Lecture 8 - University of California, Berkeleyee105/fa07/lectures...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

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

dimpedance.


Small‐Signal Analysis

• The gain of a degenerated CE stage = the total load resistance seen at the collector divided by 1/g plusresistance seen at the collector divided by 1/gm plus the total resistance placed in series with the emitter.

RRg −−

Em

C

Em

Cmv

Rg

RRgRgA

+=

+= 11

mg


Emitter Degeneration Example 1

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

2||1πrR

RAE

Cv

+−=


21

|| πg Em


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

E

Cv

R

rRA+

−= 2

1|| π


Emg 1

Input Impedance of Degenerated CE Stage

• With emitter degeneration, the input impedance is increased from r to r + (β+1)R ― a desirable effectincreased from rπ to rπ + (β+1)RE a desirable effect.

A

iRiV

)1()( ∞=

β

Ex

in

xExx

RrvR

iRirv

)1(

)1(

++=≡

++=

β

β

π

π


Ex

in i)(βπ

Output Impedance of Degenerated CE Stage

• Emitter degeneration does not alter the output impedance if the Early effect is negligibleimpedance, if the Early effect is negligible.

A

Rv

V

⇒⎞

⎜⎜⎛

++

∞=

00

)(

π

x

Emin

RvR

vRvgr

vv =⇒⎠

⎜⎜⎝

++== 00 πππ

ππ


Cx

xout R

iR =≡

Degenerated CE Stage as a “Black Box”

AV ∞= )(

E

inmout Rgr

vgi++

= − )(1 1

• If gmRE >> 1, Gm is more linear.mout

m

Em

RgiG

Rgr

+≈≡

++

1

)(1 π


gm E , mEmin Rgv +1

Degenerated CE Stage with Base Resistance

)( ∞=AV

.=

βA

out

in

A

in

out

vv

vv

vv

)1( +++−

=β

β

π BE

C

in

out

RRrR

vv

1++

−≈

BE

Cv RR

RA


1+++βE

m

Rg

Degenerated CE Stage: Input/Output ImpedancesInput/Output Impedances

• Rin1 is more important in practice, because RB is often the output impedance of the previous stagethe output impedance of the previous stage.

AV ∞= )(

Ein

A

RRRRrR+++

++=)1(

)1(1

ββπ

Cout

EBin

RRRrRR

=+++= )1(2 βπ



2

1

1)||(RR

RRAB

Cv

++

−=

2

2

)1(1RRrR

g

Bin

m

+++=+

ββ

π


1|| RRR Cout =

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

[ ])||)(1(

||)||(1

π

ππ

rRrgrRrRrrRgR

EOmOout

EOEmout

++=++=


[ ])||(1 π

π

rRgrR EmOout

EOmOout

+≈

Two Special Cases

Stage with explicit depiction of ro:

OmOoutE rrgrRrR )1( : )1 ≈+≈>> ππ β

OEE rRgRrR )1(:)2 +≈<<


OEmoutE rRgRrR )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

[ ] 12 ||)||(1 RrrRgR Omout π+=[ ] Omout rrRgR )||(1 21 π+=11 || outout RRR =

Example: Degeneration by Another BJT

[ ] 1121 )||(1 OOmout rrrgR π+=

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


, y gthat 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.


Use of Coupling Capacitor

• A capacitor is used to isolate the DC bias network from the microphone and to short (or “couple”) thefrom the microphone , and to short (or couple ) the microphone to the amplifier at higher frequencies.


DC and AC Analysis• The coupling capacitor is replaced with an open circuit for DC analysis, and then replaced with a shortcircuit for DC analysis, and then replaced with a short circuit for AC analysis.

Bin

OCmv

RrRrRgA

||)||(

=−=

π

OCout rRR ||=


Bad Output Connection• Since the speaker has an inductor with very low DC resistance, connecting it directly to the amplifier , g y pwould ~short the collector to ground, causing the BJT to go into deep saturation mode.


Use of Coupling Capacitor at Output• The AC coupling indeed allows for correct biasing. However due to the speaker’s small inputHowever, due to the speaker s small input impedance, the overall gain drops considerably.


CE Stage with Voltage‐Divider Biasing

OCmv rRgA )||(−=

OCout

in

rRRRRrR

|||||| 21

== π


CE Stage with Robust Biasing

∞=V ∞AV

)( ∞=AVC

v

R

RA+

−= 1

)( ∞AV

[ ]Ein

Em

RRRrR

Rg

++=

+

21 ||||)1(βπ

EE105 Fall 2007 Lecture 8, Slide 22 Prof. Liu, UC BerkeleyCout RR =

Elimination of Emitter Degeneration for AC Signalsfor AC Signals

• The capacitor C2 shorts out RE at higher frequencies to eliminate the emitter degenerationto eliminate the emitter degeneration.

)( ∞=AV

i

Cmv

RRrRRgA

=−=

21 ||||

)( A

Cout

in

RRRRrR

=21 ||||π


Complete CE Stage

ss

LCv RRR

RRRRRR

RRA+

⋅++

−=

21

21

21 ||||

||||1||


ssE

m

Rg +

++ 2121 ||1β

Summary of CE Concepts


Documents

Lecture 8 - University of California, Berkeleyee105/fa07/lectures...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