Problems for Amplifier Section Lecture notes: Sec. 6 F. Najmabadi, - - PowerPoint PPT Presentation

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Problems for Amplifier Section Lecture notes: Sec. 6 F. Najmabadi, - - PowerPoint PPT Presentation

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Problems for Amplifier Section Lecture notes: Sec. 6 F. Najmabadi, ECE65, Winter 2012 Exercise 1: Find the bias point and the amplifier parameters of the circuit below. (Si BJT with = 200, V A = 150 V, ignore Early effect in bias

slide-1
SLIDE 1

Problems for Amplifier Section

Lecture notes: Sec. 6

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

Exercise 1: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

  • This is a common collector amplifier

(emitter follower) .

  • Input at the base, output at the emitter.
  • It has a emitter-degeneration bias with a

voltage divider.

slide-3
SLIDE 3
  • F. Najmabadi, ECE65, Winter 2012

Bias circuit Thevenin form of the Voltage divider

V 95 . 4 9 k 18 k 22 k 22 k 90 . 9 k 18 || k 22 = × + = = =

BB B

V R

Real circuit

Exercise 1: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

slide-4
SLIDE 4
  • F. Najmabadi, ECE65, Winter 2012

Bias Calculations

A 3 . 20 / mA 05 . 4 10 7 . ) 1 /( 10 9 . 9 4.95 4.95 : KVL BE

3 3

µ β β = = ≈ = + + + × = + + = −

C B C E E E E E BE B B

I I I I I I R I V R I

V 7 . and V, 7 . : Active in is BJT Assume ≥ > =

CE C BE

V I V

V 0.7 V 5 10 10 4 9 9 : KVL CE

3 3

= > = × × + = + = −

− D CE CE E E CE

V V V R I V V 95 . 4 k 9 . 9 = =

BB B

V R

k 28 . 1 r k . 37 10 x 4 150 r mA/V 156 10 26 10 4.05

3

  • 3

3

= = = = = ≈ = × × = =

m B T

  • C

A

  • T

C m

g I V I V V I g β

π

Exercise 1: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

Thevenin form of the Voltage divider

slide-5
SLIDE 5
  • F. Najmabadi, ECE65, Winter 2012

Signal circuit Real circuit

Exercise 1: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

slide-6
SLIDE 6
  • F. Najmabadi, ECE65, Winter 2012

1 151 1 151 151 k) 100 || k 1 || k 8 . 38 ( 10 156 ) || || ( ) || || ( 1 ) || || (

3

≈ + = = × = + = =

− v L E

  • m

L E

  • m

L E

  • m

i

  • v

A R R r g R R r g R R r g v v A k 28 . 1 r k 8 . 38 r mA/V 156

  • =

= =

π m

g

[ ] [ ]

k 9 . 9 k 194 k 3 . 1 || k 9 . 9 ) || || )( 1 ( || ≈ + = + + =

i L E

  • B

i

R R R r r R R β

π

Ω = = + = 4 . 6 || || || β β

π π

r r R R r r R

  • sig

B

  • Amplifier Parameters

This is a common collector amplifier (emitter follower)

Exercise 1: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

slide-7
SLIDE 7
  • F. Najmabadi, ECE65, Winter 2012

Ω = = 13 k 9 . 9

  • i

R R k 28 . 1 r k 8 . 38 r mA/V 156

  • =

= =

π m

g

Amplifier Parameters (Cut-off frequency)

Hz 39 . 3 10 47 . ) 10 100 (6.4 2 1 ) ( 2 1 Hz 2 . 34 10 47 . ) 10 9 . 9 ( 2 1 ) ( 2 1

6 3 2 2 2 6 3 1 1 1

= × × × + = + = = × × + × = + =

− −

π π π π

p c L

  • p

p c sig i p

f C R R f f C R R f Hz 6 . 37 4 . 3 2 . 34

2 1

= + = + ≈

p p p

f f f

Exercise 1: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

slide-8
SLIDE 8
  • F. Najmabadi, ECE65, Winter 2012
  • This is a common emitter amplifier with

RE .

  • Input at the base, output at the collector.
  • It has a emitter-degeneration bias with a

voltage divider.

Exercise 2: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

slide-9
SLIDE 9

Exercise 2: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

  • F. Najmabadi, ECE65, Winter 2012

Bias circuit Thevenin form of the Voltage divider

V 22 . 2 15 k 9 . 5 k 34 k 9 . 5 k . 5 k 9 . 5 || k 34 = × + = = =

BB B

V R

Real circuit

slide-10
SLIDE 10
  • F. Najmabadi, ECE65, Winter 2012

Bias calculations

Thevenin form of the Voltage divider

A 2 . 14 / mA 84 . 2 510 7 . ) 1 /( 10 . 5 2.22 2.22 : KVL BE

3

µ β β = = ≈ = + + + × = + + = −

C B C E E E E E BE B B

I I I I I I R I V R I

V 7 . and V, 7 . : Active in is BJT Assume ≥ > =

CE C BE

V I V

V 0.7 V 5 . 10 ) 510 10 ( 10 84 . 2 15 15 : KVL CE

3 3

= > = + × × + = + + = −

− D CE CE E E CE C C

V V V R I V R I V 22 . 2 k . 5 = =

BB B

V R

k 83 . 1 r k 8 . 52 10 84 . 2 150 r mA/V 10.9 10 26 10 2.84

3

  • 3

3

= = = = × = ≈ = × × = =

m B T

  • C

A

  • T

C m

g I V I V V I g β

π

Exercise 2: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

slide-11
SLIDE 11

Exercise 2: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

  • F. Najmabadi, ECE65, Winter 2012

Signal circuit Real circuit

slide-12
SLIDE 12

Exercise 2: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

  • F. Najmabadi, ECE65, Winter 2012

k 83 . 1 r k 8 . 52 r mA/V 10.9

  • =

= =

π m

g Amplifier Parameters This is a CE amplifier with RE

[ ] [ ]

k 8 . 4 k 51 . 201 k 83 . 1 || k . 5 ) 1 ( || = × + = + + ≈

i E B i

R R r R R β

π

64 . 1 8 . 52 / 990 . 510 10 9 . 10 1 990 10 9 . 10 0.990k k 100 || k 1 || / ) || ( 1 ) || (

3 3

− = + × × + × × − = = = + + − ≈

− − i

  • L

C

  • L

C E m L C m i

  • v

v R R r R R R g R R g v v k . 1 || 1 || = ≈                 + + + ≈

C

  • sig

B E E

  • C
  • R

R R R R r R r R R

π

β 59 . 1 ) 64 . 1 ( 100 800 , 4 800 , 4 − = − × + = × + = =

v i

  • sig

i i sig

  • v

A v v R R R v v A

slide-13
SLIDE 13

Exercise 2: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

  • F. Najmabadi, ECE65, Winter 2012

k . 1 k 8 . 4 = =

  • i

R R

Amplifier Cut-off frequency (2 caps: 2 poles)

Hz 8 . 15 10 100 ) 10 100 10 ( 2 1 ) ( 2 1 Hz 91 . 6 10 7 . 4 ) 100 10 8 . 4 ( 2 1 ) ( 2 1

9 3 3 2 2 2 6 3 1 1 1

= × × × + = + = = × × + × = + =

− −

π π π π

p c L

  • p

p c sig i p

f C R R f f C R R f Hz 7 . 22 8 . 15 9 . 6

2 1

= + = + ≈

p p p

f f f k 83 . 1 r k 8 . 52 r mA/V 10.9

  • =

= =

π m

g

slide-14
SLIDE 14

Exercise 3: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

  • F. Najmabadi, ECE65, Winter 2012
  • This is a PNP common emitter amplifier (no RE ).
  • Input at the base, output at the collector (RE is

shorted out by a cap)

  • It has a emitter-degeneration bias with two

voltage sources.

slide-15
SLIDE 15

Exercise 3: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

  • F. Najmabadi, ECE65, Winter 2012

Bias circuit Real circuit

A . 5 / mA . 1 10 3 . 2 3 : KVL BE

3

µ β = = ≈ = + × = −

C B C E EB E

I I I I V I

V 7 . and V, 7 . : Active in is BJT Assume ≥ > =

EC C EB

V I V

V 0.7 V 4 . 1 10 10 6 . 4 6 3 10 3 . 2 10 3 . 2 3 : KVL CE

3 3 3 3

= > = × × − = − × + + × = −

− D EC EC C EC E

V V V I V I

k 26 . 5 r k 150 10 150 r mA/V 38.5 10 26 10

3

  • 3
  • 3

= = = = = ≈ = × = =

m B T C A T C m

g I V I V V I g β

π

slide-16
SLIDE 16

Exercise 3: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

  • F. Najmabadi, ECE65, Winter 2012

Signal circuit Real circuit 3 . 85 3 . 85 ) k 100 || k 3 . 2 || k 150 ( 10 38.5 ) || || (

3

− = = × + = − = × − = − =

− i

  • i
  • sig

i i v i

  • L

C

  • m

i

  • v

v v v R R R A v v R R r g v v k 26 . 5 r k 150 r mA/V 38.5

  • =

= =

π m

g Hz 82 16 67

2 1

= + = + ≈

p p p

f f f * Show Amplifier Parameters This is a CE amplifier with no RE k 27 . 2 k 3 . 2 || k 150 || = = =

  • C
  • R

r R R k 26 . 5 || = = =

π π

r r R R

B i

slide-17
SLIDE 17
  • F. Najmabadi, ECE65, Winter 2012
  • This is a MOS common source amplifier (no RS ).
  • Input at the gate, output at the drain (RS is

shorted out by a cap)

  • It has a source-degeneration bias with voltage

divider.

Exercise 4: Find the bias point and the amplifier parameters of this circuit. (µnCox = 100 µA/V2, (W/L) = 6/0.1, Vt = 0.5 V, λ = 0.1 V-1. Assume capacitors are large and ignore channel width modulation in biasing. )

slide-18
SLIDE 18
  • F. Najmabadi, ECE65, Winter 2012

Bias (capacitors are open circuit):

V 353 . 1 8 . 1 100 33 100 V

G

= + = ⇒ = k k k IG Assume Saturation

2 3 2

10 x 3 5 .

OV OV

  • x

n D

V V L W C I

−

= = µ V 803 . = + =

t OV GS

V V V Saturation ⇒ >

OV DS

V V mA 275 . 10 x 3

2 3

= =

− OV D

V I V 550 . = − =

GS G S

V V V V 249 . 1 8 . 1 = − =

D D D

I R V V 699 . = − =

S D DS

V V V V 303 . =

OV

V

D S t OV D S GS G

I R V V I R V V + + = + =

2 3 3

10 3 10 2 5 . 353 . 1

OV OV

V V

−

× × × + + = 853 . 6

2

= − +

OV OV

V V GS-KVL:

Exercise 4: Find the bias point and the amplifier parameters of this circuit. (µnCox = 100 µA/V2, (W/L) = 6/0.1, Vt = 0.5 V, λ = 0.1 V-1. Assume capacitors are large and ignore channel width modulation in biasing. )

slide-19
SLIDE 19
  • F. Najmabadi, ECE65, Winter 2012

Exercise 4: Find the bias point and the amplifier parameters of this circuit. (µnCox = 100 µA/V2, (W/L) = 6/0.1, Vt = 0.5 V, λ = 0.1 V-1. Assume capacitors are large and ignore channel width modulation in biasing. )

k 3 . 36 10 75 2 . 10 r mA/V 1.82 0.303 10 0.275 2 2

3

  • 3

= × = = = × × = =

  • D

A

  • OV

D m

I V V I g 45 . 3 45 . 3 ) || k 2 || k 3 . 36 ( 10 1.82 ) || || (

3

− = = × + = − = ∞ × − = − =

− i

  • i
  • sig

i i v i

  • L

D

  • m

i

  • v

v v v R R R A v v R R r g v v Amplifier Parameters This is a CS amplifier with no RS k 90 . 1 k 2 || k 3 . 36 || = = =

  • D
  • R

R r R k 8 . 24 = =

G i

R R k 8 . 24 k 33 || k 100 = =

G

R

slide-20
SLIDE 20

Exercise 5: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

  • F. Najmabadi, ECE65, Winter 2012
  • This is a common collector amplifier (emitter follower).
  • Input at the base, output at the emitter.
  • It is biased with a current source!
slide-21
SLIDE 21

Exercise 5: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

  • F. Najmabadi, ECE65, Winter 2012

Bias circuit Real circuit

V 7 . − = − =

E E BE

V V V

V 7 . and V, 7 . : Active in is BJT Assume ≥ > =

CE C BE

V I V

k 21 . 1 r k 9 . 34 10 4.3 150 r mA/V 16.5 10 26 10 4.3

3

  • 3

3

= = = = × = ≈ = × × = =

m B T

  • C

A

  • T

C m

g I V I V V I g β

π

A 5 . 21 / mA 3 . 4 µ β = = ≈ =

C B C E

I I I I V 0.7 V 7 . 4 4

0 =

> = − =

D E CE

V V V

E

V

slide-22
SLIDE 22

Exercise 5: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

  • F. Najmabadi, ECE65, Winter 2012

Signal circuit Real circuit k 21 . 1 r k 9 . 34 r mA/V 16.5

  • =

= =

π m

g 1 427 1 427 427 ) || || ( k 9 . 25 k 100 || || k 9 . 34 || || ) || || ( 1 ) || || ( ≈ + = = = = ∞ = + =

i

  • v

L E

  • m

L E

  • L

E

  • m

L E

  • m

i

  • v

v A R R r g R R r R R r g R R r g v v Amplifier Parameters This is an emitter follower (RE = ∞ ) Ω = ≈ + + ≈ 6 . 60 1 || || β β

π π

r R R r R R

sig B E

  • [

]

M 2 . 5 k 9 . 25 201 k 2 . 1 ) || || )( 1 ( || = × + = + + =

i L E

  • B

i

R R R r r R R β

π

slide-23
SLIDE 23

Exercise 5: Find the bias point and the amplifier parameters of the circuit

  • below. (Si BJT with β = 200, VA = 150 V, ignore Early effect in bias

calculations).

  • F. Najmabadi, ECE65, Winter 2012

Signal circuit k 21 . 1 r k 9 . 34 r mA/V 16.5

  • =

= =

π m

g Cut-off frequency Hz 34 . 3 10 47 . ) 61 10 100 ( 2 1 ] [ 2 1

6 3 2

= × × + × = + =

−

π π

p c

  • L

p

f C R R f

slide-24
SLIDE 24

Exercise 6: Find the bias point and the amplifier parameters of the circuit

  • below. (µpCox (W/L) = 400 µA/V2, Vtp = − 4 V, λ = 0.01 V-1. Ignore

channel width modulation in biasing).

  • This is a PMOS common drain amplifier.
  • Input at the gate, output at the source.
  • It has a source-degeneration bias with two

voltage sources.

slide-25
SLIDE 25

Exercise 6: Find the bias point and the amplifier parameters of the circuit

  • below. (µpCox (W/L) = 400 µA/V2, Vtp = − 4 V, λ = 0.01 V-1. Ignore

channel width modulation in biasing).

Bias circuit Real circuit Assume Saturation 9 2 9 10 400 5 . 10 | | 10 10 13

2 2 6 4 4 4

= − + = − + × × × + + × = + × =

− OV OV OV OV tp OV D SG D

V V V V V V I V I GS-KVL: 5 .

2 OV

  • x

p D

V L W C I µ = V 9 . 5 = + =

t OV SG

V V V Saturation ⇒ >

OV DS

V V mA 71 . 10 400 5 .

2 6

= × × =

− OV D

V I V 9 . 5 = → − =

S S SG

V V V V 9 . 10 ) 5 ( = − − =

S SD

V V V 9 . 1 =

OV

V k 141 10 0.71 01 . 1 1 r mA/V 0.747 0.303 10 0.71 2 2

3

  • 3

= × × = = = × × = =

− − D OV D m

I V I g λ

slide-26
SLIDE 26

Exercise 6: Find the bias point and the amplifier parameters of the circuit

  • below. (µpCox (W/L) = 400 µA/V2, Vtp = − 4 V, λ = 0.01 V-1. Ignore

channel width modulation in biasing).

Signal circuit Real circuit k 2 . 1 k 34 . 1 || k 10 1 || 88 . ) || || ( 1 ) || || ( = = = ∞ = = = + =

m S

  • G

i L S

  • m

L S

  • m

v

g R R R R R R r g R R r g A Amplifier Parameters This is a common collector Amp. Cut-off frequency Hz 39 . 3 10 47 . ) 10 2 . 1 10 100 ( 2 1 ] [ 2 1

6 3 3 2

= × × × + × = + =

−

π π

p c

  • L

p

f C R R f

slide-27
SLIDE 27

Exercise 7: Find the bias point and the amplifier parameters of the circuit

  • below. (µnCox (W/L) = 800 µA/V2, Vt = 1 V, λ = 0.01 V-1. Ignore

channel width modulation in biasing).

  • This is a NMOS common gate amplifier.
  • Input at the source, output at the drain.
  • It has a source-degeneration bias with

voltage divider.

slide-28
SLIDE 28

Bias circuit Assume Saturation 5 4 5 10 800 5 . 10 10 10 6

2 2 6 4 4 4

= − + = − + × × × × + + = × + = =

− OV OV OV OV D t OV D GS G

V V V V I V V I V V GS-KVL: 5 .

2 OV

  • x

n D

V L W C I µ = V . 2 = + =

t OV GS

V V V Saturation ⇒ >

OV DS

V V mA 40 . 10 800 5 .

2 6

= × × =

− OV D

V I V 7 4 4 15 10 10 15

4 4

= − − = × + + × =

DS D DS D

V I V I V . 1 =

OV

V

Exercise 7: Find the bias point and the amplifier parameters of the circuit

  • below. (µnCox (W/L) = 800 µA/V2, Vt = 1 V, λ = 0.01 V-1. Ignore

channel width modulation in biasing).

G

V V 6 15 M 8 . 1 M 2 . 1 M 2 . 1 = × + =

G

V DS-KVL:

slide-29
SLIDE 29

k 10 )] || ( 1 ( [ || k 1 . 1 / ) || ( 1 || 7 . 7 ) || k 10 || k 250 ( 10 8 . ) || || (

3

≈ + = =       + = = ∞ × = =

− sig S m

  • D
  • m
  • L

D S i v L S

  • m

v

R R g r R R g r R R R R A R R r g A Amplifier Parameters This is a common gate Amp. Cut-off frequency kHz 47 . 1 Hz 22 kHz 45 . 1 ] [ 2 1 ] [ 2 1

2 1 2 2 1 1

= + = + = + = + =

p p p c

  • L

p c sig i p

f f f C R R f C R R f π π

Exercise 7: Find the bias point and the amplifier parameters of the circuit

  • below. (µnCox (W/L) = 800 µA/V2, Vt = 1 V, λ = 0.01 V-1. Ignore

channel width modulation in biasing).

k 250 10 0.4 01 . 1 1 r mA/V 0.80 1 10 0.4 2 2

3

  • 3

= × × = = = × × = =

− − D OV D m

I V I g λ

slide-30
SLIDE 30

Exercise 8: Find the bias point and the amplifier parameters of the circuit

  • below. (µnCox (W/L) = 400 µA/V2, Vt = 3 V, λ = 0.01 V-1. Ignore

channel width modulation in biasing).

  • This is a NMOS common drain amplifier.
  • Input at the gate, output at the source.
  • It is biased with a current source.
slide-31
SLIDE 31

Bias circuit Assume Saturation

3 2

10 0.71 5 .

  • OV
  • x

n D

V L W C I × = = µ V . 4 = + =

t OV GS

V V V Saturation ⇒ >

OV DS

V V V . 1 =

OV

V

S

V mA 71 . =

D

I

Exercise 8: Find the bias point and the amplifier parameters of the circuit

  • below. (µnCox (W/L) = 400 µA/V2, Vt = 3 V, λ = 0.01 V-1. Ignore

channel width modulation in biasing).

V . 4 − = − = → − =

GS S S G GS

V V V V V V 9 4) ( 5 = − − = − =

S D DS

V V V

slide-32
SLIDE 32
  • F. Najmabadi, ECE65, Winter 2012

704 704 || 1 || 99 . ) || || ( 1 ) || || ( Ω = ∞ = = ∞ = = = + =

m S

  • G

i L S

  • m

L S

  • m

v

g R R R R R R r g R R r g A Amplifier Parameters This is a common collector Amp. Cut-off frequency Hz 36 . 3 10 47 . ) 704 10 100 ( 2 1 ] [ 2 1

6 3 2

= × × + × = + =

−

π π

p c

  • L

p

f C R R f

Exercise 8: Find the bias point and the amplifier parameters of the circuit

  • below. (µnCox (W/L) = 400 µA/V2, Vt = 3 V, λ = 0.01 V-1. Ignore

channel width modulation in biasing).

k 141 10 0.71 01 . 1 1 r mA/V 1.42 1 10 0.71 2 2

3

  • 3

= × × = = = × × = =

− − D OV D m

I V I g λ Signal circuit Real circuit