The thermal timeconstant of a cubic meter of copper is 9,000 seconds.
That is also the timconstant of a square meter of copper foil, if the heat can only flow along the sheet of metal, that is, the sides (the 2 square meter surfaces) are insulated.
The thermal timeconstant of 0.1 meter cube of copper is 90 seconds. Yes, if 10:1 smaller, the timeconstant is 100X faster.
The thermal timeconstant of 0.01 cube of copper (1cm, or 0.4 inches) is 0.9 seconds.
The thermal timeconstant of 1milliMeter of copper is 0.009 seconds.
Curiously, the thermal timeconstant of silicon (the basis of clays and ceramics) is 11,600 seconds for a cubic meter of silicon. Thus silicon and copper have about the same thermal response rate. The thermal conductivities are considerably different, but the timeconstants are similar.
Consider the distortion at DC, where the thermal-masses become filled with heat, and the distortion is maximum.
We can also predict the thermal-distortion for AC signals. Given the thermal time-constant, we can model the behavior of OpAmp differential-pairs being heated by OpAmp output transistors and causing the input-offset-voltage to change, with dVoffset/dTemperature as one specification of all opamps.
Given the gain setting function of (most) opamps uses resistors, and the internal heat of these resistors (could be the bulk carbon composition, the bulk metal film, or the laser-trimmed thin-film types of resistors), the GAIN
of our opamp stage will also change.
The screenshot includes, in lower left, the predicted thermal distortion (summing to over 100 microVolts with 1milliVolt from the sensor) is 100uV/0.34uV or nearly 300 quanta (ADC quanta) of nonlinearity, or upconverted-as-amplitude-modulation.
Notice in the center worksheets, the ability to edit the
a) opamp thermal noise, either as RootHertz or as Rnoise
b) params of the opamp thermal mass, thermal resistance, and dVoffset/dTemp
c) thermal properties of the resistors used in setting the gain.
To minimize OpAmp contribution to thermal-distortion, insert a BUFFER. The tool includes Buffered OpAmp as one stage choice.
To minimize Resistor contribution to thermal-distortion,
d) either use equal resistors for Rg and Rf (making your gain be R+R/R = 2),
e) or use identical resistors in series with equal ability to dissipate heat and dispose of heat,
f) or use the method of Walt Jung of ADI for low distortion Audio PAs: use physically large resistors so the thermal mass is large and the Tau is very long.
If you are responsible for Signal Chains with better than 10 bits SINAD, the error budget should include a line item for thermal distortion.