Several sources of noise are observed in the lab:
Technical noise:
- Electro‘static’ (fluorescent lights)
- Magneto‘static’ (ground loops and AC transformers)
- E&M radiation (room lights into PN diodes, sparks)
-Acoustic, thermoelectric, triboelectric……
George Herold, David Van Baak
TeachSpin, Inc. Buffalo NY, 14214
2
Voltage Noise versus Bandwidth
2
1E-11
Y = -15.79566+1.00293 X
1E-12
1k
10k
100k
Fig. 3 Voltage noise versus Bandwidth
l
d dh
Note this log-log plot shows a linear fit with slope
1.003, indicating <Vn2> ~ ∆f consistent with
expectations. Such a fit motivates forming the quotient
<Vn2> / ∆f, with units Volts2/ Hertz, in the graphs below.
Figure 4 shows a test of the claim that Johnson noise
is ‘white’, ie. that the noise density is independent of the
center frequency of the band pass filter.
3.00E-016
Apparatus
Noise from 10k ohm resistor
measured with band pass filter
2.50E-016
+
-
x100
RS
100Ω
1E-16
raw data
fmax = 100kHz
fmax = 33kHz
fmax = 10kHz
fmax = 3.3kHz
Theor
Theory
1E-17
1E-18
O
T = 25 C (298K)
100
1k
10k
100k
1M
Resistance (ohms)
Fig. 5 Voltage noise versus Source Resistance
Note that the amplifier noise can be successfully
subtracted to reveal the Johnson noise generated by a 10 Ω
resistor. For a large source resistance, capacitive effects
reduce the noise content for measurements with higher
maximum frequencies. The points do indeed fall on a line
computed from the textbook value of Boltzmann’s constant
and the ambient temperature.
Figure 6 shows a measurement of the shot noise current,
generated in a silicon photodiode illuminated by an
incandescent light bulb. The photocurrent’s average value
varies over a range of 104, and again the input-stage
amplifier noise can be successfully subtracted to show that
<In2> is proportional to IDC. The corrected points fall on a
line computed from the textbook value of e, the charge of
the electron.
2
1E-22
1.50E-016
1.00E-016
raw data
amp noise
resistor
5.00E-017
0.00E+000
100
1k
10k
100k
Fig. 4 Voltage noise versus Center Frequency
Low side
Filter
1E-15
2.00E-016
Frequency (Hz)
__________
*Rolf Landauer would like us to understand these separate types of fundamental noise as
Johnson Noise versus Source Resistance
10
10k ohm Resistor
raw data
amplifier
1E-13
Effective bandwidth of measurment (Hz)
The signal chain starts in the preamp stage. The
first amplifier is configured appropriately for the type
of measurement, and is followed by a x100 gain
stage. The bandwidth ∆f is defined by adjustable
low-side and high-side filters. There follows a
further ggain stage,
g , adjustable
j
from x10 to x104. An
analog multiplier generates the real-time square of
the filtered and amplified voltage. That square is
time-averaged to yield an output voltage. A model of
the whole chain is
Vin→ GVin→ (GVin)2→ G2<Vin2> = Vout
1E-14
1E-19
100
Fig. 1 An oscilloscope trace of noise
Fig. 1 An oscilloscope trace of noise
Voltage Noise Density (V /Hz.)
Figure 3 shows a test of the claim that Johnson
noise gives an output signal proportional to the
bandwidth ∆f used in the signal chain.
Time average of V (t) (V )
Any noise signal has time average <V(t)> =0, but the
mean-square value <V2(t)> is non-zero, and can
serve as a measure of the noise. Because noise is
distributed in frequency space, the noise measured
will depend on the bandwidth ∆f. White noise is
characterized by having uniform noise power per unit
bandwidth, with natural units Volts2 / Hertz (V2/Hz).
Two fundamental mechanisms do generate
(Gaussian) white noise. All resistors (R) at non-zero
temperature (T) show Johnson noise,
<Vn2> = 4 kB T R ∆f.
Some currents show shot noise,
<In2> = 2 e IDC ∆f,
where IDC is the average current.
Fundamental noise*
- Thermal motion of electrons (Johnson noise)
- Discrete size of moving electrons (Shot noise)
being related. Both are due to the motion of electrons driven either thermally or by an emf.
In certain devices (diodes) it is possible to go continuously from thermal noise to shot noise.
1E-13
Data
Theory
Shot noise from light bulb on photodiode
sense resistor = 100k Ohm
1E-23
2
What is noise? Where does it come from? Can you get rid of
it? (and can you learn something from the bits you can’t get rid
of?)
We are only talking about electronic noise: the noise caused by
the motion of electrons. Noise is generally an unwanted signal
that exists ‘on top’ of the signal you want to measure.
Note the vertical axis in Fig 4. has a linear scale, and the
corrected data display a scatter of only +/- 1% over three
decades of frequency.
Figure 5 tests the claim that Johnson noise gives a
voltage noise power proportional to source resistance.
Shot Noise Density (A / Hz)
Introduction
t oduct o
Noise Fundamentals: where noise is the signal
Johnson Nois
se Density (V^2/Hz)
Abstract
The measurement and theoretical examination of
noise is an important and underrepresented topic in the
advanced laboratory.
Noise is inherent in all
measurements and sets the lower limit of any physical
measurement Noise can also be used to determine
measurement.
fundamental constants. The Johnson voltage noise
from a resistor (vn2 = 4 R kBT ∆f) gives a measure of
the Boltzmann constant (kB) if the resistance (R) and
temperature (T) are known. The charge of the electron
(e) can be determined from a DC current (I) with full
shot noise (in2 = 2 e I ∆f).
The apparatus that will be demonstrated can be used
to measure the
h Johnson
h
noise
i from
f
resistors
i
i the
in
h
range from 10 Ω to 10 MΩ, over a calibrated frequency
range of 3 Hz to 100 kHz and temperatures from 77 to
373 K.
Shot noise can be measured in currents
ranging from 10 nA to 1 mA. The currents can be
derived from a variety of sources: a photodiode
illuminated by an incandescent light bulb or an LED; a
forward biased PN junction; a diode-connected bipolar
junction transistor; or from a zener diode. Some of the
experimental subtleties of noise measurement will be
presented, especially the effect of capacitance.
High
g side
Filter
1E-24
1E-25
Amplifier noise subtracted
raw data
Theory
1E-26
-8
10
Gain
10 to 104
1kΩ
Preamplifier
Fig. 2 Block Diagram of Apparatus
Analog
Squarer
Output
Filter
VOUT
-7
10
-6
10
DC current (A)
Fig. 6 Current noise versus DC Current
-5
10
-4
10