# Can lowering resistor temperature reduce thermal/Johnson's noise?

If resistors contribute to thermal noise (Johnson noise in the form of the formula 0.13 * Sqrt (Resistance) * Sqrt (BW). If the resistor temperature is lowered, would the noise lessened? Are there applications where ordinary (not superconductor materials) resistors or equivalent is sort of put in a a tiny heat exchanger akin operating on same principle as a refrigerator or freezer and the thermal noise diminish so much but the component still functional? Are there any resistor accessories to lower its temperature?

• The whole idea is based on the 2nd law of thermodynamics (thermal equilibrium = no heat flow) and the equi-partition law (nuanced, as the Hamiltonian here involves both position and momentum.) Lowing the temperature (such as using a thermoelectric cooler stack) does reduce the Johnson noise. However, transmission line also matters as observing this condition assumes an equal source and destination impedance (noise of source is equal to noise of load so emission equals absorption -- so thermal equilibrium is met.) Commented Mar 29 at 23:10

rms voltage noise of a resistor is: $$E_t = \sqrt{4\; k\; T\; R\; \Delta f}$$

Where:
$$\ k = \$$ Boltzmann's constant $$\ = 1.38e-23 \; W\cdot sec/°K\$$
$$\ T = \$$ temperature in °K
$$\ R = \$$ resistance in ohms
$$\ \Delta f = \$$ bandwidth in Hertz

Thus, the Johnson noise of a resistor is dependent on temperature.

Some low noise-amplifiers and imaging devices are cooled to lower noise.

• What device can lower the temperature of single resistor?
– Jtl
Commented Mar 29 at 23:35
• @Jtl For temperatures above ~200K, thermoelectric heat pumps are useful. Lower temperatures generally use cryogenic liquids (nitrogen, helium, ...). Commented Mar 30 at 0:21
• how do you put it in the resistor.. any photos?
– Jtl
Commented Mar 30 at 1:52
• @jtl you don't put it in the resistor, you put the resistor in it. Commented Mar 30 at 1:53
• Also, note that this is an approximation. Planck's black body radiation law would take over at very low temperatures and/or very high frequencies (THz). Commented Mar 30 at 1:54