Young Won Lim4/6/16

CMOS Inverter

Young Won Lim4/6/16

Copyright (c) 2011-2016 Young W. Lim.

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Inverter (2B) 3 Young Won Lim4/6/16

Operation Modes

VDSn

IDSn

nLIN

nOFF

nSAT nLIN

nSAT

nOFF

I ds ∝ V ds

I ds = const

I ds = 0

G

S

D

Inverter (2B) 4 Young Won Lim4/6/16

Operation Modes and Bias Voltages

nLIN

nSAT nOFF

I ds ∝ V ds

I ds = c

I ds = 0

V dsV gs

V dsV gs

V dsV gs

V dsV gs

nOFF

I ds = 0

G

S

D

Inverter (2B) 5 Young Won Lim4/6/16

nMOS Bias https://en.wikipedia.org/wiki/CMOS

nLINnOFF

Inverter (2B) 6 Young Won Lim4/6/16

pMOS Bias

N N

N Np p

pp

https://en.wikipedia.org/wiki/CMOS

pLINpOFF

Inverter (2B) 7 Young Won Lim4/6/16

Pinch-Of

+ +

––+–

+

––

––-

++

++

More reverse biasedMore reverse biased

Most of Vds

https://en.wikipedia.org/wiki/CMOS

nSAT

Most of Vds

nSAT

Constant flowing capacity

To prevent forward biased junction

nLIN

Inverter (2B) 8 Young Won Lim4/6/16

Notation

IDSp

IDSn

VDSp

–

+

VDSn

+

–

Current Notation

Voltage Notation

S

S

DD

G

G

S

S

DD

G

G

S

S

DD

G

G

https://en.wikipedia.org/wiki/CMOS

V i n = V GSp + V dd = V GSn

V out = V DSp + V dd = V DSn

Inverter (2B) 9 Young Won Lim4/6/16

Input Voltage

IDSn VDSn

+

–

VDSp

+

–

Vin=

Vin=

IDSp

V GSn = V Gn − V Sn

V SGp = V Sp − V Gp

+

– VGSn= V in − V ss

= V dd − V i n

S

S

DD

G

G

S

S

DD

G

G

–

+VGSp

V GSp = V Gp − V Sp

= V in − V dd

V i n = V GSp + V dd

= V GSn

https://en.wikipedia.org/wiki/CMOS

Inverter (2B) 10 Young Won Lim4/6/16

Output Voltage

VDSp

–

+

VDSn

+

–

VQ VQ

V Q = V DSp+ V Sp

= V DSp + V dd

V Q = V DSn+ V S

= V DSn + V ss

S

S

DD

G

G

S

S

DD

G

G

S

S

DD

G

G

= V DSn

V out = V DSp + V dd = V DSn

https://en.wikipedia.org/wiki/CMOS

Inverter (2B) 11 Young Won Lim4/6/16

Characteristic Curves

VDSn

IDSn

VDSp

IDSp

IDSn VDSn

+

–

Vin=

+

– VGSn

S

S

DD

G

G

VDSp

+

–

Vin=

IDSp

S

S

DD

G

G

–

+VGSp

https://en.wikipedia.org/wiki/CMOS

negative

negative

Inverter (2B) 12 Young Won Lim4/6/16

Flip up pMOS curves

VDSn

IDSn

VDSp

– IDSp

IDSn VDSn

+

–

Vin=

+

– VGSn

S

S

DD

G

G

VDSp

+

–

Vin=

S

S

DD

G

G

–

+VGSp

– IDSp

https://en.wikipedia.org/wiki/CMOS

(-1) * IDSp

Inverter (2B) 13 Young Won Lim4/6/16

Shift right pMOS curves

VDSn

IDSn

VDSp + Vdd

-IDSp

VDSn

+

–

Vin=

+

– VGSn

S

S

DD

G

G

VDSp

+

–

Vin=

S

S

DD

G

G

–

+VGSp

V Q = V DSp + V dd

V Q = V DSn

https://en.wikipedia.org/wiki/CMOS

VDSp + Vdd

Inverter (2B) 14 Young Won Lim4/6/16

Overlay pMOS & nMOS curves

VDSn

IDSn

VDSp + Vdd

IDSn VDSn

+

–

Vin=

+

– VGSn

S

S

DD

G

G

VDSp

+

–

Vin=

- IDSp

S

S

DD

G

G

–

+VGSp

V i n = V GSp + V dd = V GSn

V out = V DSp + V dd = V DSn

-IDSp

https://en.wikipedia.org/wiki/CMOS

Inverter (2B) 15 Young Won Lim4/6/16

[Ids–Vgs], [Ids–Vds] Characteristic Curves

IDSn

VDSn

VDSp + Vdd

-IDSp

IDSn

V GSn = 1

V GSn = 2

V GSn = 3

V GSn = 4

V GSn = 5

1 2 3 4 5 VGSn

-IDSp

1 2 3 4 5 V GSp + V dd

V GSp = −1

V GSp = −2

V GSp = −3

V GSp = −4

V GSp = −5

Inverter (2B) 16 Young Won Lim4/6/16

Vin : L → H

V i n = V GSp + V dd = V GSn

V out = V DSp + V dd = V DSn0 1 2 3

-5 -4 -3 -2

0 1 2 3

4 5

-1 0

4 5V i n

V GSp

V GSn

V dd

V ssV i n

V GSp V GSnV

in=

+

– VGSn

S

S

DD

G

G

–

+VGSp

VDSp

–

+

VDSn

+

–

Inverter (2B) 17 Young Won Lim4/6/16

Intersect Points

IDSnIDSn IDSn

IDSnIDSn IDSn

V i n =+0V GSp =−5V GSn =+0

V i n =+1V GSp =−4V GSn =+1

V i n =+2V GSp =−3V GSn =+2

V i n =+3V GSp =−2V GSn =+3

V i n =+4V GSp =−1V GSn =+4

V i n =+5V GSp =−0V GSn =+5

Inverter (2B) 18 Young Won Lim4/6/16

Intersect Points in [Ids–Vgs], [Ids–Vds] Curves

VDSn

IDSn

VDSp + Vdd

-IDSp

0

-1-2-3

-4

-5

0

123

4

5

VGSnIDSn

V GSn

-IDSp

VGSp + V dd

0

-1-2-3

-4

-5

0

123

4

5

VGSp

Inverter (2B) 19 Young Won Lim4/6/16

Mode Changes

0 1 2 3

-5 -4 -3 -2

0 1 2 3

4 5

-1 0

4 5V i n

V GSp

V GSn

pLIN

nSAT

pLINnSATpLIN

nLINpSAT pSAT pOFF

nLIN nLIN

IDSn

1 2 3 4 5 VGSn

V GSp+V ddnOFF

pLIN

nSAT

pLINnSATpLIN

nLINpSAT pSAT pOFF

nLIN nLINnOFF

VDSn

IDSn

-IDSp

0

123

4

5

VGSnIDSn

VDSp + Vdd

-IDSp

0

-1-2-3

-4

-5

VGSp

pOFF pSAT pSAT pLIN pLIN pLIN nLIN nLIN nLIN nSAT nSAT nOFF

IDSn

-IDSp

Inverter (2B) 20 Young Won Lim4/6/16

Resistance and Mode Changes

nSAT nSAT nLIN nLIN nLINnOFF

pLIN pLIN pLIN pSAT pSAT pOFF

VDSn

IDSn

VDSp + Vdd

-IDSp

0

-1-2-3

-4

-5

0

123

4

5

VGSnVGSp

Inverter (2B) 21 Young Won Lim4/6/16

Abruptly Changing Region

nSAT nSAT nSAT nLIN nLINnOFF

pLIN pLIN pSAT pSAT pSAT pOFF

pLINnOFF

pSATnSAT

pOFFnLIN

VIL

VIH

VOL

VOH

VDSn

IDSn

-IDSp

0

-1-2-3

-4

-5

0

123

4

5

VGSnVGSp

IDSn

V GSn

-IDSp

VGSp + V dd

Inverter (2B) 22 Young Won Lim4/6/16

Input Switching 1 → 0

time

vin

vin

vout

nOFF

vout

nSAT

nLIN

time

H H

L L

Decreasinginput voltage

Increasing output voltage

Increasing output voltage

Decreasing input voltage

Inverter (2B) 23 Young Won Lim4/6/16

Input Switching 0 → 1

time

vin

vin

vout

nOFF

vout

nSAT

nLIN

time

HH

LL

Increasinginput voltage

Decreasing output voltage

Decreasing output voltage

Increasing input voltage

Inverter (2B) 24 Young Won Lim4/6/16

[VIL, VIH] & [VOL, VOH]

can be considered as a logic “L” input

can be considered as a logic “H” input

the worst case output when the worst “L” input is applied

the worst case output when the worst “H” input is applied

pLINnOFF

pSATnSAT

pOFFnLIN

VIL

VIH

VOL

VOH

Inverter (2B) 25 Young Won Lim4/6/16

Noise Margin

VOL

VOH

VIH

VIL

NMH

NML

VOH

VOL

VIH

VIL

Noise

can be considered as a logic “L” input

can be considered as a logic “H” input

pLINnOFF

pSATnSAT

pOFFnLIN

VIL

VIH

VOL

VOH

Inverter (2B) 26 Young Won Lim4/6/16

Simple Transistor Model

Cutoff, subthreshold, or weak-inversion mode

When VGS

< Vt:

Triode mode or linear region (the ohmic mode)

When VGS

> Vt and V

DS < ( V

GS – V

t )

Saturation or active mode

When VGS

> Vt and V

DS ≥ ( V

GS – V

t )

I d = k 'WL [(v gs − v t)v ds −

12

vds2 ]

I d =12

k 'WL

(v gs − v t)2

I d = 0

https://en.wikipedia.org/wiki/CMOS

Inverter (2B) 27 Young Won Lim4/6/16

Linear and Saturation Models

I d = k 'WL [(v gs − v t)v ds −

12

vds2 ]

I d =12

k 'WL

(v gs − v t)2

linear region

When VGS

> Vt and V

DS < ( V

GS – V

t )

Saturation or active mode

When VGS

> Vt and V

DS ≥ ( V

GS – V

t )

https://en.wikipedia.org/wiki/CMOS

VDS

IDS

2(vgs − v t)

(vgs − v t)

VDS

IDS

Inverter (2B) 28 Young Won Lim4/6/16

Bias Conditions

Cutoff V

GS < V

t:

Linear region V

GS > V

t

VDS

< ( VGS

– Vt )

Saturation V

GS > V

t

VDS

> ( VGS

– Vt )

VDS

VGS

IDS

https://en.wikipedia.org/wiki/CMOS

Inverter (2B) 29 Young Won Lim4/6/16

Characteristic Curve

Young Won Lim4/6/16

References

[1] http://en.wikipedia.org/[2] http://www.allaboutcircuits.com/[3] W. Wolf, “Modern VLSI Design : Systems on Silicon[4] N. Weste, D. Harris, “CMOS VLSI Design: A Circuits and Systems Perspective”[5] J. P. Uyemura, “Introduction to VLSI Circuits and Systems”[6] https://en.wikiversity.org/wiki/The_necessities_in_SOC_Design[7] https://en.wikiversity.org/wiki/The_necessities_in_Digital_Design[8] https://en.wikiversity.org/wiki/The_necessities_in_Computer_Design[9] https://en.wikiversity.org/wiki/The_necessities_in_Computer_Architecture[10] https://en.wikiversity.org/wiki/The_necessities_in_Computer_Organization[11] https://en.wikiversity.org/wiki/Verilog_programming_in_plain_view