#### Transcript lec12-elec

```Current Mirrors
OUTLINE

Cascode Stage (cont’d)


supplementary remarks
Current Mirrors
Review: Cascode Stage Rout

The impedance seen looking into the collector can be boosted
significantly by using a BJT for emitter degeneration, with a
Rout  [1  g m (rO 2 || r 1 )]rO1  rO 2 || r 1
Rout  g m1rO1 rO 2 || r 1 
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
R2

VCC
R1  R2
Concept of a Current Mirror

Circuit designs to provide a supply- and
temperature-independent 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.
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 
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

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.

Although it provides a path for base currents to flow,
this biasing approach is no better than a resistive
voltage divider.
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 
IS, j
I S , REF
I REF
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
Example: Scaled Currents
Fractional Scaling

I REF
A fraction of IREF can be created in Q1 by scaling up
the emitter area of QREF.
 VX
 3I S exp 
 VT



I copy
I copy
1
 I REF
3
 VX
 I S exp 
 VT



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).
Effect of Base Currents
I REF  I C , REF 
I C , REF 
I copy
n
I copy
nI REF

1
1  n  1

I copy
n

I copy

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
I copy I copy
IC ,F  I E ,F 

n

I C , REF 
I copy
n
I B,F
I copy  1 
 2   1
 n 
I copy
nI REF

1
1  2 n  1

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

PNP Current Mirror

A PNP BJT current mirror can be used as a currentsource load for an NPN BJT amplifier stage.
Generation of IREF for a
PNP-BJT Current Mirror

Neglecting base currents, the currents flowing
through QM and QREF2 are the same.
Current Mirror with Discrete BJTs

If QREF and Q1 are discrete NPN BJTs, IREF and Icopy1
can differ dramatically, due to IS mismatch.
```