IEEE Solid-States Circuits Magazine - Summer 2021 - 6

THE ANALOG MIND
Behzad Razavi
M
The Design of a Low-Voltage Bandgap Reference
Most integrated circuits incorporate
bandgap references (often simply
called bandgaps) to define certain dc
voltages or currents that serve various
building blocks. In this article, we
introduce a step-by-step procedure
for the design of low-voltage bandgaps.
As presented in Figure 1, a typical
power-management environment
employs a low-dropout (LDO) circuit
that, from a global supply of 1.2 V,
generates a moderately regulated
voltage around 1 V. This voltage acts
as a local supply for the bandgap circuit
and some other building blocks.
It is desirable for the bandgap to provide
substantial supply rejection to
minimize corruption in its output due
to the electronic noise produced by
the LDO and the transient perturbations
caused by the switching activities
within the other building blocks.
We target the following specifications:
■
output voltage = 0.5 V
■ output voltage variation 1 5 mV
from 0Cc to 100Cc
■ supply rejection 2 40 dB
■ power consumption 1 1 mW
■ supply voltage
=15 %.V!
We design the circuit in 28-nm
CMOS technology. The reader
is
referred to [1]-[12] for background
information.
Basic Operation
We wish to generate a voltage that
is nominally independent of the
Digital Object Identifier 10.1109/MSSC.2021.3088963
Date of current version: 25 August 2021
6
Q ,2
VTln =+ (2)
I
I
where IS1
S
D
1
1
VTln
and IS2
I
I
S
D
2
2
|| ,
IR
D21
ter saturation currents of Q1
respectively. Viewing Q1
21
=
||
SUMMER 2021
IEEE SOLID-STATE CIRCUITS MAGAZINE
denote the emitand
unit
and Q2 as n units in parallel, we
have InISS and
IR ln ,Vn21 =
DT
(3)
The key to the circuit's low-voltage
operation is that Vout
as a VV .
T .
arbitrarily small even though
||
BE +17 12V at
T 25 C=
c
.
Design Issues
The topology of Figure 2(c) entails several
issues. First, noting that the TC of
can be
Hence,
1.2 V
1 V
LDO
Bandgap
Reference
FIGURE 1: A typical power-management
environment.
temperature. This can be accomplished
by summing two voltages
that have opposite temperature coefficients
(TCs), as practiced in [1], [3],
and [11]. Alternatively, we can first
sum two currents of opposite TCs
and then allow the result to flow
through a resistor [9]. We pursue the
latter here.
The bandgap core is typically
realized as illustrated in Figure 2(a),
where the emitter areas of Q1
Q2 differ by a factor of n, and amplifier
A1 adjusts the gate voltage of
M1 and M2
and
to equalize VX
We thus obtain
VV || .
BE12 IRD21BE
=+
(1)
and V .Y
where M1
and M2
identical. The voltage across R1
are assumed to be
is
therefore proportional to the absolute
temperature (PTAT) and so are
the drain currents of M1
R1 has a zero TC.
It is possible to make ID1 and ID2
independent of the temperature by
attaching two resistors from X and Y
to the ground [see Figure 2(b)] [9]. Let
us formulate the circuit's behavior,
assuming that
RR .23
T
= SinceVV ,XY
.
(1) still holds, and the current through
R1
is still equal to () ./ln
we have
|| ||
DD
12
Vn R1 Summing
this current and that through
R ,3
II Vn VBE1
R13
== +
=+
31
3
RR
1 R Vn V
Tln ||
R
BE1
(4)
cm (5)
Tln || .
The two terms on the right-hand
side of (5) represent currents with
opposite TCs. For ||ID2
of zero, we select ()/
be approximately V17 T
RR ln
to have a TC
31 VnT
to
[12]. Now, as
depicted in Figure 2(c), this current
is copied and applied to a resistor to
yield a nominally constant output
voltage [9],
V cm (6)
Tln || .
out=+ BE1
R
R
R
L R Vn V
31
3
and M2 if
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