						1		C						T

Allen and Holberg - CMOS Analog Circuit Design

Page V.2-8

Single-MOSFET, Differential Resistor Realization

i1	r ac/2
v1	v2
	r ac/2
- v1	v2
i2	R

Voltage-Current Characteristics

1.0mA

0.6mA

0.2mA

ID(M1)

-0.2mA

-0.6mA

-1.0mA

VC i1

v1 v2

VCC

- v1 v2 i2

VC= 7V 6V

4V 3V

-2

-1

Single MOSFET Differential Resistor Realization M1 1 2 3 4 MNMOS1 W=15U L=3U

M2 5 2 3 4 MNMOS1 W=15U L=3U VC 2 0

VCC 4 0 DC -5V V1 1 0

E1 5 0 1 0 -1

.MODEL MNMOS1 NMOS VTO=0.75 KP=25U +LAMBDA=0.01 GAMMA=0.8 PHI=0.6

.DC V1 -2.0 2.0 0.2 VC 3 7 1

.PRINT DC ID(M1)

.PROBE

.END

Allen and Holberg - CMOS Analog Circuit Design Page V.2-9

The Double MOSFET Differential Resistor

VC1

iD1

iD2

VC2

iD3

iD4

VC1

-v-V

)(v

-v) -

= β (V

-v)2

-v-V

)(v

-v) -

= β (V

-v)2

-v-V

)(v

-v) -

= β (V

-v)2

-v-V

)(v

-v) -

= β (V

-v)2

-v-V

)(v

-v)-

-v)2+(V

-v-V

)(v

-v)-

=β (V

-v)2

-v-V

)(v

-v)-

-v)2+(V

-v-V

)(v

-V)-

=β (V

-v)2

- i2 =

β[(VC1-v-VT)(v1-v) + (VC2-v-VT)(v2-v)

-(VC2-v-VT)(v1- v) - (VC1-v-VT)(v2-v)]

=β[v1(VC1-VC2) + v2(VC2-VC1)] = β(VC1-VC2)(v1-v2)

Rin =

v1-v2

β(VC1-VC2)(v1-v2)

i1-i2

(VC1-VC2)

or R

≤ min [(V

-V

),(V

-V

)]

i n

(VC1-VC2)

Allen and Holberg - CMOS Analog Circuit Design

Page V.2-10

Double-MOSFET, Differential Resistor Realization

VC1

iD1	M1	i1
v1		v3

1	r ac/2	iD2	VSS
1	r ac/2	v3
		v3	M2
	r ac/2	VC2
		v4
2	R	iD3	M3
		iD3	M3

iD4	VSS
v2		v4
	M4	i2

VC1

Voltage-Current Characteristics

150uA
100uA		VBC	=-5V

		V3 =0V
50uA		VC1 =7V

I(VSENSE)	0

- 50uA

-100uA

-150uA

VC2 = 6V

3V 2V

Double MOSFET Differential Resistor Realization M1 1 2 3 4 MNMOS1 W=3U L=3U

M2 1 5 8 4 MNMOS1 W=3U L=3U

M3 6 5 3 4 MNMOS1 W=3U L=3U

M4 6 2 8 4 MNMOS1 W=3U L=3U VSENSE 3 8 DC 0

VC1 2 0 DC 7V VC2 5 0

VSS 4 0 DC -5V V12 1 6

.MODEL MNMOS1 NMOS VTO=0.75 KP=25U +LAMBDA=0.01 GAMMA=0.8 PHI=0.6

.DC V12 -3 3 0.2 VC2 2 6 1

.PRINT DC I(VSENSE))

.PROBE

.END

-3

-2

-1

V1-V2

Allen and Holberg - CMOS Analog Circuit Design

Page V.2-11

SUMMARY OF ACTIVE RESISTOR REALIZATIONS

AC Resistance

Realization

Single MOSFET

Parallel MOSFET

Single-MOSFET, differential resistor

Double-MOSFET, differential resistor

Linearity	How	Restrictions
Linearity	Controlled	Restrictions
	Controlled

Poor	VGS or W/L	vBULK < Min (vS, vD)

Good	VC or W/L	v ≤ (VC - VT)

Good	VC or W/L	\|v1\| < VC - VT
Good	VC or W/L	vBULK < -v1
		Differential around v1
	VC1 - VC2 or	v1, v2 < min(VC1-VT,
Very Good	VC1 - VC2 or	VC2-VT)
	W/L	vBULK < min(v1,v2)
		Transresistance only

Allen and Holberg - CMOS Analog Circuit Design

Page V.3-1

V.3 - CURRENT SINKS & SOURCES

CHARACTERIZATION OF SOURCES & SINKS

1). Minimum voltage (vMIN) across sink or source for which the current is no longer constant.

2). Output resistance which is a measure of the "flatness" of the current sink or source.

CMOS Current Sinks & Sources

VDD

iD +

VGG -

VDD

VGG

+ v

1 rOUT = λID

VG = VGG

vMIN

iD	VG = VGG

0		vMIN
0		v
		v
	0	VDD
	0

vMIN = vDS(SAT.) = vON

where vON = vGS - VT

Allen and Holberg - CMOS Analog Circuit Design									Page V.3-2
SMALL SIGNAL MODEL FOR THE MOSFET
		D	G	B					D
		D	+	+
			+	+
	G	B	vgs	vbs	g v	g	v	r	ds
	G	B			m gs	mbs bs			ds
			-	-
		S	S						S
gm =		2K'WID
gm =		L
gmbs	=	gmγ
gmbs	=	2φF + \|VBS \|
	2	2φF + \|VBS \|
rds ≈	1	= 1
	gds	λID

Allen and Holberg - CMOS Analog Circuit Design

Page V.3-3

INCREASING THE ROUT OF A CURRENT SOURCE

MOS

	Circuit		Small-Signal Model
		+
		iOUT			+
	M2			iout	+
				r ds2
		gm2vgs2			vout
+		vOUT	gmbs2vbs2		vout
+	r		+
-	r		+	r
	VGG	-	vS2	r	-
		-	-
Loop equation:
	vout =	[iout - (gm2vgs2 + gmbs2vbs2)]rds2 + iout r
But, vgs2 = -vs2 and vbs2 = - vs2.
	vout = [iout + gm2vs2 + gmbs2vs2]rds2 + iout r
Replace vs2 by ioutr-
	vout =	iout [ rds2 + gm2rds2r + gmbs2rds2r + r ]

Therefore,

rout = rds2 + r [1 + gm2rds2 + gmbs2rds2]

MOS Small Signal Simplifications

Normally,

gm ≈ 10gmbs ≈ 100gd s

Continuing

rout rgm2rds2

rout ≈ r x (voltage gain of M2 from source to drain)

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