Determination of the temperature vs power dynamic behavior of a cryocooler via two independent methods in time and frequency domain

Abstract

This report deals with the analysis of a cryocooler as a linear dynamical system around a set point, over a range of temperatures where the thermal properties can be considered constant. The accurate knowledge of the cryocooler temperature dependence with a time dependent power stimulus allows to analyze the thermodynamical properties of the system and understand the power flow related, for example, to the cryocooler temperature fluctuations. This is useful for the design of efficient thermal dampers that are necessary for the thermal stabilization of the device under test Sosso et al. [1], Trinchera et al. [2]. Two different and independent methods for deriving the cooler dynamic (i.e. non-stationary) behavior are described using the two main approaches to mathematically represent a dynamical system: step response and transfer function. •Using both approaches we were able to cross check results and provide an estimate of the accuracy of each method.•The instrumentation required is typically available in physics and engineering laboratories.•These results provide insights on cryocooler thermodynamics and design tools for cryocooler engineering.

Keywords: Cryocooler analysis; Step response; Temperature to power dynamic response of a cryocooler with both time and frequency domain analyses; Transfer function.

Graphical abstract

Fig. 1

Picture of a cryocooler cold plate. A SMD resistor and a diode temperature sensor are suitably tightened to the cold plate through a brass screw. The SMD resistor is covered by a thin kapton layer to avoid accidental short-circuits.

Fig. 2

One period of the (100 s duration) step input power (yellow) and diode voltage (red) as visualized with the oscilloscope. Ascending and descending exponential decays are averaged and saved.

Fig. 3

Sampled temperature-to-time response to the ascending power step input as in Fig. 1. Full temperature variation ΔT is subdivided into M = 5 equal intervals.

Fig. 4

Skimmed temperature-to-time response to the ascending power step input as in Fig. 1. Full temperature variation ΔT is subdivided into M = 5 equal intervals.

Fig. 5

Left: diode voltage response (red) to a power sinewave over the set of frequencies in the range of interest [5] input as visualized with the oscilloscope. Sine square-root input voltage (yellow) is also measured for phase evaluation through Δt measurement. Right: input power sinewave (red) calculated as V(t)²/R and temperature variation (blue) measured by the diode according to its calibration curve.