ECE 342 – Jose Schutt‐Aine
ECE 342Solid‐State Devices & Circuits
4. CMOS
Jose E. Schutt-AineElectrical & Computer Engineering
University of [email protected]
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ECE 342 – Jose Schutt‐Aine
Digital Circuits
VIH: Input voltage at high state VIHminVIL: Input voltage at low state VILmaxVOH: Output voltage at high state VOHminVOL: Output voltage at low state VOLmin
Currents into input
IIH IIHmaxIIL IILmax
IOH IOHmaxIOL IOLmax
Likewise for current we can define
Currents into output
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ECE 342 – Jose Schutt‐Aine 3
NMHNML
Voltage Transfer Characteristics (VTC)The static operation of a logic circuit is determined by its VTC
• In low state: noise margin is NML
• In high state: noise margin is NMH
L IL OLNM V V
H OH IHNM V V VIL and VIH are the points where the slope of the VTC=-1
• An ideal VTC will maximize noise margins
/ 2 L H DDNM NM VOptimum:
ECE 342 – Jose Schutt‐Aine
Switching Time & Propagation Delay
input
output
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ECE 342 – Jose Schutt‐Aine
tr=rise time (from 10% to 90%)tf=fall time (from 90% to 10%)tpLH=low-to-high propagation delaytpHL=high-to-low propagation delay
Inverter propagation delay: 12p pLH pHLt t t
Switching Time & Propagation Delay
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ECE 342 – Jose Schutt‐Aine 6
For a logic-circuit family employing a 3-V supply, suggest an ideal set of values for Vth, VIL, VIH, VOH, NML, NMH. Also, sketch the VTC. What value of voltage gain in the transition region does your ideal specification imply?
3.0 ; 0.0OH DD OLV V V V V
Ideal 3V logic implies:
/ 2 3.0 / 2 1.5 ;th DDV V V
/ 2 1.5 ; / 2 1.5IL DD IH DDV V V V V V
VTC and Noise Margins
ECE 342 – Jose Schutt‐Aine 7
3.0 1.5 1.5H OH IHNM V V V
1.5 0.0 1.5L IL OLNM V V V
The gain in the transition region is:
/ 3.0 0.0 / 1.5 1.5OH OL IH ILV V V V
3 / 0 /V V
VTC and Noise Margins
Inverting transfer characteristics
ECE 342 – Jose Schutt‐Aine
When inverter threshold is at VDD/2, the noise margin NMH and NML are equalized
3 28 3H L DD thNM NM V V
Noise margins are typically around 0.4 VDD; close to half power-supply voltage CMOS ideal from noise-immunity standpoint
: noise margin for high inputNML: noise margin for low inputVth: threshold voltage
CMOS Noise Margins
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ECE 342 – Jose Schutt‐Aine
Switching Circuit
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ECE 342 – Jose Schutt‐Aine
Nonideal Switch
1sc
lowsc L
RV VR R
1
sohigh
so L
RV VR R
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ECE 342 – Jose Schutt‐Aine
IV Characteristics of Switches
Ideal switch Non-ideal switch
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ECE 342 – Jose Schutt‐Aine
Complementary Switches
1sc
lowsc so
RV VR R
1
sohigh
so sc
RV VR R
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ECE 342 – Jose Schutt‐Aine
Problem
CC Sout
L S
V RVR R
6: 10 10 5S outOpen R V V
A switch has an open (off) resistance of 10M and close (on) resistance of 100 .Calculate the two voltage levels of Vout for the circuit shown. Assume RL=5 k
22 5 10: 10 0.098
5000 100S outShort R V V
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ECE 342 – Jose Schutt‐Aine
Problem
100 , 10S SR on R off M
If two switches are used as shown, calculate the two output voltage levels. Assume switches are complementary
2
1 2
CC Sout
S S
V RVR R
State 1: S1 off, S2 on RS1=10 M, RS2=100
6
5 100 5 010 10 100outV V V
State 2: S1 on, S2 off RS1=100 , RS2=10 M
6 7
6 7
5 10 10 5 10 510 10 100 10 100outV V
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ECE 342 – Jose Schutt‐Aine
MOSFET Switch
NMOS PMOS
• Characteristics of MOS Switch – MOS approximates switch better than BJT in off state– Resistance in on state can vary from 100 to 1 k
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ECE 342 – Jose Schutt‐Aine
NMOS Switch
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ECE 342 – Jose Schutt‐Aine
CMOS Switch
CMOS switch is called an inverter
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The body of each device is connected to its source NO BODY EFFECT
ECE 342 – Jose Schutt‐Aine
CMOS Switch – Off State
• OFF State (Vin: low)– nMOS transistor is off– Path from Vout to V1 is through PMOS Vout: high
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ECE 342 – Jose Schutt‐Aine
CMOS Switch – Input Low
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ECE 342 – Jose Schutt‐Aine
CMOS Switch – Input LowNMOS
GSN TNV V OFF
rdsn high
PMOS
'
1dsp
p DD TPp
rWk V VL
rdsp is low
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ECE 342 – Jose Schutt‐Aine
CMOS Switch – On State
• ON State (Vin: high)– pMOS transistor is off– Path from Vout to ground is through nMOSVout: low
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ECE 342 – Jose Schutt‐Aine
CMOS Switch – Input High
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ECE 342 – Jose Schutt‐Aine
PMOS
GSP TPV V OFF
rdsp high
CMOS Switch – Input HighNMOS
'
1dsn
n DD TNn
rWk V VL
rdsn is low
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ECE 342 – Jose Schutt‐Aine
CMOS Inverter
'
1dsn
N DD Tn
rWk V VL
'
1dsp
P DD Tp
rWk V VL
Short switching transient current low power
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ECE 342 – Jose Schutt‐Aine 25
Load driving capability of CMOS is high. Transistors can sink or source large load currents that can be used to charge and discharge load capacitances.
CMOS Inverter
Advantages of CMOS inverter Output voltage levels are 0 and VDDsignal swing is
maximum possible Static power dissipation is zero Low resistance paths to VDD and ground when needed High output driving capability increased speed Input resistance is infinite high fan-out
ECE 342 – Jose Schutt‐Aine 26
CMOS Inverter VTC
QP and QN are matched
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Derivation Assume that transistors are matched Vertical segment of VTC is when both QN and QP are saturated No channel length modulation effect = 0 Vertical segment occurs at vi=VDD/2 VIL: maximum permitted logic-0 level of input (slope=-1) VIH: minimum permitted logic-1 level of input (slope=-1)
CMOS Inverter VTC
To determine VIH, assume QN in triode region and QP in saturation region
221 12 2I t o o DD I tv V v v V v V
Next, we differentiate both sides relative to vi
o oI t o o DD I t
I I
dv dvv V v v V v Vdv dv
ECE 342 – Jose Schutt‐Aine 28
CMOS Inverter VTC
Substitute vi=VIH and dvo/dvi = -1
2DD
o IHVv V
After substitutions, we get
1 5 28IH DD tV V V
Same analysis can be repeated for VIL to get
1 3 28IL DD tV V V
ECE 342 – Jose Schutt‐Aine 29
CMOS Inverter Noise Margins
1 5 28IH DD tV V V
1 3 28IL DD tV V V
1 3 28H DD tNM V V
1 3 28L DD tNM V V Symmetry in VTC equal
noise margins
ECE 342 – Jose Schutt‐Aine
Matched CMOS Inverter VTC
n
p np
W WL L
CMOS inverter can be made to switch at specific threshold voltage by appropriately sizing the transistors
Symmetrical transfer characteristics is obtained via matching equal current driving capabilities in both directions (pull-up and pull-down)
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ECE 342 – Jose Schutt‐Aine 31
VTC and Noise Margins - ProblemAn inverter is designed with equal-sized NMOS and PMOS transistors and fabricated in a 0.8-micron CMOS technology for which kn’ = 120 A/V2, kp’ = 60 A/V2, Vtn =|Vtp|=0.7 V, VDD= 3V, Ln=Lp = 0.8 m, Wn = Wp = 1.2 m, find VIL, VIH and the noise margins.
2' 2 '1 12 2n I t o o p DD I t
n p
W Wk V V V V k V V VL L
Equal sizes NMOS and PMOS, but kn’=2kp’
Vt = 0.7V
For VIH: QN in triode and QP in saturation
ECE 342 – Jose Schutt‐Aine 32
224 2I t o o DD I tV V V V V V V
Differentiating both sides relative to VI results in:
: 4 4 4 2 ( 1)o oI t o o DD I t
I I I
V VV V V V V V VV V V
Substitute the values together with:
and 1oI IH
I
VV VV
VTC and Noise Margins – Problem (cont’)
(1)
ECE 342 – Jose Schutt‐Aine 33
4 0.7 1 4 4 2 3 0.7IH o o IHV V V V
8 7.4 1.33 1.236
oIH o
VV V
22From (1) : 4 0.7 2 3 0.7IH o o IHV V V V
224 0.7 2 2.3IH o o IHV V V V
2solving (2) & (3) : 1.55 4.97 1.14 0o oV V
0.22oV V 1.52IHV V
VTC and Noise Margins – Problem (cont’)
(2)
(3)
ECE 342 – Jose Schutt‐Aine 34
2 2' '1 12 2n I t p DD I t DD o DD o
n p
W Wk V V k V V V V V V VL L
For VIL: QN is in saturation and QP in triode
2 210.7 3 0.7 3 32I I o oV V V V
2 210.7 2.3 3 32I I o oV V V V
2 0.7 2.3 3 3o oI I o o
I I I
V VV V V VV V V
VTC and Noise Margins – Problem (cont’)
(1)
ECE 342 – Jose Schutt‐Aine 35
and 1oI IL
I
VV VV
2 1.4 2.3 3 3IL IL o oV V V V
2 1.153IL oV V
2 21From (1) : 0.7 2.3 3 32IL IL o oV V V V
2 210.66 1.85 3.45 0.66 3 32o o o oV V V V
VTC and Noise Margins – Problem (cont’)
ECE 342 – Jose Schutt‐Aine 36
2.96oV V 0.81ILV V
Noise Margins:
3 1.52 1.48HNM V
0.81 0 0.81LNM V
VTC and Noise Margins – Problem (cont’)
Since QN and QP are not matched, the VTC is not symmetric
ECE 342 – Jose Schutt‐Aine 37
CMOS Dynamic Operation
Exact analysis is too tedious Replace all the capacitances in the circuit by a single
equivalent capacitance C connected between the output node of the inverter and ground
Analyze capacitively loaded inverter to determine propagation delay
ECE 342 – Jose Schutt‐Aine 38
CMOS – Dynamic Operation
1 2 1 2 3 42 2gd gd db db g g wC C C C C C C C
ECE 342 – Jose Schutt‐Aine 39
CMOS – Dynamic Operation
ECE 342 – Jose Schutt‐Aine 40
CMOS Dynamic Operation
Need interval tPHL during which vo reduces from VDD to VDD/2
/ 2av PHL DD DDI t C V V
Which gives
Iav is given by2
DDPHL
av
CVtI
12av DN DNI i E i M
ECE 342 – Jose Schutt‐Aine 41
CMOS Dynamic Operationwhere
2'12DN n DD tn
n
Wi E k V VL
and
' /n
PHLn DDn
Ctk W L V
2
' 12 2 2DD DD
DN n DD tnn
W V Vi M k V VL
this gives
ECE 342 – Jose Schutt‐Aine 42
CMOS Dynamic OperationWhere a is given by
2
2
374
n
tn tn
DD DD
V VV V
Likewise, tPLH is given by
' /p
PLHp DDp
Ct
k W L V
with 2
237
4
ptp tp
DD DD
V VV V
ECE 342 – Jose Schutt‐Aine 43
CMOS Dynamic OperationWhere a is given by
12P PHL PLHt t t
Components can be equalized by matching transistors tP is proportional to C reduce capacitance Larger VDD means lower tp Conflicting requirements exist
ECE 342 – Jose Schutt‐Aine 44
CMOS – Propagation Delay
ECE 342 – Jose Schutt‐Aine 45
CMOS – Propagation Delay
Capacitance C is the sum of:– Internal capacitances of QN and QP– Interconnect wire capacitance– Input of the other logic gate
'
1.6/PHL
n DDn
Ctk W L V
To lower propagation delay– Minimize C– Increase process transconductance k’– Increase W/L– Increase VDD
ECE 342 – Jose Schutt‐Aine 46
A CMOS inverter for which kn=10 kp=100 A/V2 and Vt =0.5 V is connected as shown to a sinusoidal signal source having a Thevenin equivalent voltage of 0.1-V peak amplitude and resistance of 100 k. What signal voltage appears at node Awith vI = +1.5 V and vI = -1.5 V?
CMOS Inverter Problem
ECE 342 – Jose Schutt‐Aine 47
For vI = 1.5 V, the NMOS operates in the triode region while the PMOS is off.
6
1 1 10100 10 1.5 0.5DSn
n I t
r kk v V
3 4
4 5
100 10 10 9.0910 10Av mV
CMOS Inverter Problem (cont’)
ECE 342 – Jose Schutt‐Aine 48
For vI = -1.5 V, the PMOS operates with
5
61 1 10
100 10 1.5 0.510
DSPp I t
rk v V
3 5
5 5
100 10 10 5010 10Av mV
CMOS Inverter Problem (cont’)
ECE 342 – Jose Schutt‐Aine 49
Propagation Delay - ExampleFind the propagation delay for a minimum-size inverter for which kn’=3kp’=180 A/V2 and (W/L)n = (W/L)p=0.75 m/0.5 m, VDD = 3.3 V, Vtn = -Vtp = 0.7 V, and the capacitance is roughly 2fF/mm of device width plus 1 fF/device. What does tpbecome if the design is changed to a matched one? Use the method of average current.
2 237 7 3 0.7 0.72 2 1.734 4 3.3 3.3
tn tnn
DD DD
V VV V
Solution
'6
1.73 2 0.75 10.75/ 180 10 3.30.5
nPHL
n DDn
fF fFCtk W L V
13.38
ECE 342 – Jose Schutt‐Aine 50
4.85PHLt ps
Since , then 1.73tn tp n pV V
We also have , hencen p
W WL L
'
' 4.85 3 14.55nPLH PHL
n
kt t psk
1 1 4.85 14.55 9.72 2P PHL PLHt t t ps
Propagation Delay - Example
ECE 342 – Jose Schutt‐Aine 51
If both devices are matched, then
' 'p nk k
PLH PHLt t
and
1 4.852p PHL PLH PHLt t t t ps
Propagation Delay - Example
ECE 342 – Jose Schutt‐Aine 52
CMOS – Dynamic Power Dissipation
In every cycle– QN dissipate ½ CVDD
2 of energy– QP dissipate ½ CVDD
2 of energy – Total energy dissipation is CVDD
2
If inverter is switched at f cycles per second, dynamic power dissipation is: 2
D DDP fCV
ECE 342 – Jose Schutt‐Aine 53
Power Dissipation - Example
In this problem, we estimate the inverter power dissipation resulting from the current pulse that flows in QN and QP when the input pulse has finite rise and fall times. Let Vtn=-Vtp=0.5 V, VDD = 1.8V, and kn=kp=450A/V2. Let the input rising and falling edges be linear ramps with the 0-to-VDD and VDD-to-0 transitions taking 1 ns each. Find Ipeak.13.44
ECE 342 – Jose Schutt‐Aine 54
To determine the energy drawn from the supply per transition, assume that the current pulse can be approximated by a triangle with a base corresponding to the time for the rising or falling edge to go from Vt to VDD-Vt, and the height equal to Ipeak. Also, determine the power dissipation that results when the inverter is switched at 100 MHz.
Power Dissipation - Example
ECE 342 – Jose Schutt‐Aine 55
212 2
DDPeak n ox tn
n
W VI C VL
2
2
1 1.8450 0.5 362 2Peak
AI AV
Power Dissipation - Example
ECE 342 – Jose Schutt‐Aine 56
The time when the input reaches Vt is:
0.5 1 ns 0.28 ns1.8
The time when the input reaches VDD - Vt is:
1.8 0.5 1 ns 0.72 ns1.8
The base of the triangle is
0.72 0.28 0.44 ns widet
Power Dissipation - Example
ECE 342 – Jose Schutt‐Aine 57
1 1 36 1.8 0.44 ns2 2Peak DDE I V t A
14.3E femtoJoules
6 15100 10 14.3 10 1.43P f E W
Power Dissipation - Example
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