IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, VOL. 37, NO. 9, SFPTEMBER 1990
Power Supply Rejection Ratio in
Operational Transconductance Amplifiers
amplifiers is analyzed. An analyzing technique based on cuts in suhcir-
cuits is presented that allows hand calculation of PSRR of any circuit.
In this paper it is shown that the PSRR of the single stage operational
amplifier (OTA) has an order of magnitude better PSRR than the
commonly used Miller OTA. The analyses are compared with hand
calculations and SPICE level-2 simulations on a realized improved
Miller OTA structure.
power supply rejection ratio (PSRR) of operational
HE DESIGN of complex systems with analog, digital,
one chip suffers from large signal variations on the power
supply lines (up to 100 mVpeak [l]) that are introduced by
the digital and the switched-capacitor networks.
Especially in those cases where low-level signals have to
be measured, the use and development of high perfor-
mance amplifiers are necessary. In analog building blocks
and switched-capacitor structures, the main building
blocks are operational transconductance amplifiers
(OTA's). For this reason the performance of such ampli-
fiers must be studied and analyzed as function of the
power supply variations. The power supply rejection ratio
(PSRR) is very often only specified at dc or at very low
frequencies ( f < 1 Hz). In order to reduce the influences
of 50/60 Hz clock-frequencies and high frequency power
supply noise, the performance at frequencies up to the
bandwidth of the system, which is for amplifiers the gain
bandwidth (GBW), must be studied. This is especially
important in aliasing (sampled data) contexts where high
frequency power ~ ~ p p l y noise can be folded back into the
signal band. This effect can drastically decrease the PSRR
performance, as has been demonstrated in switched-
capacitor filters [ll.
The performance of a system influenced by power-
supply variations can be described by the PSRR. In the
next section the definition of the PSRR is described.
From this definition it can be concluded that for ampli-
fiers, the PSRR at high frequencies (f do mini,n, < f < GBW)
can be improved by increasing the GBW of the amplifier.
Therefore, the PSRR can be best normalized to 2. T.
and switched-capacitor building blocks integrated on
Manuscript received August 19. 1987; revised February 6, 1989. This
paper was recommended by Associate Editor C. A. T. Salama.
The authors are with the Department of Electrical Engineering,
Katholieke Universiteit Leuven, 3030 Heverlee. Belgium.
IEEE Log Number 9037126.
Fig. 1. A block diagram of a general electrical circuit.
GBW/s in order to be able to compare different ampli-
fier structures. This normalization results in the parame-
ter l/Ap(sl: i.e., the reciprocal of the power supply gain
(PSR, as distinct from PSRR). Secondly, a technique to
calculate the PSRR is discussed. Using this technique,
several op-amps, such as an OTA and a Miller op-amp,
are analyzed. Finally, an improved two-stage amplifier is
studied and analyzed.
OF THE PSRR
A general electrical circuit as presented in Fig. 1 has an
input, an output, and a power node. Hence it has voltage
transfer functions from any node to any other node. In
many cases, only the transfer function from the input to
the output and from the power node to the output node
are important. If the transfer function of the power node
to the output node is called the power supply gain (Ap),
and the transfer function of the input node to the output
node is called the open-loop transfer function (A), the
PSRR is defined as (in the frequency domain s = j . 01
which is normally given in decibels ( = 20.log(A /Ap)).
By increasing the GBW of an amplifier, A b ) increases
( A h ) = 2..sr.GBW/s for f > fdominant), and as a result the
PSRR increases, too. Thus to compare different amplifier
structures, the PSRR can be best normalized to 2 . 7 ~
GBW/s. From the definition, this results in the parame-
ter l/Ap(s), i.e., the reciprocal of the power supply gain.
In this text this parameter is called the PSR. If both
functions (A(s) and PSRR(s)) are assumed to be first-
order, the PSR at high frequencies is a constant (see Fig.
2). The smaller A,(s) is (or the higher the PSR is), the
better the structure performance is.
The equivalent mathematical equation for the output
node as function of the input and of the power supply
node is described by the superposition of the power
supply gain and the open-loop gain, or uOut = A;u, +
0098-4094/90/0900-1077$01.00 01990 IEEE
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, VOL. 37, NO. 9, SEPTEMBER. 1990
49 5dB+O 5dB
20dB 19dBk.O 5dB
process, this effect can be cancelled if the output stage is
inverted (PMOS transistors M11 and M14 in Fig. 12
become nMOS transistors and the nMOS transistor M13
in Fig. 12 becomes a PMOS transistor). The relation for
the PSRR,v,, is in that case given by (see also (30))
g m 1
and for the PSRR,u,, it becomes (see also (10))
It was found from hand calculations and SPICE simula-
tions that such a structure has a PSR, Udd of more than 20
dB and a PSR,v,, of more than 25 dB.
In large systems, where different structures are inte-
grated on one chip, the PSRR specification of the differ-
ent blocks is very important. Therefore the most used
building block in analog design, the transconductance
amplifier, has been analyzed.
First an analysis technique based on cuts in subcircuits
was presented. By this technique the power supply
transconductances of each network branch can be calcu-
lated. The summation of these power supply transconduc-
tances of each branch results in the total power supply
transconductance. The PSRR is thereby given by the ratio
of the signal transconductance and the power supply
Using the presented technique, different amplifier
structures have been compared on the basis of hand
calculations and SPICE simulations. It has been shown
that the PSRR specifications of a single-stage OTA are
an order of magnitude better than for the widely used
two-stage Miller OTA. Also, the cause of this bad PSRR
specification in the two-stage Miller OTA has been inves-
tigated. It is shown that it is due to a complex feedback
loop in the output stage and not to a signal feedthrough
through a gate-source capacitance and the compensation
capacitance, as is usually suspected.
With these analyses it is shown that the problem in the
two-stage Miller OTA can be solved by inserting an extra
cascode transistor in the circuit. This improved amplifier
has been designed in a 3-pm p-well process. The mea-
surements on PSRR specifications have been compared
with the hand calculations and SPICE simulations. It is
found that the structure has excellent PSRR specifica-
tions, compared with the commonly used Miller amplifier
structure, even at higher frequencies.
K. Halonen and W. Sansen, “Effect of current spikes in power
supply rails on PSRR performances of switched-capacitor filters,”
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in het frequentie-en tijdsdomein,” Masters thesis, Katholieke Uni-
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Michel S. J. Steyaert (S’85-A’89) received the
engineer’s degree in electrical and mechanical
engineering from the Katholieke Universiteit
Leuven, Heverlee, Belgium in 1983 and the
Ph.D. degree in electronics from the Katholieke
Universiteit Leuven in 1987.
From 1983 to 1986 he received an IWNOL
fellowship, which allowed him to work as a
research assistant at the Laboratory ESAT, K.U.
Leuven. In 1987 he was responsible for several
industrial proiects in the field of analog micro-
power circuits,at the Laboratory-ESAT, K.U. Leuven as an TWONL
project-researcher. In 1988, he was a visiting assistant professor at the
University of California, Los Angeles. Since 1989 he has been at the
Laboratory ESAT, K.U. Leuven as an NFWO research associate. His
current research interests are in high frequency analog integrated cir-
cuits for telecommunications.
Willy M. C. Sansen (S’66-M72-SM’86) re-
ceived the engineering degree in electronics
form the Katholieke Universiteit Leuven, Hev-
erlee, Belgium, in 1967 and the Ph.D. degree in
electronics from the University of California,
Berkeley, in 1972.
In 1968 he was employed as an Assistant at
the Katholieke Universiteit Leuven. In 1971 he
was employed as a Teaching Fellow at the Uni-
versity of California. In 1972 he was appointed
by the Belgian National Foundation as a Re-
search Associate at the Laboratory Elektronika, Systemen, Automati-
satie, Technologie, Katholieke Universiteit Leuven, where he has been
Full Professor since 1981. Since 1984 he has been the head of the
Department of Electrical Engineering. His interests are in device model-
ing, design of integrated circuits, and medical electronics and sensors.
Dr. Sansen is a member of the Koninklijke Vlaamse Ingenieurs
Vereniging, the Audio Engineering Society, the Biotelemetry Society,
and Sigma Xi. In September 1969 he received a CRB Fellowship from
the Belgian American Educational Foundation, in 1970 a G.T.E. Fellow-
ship, and in 1978 a NATO Fellowship.