Noise is everywhere -- the audible noise we hear, the electronic noise we
measure and, usually, try to avoid. Noise reminds us that we live in a real
universe. On this page I'm going to look at some of the sources of unwanted noise that
are found in electronic circuits.
Note: I say unwanted noise as dedicated noise sources will not be covered on this page.
Thermal noise, or Johnson Noise, is noise energy generated in conducting materials
due to thermal effects. The simplified relation between noise power, Pn Watts,
temperature, T Kelvin, and bandwidth, B Hz, is
where k is Boltmann's constant, 1.38x10-23.
Note there is no mention of resistance. Since
It follows that the thermal noise voltage generated by a resistor R
for a given bandwidth B Hz at temperature T Kelvin is then
An excellent article on resistor noise is
"Resistor NoiseŚreviewing basics, plus a Fun Quiz" recently published in EDN. One interesting thing to note is shown in the graph in figure 1: due to temperature, T, being in degress Kelvin, changes in ambient temperature from -55°C to +125°C have very little effect on a resistor's thermal noise voltage.
E24 Rresistor Values, Noise Density and Noise Voltage
The table below lists the voltage noise densities and voltage noises for two decades
in the E24 resistor series. These figures have been calculated at T=296K (about 23°C),
and the noise voltages for the a bandwidth of 20Hz-20kHz (B = 19980Hz).
For other resistance decades you can use this table and scale the noise voltages
accordingly. Since noise voltage is proportional to the square root of resistance
you need to do a double-decade jump. For example, for a 100Ω resistor we
look at the row for 10kΩ (100 x 102) and divide the voltages
by 10 to give a noise voltage
density of 1.279nV/√Hz, or 180.7nV over the audio bandwidth. For signal
levels in dBu add or subtract 10dB per resistor decade. So our 100Ω
resistor being two decades below 10k has -112.6dBu - 20db = -132.6dBu noise.
|Resistance||Noise Density||Noise Voltage (20Hz to 20kHz)||dBu (0dBu = 775mV)|
|1k0 ||4.04 nV√Hz ||0.57 μV||-122.6|
|1k1 ||4.24 nV√Hz ||0.60 μV||-122.2|
|1k2 ||4.43 nV√Hz ||0.63 μV||-121.8|
|1k3 ||4.61 nV√Hz ||0.65 μV||-121.5|
|1k5 ||4.95 nV√Hz ||0.70 μV||-120.9|
|1k6 ||5.11 nV√Hz ||0.72 μV||-120.6|
|1k8 ||5.42 nV√Hz ||0.77 μV||-120.1|
|2k0 ||5.72 nV√Hz ||0.81 μV||-119.6|
|2k2 ||6.00 nV√Hz ||0.85 μV||-119.2|
|2k4 ||6.26 nV√Hz ||0.89 μV||-118.8|
|2k7 ||6.64 nV√Hz ||0.94 μV||-118.3|
|3k0 ||7.00 nV√Hz ||0.99 μV||-117.9|
|3k3 ||7.34 nV√Hz ||1.04 μV||-117.4|
|3k6 ||7.67 nV√Hz ||1.08 μV||-117.1|
|3k9 ||7.98 nV√Hz ||1.13 μV||-116.7|
|4k3 ||8.38 nV√Hz ||1.19 μV||-116.3|
|4k7 ||8.77 nV√Hz ||1.24 μV||-115.9|
|5k1 ||9.13 nV√Hz ||1.29 μV||-115.6|
|5k6 ||9.57 nV√Hz ||1.35 μV||-115.2|
|6k2 ||10.07 nV√Hz ||1.42 μV||-114.7|
|6k8 ||10.54 nV√Hz ||1.49 μV||-114.3|
|7k5 ||11.07 nV√Hz ||1.57 μV||-113.9|
|8k2 ||11.58 nV√Hz ||1.64 μV||-113.5|
|9k1 ||12.20 nV√Hz ||1.72 μV||-113.0|
|10k ||12.79 nV√Hz ||1.81 μV||-112.6|
|11k ||13.41 nV√Hz ||1.90 μV||-112.2|
|12k ||14.01 nV√Hz ||1.98 μV||-111.8|
|13k ||14.58 nV√Hz ||2.06 μV||-111.5|
|15k ||15.66 nV√Hz ||2.21 μV||-110.9|
|16k ||16.17 nV√Hz ||2.29 μV||-110.6|
|18k ||17.15 nV√Hz ||2.42 μV||-110.1|
|20k ||18.08 nV√Hz ||2.56 μV||-109.6|
|22k ||18.96 nV√Hz ||2.68 μV||-109.2|
|24k ||19.81 nV√Hz ||2.80 μV||-108.8|
|27k ||21.01 nV√Hz ||2.97 μV||-108.2|
|30k ||22.15 nV√Hz ||3.13 μV||-107.9|
|33k ||23.23 nV√Hz ||3.28 μV||-107.4|
|36k ||24.26 nV√Hz ||3.43 μV||-107.1|
|39k ||25.25 nV√Hz ||3.57 μV||-106.7|
|43k ||26.51 nV√Hz ||3.75 μV||-106.3|
|47k ||27.72 nV√Hz ||3.92 μV||-105.9|
|51k ||28.87 nV√Hz ||4.08 μV||-105.6|
|56k ||30.26 nV√Hz ||4.28 μV||-105.2|
|62k ||31.84 nV√Hz ||4.50 μV||-104.7|
|68k ||33.34 nV√Hz ||4.71 μV||-104.3|
|75k ||35.01 nV√Hz ||4.95 μV||-103.9|
|82k ||36.61 nV√Hz ||5.18 μV||-103.5|
|91k ||38.57 nV√Hz ||5.45 μV||-103.0|
Op-Amp Noise Voltage, Noise Current, and Noise Resistance
When considering an op-amp for low-noise design we find two useful numbers
in the datasheet: equivalent input noise voltage, and equivalent input noise current.
The equivalent input noise voltage represents the internal noise voltages inherent
inside the op-amp, and is modelled as a single voltage source in series with the
The equivalent input noise current represents the current noise inside the
op-amp, and is modelled as a current source placed across the input terminals.
The optimal external source resistance (i.e., the resistance
seen by the op-amp terminals) is the ratio of noise voltage to noise current:
What this tells us is that lower source resistor values will not help much since the noise
performance will be dominated by the noise voltage, while a higher source resistance
will generate increasing levels of noise voltage due to the noise current flowing
in them. We also want to keep the external resistors low to minimize thermal noise.
Some examples (figures are typical, at 1kHz unless stated) sorted in order
of noise voltage:
|Op-amp||en (nV√Hz)||in (pA√Hz)||rn (Ω)|
|AD797A ||0.9||2.0 ||450|
|LM4562 ||2.7||1.6 ||1k7|
|NE5534A ||3.5||0.4 ||8k8|
|LM833 ||4.5||0.5 ||9k0|
|NE5532A ||5 ||0.7 ||7k1|
|OP275 ||6 ||1.5 ||4k0|
|OPA2134 ||8 ||0.003||2M7|
|TL072 ||18 ||0.01 ||1M8|
A Word on Noise Gain
As mentioned above, the internal noise sources within an op-amp are referred
to the non-inverting (+) input. While this sounds innocuous enough, it has an
important ramification: the gain applied to the op-amp noise, the Noise Gain,
is that of a non-inverting amplifier, which is 1 greater than that of an inverting
amplifier! At low gains this can make a huge difference: for example,
a unity-gain inverting buffer has a Noise Gain of 2.
Minimising Thermal Noise
Thermal noise is characterised by three parameters: bandwidth, temperature, and resistance.
It has no dependence on the resistor type, so a carbon composition resistor will have the
same thermal noise as a super-expensive metal foil resistor (excess noise
(see below) will be different though).
Bandwidth is a system parameter so will be determined by the design parameters.
Temperature is a little more controllable, although unless you're prepared to
emerse your circuit in liquid nitrogen there's not much you can really do.
So the main parameter for controlling thermal noise is resistance. And from
the table above it is clear that lower resistance is better with less thermal
Work in progress!
Due to structure of resistive materials. Carbon comp the worst, then CF, then MF, then metal foil (very expensive!)
Larger physical size has lower excess noise. 0.5W better than 0.25W better than 0.125W.
Also lower resistance has lower excess noise. Check manufacturer datasheets.