The Curve and Why It Flattens
When you power up an analog oscillator, the pitch isn't wrong — it's moving. Transistors, resistors, and capacitors all change their electrical characteristics as they heat from room temperature toward their operating temperature. The core circuit element driving pitch in most analog VCOs is an exponential converter built around a matched transistor pair. The transconductance of those transistors is strongly temperature-dependent: a few degrees of change shifts the scaling of the volt-per-octave response measurably. That shift is the drift you hear.
The warm-up curve follows a predictable shape. It's steep in the first few minutes, because the components are furthest from equilibrium and absorbing heat fastest. Then it flattens — not because the temperature stops rising, but because the rate of change slows as the module approaches thermal equilibrium with its enclosure and neighbors. That plateau is what stable operation actually means: not zero temperature, but stable temperature. A well-designed oscillator with a temperature-compensated exponential converter — the classic approach using a tempco resistor whose positive coefficient offsets the transistors' negative one — minimizes how much the pitch shifts across that curve, but it doesn't eliminate the curve itself.
Cool-down is the mirror image. Pull the module from the case, or power everything down in a cold room, and the same process runs in reverse. If you power back up quickly before the board has fully cooled, you start from a different initial condition and the drift pattern will look slightly different.
What calibration can and cannot do here is important to understand clearly. Calibrating an oscillator at cold fixes the 1V/oct tracking at cold. Calibrating at full operating temperature fixes it at heat. Neither fixes the interval in between. The right practice is to let the system warm up fully — typically fifteen to twenty minutes under power — and then calibrate. Trimmer adjustments made cold will be slightly off once the circuit settles. That's not a fault; it's thermodynamics.