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NOISE ANALYSIS FOR HIGH SPEED OP AMPS
by Michael Steffes
As system bandwidths have increased, an accurate estimate
of the noise contribution for each element in the signal
channel has become increasingly important. Many design-
ers are not, however, particularly comfortable with the
calculations required to predict the total noise for an op
amp, or in the conversions between the different descrip-
tions of noise. Considerable inconsistency between manu-
facturers in describing noise and, in some cases, incomplete
specifications, have contributed to this confusion. A thor-
ough description of the op amp noise model will be devel-
oped here with a detailed discussion of the key differences
between current and voltage feedback amplifiers. The con-
versions between several different measures for noise used
in the industry will also be described. Broadband effects will
be covered for both low frequencies (the 1/f region) and high
frequencies (noise power bandwidth).
FUNDAMENTALS OF NOISE ANALYSIS
Random electrical noise (either a current or a voltage) is
present in almost every type of component used in a circuit.
This noise may be considered as either a frequency domain
phenomena or something that occurs over time. The most
common models approach noise from the frequency domain
first then convert to the time domain using the shape of the
noise density curve combined with a noise power bandwidth
analysis. This is the approach that will be used here.
Another useful view of op amp noise is to consider the input
voltage and current noises to be the time varying component
of the input offset voltage and bias currents respectively.
Working from the frequency domain to the time domain, as
will be done here, develops the required tools to predict the
amplitude of this time varying component. Only the random
electrical noise generated by the components themselves
will be considered. Other sources of 鈥渘oise鈥?that will
not
be
considered here, (but are nevertheless of interest to the
system designer), include conducted noise through the power
supplies that appear at the output due to finite PSRR, various
sources of radiated emission pickup (EMI), micro-phonic
effects due to system vibration, and high narrowband noise
that is in fact a parasitic oscillation.
The starting point for a frequency domain analysis of noise
is the noise density. This is the noise power normalized to
1Hz bandwidth (at a particular center frequency) and is
sometimes called the 鈥渟pot鈥?noise. 鈥淲hite鈥?noise has a flat
(or constant) noise power over frequency. Most amplifiers
and resistors show a flat noise region that extends over many
frequency decades. Most, however, also show an increasing
漏
noise power density at low frequencies. This is often called
the 1/f region since the noise power density will often
increase as the inverse of frequency. 鈥淧opcorn鈥?noise is a
random long term shift in voltage or current (that sounds like
popcorn if fed into an audio speaker). This phenomena
doesn鈥檛 fit well into a frequency domain description and is
best observed over time.
To analyze noise in the frequency domain, equivalent noise
voltage or current generators are introduced into the circuit
that represent the noise density over frequency for that
element. These voltages or currents are the square root of the
noise power densities. We work with voltages and current in
order to avail ourselves of standard circuit analysis tech-
niques. One key caveat to using noise voltages and currents
is that they do not add algebraically. Each individual noise
source has a random phase to any other (with the exception
of correlated sources). This means that, although we can use
superposition to get the contribution of each noise term to a
particular point in the circuit, the voltages or currents them-
selves cannot simply be added at that point. It is the powers
that are added to get to a total noise power.
OP AMP NOISE MODEL
Figure 1 shows the analysis circuit that will act as a starting
point for the subsequent noise analysis. This schematic
includes the three equivalent input noise terms for the op
amp and the three resistor noise terms that must always be
considered for a complete op amp noise analysis. Any
particular op amp application circuit can typically be re-
duced to that of Figure 1 by shorting any input voltage
sources and/or opening any input current sources that might
be driving the circuit and reducing the remaining imped-
ances to the three elements shown in Figure 1. Reactive
elements (capacitors, inductors, transformers) are normally
considered to be noiseless. They can, however, strongly
influence the frequency response for the noise generators in
a circuit. Examples of this will be shown later. At this point
consider the elements around the op amp to be purely
resistive. Remember that the Johnson noise of the resistor
may be represented as either a current or a voltage. The
analysis circuit of Figure 1 uses both forms (current noise for
R
G
and voltage noise for R
F
) to simplify later computations.
Most of the discrepancies between different noise analysis
come from neglecting as insignificant some of the noise
sources in Figure 1. In general, there will in fact be a
dominant noise source for a particular op amp in a particular
application circuit. However, to maintain the required gen-
AB-103
Printed in U.S.A. October, 1996
1996 Burr-Brown Corporation
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