Lecture 12
ANNOUNCEMENTS
• Review session: 3-5PM Friday (10/5) in 306 Soda (HP Auditorium)
• Midterm #1 (Thursday 10/11, 3:30PM-5:00PM) location:
• 106 Stanley Hall: Students with last names starting with A-L
• 306 Soda Hall: Students with last names starting with M-Z
OUTLINE
• Cascode Stage (cont’d)
– supplementary remarks
• Current Mirrors
Reading: Chapter 9.2
EE105 Fall 2007
Lecture 12, Slide 1
Prof. Liu, UC Berkeley
Review: Cascode Stage Rout
• The impedance seen looking into the collector can be boosted
significantly by using a BJT for emitter degeneration, with a
relatively small reduction in headroom.
Rout  [1  g m (rO 2 || r 1 )]rO1  rO 2 || r 1
Rout  g m1rO1 rO 2 || r 1 
EE105 Fall 2007
Lecture 12, Slide 2
Prof. Liu, UC Berkeley
Another View of a Cascode Stage
• Instead of considering a cascode as Q2 degenerating
Q1, we can also think of it as Q1 stacked on top of Q2
(current source) to boost Q2’s output impedance.
EE105 Fall 2007
Lecture 12, Slide 3
Prof. Liu, UC Berkeley
Temperature and Supply-Voltage
Dependence of Bias Current
• Circuits should be designed to operate properly over
a range of supply voltages and temperatures.
• For the biasing scheme shown below, I1 depends on
the temperature as well as the supply voltage, since
VT and IS depend on temperature.
I1  I S e
VBE / VT
VBE
EE105 Fall 2007
R2

VCC
R1  R2
Lecture 12, Slide 4
Prof. Liu, UC Berkeley
Concept of a Current Mirror
• Circuit designs to provide a supply- and temperatureindependent current exist, but require many
transistors to implement.
 “golden current source”
• A current mirror is used to replicate the current from
a “golden current source” to other locations.
EE105 Fall 2007
Lecture 12, Slide 5
Prof. Liu, UC Berkeley
Current Mirror Circuitry
• Diode-connected QREF produces an output voltage VX that
forces Icopy1 to be equal to IREF, if Q1 is identical to QREF.
Current mirror concept
Generation of required VBE
I copy1 
EE105 Fall 2007
I S ,1
I S , REF
Current Mirror Circuitry
 I copy1 
 I REF 
  VT ln 

VX  VT ln 



I
I
S
,
1
S
,
REF




I REF
Lecture 12, Slide 6
Prof. Liu, UC Berkeley
Bad Current Mirror Example 1
• If the collector and base of QREF are not shorted
together, there will not be a path for the base
currents to flow, so that Icopy is zero.
EE105 Fall 2007
Lecture 12, Slide 7
Prof. Liu, UC Berkeley
Bad Current Mirror Example 2
• Although it provides a path for base currents to flow,
this biasing approach is no better than a resistive
voltage divider.
EE105 Fall 2007
Lecture 12, Slide 8
Prof. Liu, UC Berkeley
Multiple Copies of IREF
• Multiple copies of IREF can be generated at different
locations by applying the current mirror concept to
multiple transistors.
I copy , j 
EE105 Fall 2007
IS, j
I S , REF
Lecture 12, Slide 9
I REF
Prof. Liu, UC Berkeley
Current Scaling
• By scaling the emitter area of Qj by a factor of n with
respect to the emitter area of QREF, Icopy,j is scaled by a
factor of n with respect to IREF.
– This is equivalent to placing n unit-sized transistors in parallel.
I copy , j  nI REF
EE105 Fall 2007
Lecture 12, Slide 10
Prof. Liu, UC Berkeley
Example: Scaled Currents
EE105 Fall 2007
Lecture 12, Slide 11
Prof. Liu, UC Berkeley
Fractional Scaling
• A fraction of IREF can be created in Q1 by scaling up
the emitter area of QREF.
I REF
 VX
 3I S exp 
 VT



I copy
I copy
EE105 Fall 2007
 VX
 I S exp 
 VT
1
 I REF
3
Lecture 12, Slide 12
Prof. Liu, UC Berkeley



Example: Different Mirroring Ratios
• Using the concept of current scaling and fractional
scaling, Icopy1 = 0.05mA and Icopy2 = 0.5mA, derived
from a single 0.2mA reference current source (IREF).
EE105 Fall 2007
Lecture 12, Slide 13
Prof. Liu, UC Berkeley
Effect of Base Currents
I REF  I C , REF 
I C , REF 
I copy
n

I copy

I copy
n
I copy
nI REF

1
1  n  1

EE105 Fall 2007
Lecture 12, Slide 14
Prof. Liu, UC Berkeley
Improved Mirroring Accuracy
• Use QF (rather than IREF) to supply the base currents of
QREF and Q1, reduce the mirroring error by a factor of .
I REF  I B , F  I C , REF
IC ,F  I E ,F 
I C , REF 
I B,F
I copy
n
I copy
n

I copy

I copy  1 
 2   1
 n 
I copy
nI REF

1
1  2 n  1

EE105 Fall 2007
Lecture 12, Slide 15
Prof. Liu, UC Berkeley
Different Mirroring Ratio Accuracy
I REF  I B , F  4 I C , REF
IC ,F 
I copy1


I copy2

4
I B,F 
I copy1
I C , REF

15I copy1
2
I REF

15
4 2

I C , REF  I copy1
I copy 2
10I REF

15
4 2

EE105 Fall 2007
Lecture 12, Slide 16
Prof. Liu, UC Berkeley
PNP Current Mirror
• A PNP BJT current mirror can be used as a currentsource load for an NPN BJT amplifier stage.
EE105 Fall 2007
Lecture 12, Slide 17
Prof. Liu, UC Berkeley
Generation of IREF for a
PNP-BJT Current Mirror
• Neglecting base currents, the currents flowing
through QM and QREF2 are the same.
EE105 Fall 2007
Lecture 12, Slide 18
Prof. Liu, UC Berkeley
Current Mirror with Discrete BJTs
• If QREF and Q1 are discrete NPN BJTs, IREF and Icopy1 can
differ dramatically, due to IS mismatch.
EE105 Fall 2007
Lecture 12, Slide 19
Prof. Liu, UC Berkeley