Problems for MOS Section Lecture notes: Sec. 4 F. Najmabadi, ECE65, - - PowerPoint PPT Presentation

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Problems for MOS Section Lecture notes: Sec. 4 F. Najmabadi, ECE65, - - PowerPoint PPT Presentation

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Problems for MOS Section Lecture notes: Sec. 4 F. Najmabadi, ECE65, Winter 2012 Exercise 1: Compute i D ( p C ox ( W/L ) = 0.4 m A/V 2 , V tp = 3 V and = 0 ). PMOS with v SG = 5 V and v GD = 6 V. V OV = v SG | V tp | = 5

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SLIDE 1

Problems for MOS Section

Lecture notes: Sec. 4

  • F. Najmabadi, ECE65, Winter 2012
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SLIDE 2
  • F. Najmabadi, ECE65, Winter 2012

Exercise 1: Compute iD (µpCox (W/L) = 0.4 mA/V2 , Vtp = −3 V and λ = 0 ).

  • PMOS with vSG = 5 V and vGD = 6 V.
  • VOV = vSG – | Vtp|= 5 – 3 = 2 V
  • VOV > 0 → MOS is ON
  • vSD = vSG + vGD = 5 + 6 = 11 V
  • vSD = 11 > VOV = 2 → MOS in saturation
  • mA

0.8 (2) 10 0.4 0.5 5 .

2 3

  • 2

= × × = =

OV

  • x

p D

V L W C i µ

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SLIDE 3
  • F. Najmabadi, ECE65, Winter 2012

Exercise 2: Find VS (µnCox (W/L) = 0.5 mA/V2 , Vtn = 0.8 V and λ = 0 ).

  • Since iD = 10 µA, MOS is ON
  • Assume MOS in saturation

V 2 . 10 0.5 0.5 10 10 5 .

2 3

  • 6
  • 2

= → × × = × =

OV OV OV

  • x

n D

V V V L W C i µ V 1 V 1 8 . 2 . − = → − = − = = + = + =

S S S G GS t OV GS

V V V V v V V v ) saturation in (MOS V 0.2 8 V 8 ) 1 ( 7 = > = = − − = − =

OV DS S D DS

V v V V v

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SLIDE 4

A) Range of VG for MOS ON? V 4 4 ≤ → ≥ − → ≥

G G OV

V V V

  • F. Najmabadi, ECE65, Winter 2012

Exercise 3: Consider this PMOS with µpCox (W/L) = 0.6 mA/V2 , Vtp = −1 V and λ = 0 . A) For what values of VG, PMOS will be ON? B) For what values of VD, PMOS will be in triode? (in terms of VG) C) For what values of VD, PMOS will be in saturation? (in terms of VG)

G tp G tp SG OV D D S SD G G S SG

V V V V v V V V V v V V V v − = − − = − = − = − = − = − = 4 | | 5 | | 5 5 B) Range of VD for MOS in triode? 1 4 5 + ≥ → − ≤ − → ≤

G D G D OV SD

V V V V V v C) Range of VD for MOS in saturation? 1 4 5 + ≤ → − ≥ − → ≥

G D G D OV SD

V V V V V v

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SLIDE 5
  • F. Najmabadi, ECE65, Winter 2012

Exercise 4: Find vGS , vDS , and iD (µnCox (W/L) = 0.4 mA/V2 , Vtn = 3 V and λ = 0 ).

  • Not in cut-off as for iD = 0, GS-KVL gives VOV =12 V > 0.
  • Assume MOS in saturation

V 64 . 8 V 64 . 5 0) need incorrect, ( V 64 . 10 12 0.2 10 0.4 0.5 10 12 : KVL

  • GS

5 .

2 2 3

  • 3

2

= → = > − = = − + × × × + = =

GS OV OV OV OV OV OV OV OV

  • x

n D

v V V V V V V V V L W C i µ ) saturation in (MOS V 5.64 17.3 = > =

OV DS

V v V 27 17 10 2 30 : KVL

  • DS

mA 36 . 6 10 12 : KVL

  • GS

3 3

. v i v i i V

DS D DS D D OV

= → × + = = → + =

D DS D DS D D OV D t OV D GS G

i v i v i i V i V V i v i 10 2 30 15 10 10 15 : KVL

  • DS

10 12 15 10 15 10 10 : KVL

  • GS

3 3 3 3 3 3 6

× + = → − + + = + = → − + + = − + + =

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SLIDE 6
  • F. Najmabadi, ECE65, Winter 2012

Exercise 5: Find R such that PMOS is in saturation with VOV = 0.6 V (µpCox = 0.1 mA/V2 , W/L = 10/0.18 , Vtp = −0.4 V and λ = 0) .

mA 1 ) 6 . ( ) 18 . / 10 ( 10 0.1 0.5 5 .

2 3

  • 2

= × × × × = =

OV

  • x

p D

V L W C i µ Ω = + + = + + = + =

− −

800 4 . 6 . 10 1.8 | | 10 1.8 : KVL

  • SG

3 3

R R V V R v Ri

tp OV SG D

saturation in MOS 6 . . 1 V . 1 1.8 : KVL

  • SD

→ = > = = → + = V v v v i R

OV SD SD SD D

In an IC, W/L (typically specified as a fraction) is a design parameter for MOS circuits.

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SLIDE 7
  • F. Najmabadi, ECE65, Winter 2012

Exercise 6: Find VD (µnCox (W/L) = 0.5 mA/V2 , Vt = 0.8 V and ignore channel-width modulation).

  • When the gate and drain of a MOS are connected to each
  • ther, MOS becomes a 2-terminal device.
  • Called diode-connected transistor
  • If MOS is ON (vDS = vGS ≥ Vt ), MOS will always be in

saturation!

  • vDS = vGS ≥ vGS − Vt = VOV

V 36 . 3 V 56 . 2 0) need incorrect, ( V 56 . 6 2 . 4 0.25 10 0.5 0.5 10 10 5 5 .

2 2 3

  • 3

3 2

: KVL

  • DS/GS

= = = → + = = > − = = − + + + × × × = + = =

GS DS D t OV GS OV OV OV OV OV t OV OV GS D OV

  • x

n D

v v V V V v V V V V V V V V v i V L W C i µ

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SLIDE 8
  • F. Najmabadi, ECE65, Winter 2012

Exercise 7: Find V1 and V2 (µnCox (W/L) = 5 mA/V2 , Vt = 1 V and ignore channel-width modulation).

D D D D DS DS D DS GS D OV D t OV D GS

i i i i v v i v v i V i V V i v = = − + + = − + + = = + → − + + = − + =

2 1 3 1 2 3 1 2 3 1 3 1 3 1

5 . 2 10 2.5 5 . 2 10 2.5 5 . 1 10 5 . 2 10 5 . 2 10

: KCL : KVL

  • DS

: KVL

  • GS2

: KVL

  • GS1
  • Q1 is not in cut-off as for iD1 = 0, GS1-KVL

gives VOV =1.5 V > 0.

  • Q2 is not in cut-off either as iD1 = iD2 > 0
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SLIDE 9
  • F. Najmabadi, ECE65, Winter 2012

Exercise 7 (cont’d) : Find V1 and V2 (µnCox (W/L) = 5 mA/V2 , Vt = 1 V and ignore channel-width modulation).

V 60 . 0) need incorrect, ( V . 1 5 . 1 2.5 10 5 0.5 10 10 1.5 5 .

1 1 1 2 1 2 3

  • 3

1 3 1 2 1 1

: KVL

  • GS1

= > − = = − + × × × + = + = = =

OV OV OV OV OV OV OV D OV OV

  • x

n D D

V V V V V V V i V V L W C i i µ Assume both MOS in saturation Both MOS in saturation, iD2 = iD1 and λ = 0: VOV2 = VOV1 = 0.60 V V 6 . 1 V 6 . 1 1 6 .

2 2 1 1 1 1 1

− = → − = − = = + = + = V V V V v V V v

S G GS t OV GS

V 9 . 5 . 2 V 6 . 1 1 6 .

1 1 2 2 2 2 2

= → − = − = = + = + = V V V V v V V v

S G GS t OV GS

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SLIDE 10
  • F. Najmabadi, ECE65, Winter 2012

Exercise 7 (cont’d) : Find V1 and V2 (µnCox (W/L) = 5 mA/V2 , Vt = 1 V and ignore channel-width modulation).

Need to confirm our assumption of both MOS in saturation V 6 . 5 . 2 V 5 . 2 ) 6 . 1 ( 90 .

1 1 2 1 1 1 1

= > = = − − = − = − =

OV DS S D DS

V v V V V V v

For circuits with multiple transistors, it is usually advantageous to keep track of node voltages (at transistor terminals!

V 6 . 6 . 1 V 6 . 1 9 . 5 . 2 5 . 2

2 2 1 2 2 2

= > = = − = − = − =

OV DS S D DS

V v V V V v