The system considered in this document comprises an electrical heater
of heat capacity Ch connected via a thermal
resistance Rho to the oven, heat capacity
Co. The oven loses heat to the environment, at
temperature Te, through the thermal resistance
Ro of its insulation. The temperature
controller adjusts the power dissipated in the heating elements,
W, by comparing the oven temperature,
To, with the set-point temperature
Figure 1. Equivalent circuit representation of system model.
The red symbols on the diagram are thermal components; the black ones are
electrical devices. Dashed lines represent transducers: a thermometer in one case,
conversion of electrical current
flowing through the heater into heat (thermal current W) in the other.
With the notable exception of cryogenic systems, the thermometer
time constant is usually very small so its effects
will be tacitly assumed to be negligible during much of the following discussion. However, it will
be mentioned in the final section which discusses the frequency domain
behaviour of the system.