# Lecture 8 ```Lecture 8
ANNOUNCEMENTS
• A
A summary of frequently misunderstood/missed concepts is summary of frequently misunderstood/missed concepts is
now posted on the class website, and will be updated regularly.
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
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 impedance. d
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/gm plus resistance seen at the collector divided by 1/g
plus
the total resistance placed in series with the emitter. − g m RC
− RC
Av =
=
1
1 + g m RE
+ RE
gm
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. RC
Av = −
1
+ RE || rπ 2
gm1
EE105 Fall 2007
Lecture 8, Slide 4
Prof. Liu, UC Berkeley
Emitter Degeneration Example 2
Note that the input impedance of Q2 is in parallel with RC.
RC || rπ 2
Av = −
1
+ RE
g m1
EE105 Fall 2007
Lecture 8, Slide 5
Prof. Liu, UC Berkeley
Input Impedance of Degenerated CE Stage
• With emitter degeneration, the input impedance is increased from rπ to r
increased from r
to rπ + (
+ (β+1)RE ― a desirable effect.
a desirable effect
(VA = ∞)
vx = rπ ix + RE (1+ β )ix
vx
Rin ≡ = rπ + (β +1)RE
ix
EE105 Fall 2007
Lecture 8, Slide 6
Prof. Liu, UC Berkeley
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.
(VA = ∞)
⎛ vπ
⎞
vin = 0 = vπ + ⎜⎜ + g mvπ RE ⇒ vπ = 0
⎝ rπ
⎠
vx
Rout ≡ = RC
ix
EE105 Fall 2007
Lecture 8, Slide 7
Prof. Liu, UC Berkeley
Degenerated CE Stage as a “Black Box”
(VA = ∞)
iout
vin
= gm
1 + (rπ−1 + g m ) RE
iout
gm
≈
Gm ≡
vin 1 + g m RE
EE105 Fall 2007
• If g
gmRE &gt;&gt; 1, G
, m is more linear.
Lecture 8, Slide 8
Prof. Liu, UC Berkeley
Degenerated CE Stage with Base Resistance
(V A = ∞ )
vout v A vout
=
.
vin
vin v A
vout
− β RC
=
vin
rπ + ( β + 1) R E + R B
Av ≈
− RC
1
RB
+ RE +
gm
β +1
EE105 Fall 2007
Lecture 8, Slide 9
Prof. Liu, UC Berkeley
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.
(V A = ∞ )
Rin1 = rπ + ( β + 1) RE
Rin 2 = RB + rπ + ( β + 1) RE
Rout = RC
EE105 Fall 2007
Lecture 8, Slide 10
Prof. Liu, UC Berkeley
Emitter Degeneration Example 3
− (RC || R1 )
Av =
1
RB
+ R2 +
β +1
gm
Rin =r π +(β +1) R2 + RB
Rout = RC || R1
EE105 Fall 2007
Lecture 8, Slide 11
Prof. Liu, UC Berkeley
Output Impedance of Degenerated CE Stage with VA&lt;∞
with V
• Emitter degeneration boosts the output impedance.
– This
This improves the gain of the amplifier and makes the improves the gain of the amplifier and makes the
circuit a better current source. R out = [1 + g m ( R E || rπ ) ]rO + R E || rπ
R out = rO + ( g m rO + 1)( R E || rπ )
R out ≈ rO [1 + g m ( R E || rπ ) ]
EE105 Fall 2007
Lecture 8, Slide 12
Prof. Liu, UC Berkeley
Two Special Cases
Stage with explicit depiction of ro:
1) RE &gt;&gt; rπ : Rout ≈ rO (1 + g m rπ ) ≈ βrO
2) RE &lt;&lt; rπ : Rout ≈ (1 + g m RE )rO
EE105 Fall 2007
Lecture 8, Slide 13
Prof. Liu, UC Berkeley
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.
Rout = R1 || Rout 1
EE105 Fall 2007
Rout 1 = [1 + g m ( R2 || rπ )]rO
Lecture 8, Slide 14
Rout = [1 + g m ( R2 || rπ )]rO || R1
Prof. Liu, UC Berkeley
Example: Degeneration by Another BJT
Rout = [1 + gm1 (rO2 || rπ 1 )]rO1
• Called a “cascode”, this circuit offers many advantages ,
y
g
that we will study later...
EE105 Fall 2007
Lecture 8, Slide 15
Prof. Liu, UC Berkeley
• Since the microphone has a very low resistance ((connecting the base of Q
g
g
)
1 to ground), it attenuates 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”)
from the microphone , and to short (or couple ) the 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.
Av = − g m ( RC || rO )
Rin = rπ || RB
Rout = RC || rO
EE105 Fall 2007
Lecture 8, Slide 18
Prof. Liu, UC Berkeley
• 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’ss small input However, due to the speaker
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
Av = −gm (RC || rO )
Rin = rπ || R1 || R2
Rout = RC || rO
EE105 Fall 2007
Lecture 8, Slide 21
Prof. Liu, UC Berkeley
CE Stage with Robust Biasing VA = ∞
(V A = ∞ )
− RC
Av =
1
+ RE
gm
Rin = [rπ + (β + 1) RE ] || R1 || R2
Rout = RC
EE105 Fall 2007
Lecture 8, Slide 22
Prof. Liu, UC Berkeley
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.
(V A = ∞ )
Av = − g m R C
R ini = rπ || R1 || R 2
R out = R C
EE105 Fall 2007
Lecture 8, Slide 23
Prof. Liu, UC Berkeley
Complete CE Stage
Av =
EE105 Fall 2007
− RC || RL
R1 || R2
⋅
R || R || R
1
+ RE + s 1 2 R1 || R2 + Rs
gm
β +1
Lecture 8, Slide 24
Prof. Liu, UC Berkeley
Summary of CE Concepts
EE105 Fall 2007
Lecture 8, Slide 25
Prof. Liu, UC Berkeley
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