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Amplifier Noise Sources
Input noise
The input noise of the SR570 current amplifier
varies depending upon the sensitivity setting. On
the 1 mA/V setting, the noise is dominated by
the voltage noise of the op amps in the circuit.
Typically, this figure is about 100 nV/√Hz,
which, when divided by the 1 kW feedback
resistor, gives a current noise of 100 pA/√Hz.
On the other hand, the noise on the higher
sensitivity ranges is dominated by the Johnson
noise of the feedback resistor. On the 1 nA/V
scale, the 1 GW resistor alone produces an input
current noise of 4 pA/√Hz, while the 100
nV/√Hz of amplifier voltage noise gives an input
current noise of about 0.1 fA/√Hz. Therefore, all
the possible sources of noise must be considered
in order to calculate a noise figure for a current
amplifier.
Noise Sources
There are two types of noise we have to worry
about in laboratory situations, intrinsic noise and
external noise. Intrinsic noise sources like
Johnson noise and shot noise are inherent to all
physical processes. Though we cannot get rid of
intrinsic noise sources, by being aware of their
nature their effects can be minimized. External
noise sources are those found in the
environment, such as power line noise and
broadcast stations. The effect of these noise
sources can be minimized by careful attention to
grounding, shielding and other aspects of
experimental design. We will first discuss some
sources of intrinsic noise.
Johnson noise
Every resistor generates a noise voltage across
its terminals due to thermal fluctuations in the
electron density within the resistor itself. These
fluctuations give rise to an open-circuit noise
voltage:
APPENDIX A
where k=Boltzmann's constant (1.38x10
is the temperature in Kelvin (typically 300 K), R is
the resistance in Ohms, and Df is the bandwidth of
the measurement in Hz. Using this formula, the
Johnson current noise is given by:
I
noise
For example, a 100 MW resistor will produce a
Johnson current noise of about 13 fA/√Hz. It is
important to remember that Johnson voltage noise is
proportional to the square root of the measurement
bandwidth. Therefore, using signal filters in a
measurement will affect the actual value of noise
measured in the circuit.
Shot noise
Electric current has noise due to the finite nature of
the charge carriers. There is always some non-
uniformity in the electron flow which generates
noise in the current. This noise is called shot noise.
This can appear as voltage noise when current is
passed through a resistor, or as noise in a current
measurement. The shot noise, or current noise, is
given by:
where q is the electron charge (1.6x10
I is the RMS AC current or DC current depending
upon the circuit, and Df is the bandwidth.
Shot noise is usually not a problem in typical
measurement setups. For example, a 1 µA current,
measured with a 100 kHz bandwidth, will have only
180 pA of shot noise or 0.02% of the signal
amplitude. For very small currents, shot noise will
be more appreciable. Take, for instance, a 1 pA
current measured with a bandwidth of 100 Hz. The
shot noise will be 6 fA or 0.6% of the signal
amplitude, which might be important.
A-1
V
(rms)
4k TR f
noise
10
(rms)
1. 27x10
R
1/2
I
(rms)
2q I f
noise
1/2
-23
J/°K), T
1/2
A/
Hz
-19
Coulomb),
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