IEEE Solid-State Circuits Magazine - Summer 2016 - 11

current, we observe that 2Vout /2T can
be zero but Vout is still around 1.25 V.
How do we create a fraction of this
value without first generating such
a high voltage? Let us tie a resistor
from the output node to ground [Figure 7(b)], surmising that the resulting
voltage division creates a zero-TC
output with a smaller magnitude.
Since (Vout - VBE3) /R 4 + Vout /R 5 = I 1,
we have

poor supply rejection, especially due
First, a CMOS op amp directly drivto that of the op amp, 3) if driving a
ing the feedback resistors must deal
heavy load capacitance
with gain-power-stabilat the output, the circuit
ity trade-offs. Second,
can become unstable, esit is difficult to realIn this article,
pecially in cases where
ize bipolar transistors
we study the
A 1 itself contains more
whose collectors are not
principles of
than one stage, and
grounded; the vertical
bandgap circuit
4) if the op amp begins
structure available in
design.
with a high output level
typical CMOS processes
at power-up, the two
utilizes the p-substrate
branches may remain off
as the collector. Third,
indefinitely. The remedies include the
the op amp offset is amplified by a
use of large MOS transistors to address
factor of 1 + R 2 /R 3 as it appears in
Vout , causing error and temperature
the first issue, the choice of an op
drift. For example, n = 10 translates
amp topology for high supply rejecto 1 + R 2 /R 3 . 7.5.
tion for the second issue, and adding
To address these issues, we first
a start-up circuit to deal with the third.
recognize that resistors R 1 and R 2
As shown in Figure 6(b), a weak adin Figure 5 provide equal bias curditional branch creates a large initial
rents, a function that can be realimbalance at the input of the op amp,
ized by controlled current sources.
forcing its output to go low. After
In the spirit of Figure 3, we arrive
the circuit turns on and reaches
at the topology depicted in Figthe desired operating point, M 3 and M 4
turn off.
ure 6(a). If M 1 and M 2 are identical, then VBE1 - VBE2 = VT ln n and
Vout = VBE2 + (1 + R 2 /R 3) VT ln n. The
Low-Voltage Bandgap References
The basic bandgap expression,
bipolar transistors are implemented
VBE + 17.2VT , takes on a value of about
as vertical pnp structures. As with
1.25 V at T = 300 K, defying direct
Figure 3, resistor Rl2 = R 2 can be
inserted to ensure VDS1 = VDS2, supimplementation in today's low-voltage
pressing current mismatch due to
technologies. We describe one lowchannel-length modulation.
voltage example and refer the reader
The op amp offset is still amplito [10] and [11] for others.
fied by a factor of 1 + R 2 /R 3 . This
For a low-voltage bandgap reference
issue is ameliorated by choosing a
to have a zero TC, it must produce an
large n, say, 20-30, and/or establishoutput of the form a (VBE + 17.2VT ),
where a 1 1 is a scaling factor. For
ing a nonunity ratio between I E1 and
I E2. Specifically, if (W/L) 1 = m (W/L) 2,
example, beginning with the branch
the bipolar transistor current denshown in Figure 7(a) and writing
Vout = VBE3 + R 4 I 1, where I 1 is a PTAT
sities differ by another factor of m,
leading to

Vout =

R5
(R I + VBE3),
R5 + R4 4 1

concluding that the output can be
arbitrarily small and have a zero TC.
We now derive the PTAT current, I 1,
from the circuit of Figure 6(a) and
arrive at the topology shown in Figure 7(c) [12]. With a voltage drop of
VT ln n across R 3, we have
Vout =

R5
(V + R 4 V ln n), (13)
R 5 + R 4 BE3 R 3 T

where the MOSFETs are assum ed
identical.

VDD
M1
R2′

M2
Vout

A1
- +

R2

Q1

Q2

A

VDD

Y
R3

X

M3

nA

M4
X

(a)

(b)

Figure 6: (a) A CMoS bandgap circuit and
(b) a start-up branch.

Vout = VBE2 + (1 + R 2 ) VT ln (n ·m) . (11)
R3
For example, with n = 20 and
m = 5, we require 1 + R 2 /R 3 . 3.7.
This means that the designer must
still pay close attention to the op
amp's offset.
While simple and robust, the bandgap reference in Figure 6(a) suffers
from several undesirable effects:
1)  the output tends to contain substantial flicker (and thermal) noise contribution from the op amp and M 1 and
M 2, 2) the circuit potentially exhibits

(12)

VDD
VDD
I1

VDD

PTAT

I1

Vout

Q3
(a)

PTAT

R4

R4

Q3
(b)

M1
- +

Vout
R5

M3

M2

A1

Vout
R4

R3
Q1

A

Q2

nA

Q3

R5

(c)

Figure 7: (a) A single branch generating a ti voltage, (b) the use of voltage division to lower
the output, and (c) a complete low-voltage reference.

IEEE SOLID-STATE CIRCUITS MAGAZINE

Su m m e r 2 0 16

11



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