CNIC Information System with Pakdata Cf In Pakistan
Β
Ch16p
1. Chapter 16
Exercise Solutions
EX16.1
( 3.9 ) (8.85 Γ10β14 )
COX = = 1.726 Γ10β7 F / cm 2
200 Γ 10β8
2 (1.6 Γ 10β19 ) (11.7 ) ( 8.85 Γ10 β14 )(1015 ) 1
Ξ³ = = 0.1055 V 2
1.726 Γ 10β7
ΞVTN = r β‘ 0.576 + VSB β 0.576 β€ = ( 0.1055 ) β‘ 0.576 + 5 + 0.576 β€
β£ β¦ β£ β¦
ΞVTN = 0.169 V
EX16.2
(a)
vo = VDD β I D RD
β kβ² ββ W β
vo = 3 β β n β β β β£ 2 ( 3 β 0.5 ) vo β vo β¦ RD
β‘ β€
2
β 2 β β L β
vo = 0.1
β 0.06 β β‘
β ( 5 ) β£( 5 )( 0.1) β ( 0.1) β€ RD
2
0.1 = 3 β β
β 2 β β¦
0.1 = 3 β 0.0735RD
RD = 39.5 K
(b)
β 0.06 β
β ( 5 )( 39.5 )(VIt β 0.5 ) + (VIt β 0.5 ) β 3 = 0
2
β
β 2 β
5.925 (VIt β 0.5 ) + (VIt β 0.5 ) β 3 = 0
2
β1 Β± 1 + 4 ( 5.925 )( 3)
(VIt β 0.5 ) = VOt =
2 ( 5.925 )
VOt = 0.632 V
VIt = 1.132 V
EX16.3
(a)
(i)
vo = VDD β VTNL = 3 β 0.4
vo = 2.6 V
(ii)
βW β βW β
β β β‘ 2 ( vI β 0.4 ) vo β vo β€ = β β [VDD β vo β 0.4]
2 2
β£ β¦
β L β D β L β L
16 β‘ 2 ( 2.6 β 0.4 ) vo β vo β€ = 2 [3 β vo β 0.4]
2 2
β£ β¦
35.2vo β 8vo = 6.76 β 5.2vo + vo
2 2
9vo β 40.4vo + 6.76 = 0
2
40.4 Β± 1632.16 β 4 ( 9 )( 6.76 )
vo =
2 (9)
vo = 0.174 V
2. (b)
β 60 β
iD = β β (2) [3 β 0.174 β 0.4]
2
β 2 β
iD = 353.1 ΞΌ A
P = iD β VDD = 1.06 mW
EX16.4
(a)
βW β βW β
β β β‘ 2 ( vI β 0.4 ) vo β vo β€ = β β ( β ( β0.8 ) )
2 2
β L β D β£ β¦
β L β L
6 β‘ 2 ( 3 β 0.4 ) vo β vo β€ = 2 ( 0.64 )
β£
2
β¦
6vo β 31.2vo + 1.28 = 0
2
31.2 Β± 973.44 β 4 ( 6 )(1.28 )
vo =
2(6)
vo = 41.4 mV
(b)
βW β βW β
β β ( vIt β 0.4 ) = β β ( β(β0.8) )
2 2
β L β D β L β L
6 ( vIt β 0.4 ) = 2 ( 0.64 )
2
β vIt = 0.862 V β«
β¬ Driver
vOt = 0.862 β 0.4 = 0.462 V β
vIt = 0.862 V β«
β¬ Load
vOt = VDD + VTNL = 3 β 0.8 = 2.2 V β
(c)
β 60 β
iD = β β (2) ( β ( β0.8 ) ) = 38.4 ΞΌ A
2
β 2 β
P = iD β VDD = 115.2 ΞΌ W
EX16.5
We have
{
VOH = VDD β VTNLO + r β‘ 2Ο fP + VSB β 2Ο fP β€
β£ β¦ }
{
VOH = 5 β 0.8 + 0.35 β‘ 0.73 + VOH β
β£ 0.73 β€}
β¦
VOH β 4.499 = β0.35 0.73 + VOH
Squaring both sides
VOH β 8.998VOH + 20.241 = 0.1225(0.73 + VOH )
2
VOH β 9.1205VOH + 20.15 = 0
2
9.1205 Β± 83.1835 β 4(20.15)
VOH =
2
VOH = 3.76 V
EX16.6
a.
i. A = logic 1 = 10 V, B = logic 0 βAβ driver in nonsaturation. βBβ driver off
3. β²
β kn β β W β β kβ² ββ W β
β 2 β β L β ( βVTNL ) = β 2 β β L β β‘ 2 ( vI β vTND ) VOL β VOL β€
2 2
β£ β¦
β β β β L β β β β D
2 ( 3) = (10 ) β‘ 2 (10 β 1.5 ) V0 L β V02L β€
2
β£ β¦
9 = 5 (17V0 L β V02L )
5V02L β 85V0 L + 9 = 0
(85 ) β 4 ( 5 )( 9 )
2
85 Β±
V0 L = β V0 L = 0.107 V
2(5)
ii. A = B = logic 1
β²
β kn β β W β β kβ² ββ W β
β 2 β β L β ( βVTNL ) = 2 β 2 β β L β β£ 2 ( vI β vTND )VOL β VOL β€
β‘
2 2
β¦
β β β β L β β β β D
2 ( 3) = ( 2 )(10 ) β‘ 2 (10 β 1.5 ) V0 L β V02L β€
2
β£ β¦
9 = 10 (17V0 L β V02L )
10V02L β 170V0 L + 9 = 0
(170 ) β 4 (10 )( 9 )
2
170 Β±
V0 L = β V0 L = 0.0531 V
2 (10 )
b. Both cases.
35
iD = β ( 2 )( 3) = 315 ΞΌ A β P = iD β VDD β P = 3.15 mW
2
2
EX16.7
800
P = iD β VDD β iD = = 160 ΞΌ A
5
35 β W β βW β βW β
iD = 160 = β β β (1.4 ) = 34.3 β β β β β = 4.66
2
2 β L β L β L β L β L β L
35 β W β β‘ βW β
β β β 2 ( 5 β 0.8 )( 0.12 ) β ( 0.12 ) β€ β β β = 9.20
2
iD = 160 =
2 β L β D β£ β¦ β L β D
EX16.8
VDD 2.1
(a) VIt = = = 1.05 V
2 2
VOPt = VIt β VTD = 1.05 β (β0.4) = 1.45 V
VONt = VIt β VTN = 1.05 β 0.4 = 0.65 V
2.1 + (β0.4) + 0.5(0.4)
(b) VIt = = 1.16 V
1 + 0.5
VOPt = 1.16 + 0.4 = 1.56 V
VONt = 1.16 β 0.4 = 0.76 V
2.1 + (β0.4) + 2(0.4)
(c) VIt = = 0.938 V
1+ 2
VOPt = 0.938 + 0.4 = 1.338 V
VONt = 0.538 V
EX16.9
4. P = f β CL β VDD
2
( 0.10 Γ10 ) = f ( 0.5 Γ10 ) ( 3)
β6 β12 2
f = 2.22 Γ 104 Hz β f = 22.2 kHz
EX16.10
a.
10 β 2 + 2.5(2)
K n / K p = 200 / 80 = 2.5 β VIt = β VIt = 4.32 V
1 + 2.5
V0 Pt = 6.32 V
V0 Nt = 2.32 V
b.
10 β 2 β 2 β‘ 2.5 β€
VIL = 2 + β β’2 β 1β₯ β VIL = 3.39 V
2.5 β 1 β£ 2.5 + 3 β¦
1
V0 HU = {(1 + 2.5)(3.39) + 10 β (2.5)(2) + 2}
2
V0 HU = 9.43 V
10 β 2 β 2 β‘ 2(2.5) β€
VIH = 2 + β β’ β 1β₯ β VIH = 4.86 V
2.5 β 1 β’ 3(2.5) + 1 β₯
β£ β¦
(4.86)(1 + 2.5) β 10 β (2.5)(2) + 2
V0 LU =
2(2.5)
V0 LU = 0.802 V
c.
NM L = VIL β V0 LU = 3.39 β 0.802 β NM L = 2.59 V
NM H = V0 HU β VIH = 9.43 β 4.86 β NM H = 4.57 V
EX16.11
3 PMOS in series and 3 NMOS in parallel.
Worst Case: Only one NMOS is ON in Pull-down mode β same as the CMOS inverter β Wn = W .
All 3 PMOS are on during pull-up mode β W p = 3(2W ) = 6W .
EX16.12
NMOS: Worst Case, M NA , M NB on, Wn = 2(W ) or M NC , M ND or M NC , M NE on β Wn = 2(W ).
PMOS: M PA and M PC on or M PA and M PB on β WP = 2(2W ) = 4W
If M PD and M PE on, need WP = 2(4W ) = 8W
EX16.13
a. vI = Ο = 5 V β v0 = 4 V
b. vI = 3 V, Ο = 5 V β v0 = 3 V
c. vI = 4.2 V, Ο = 5 V β v0 = 4 V
d. vI = 5 V, Ο = 3 V β v0 = 2 V
EX16.14
(a) vI = 8V , Ο = 10V β vGSD = 8 V
M D in nonsaturation
6. 800
P = iD β VDD β iD = = 160 ΞΌ A
5
35 β W β βW β
iD = 160 = β β β (1.4 ) β β β = 4.66
2
2 β L β L β L β L
35 1 β W β β‘ βW β
iD = 160 ΞΌ A = β β β β 2 ( 5 β 0.8 )( 0.12 ) β ( 0.12 ) β€ β β β = 27.6
2
2 3 β L β D β£ β¦ β L β D
TYU16.4
a. From the load transistor:
β β²
kn β β W β 35
I DL = β β β β (VGSL β VTNL ) = ( 0.5 )( 5 β 0.15 β 0.7 )
2 2
β 2 β β L β L 2
or
I DL = 150.7 ΞΌ A
Maximum v0 occurs when either A or B is high and C is high. For the two NMOS is series, the effective
k N is cut in half, so
1 β‘β k n β β W β β€
β²
I DL = β’β β β β β₯ β‘ 2 (VGSD β VTND ) VDS β VDS β€
2
2 β£β 2 β β L β D β¦ β£ β¦
or
1 β‘ 35 β W β β€ β‘
β’ β β β β₯ 2 ( 5 β 0.7 )( 0.15 ) β ( 0.15 ) β€
2
150.7 =
2 β£ 2 β L β D β¦ β£ β¦
which yields
βW β
β β = 13.6
β L β D
b. P = iD β VDD = (150.7 )( 5 ) β P = 753 ΞΌ W
TYU16.5
a. v0 (max) occurs when A = B = 1 and C = D = 0 or A = B = 0 and C = D = 1
βW β 1 βW β
β β (βVTNL ) = β β β β‘ 2(vI β VTND )vO β vO β€
2 2
β L β L 2 β L β D β£ β¦
1 βW β
β‘ β€
(0.5)(1.2)2 = β β β β£ 2(5 β 0.7)(0.15) β (0.15) 2 β¦
2 β L β D
βW β βW β
0.72 = (0.634) β β β β β = 1.14
β L β D β L β D
b.
β kβ² ββ W β β 35 β
iD = β n β β β (βVTNL ) 2 = β β (0.5) [ β(β1.2) ]
2
β 2 β β L β L β 2β
iD = 12.6 ΞΌ A
P = iD β VDD = (12.6)(5) β P = 63 ΞΌ W
TYU16.6
a.
K n = K p = 50 ΞΌ A / V 2
VIt = 2.5 V
iD (max) = K n (VIt β VTN ) 2 = 50(2.5 β 0.8) 2 β iD (max) = 145 ΞΌ A
7. b.
K n = K p = 200 ΞΌ A / V 2
VIt = 2.5 V
iD (max) = (200)(2.5 β 0.8) 2 β iD (max) = 578 ΞΌ A
TYU16.7
a.
5 β 2 + (1)(0.8)
VIt =
1+1
VIt = 1.9 V
V0 Pt = 3.9 V
V0 Nt = 1.1 V
b.
3
VIL = 0.8 + β [5 β 2 β 0.8] β VIL = 1.63 V
8
1
V0 HU = {2(1.63) + 5 β 0.8 + 2}
2
V0 HU = 4.73 V
5
VIH = 0.8 + (5 β 2 β 0.8) β VIH = 2.18 V
8
1
V0 LU = {2(2.18) β 5 β 0.8 + 2}
2
V0 LU = 0.275 V
c.
NM L = VIL β V0 LU = 1.63 β 0.275 β NM L = 1.35 V
NM H = V0 HU β VIH = 4.73 β 2.18 β NM H = 2.55 V
TYU16.8
8. TYU16.9
NMOS β 2 transistors in series
Wn = 2 (W ) = 2W
PMOS β 2 transistors in series
W p = 2 ( 2W ) = 4W
TYU16.10
The NMOS part of the circuit is:
9. TYU16.11
The NMOS part of the circuit is:
TYU16.12
Exclusive-OR
A B f
0 0 0
1 0 1
0 1 1
1 1 0
10. TYU16.13
NMOS conducting for 0 β€ vI β€ 4.2 V
β NMOS Conducting: 0 β€ t β€ 8.4 s
NMOS Cutoff: 8.4 β€ t β€ 10 s
PMOS cutoff for 0 β€ vI β€ 1.2 V
β PMOS Cutoff: 0 β€ t β€ 2.4 s
PMOS Conducting: 2.4 β€ t β€ 10 s
TYU16.14
(a) 1 K β 32 Γ 32 array
Each row and column requires a 5-bit word β 6 transistors per row and column, β 32 Γ 6 + 32 Γ 6 = 384
transistors plus buffer transistors.
(b) 4 K β 64 Γ 64 array
Each row and column requires a 6-bit word β 7 transistors per row and column β 64 Γ 7 + 64 Γ 7 = 896
transistors plus buffer transistors.
(c) 16 K β 128 Γ 128 array
Each row and column requires a 7-bit word β 8 transistors per row and column
β 128 Γ 8 + 128 Γ 8 = 2048 transistors plus buffer transistors.
TYU16.15
From Equation (16.84)
(W / L )nA 2 (VDDVTN ) β 3VTN 2(2.5)(0.4) β 3(0.4) 2
2
= = = 0.526
(W / L )n1 (VDD β 2VTN )
2
( 2.5 β 2(0.4) )
2
From Equation (16.86)
11. (W / L ) p kn 2 (VDDVTN ) β 3VTN
β² 2
β‘ 2(2.5)(0.4) β 3(0.4) 2 β€
= β = (2.5) β’ β₯ = 0.862
(W / L )nB kβ²
p (VDD + VTP )
2
β£ (2.5 β 0.4) 2 β¦
βW β βW β
So β β of transmission gate device must be < 0.526 times the β β of the NMOS transistors in the
β Lβ βLβ
βW β βW β
inverter cell. The β β of the PMOS transistors must be < 0.862 times the β β of the transmission gate
βLβ βLβ
β Wβ β Wβ
devices. Then the β β of the PMOS devices must be < 0.453 times β β of NMOS devices in cell.
βLβ βLβ
TYU16.16
Initial voltage across the storage capacitor = VDD β VTN = 3 β 0.5 = 2.5 V .
Now
dV I
βI = C or V = β β t + K
dt C
2.5
where K = 2.5 V , t = 1.5 ms, V = = 1.25 V , and C = 0.05 pF . Then
2
I (1.5 Γ 10β3 )
1.25 = 2.5 β β
(0.05 Γ 10β12 )
I = 4.17 Γ 10β11 A β I = 41.7 pA