Transcript Lecture 1 - Ilam university

BJT Amplifier
Amplifier topologies
Possible BJT Amplifier Topologies


There are 3 possible ways to apply an input to an
amplifier and 3 possible ways to sense its output.
In practice, only 3 out of the possible 6 input/output
combinations are useful.
Common-Emitter (CE) Topology
Small Signal of CE Amplifier
vout
Av 
vin
Limitation on CE Voltage Gain


Since gm = IC/VT, the CE voltage gain can be written
as a function of VRC , where VRC = VCC - VCE.
VCE should be larger than VBE for the BJT to be
operating in active mode.
I C RC VRC
Av 

VT
VT
Voltage-Gain / Headroom Tradeoff
I/O Impedances of CE Stage

When measuring output impedance, the input port
has to be grounded so that vin = 0.
vX
Rin   r
iX
vX
Rout 
 RC
iX
CE Stage Design Trade-offs
Inclusion of the Early Effect

The Early effect results in reduced voltage gain of
the CE amplifier.
Av   g m ( RC || rO )
Rout  RC || rO
Intrinsic Gain


As RC goes to infinity, the voltage gain approaches its
maximum possible value, gm × rO, which is referred to
as the intrinsic gain.
The intrinsic gain is independent of the bias current:
Av   g m rO
VA
Av 
VT
Current Gain, AI


The current gain is defined as the ratio of current
delivered to the load to current flowing into the input.
For a CE stage, it is equal to .
iout
AI 
iin
AI
CE

Emitter Degeneration


By inserting a resistor in series with the emitter, we
“degenerate” the CE stage.
This topology will decrease the gain of the amplifier but
improve other aspects, such as linearity, and input
impedance.
Small-Signal Analysis

The gain of a degenerated CE stage = the total load
resistance seen at the collector divided by 1/gm plus
the total resistance placed in series with the emitter.
 g m RC
 RC
Av 

1
1  g m RE
 RE
gm
Emitter Degeneration Example 1
Note that the input impedance of Q2 is in parallel with RE.
Av  
RC
1
 RE || r 2
g m1
Emitter Degeneration Example 2
Note that the input impedance of Q2 is in parallel with RC.
RC || r 2
Av  
1
 RE
g m1
Input Impedance of Degenerated CE Stage

With emitter degeneration, the input impedance is
increased from r to r + (+1)RE ― a desirable
effect.
(VA  )
vx  r ix  RE (1   )ix
vx
Rin   r  (   1) RE
ix
Output Impedance of Degenerated CE Stage

Emitter degeneration does not alter the output
impedance, if the Early effect is negligible.
(VA  )
 v

vin  0  v    g m v  RE  v  0
 r

vx
Rout   RC
ix
Degenerated CE Stage as a “Black Box”
(VA  )
iout
vin
 gm
1
1  (r  g m ) RE
iout
gm
Gm 

vin 1  g m RE

If gmRE >> 1, Gm is more
linear.
Degenerated CE Stage with Base Resistance
(VA  )
vout v A vout

.
vin vin v A
vout
 RC

vin r  (   1) RE  RB
Av 
 RC
1
RB
 RE 
gm
 1
Degenerated CE Stage:
Input/Output Impedances

Rin1 is more important in practice, because RB is
often the output impedance of the previous stage.
(VA  )
Rin1  r  (   1) RE
Rin2  RB  r  (   1) RE
Rout  RC
Emitter Degeneration Example 3
 ( RC || R1 )
Av 
1
RB
 R2 
gm
 1
Rin r  (   1) R2  RB
Rout  RC || R1
Output Impedance of Degenerated CE
Stage with VA<∞

Emitter degeneration boosts the output impedance.

This improves the gain of the amplifier and makes the
circuit a better current source.
Rout  1  g m ( RE || r )rO  RE || r
Rout  rO  ( g m rO  1)( RE || r )
Rout  rO 1  g m ( RE || r )
Two Special Cases
Stage with explicit depiction of ro:
1) RE  r : Rout  rO (1  g m r )  rO
2) RE  r : Rout  (1  g m RE )rO
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 || Rout1
Rout1  1  g m ( R2 || r )rO
Rout  1  g m ( R2 || r )rO || R1
Example: Degeneration by Another BJT
Rout  1  g m1 (rO 2 || r 1 )rO1

Called a “cascode”, this circuit offers many
advantages 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
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”) 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
short circuit for AC analysis.
Av   g m ( RC || rO )
Rin  r || RB
Rout  RC || rO
Bad Output Connection

Since the speaker has an inductor with very low DC
resistance, connecting it directly to the amplifier
would ~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 input
impedance, the overall gain drops considerably.
CE Stage with Voltage-Divider Biasing
Av   g m ( RC || rO )
Rin  r || R1 || R2
Rout  RC || rO
CE Stage with Robust Biasing
VA  
(VA  )
 RC
Av 
1
 RE
gm
Rin  r  (   1) RE  || R1 || R2
Rout  RC
Elimination of Emitter
Degeneration for AC Signals

The capacitor C2 shorts out RE at higher frequencies
to eliminate the emitter degeneration.
(VA  )
Av   g m RC
Rin  r || R1 || R2
Rout  RC
Complete CE Stage
Av 
 RC || RL
R1 || R2

R || R || R
1
 RE  s 1 2 R1 || R2  Rs
gm
 1
Summary of CE Concepts