IEEE Solid-States Circuits Magazine - Summer 2021 - 18

want a microamp, and supplies were
30 V in those days, so you'd need a
30-MΩ resistor. That won't work.
I t probably wouldn't even fit in
the package.
A popular solution to this dilemma
came from that Granddaddy of IC
design, the irascible Bob Widlar.
He invented the topology shown in
Figure 3(a), and it bears his name
to this day. The idea was to degenerate
the output of a current mirror,
so the gain was much less than
one. Now you could run a much
higher current in your supply resistor
and still get a microamp output.
To modern eyes, this looks hideously
wasteful. Basically, you're
throwing away most of the current.
But in those days, it was no biggie
because everybody was still getting
over vacuum tubes that would
keep the room warm. Power was
not an issue.
The Widlar mirror still had one
shortcoming, though. Putting the
degeneration in the output part of
the mirror meant that the degeneration
resistor was running at a
tiny current. To get a mirror ratio
of 1,000:1 using bipolar transistors,
you need to drop 180 mV in the
degeneration resistor. If the output
current was to be 1 µA,
then the
resistor had to be 180 kΩ. That was
still pretty big in ancient technology.
There was another problem. Not
only was the degeneration resistor
still substantial, but the input current
was still supplied from a resistor
to the positive supply, and thus
yielded a current proportional to the
supply voltage. That was also suboptimal.
The operating bias and, hence,
the performance would depend on
the supplies you used, and,
of course, it was a great way
to get supply noise into the
system. What designers
really wanted to use was
a parasitic junction fieldeffect
transistor (JFET)
that could be built on the
epi layer and pinched
off to provide a supplyindependent
current.
Unfortunately, such JFETs were too
process sensitive, even for the relaxed
manufacturing standards of the day.
About
this time, a young Hitachi
engineer named Minoru Nagata
(see " A Mirror That Reflects Well on
Its Inventor " ), fresh from a stint at
Stanford's fledgling IC Laboratory,
came up with a solution [1], [2]. His
idea was to put the limiting resistor
on the input side of the mirror as
shown in Figure 3(b). The immediate
advantage is that, compared to the
Widlar mirror, the resistor is on the
high-current, input side of the mirror,
and so substantially less resistance
is needed for the same voltage
drop. Yay.
However, Nagata was actually in
You may swear
that you've never
seen anything
so stupid in
your entire
life, but I'll bet
you have-and
you've probably
even used it!
pursuit of something else. While the
primary objective of the Widlar mirror
was to attenuate the bias current
without huge resistors or ridiculous
transistor size ratios, it also had the
property that it could limit the current
somewhat. That's
a very good thing if
your bias current is
derived from the supply
voltage. The Nagata
mirror has this property
Figure 3(c),
in spades.
As you can see from
the output
increases with input only
up to a specific bias, and
then it declines. This happens because
the drop in the resistor is linear with
input current, but the gate-to-source
voltage (Vgs) of M1
is not. It works if
the transistor is in weak or strong
inversion but will not work if the transistor
goes into the triode region or
is driven into velocity saturation. If
either of those two conditions exists,
the Vgs also becomes a linear function
of current, and the fun's over.
The peak in the output current
of the Nagata mirror means that the
derivative of the output current (the
small-signal current gain) is zero at
the peak. Therefore, when biased at
Iin
Iin
Iout
R
M2
M1
R
M1
M2
Iout
20
15
10
5
Widlar
Current Mirror
(a)
Nagata
Current Mirror
(b)
Widlar
Nagata
020406080 100 120 140
Input Current , Iin (µA)
(c)
FIGURE 3: Two nonlinear current mirrors: (a) Widlar and (b) Nagata. (c) The examples shown emphasize the current-regulating characteristics,
not the attenuation potential of the mirrors.
18 SUMMER 2021
IEEE SOLID-STATE CIRCUITS MAGAZINE
Output Current, Iout (µA)

IEEE Solid-States Circuits Magazine - Summer 2021

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