Lecture 8 ANNOUNCEMENTS A summary of frequently - - PowerPoint PPT Presentation

Lecture 8

ANNOUNCEMENTS

• A summary of frequently misunderstood/missed concepts is
• A summary of frequently misunderstood/missed concepts is

now posted on the class website, and will be updated regularly.

• Graded HW assignments can be picked up in lab (353 Cory).

OUTLINE

Please indicate your lab section on your HW assignments!

OUTLINE

• BJT Amplifiers (cont’d)

– Common‐emitter topology – CE stage with emitter degeneration – Impact of Early effect (ro)

EE105 Fall 2007 Lecture 8, Slide 1

• Prof. Liu, UC Berkeley

Reading: Finish Chapter 5.3.1

Emitter Degeneration

• By inserting a resistor in series with the emitter, we

“degenerate” the CE stage. g g

• This topology will decrease the gain of the amplifier but

improve other aspects, such as linearity, and input d impedance.

EE105 Fall 2007 Lecture 8, Slide 2

• Prof. Liu, UC Berkeley

Small‐Signal Analysis

• The gain of a degenerated CE stage = the total load

resistance seen at the collector divided by 1/g plus resistance seen at the collector divided by 1/gm plus the total resistance placed in series with the emitter.

R R g − −

E m C E m C m v

R g R R g R g A + = + = 1 1

m

g

EE105 Fall 2007 Lecture 8, Slide 3

• Prof. Liu, UC Berkeley

Emitter Degeneration Example 1

Note that the input impedance of Q2 is in parallel with RE.

2

|| 1

π

r R R A

E C v

+ − =

EE105 Fall 2007 Lecture 8, Slide 4

• Prof. Liu, UC Berkeley

2 1

|| π g

E m

Emitter Degeneration Example 2

Note that the input impedance of Q2 is in parallel with RC.

E C v

R r R A + − =

2

1 ||

π EE105 Fall 2007 Lecture 8, Slide 5

• Prof. Liu, UC Berkeley

E m

g

1

Input Impedance of Degenerated CE Stage

• With emitter degeneration, the input impedance is

increased from r to r + (β+1)R ― a desirable effect increased from rπ to rπ + (β+1)RE a desirable effect.

A

i R i V ) 1 ( ) ( ∞ = β

E x in x E x x

R r v R i R i r v ) 1 ( ) 1 ( + + = ≡ + + = β β

π π

EE105 Fall 2007 Lecture 8, Slide 6

• Prof. Liu, UC Berkeley

E x in

i ) (β

π

Output Impedance of Degenerated CE Stage

• Emitter degeneration does not alter the output

impedance if the Early effect is negligible impedance, if the Early effect is negligible.

A

R v V ⇒ ⎞ ⎜ ⎜ ⎛ + + ∞ = ) (

π x E m in

R v R v R v g r v v = ⇒ ⎠ ⎜ ⎜ ⎝ + + = =

π π π π π

EE105 Fall 2007 Lecture 8, Slide 7

• Prof. Liu, UC Berkeley

C x x

• ut

R i R = ≡

Degenerated CE Stage as a “Black Box”

A

V ∞ = ) (

E in m

• ut

R g r v g i + + =

−

) ( 1

1

• If gmRE >> 1, Gm is more linear.

m

• ut

m E m

R g i G R g r + ≈ ≡ + + 1 ) ( 1

π

EE105 Fall 2007 Lecture 8, Slide 8

• Prof. Liu, UC Berkeley

gm

E

,

m

E m in

R g v + 1

Degenerated CE Stage with Base Resistance

) ( ∞ =

A

V . = β

A

• ut

in A in

• ut

v v v v v v ) 1 ( + + + − = β β

π B E C in

• ut

R R r R v v 1 + + − ≈

B E C v

R R R A

EE105 Fall 2007 Lecture 8, Slide 9

• Prof. Liu, UC Berkeley

1 + + + β

E m

R g

Degenerated CE Stage: Input/Output Impedances Input/Output Impedances

• Rin1 is more important in practice, because RB is often

the output impedance of the previous stage the output impedance of the previous stage.

A

V ∞ = ) (

E in A

R R R R r R + + + + + = ) 1 ( ) 1 (

1

β β

π C

• ut

E B in

R R R r R R = + + + = ) 1 (

2

β

π

EE105 Fall 2007 Lecture 8, Slide 10

• Prof. Liu, UC Berkeley

Emitter Degeneration Example 3

2 1

1 ) || ( R R R R A

B C v

+ + − =

2 2

) 1 ( 1 R R r R g

B in m

+ + + = + β β

π

EE105 Fall 2007 Lecture 8, Slide 11

• Prof. Liu, UC Berkeley

1

|| R R R

C

• ut =

Output Impedance of Degenerated CE Stage with VA<∞ with VA

• Emitter degeneration boosts the output impedance.

– This improves the gain of the amplifier and makes the This improves the gain of the amplifier and makes the circuit a better current source.

[ ]

) || )( 1 ( || ) || ( 1

π π π

r R r g r R r R r r R g R

E O m O

• ut

E O E m

• ut

+ + = + + =

EE105 Fall 2007 Lecture 8, Slide 12

• Prof. Liu, UC Berkeley

[ ]

) || ( 1

π π

r R g r R

E m O

• ut

E O m O

• ut

+ ≈

Two Special Cases

Stage with explicit depiction of ro:

O m O

• ut

E

r r g r R r R ) 1 ( : ) 1 ≈ + ≈ >>

π π

β

O E E

r R g R r R ) 1 ( : ) 2 + ≈ <<

EE105 Fall 2007 Lecture 8, Slide 13

• Prof. Liu, UC Berkeley

O E m

• ut

E

r R g R r R ) 1 ( : ) 2 + ≈ <<

π

Analysis by Inspection

• This seemingly complicated circuit can be greatly

simplified by first recognizing that the capacitor creates an AC short to ground, and gradually transforming the circuit to a known topology.

[ ] [ ]

EE105 Fall 2007 Lecture 8, Slide 14

• Prof. Liu, UC Berkeley

[ ]

1 2

|| ) || ( 1 R r r R g R

O m

• ut

π

+ =

[ ] O

m

• ut

r r R g R ) || ( 1

2 1 π

+ =

1 1 ||

• ut
• ut

R R R =

Example: Degeneration by Another BJT

[ ]

1 1 2 1

) || ( 1

O O m

• ut

r r r g R

π

+ =

• Called a “cascode”, this circuit offers many advantages

EE105 Fall 2007 Lecture 8, Slide 15

• Prof. Liu, UC Berkeley

, y g that we will study later...

Bad Input Connection

• Since the microphone has a very low resistance

(connecting the base of Q1 to ground), it attenuates ( g

1

g ) the base voltage and renders Q1 with a very small bias current.

EE105 Fall 2007 Lecture 8, Slide 16

• Prof. Liu, UC Berkeley

Use of Coupling Capacitor

• A capacitor is used to isolate the DC bias network

from the microphone and to short (or “couple”) the from the microphone , and to short (or couple ) the microphone to the amplifier at higher frequencies.

EE105 Fall 2007 Lecture 8, Slide 17

• Prof. Liu, UC Berkeley

DC and AC Analysis

• The coupling capacitor is replaced with an open

circuit for DC analysis, and then replaced with a short circuit for DC analysis, and then replaced with a short circuit for AC analysis.

B in O C m v

R r R r R g A || ) || ( = − =

π O C

• ut

r R R || =

EE105 Fall 2007 Lecture 8, Slide 18

• Prof. Liu, UC Berkeley

Bad Output Connection

• Since the speaker has an inductor with very low DC

resistance, connecting it directly to the amplifier , g y p would ~short the collector to ground, causing the BJT to go into deep saturation mode.

EE105 Fall 2007 Lecture 8, Slide 19

• Prof. Liu, UC Berkeley

Use of Coupling Capacitor at Output

• The AC coupling indeed allows for correct biasing.

However due to the speaker’s small input However, due to the speaker s small input impedance, the overall gain drops considerably.

EE105 Fall 2007 Lecture 8, Slide 20

• Prof. Liu, UC Berkeley

CE Stage with Voltage‐Divider Biasing

O C m v

r R g A ) || ( − =

O C

• ut

in

r R R R R r R || || ||

2 1

= = π

EE105 Fall 2007 Lecture 8, Slide 21

• Prof. Liu, UC Berkeley

CE Stage with Robust Biasing

∞ = V ∞

A

V

) ( ∞ =

A

V

C v

R R A + − = 1

) ( ∞

A

V [ ]

E in E m

R R R r R R g + + = +

2 1 ||

|| ) 1 (β

π EE105 Fall 2007 Lecture 8, Slide 22

• Prof. Liu, UC Berkeley

C

• ut

R R =

Elimination of Emitter Degeneration for AC Signals for AC Signals

• The capacitor C2 shorts out RE at higher frequencies

to eliminate the emitter degeneration to eliminate the emitter degeneration.

) ( ∞ =

A

V

i C m v

R R r R R g A = − =

2 1 ||

||

) (

A

C

• ut

in

R R R R r R =

2 1 ||

||

π

EE105 Fall 2007 Lecture 8, Slide 23

• Prof. Liu, UC Berkeley

Complete CE Stage

s s L C v

R R R R R R R R R R R A + ⋅ + + − =

2 1 2 1 2 1

|| || || || 1 ||

EE105 Fall 2007 Lecture 8, Slide 24

• Prof. Liu, UC Berkeley

s s E m

R g + + +

2 1 2 1

|| 1 β

Summary of CE Concepts

EE105 Fall 2007 Lecture 8, Slide 25

• Prof. Liu, UC Berkeley