A precision liquidhyphen;helium temperature proportional thermostat designed for use with a superconducting cavity stabilized oscillator is described, where temperature of the Xhyphen;band superconducting Nb cavity mounted inside a vacuum can is regulated at the temperature below 2 K. By noticing the fact that the time for establishment of thermal equilibrium is very short at liquidhyphen;helium temperature and thermal transfer properties can, therefore, be measured in the frequency domain, the frequency domain technique rather than the conventional time domain technique is used to design and measure feedback loops of a thermostat. The application of a secondhyphen;order loop to the design of thermostats is discussed in order to obtain better transient and steadyhyphen;state performance. In the thermostat constructed, temperature is measured with a germanium resistance thermometer in the ac Wheatstone bridge, a commercial lockhyphen;in amplifier is used as a null detector, and the secondhyphen;order loop is used. The loop characteristics were confirmed by measuring the Bode plot of the feedback loop which also contains the frequency response of the thermal interface, and the gain crossover frequency and the phase margin were 26 Hz and 52deg;, respectively, at the operating temperature near 1.7 K. The thermostat has achieved the longhyphen;term temperature drift of less than 3.2 mgr;K, where the drift caused by the instability of the bridge itself is excepted, in the presence of the liquidhyphen;helium temperature fluctuation of 35 mK for periods more than 10 h; it has also shown very fast and good transient response. In addition, the Bode plots of the closed loops have shown that the loop is stable to the variation of the gain crossover frequency of more than four octaves. It has been shown that the method of designing a precision thermostat by measuring its thermal properties in the frequency domain can be useful and can give very reliable results at liquidhyphen;helium temperature.
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