1) The document discusses the static characteristics of MOS inverters, including their voltage transfer characteristic (VTC), noise margins, and calculations of key voltages like VOH, VOL, VIL and VIH. 2) It describes the general circuit structure of an nMOS inverter using an nMOS transistor as the driver and either a resistor or depletion-mode nMOS as the load. 3) Key parameters that determine the VTC shape include knRL (the product of transconductance and load resistance) and the load used - resistive or depletion-mode nMOS, with the latter providing better noise margins and smaller area.

1. CMOS
Digital Integrated
Circuits
Analysis and Design
1
Unit-2
MOS Inverters: Static Characteristics

2. Introduction
• Positive logic convention
– “1” represents high voltage of
VDD
– “0” represents low voltage of 0
• The inverter threshold voltage,
Vth
– The input voltage,
0<Vin<Vth output VDD
– The input voltage,
Vth<Vin<VDD output 0
2

3. General circuit structure of an nMOS inverter
• The driver transistor
– The input voltage
Vin=VGS
– The output voltage
Vout=VDS
– The source and the
substrate are ground,
VSB=0
• The load device
– Terminal current IL,
terminal voltage VL
3

5. Voltage transfer characteristic (VTC)
• The VTC describing Vout as a function of Vin under DC condition
• Very low voltage level
– Vout=VOH
– nMOS off, no conducting current, voltage drop across the load is very
small, the output voltage is high
• As Vin increases
– The driver transistor starts conducting,
the output voltage starts to decrease
– The critical voltage point, dVout/dVin=-1
• The input low voltage VIL
• The input high voltage VIH
• Determining the noise margins
• Further increase Vin
– Output low voltage VOL, when the input
voltage is equal to VOH
– The inverter threshold voltage Vth
• Define as the point where Vin=Vout
5

8. Noise immunity and noise margin
• NML=VIL-VOL
• NMH=VOH-VIH
• The transition region, uncertain
region
8

9. 9
Power and area consideration
• The DC power dissipation
– The product of its power supply voltage and the
amount of current down from the power supply during
steady state or in standby mode
– PDC=VDDIDC=(VDD/2)[IDC(Vin=low)+IDC(Vin=high)]
– In deep submicron technologies
• Subthreshold current is high therefore more power
consumption
• The chip area
– To reduce the area of the MOS transistor
• The gate area of the MOS transistor
• The product of W and L

10. Resistive-load inverter
• Operation mode
– Vin<VT0, cut off
• No current, no voltage drop
across the load resistor
• Vout=VDD
– VT0Vin<Vout+VT0, saturation
• Initially, VDS>Vin-VT0
•
• With Vin↑Ð Vout↓
– VinVout+VT0, linear
• The output voltage
continues to decrease
2
2
in T0
n
R
k
V V
I  
2
out
in T 0 out
n
R
k
• I 2V V V V 2


1
0

11. Calculation of VOH, VOL
• Calculation of VOH
– Vout=VDD-RLIR
– When Vin is low ID=IR=0 VOH=VDD
• Calculation of VOL
– Assume the input voltage is equal to VOH
– Vin-VT0≥Vout  linear region
–
n L
L
L
R
kn RL
k R
k R
R
R
I
2V
1
1
2
1
2
0L
DD T0
2
0L
2
0L
DD T 0 0L
 DD
knRL

kn RL 

2

 VDD VT 0 

V0 L  VDD VT 0 
VDD  0
V 

n L 





V  2 V V
V V

kn
 2V V 
VDD VOL
Using KCLfor the output node,i.e.IR  ID

VDD Vout
1
1

14. 9
Calculation of VIL, and VIH
n L
out in IH
n L
n L
out
L
out
out
in
out
out n
L in
L
n L
L
out
L in
k R
k R
R
dV
dV
dV
dV
k R
R
R dV
3 k R
R 2
To determine the unknownvariables
1
R dV 2
1 dV k
R 2
2knRL
1
1
2 kn RL
1
1 dV
2
R
V - V k
T 0 out
L
VDD -Vout
IH T 0 out
n in T0
in T0
2
in T 0 out out
IL T0
n in T0
n in T0
2
in T0
L
DD out n
2

VDD
V (V  V ) 

2

  


kn
  1
VT 0
 Vout Vout 
 2V 
  2V
V  V  2V 
V  1 2V 

1
 1  k V

in 




 2V 
V V 
  2  
 
VDD-Vout

kn
 2 V V V V 
VIH is the larger of the two voltage points on the VTC at which the slope is equal to -1
Vout  Vin - VTO , linearregion

2

k R 
VT 0   VDD

Vout (Vin  VIL )  VDD  n L
VT 0 
V  V 
V V  
1
 1  k  VV 
 k 
 
  VV
By definition, VIL is the smaller of the two input voltage at which the slope of the
VTC becomes equal to -1.i.e.dVout/dVin  -1
Vout  Vin - VT0 , saturationregion

18. VTC for different knRL
• The term knRL plays an important role in determining the shape of
the voltage transfer characteristic
• knRL appears as a critical parameter in expressions for VOL, VIL, and
VIH
• knRL can be adjusted by circuitdesigner
• VOH is determine primarily by the power supply voltage, VDD
• The adjustment of VOL receives primarily attention than VIL, VIH
• Larger knRL VOL becomes smaller, larger transition slope
18

19. Example 5.1
19

20. L
20
Power consumption
• The average power consumption
– When input low, VOL
• The driver cut-off, no steady-state current flow, DC
power consumption is zero
– When input high, VOH
• Both driver MOSFET and the load resistor conduct
a nonzero current
• The output voltage VOL, so the current ID=IR=(VDD-
VOL)/RL
– P 
VDD

VDD VOL
2 R
DC(average)

21. Chip area
• The chip area depend on two
parameters
– The W/L ratio of the driver
transistor
• Gate area WxL
– The value of the resistor RL
• Diffused resistor
– Sheet resistance 20 to 100Ω/□
– Very large length-to-width rations
to achieve resistor values on the
order if tens to hundreds of kΩ
• Ploysilicon resistor
– Doped polysilicon (for gate of the
transistor), Rs~20 to 40 Ω/□
– Undoped polysilicon, Rs Rs~10M
Ω/□
– The resistance value can not be
controlled very accurately Ð large
variation of the VTC
– Low power static random access
memory (SRAM)
21

22. Example 5.2
22

23. Inverters with n-type MOSFET load
• The resistive-load inverter
– The large area occupied by the load resistor
• The main advantage of using a MOSFET as
the load device
– Smaller silicon area occupied by the transistor
– Better overall performance
• Enhancement-load nMOS inverter
– The saturated enhancement-load inverter
• A single voltage supply
• A relative simple fabrication process
• VOH=VDD-VT,load
– The linear enhancement-type load
• VOH=VDD
• Higher noise margins
• Two separate power supply voltage (drawback)
– Both type suffer from relatively high stand-by
(DC) power dissipation
• Not used in any large-scale digital applications
23

25. – The linear enhancement-type load

26. Depletion-load nMOS inverter

27. 16
Depletion-load nMOS inverter
• Slightly more complicated
– Channel implant to adjust the
threshold voltage
• Advantages
– Sharp VTC transition better
noise margins
– Single power supply
– Smaller overall layout area
– Reduce standby (leakage)
current
• The circuit diagram
– Consisting
• A nonlinear load resistor,
depletion MOSFET, VT0,load<0
• A nonideal switch (driver) ,
enhancement MOSFET,
VT0,load>0
– The load transistor
GS
• V =0, always on
–
2
The load transistor operates in the linear region
2 2
T ,load out
T ,load out
n,load
D,load
F out F
T ,load T 0,load
V
k
For larger output voltage level,Vout VDD VT,load
2

kn,load
 V
V V
I 
When the output voltage is small,Vout  VDD VT,load
The load transistor is in saturation region
V V  r 
2 V  2
ϒ=substrate-bias (or body-effect) coefficient. 2
out
DD
T ,load out DD out
n,load
D,load
k

2V V V V  V V 2

I 

29. 17
2
2
2
2
2
2
T ,load OL
load
OL
OL
T0
OH
driver
OH DD OH
DD
T ,load OH
n,load
D,load
VOH
k
k
k
 VT ,load VOL 

 driver 
 kload

k
VT 0
VT 0 
VOL  VOH
 V

2V V V V
   V 2
To calculate the output low VOL
assume,Vin  VOH  VDD  driver  linear region, load  saturation region
2V V V V V
 V 2
 0
I 
Calculation of VOH, VOL, VIL, ViH
When Vin is smaller thanVT0  driver  off, load  linear region
zero drain current,VOH VDD

30. 18
Calculation of VOH, VOL, VIL, VIH
DD out
out
DD out DD out
load
driver
dV
dV
dV
k
k k
out DD T ,load out
T ,load out
driver in T0
T ,load out
2
in T0
load
2
2 2

V V  V V 
 kload 
VIL  VT 0 
sbustitute dVout /dVin  -1







Differential both sides with respect toVin

out 

 dV 
T ,load

 2V V




dVT ,load 


  2VDD Vout 
out 
dVT ,load 

2V V 


k  VV 
2V V V V V
 V 2

 VV  
Calculation of VIL
The driver  saturation region, the load  linear region
load
dVout
dV
k
k
Vout

 out 
V 
V
 driver 
 kload 
 
 dVout   dVin 
 k V V 



 dVin 
 Vout  
 dVin 
 dVout   dVout 
V 
V V
2 2F
V V  2V 
sbustitute dVout /dVin -1
Differentialboth sides with respect toVin
kdriver
2V
2 2
 kdriver 
Calculation of VIH
The driver  linear region, the load  saturation region
dVT,load


 dVT ,load 
T ,load out
IH T 0 out
 dVT ,load   dVout 
T ,load out
kdriver Vout  Vin VT 0 
V V 2
T ,load out
2 load
in T 0 out out

31. VTC of depletion load inverters
• The general shape of the
inverter VTC, and ultimately,
the noise margins, are
determined by
– The threshold voltage of the
driver and the load
• Set by the fabrication process
– The driver-to-load ratio
kR=(kdriver/kload)
• Determined by the (W/L)
ratios of the driver and the
load transistor
• One important observation
– A sharp VTC transition and
larger noise margins can be
obtained with relative small
driver-to-load ratios
• Much small area occupation
31

32. Design of depletion-load inverters
• The designable parameters in the inverter circuit are
– The power supply voltage VDD
• Being determined by other external constrains
• Determining the output level high VOH=VDD
– The threshold voltages of the driver and the load
• Being determined by the fabrication process
– The (W/L) ratios of the driver and the load transistor
•
• Since the channel doping densities are not equal
– The channel electron mobilities are not equal
– K’n,load≠k’n,driver
• The actual sizes of the driver and the load transistor are
usually determined by other constrains
– The current-drive capability
– The steady state power dissipation
– The transient switching speed
R
32
R
load
R
L
V V
k
k
k
 W
driver
 
   
 L load  Lload
 W
  
L


W   W
 driver
 driver
,k
,k 
kn,load 
kn,driver 
2V V V V 2
OH T 0 OL OL
2
T ,load OL

33. Power consideration
• The steady-state DC power consumption
– Input voltage low
• The driver off, Vout=VOH=VDD
• No DC power dissipation
– Input voltage high, VinVDD and Vout=VOL
•
Assume the input voltage levellow 50% operation
time and high during the other 50%
33
2
2
DC
OH T 0 OL OL
driver
T ,load OL
P
K
V V 2
T ,load OL

VDD

kload
2 2
2V V V V 2


V V 2

Kload
IDC Vin  VDD

34. Area consideration
• Figure (a)
– Sharing a common n+
diffusion region
• Saving silicon area
– Depletion mode
• Threshold voltage adjusted by
a donor implant into the
channel
– (W/L)driver>(W/L)load, ratio
about 4
• Figure (b)
– Buried contact
• Reducing area
• For connecting the gate and
the source of the load
transistor
– The polysilicon gate of the
depletion mode transistor
makes a direct ohmic with
the n+ source diffusion
– The contact window on the
intermediate diffusion area
can be omitted
34

35. Example 5.3 (1)
35

36. Example 5.3 (2)
36

37. Example 5.3 (3)
37

47. Circuit operation
• Region A: Vin<VT0,n
– nMOS off, pMOS on Ð ID,n=ID,p=0,
Vout=VOH=VDD
• Region B: Vin>VT0,n
– nMOS saturation, the output
voltage decreases
– The critical voltage VIL, (dVout/dVin)=-1
is located within this region
– As the output further decreases
ÐpMOS enter saturation, boundary
of region C
• Region C:
– If nMOS saturation Ð VDS,nVGS,n-
VT0,n  Vout Vin-VT0,n
– If pMOS saturation Ð VDS,nVGS,p-
VT0,p  Vout Vin-VT0,p
– Both of these conditions for device
saturation are illustrated graphically as
shaded areas
• Region D: Vout<Vin-VT0,p
– The criical point VIH
• Region E: Vin>VDD+VT0,p
– Vout=VOL=0
47

48. 48
Circuit operation
• The nMOS and the pMOS transistors an be
seen as nearly ideal switches
– The current drawn from the power supply in both
these steady state points region A and region E
• Nearly equal to zero
• The only current Ðreverse biased S, D leakage current
– The CMOS inverter can drive any load
• Interconnect capacitance
• Fan-out logic gates
• Either by supplying current to the load, or by sinking current
from the load

51. 30
Calculation of VIL, VIH
p
R
R
IL
p
out DD
n
n
k
V
k
k
k

kn




 dVin 
 dVout 
  Vout VDD  Vout VDD 
 dVin 
 dVout 
V V V 
k V V  k  
V V V
V V 
1 k
k V V  k 2V V V V 
substituting Vin  VIL and (dVout /dVin )  -1
2
2
2
2
nMOSsaturation, pMOSlinear

2Vout  VT 0, p VDD  kRVT 0,n
wherek
n IL T 0.n p out IL T 0, p DD
in DD T 0, p
n in T0,n
V  V V 2

in DD T 0, p out DD

V V 2

kp

2
V
in T0,n
2V V V V 2

GS , p T 0, p DS,P DS,p
2 p
GS ,n T0,n
n
out
k
V 
V V V 
 k  



  dVout 
 dVin   dVin 
 dVout 
V V   V V  
out out
k  

V V V
V 
V V
V
V V
V V  k 2V V 
k V V  2V  k 
V V V 
substitingVin VIH and(dVout /dVin )  -1
2
kn
 2V
2
2 2
nMOSlinear, pMOSsaturation
out T0,n
DD T 0,p R
out p IH DD T0,p
IH T0,n
p in DD T0,p
n in T0,n
2
in DD T0,p
2 p
in T 0,n out
2
GS, p T0,p
kn
 2V V 2

kp
V
GS,n T 0,n DS,n DS,n

55. Threshold voltage
• The Region C of VTC
– Completely vertical
• If the channel length modulation effect is neglected, i.e. if =0
– Exhibits a finite slope
• If >0
• Fig 5.22 shows the variation of the inversion (switching) threshold
voltage Vth as function of the transconductance ratio kR
55

59. VTC and power supply current
• If input voltage is either
smaller than VT0,n, or
larger than VDD+VT0,p
– Does not draw any
significant current from the
power supply
– Except for small leakage
current and subthreshold
currents
• During low-to-high and
high-to-low transitions
– Regions B, C, and D
– The current being drawn
from the power source
– Reaching its peak value
when Vin=Vth (both
saturation mode)
59

61. 35
Example 5.4

62. 36
Supply voltage scaling in CMOS inverters
• The static characteristics of the CMOS
inverter allow significant variation of supply
voltage without affecting the functionality of
the basic inverter
• The CMOS inverter will continue to operate
correctly with a supply voltage limit value
– Correct inverter operation will be sustained if
at least one of the transistors remains in
conduction, for any given voltage
– The exact shape of the VTC near e limit
value is essentially determined by
subthreshold conduction properties
• If the power supply voltage is reduced
below the sum of the two threshold
– The VTC will contain a region in which none
of the transistors is conducting
– The output voltage level is determine by the
previous state of the output
– The VTC exhibits a hysteresis behavior
DD T 0,n T 0, p
 V
– V min
V

63. 37
Power and area consideration
• Power consideration
– DC power dissipation of the circuit is almost negligible
– The drain current
• Source and drain pn junction reverse leakage current
• In short channel leakage current
• Subthreshold current
– However, that the CMOS inverter does conduct a significant amount of current
during a switching event
• Area consideration