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cur mir 2
PROBLEM DESCRIPTION
Design a cascode current mirror with the following requirements:
(a) Transistor at the output stage must operate in the active
region for values of output voltage to within 0.2 V of ground,
(b) the output current must be 50 A, and (c) the output
currentchange less than 0.02 % for a 1 V change in the output
voltage.
SOLUTION
Theory
The real current mirror suffers from various non-idealities. For
example, The gain of current mirror is never independent of
the input frequency. The following are few of low frequency
factors causing non-idealities.
The output current change with change in the voltage a the
output terminal. This effect is represented by the small-signal
output resistance of current mirror. It is given that the output
current changes up to 0.02% for a 1 V change in the output
voltage. So, the small signal output resistance, Ro = VoIo
= 10.0002 Io . This output resistance affects the performance
ofmany circuits that use current mirror. Higher the output
resistance of a current mirror, lower is the dependence of the
output current on the output voltage. Therefore, high output
resistance is desirable.
The difference between input current and output current of
current mirror is the gain error. There are two parts of gain
error (a) systematic gain error, and (b) random gain error. The
systematic gain error arises even when all matched elements
are matched. The random gain error is caused by the unintended
mismatches between matched elements.
When input current source is connected to the input terminal of
a current mirror, it creates a voltage drop VIN. Thisvoltage drop
reduces the voltage available across the input current source. To
reduce VIN, current mirrors sometimes havemore than one input
terminal. Cascode current mirror have high output resistance and
some provisions are incorporated
to make it high-swing cascode current mirror.
There is minimum output voltage VOU T(min) that allows the
output devices to operate in the active region. Aim is tominimizes
VOU T(min) to have wider range of output voltages for which the
current-mirror output resistance is constant.
Therefore, minimum systematic gain error (), higher output
resistance (Ro), minimum input voltage drop across the inputdevices
(VIN) and minimizing minimum output voltage (VOU T(min)) are the
important factors to be considered while designinga current
mirror.
In practice, all transistors except M4 are identical and(W/L)4
< 14(W/L)is selected for two main reasons. First, the output
transistorM1 should operate slightly above Vov1 by a few
hundreds of millivolts to realize high incremental output
resistance.Second, body effect reduces the drain-source voltage on
M1.
VDS1 = VGS3+ VGS4 VGS2 VGS5Since source body voltage ofM5 is
higher than that ofM4, Vt5 > Vt4. Similarly, source-body voltage
ofM2 is higher thanthat ofM3, Vt2 > Vt3.
Advantages of MOS Cascode Current Mirror
Cascode configuration achieves a very high output resistance.
Therefore, the use of cascodes for high performance current
mirrors is natural. The small-signal output resistance of a
cascode current mirror is given by the following expression
Ro= ro1+ ro2[1 + (gm+ gmb)ro1]
wherero1 andro2 are the output resistance of MOS transistors in
the output stage. Bipolar cascode current mirror cannot realize an
output resistance larger than 0ro/2 because 0 is finite and
nonzero
small-signal base current flows in the cascode transistor. In
contrast, the MOS cascode is capable of realizing arbitrarily
high output resistance by increasing the number of stacked
cascode devices because 0
for MOS transistors.
However, the MOS substrate leakage current can create a
resistive shunt to ground from the output node, which can
dominate the output resistance for VOU T > VOU T(min).
Computations
The output voltage 0.2 V when both transistorsM1 andM2 operate
in active (saturation) region. Therefore Vov1 = Vov2 =0.1V
NMOS device paramter,
kn= nCox= n 3.9 8.864 1014 Fcm 1tox = 450 3.9 8.864 1014 180108
= 194.5A/V2
The output current,
IOU T = 50 106 = 194.5106
2 (W/Leff)(VGS2 VT)2
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