# Lecture 23 ANNOUNCEMENTS

```Lecture 23
ANNOUNCEMENTS
6
44
• Midterm #2 results (undergrad. scores only):
• N=73; mean=63; median=63.5; std.dev.=8.42
• You may pick up your exam during any TA office hour.
• The list of misunderstood/forgotten points has been updated.
OUTLINE
• BJT Differential Amplifiers (cont’d)
– Cascode differential amplifiers
– Common-mode rejection
– Differential pair with active load
EE105 Fall 2007
Lecture 23, Slide 1
Prof. Liu, UC Berkeley
21
Cascode Differential Pair
Rout  [1  g m3 (rO1 || r 3 )]rO 3  rO1 || r 3
Rout  g m3 rO1 || r 3 rO 3  rO1 || r 3
Half circuit for ac analysis
Av   g m1Rout   g m1g m3 rO1 || r 3 rO3  rO1 || r 3 
EE105 Fall 2007
Lecture 23, Slide 2
Prof. Liu, UC Berkeley
Telescopic Cascode Differential Pair
Half circuit for ac analysis
Av   g m1 g m3 rO3 rO1 || r 3  || g m5 rO5 (rO7 || r 5 )
EE105 Fall 2007
Lecture 23, Slide 3
Prof. Liu, UC Berkeley
Example

R1 
R

Rop  1  g m5  rO 7 || r 5 ||  rO 5  rO 7 || r 5 || 1
2 
2


Av   g m1 g m3rO 3 (rO1 || r 3 ) || Rop 
Half circuit for ac analysis
EE105 Fall 2007
Lecture 23, Slide 4
Prof. Liu, UC Berkeley
Effect of Finite Tail Impedance
• If the tail current source is not ideal, then when an input
common-mode voltage is applied, the currents in Q1 and Q2
and hence the output common-mode voltage will change.
Vout,CM
Vin,CM
EE105 Fall 2007

RC / 2
1
 REE
2gm
Lecture 23, Slide 5

RC
1
 2 REE
gm
Prof. Liu, UC Berkeley
Effect of Input CM Noise
Ideal Tail Current
• There is no effect of the input CM noise at the output.
EE105 Fall 2007
Lecture 23, Slide 6
Prof. Liu, UC Berkeley
Effect of Input CM Noise
Non-Ideal Tail Current
• The single-ended outputs are corrupted by the input CM noise.
EE105 Fall 2007
Lecture 23, Slide 7
Prof. Liu, UC Berkeley
Comparison
Ideal Tail Current
Non-Ideal Tail Current
• The differential output
voltage signal is the same
for both cases.
 For small input CM
noise, the differential
pair is not affected.
EE105 Fall 2007
Lecture 23, Slide 8
Prof. Liu, UC Berkeley
CM to DM Conversion; gain ACM-DM
• If finite tail impedance and asymmetry (e.g. in load resistance)
are both present, then the differential output signal will
contain a portion of the input common-mode signal.
VCM  VBE  2I C REE 
 I C 
I C
 2I C REE
gm
VCM
1
 2 REE
gm
Vout1  I C RC
Vout 2  I C RC  RC 
Vout  Vout1  Vout 2  I C RC
Vout
RC

VCM 1 / g m   2 REE
EE105 Fall 2007
Lecture 23, Slide 9
Prof. Liu, UC Berkeley
Example
ACM  DM 
EE105 Fall 2007
R C
1
 2[1  g m3 ( R1 || r 3 )]rO 3  R1 || r 3 
g m1
Lecture 23, Slide 10
Prof. Liu, UC Berkeley
Common-Mode Rejection Ratio
• CMRR is the ratio of the wanted amplified differential input
signal to the unwanted converted input common-mode noise
that appears at the output.
CMRR 
EE105 Fall 2007
Lecture 23, Slide 11
ACM  DM
Prof. Liu, UC Berkeley
Differential to Single-Ended Conversion
• Many circuits require a differential to single-ended conversion.
• This topology is not very good; its most critical drawback is
supply noise corruption, since no common-mode cancellation
mechanism exists. Also, we lose half of the voltage signal.
EE105 Fall 2007
Lecture 23, Slide 12
Prof. Liu, UC Berkeley
… A Better Alternative
• This circuit topology performs differential to single-ended
conversion with no loss of gain.

vout
 g m ro, NPN ro, PNP
vin1  vin2
EE105 Fall 2007
Lecture 23, Slide 13
Prof. Liu, UC Berkeley

• With a current mirror as the load, the signal current produced
by Q1 can be replicated onto Q4.
• This type of load is different from the conventional “static
EE105 Fall 2007
Lecture 23, Slide 14
Prof. Liu, UC Berkeley
• The input differential pair decreases the current drawn from
RL by I, and the active load pushes an extra I into RL by
current mirror action; these effects enhance each other.
EE105 Fall 2007
Lecture 23, Slide 15
Prof. Liu, UC Berkeley