Compensating circuits and systems for changes in temperature is often a major part of the engineer's challenge, especially though not exclusively for analog designs. There are several tactics used:
- Use materials with low temperature coefficient (tempco), which works especially for passives such as resistors
- Use circuit elements with opposite tempcos, to counter each other
- Use matched circuit elements in a differential or balanced topology, such as the Wheatstone bridge
- Measure the temperature via a diode or thermocouple, and then use the data to correct in software for anticipated drift
- Stabilize the critical components in an oven
Of course, super-critical designs may use several of these techniques, in combination.
But if you think you have tempco challenges, think about the designers of pendulum-based clocks. Using the fact that, for small excursions, the period of a pendulum is a function only its length, mechanical engineers and horologists (clock designers) were able to develop some amazingly precise clocks. In addition to friction, air resistance, and other second- and third-order error sources, the change in length of the pendulum to temperature variations was a major problem. Solutions included using mercury in the pendulum bob to change its effective length as the temperate changed, and using a parallel combination of rods of different tempcos in a gridiron cage arrangement, to work “against” each other and so cancel out the length changes.
But even this solution had into problems. The static friction (stiction) of the rods in their sliding gridiron cage supports caused tiny, sudden jumps in the correction rather than smooth, continuous action.
Amazingly, the designers were able to identify and compensate for many subtle sources of error, and produce clocks with accuracy of better than 1 second/month, which is very impressive. The high-end pendulum clock was the best standard until crystal-based clocks were developed in the early 1900s; you can read more about pendulum subtleties and analysis here.
But what I also find amazing is that they achieved this performance while facing the eternal metrology challenge: how did they verify the accuracy of these clocks? Did they have to wait 24 hours for the next sunrise? What “better” standard could they use?
We're spoiled now: for a modest sum you can get a secondary time standard that is good to a few parts per million, and only takes a few moments to provide a reading. Think about their test and measurement challenge in correcting for tempco, next time you have tempco problems!♦