Stanford Research Systems SR844, User Manual

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SR844 Basics 2-25
SR844 RF Lock-In Amplifier
Intrinsic (Random) Noise Sources
Random noise finds its way into experiments in a variety of ways. Good experimental design
can reduce these noise sources and improve the measurement stability and accuracy.
There are a variety of intrinsic noise sources which are present in all electronic signals.
These sources are physical in origin.
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
V
NOISE
(rms) =
√
(4kTR
∆
f)
(2-20)
where k is Boltzmann’s constant (1.38 x10
–23
JK
–1
), T is the absolute temperature (typically
300 K), R is the resistance in ohms and
∆
f is the measurement bandwidth in Hz.
The amount of noise measured by the lock-in is determined by the measurement bandwidth.
In a lock-in the equivalent noise bandwidth (ENBW) of the time constant filters sets the
measurement bandwidth. The ENBW is determined by the time constant and slope as shown
previously.
The Johnson noise of a 50
Ω
input on the SR844 is simply
V
NOISE
(rms) = 0.91 nV
× √
(ENBW)
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. The
shot noise or current noise is given by
I
NOISE
(rms) =
√
(2qI
RMS
∆
f)
(2-21)
where q is the electron charge (1.6
×
10
–19
C), I
RMS
is the rms current and
∆
f is the
measurement bandwidth.
1/f Noise
Every 68
Ω
resistor, no matter what it is made of, has the same Johnson noise. However there
is additional noise, aside from the Johnson noise, which arises from resistance fluctuations
due to the current flowing through the resistor. This noise has spectral power density
inversely proportional to the frequency, hence the name. The amount of 1/f noise is
dependent on the resistor material and even manufacturing details. For carbon composition
resistors this noise is typically 0.3
µ
V/V per decade of frequency, while for leaded metal film
resistors 0.01
µ
V/V is more typical. These numbers are for low resistance values 10–1000
Ω
, the
µ
V/V numbers are worse for large resistances.
Total Noise
All of these noise sources are incoherent. The total random noise is the square root of the
sum of the squares of all the incoherent noise sources.