November 6, 1997

Bang-bang thermostat is simple and efficient

W Stephen Woodward, University of North Carolina--Chapel Hill

Perhaps the simplest and oldest feedback loop is the nonproportional, all-or-nothing, "bang-bang" thermostat. Fully turning on a heater when the temperature is below setpoint and off when it's above setpoint is a straightforward example of a servomechanism. Yet, elementary and crude as servomechanisms are, examples surround us in virtually every household-room thermostat, clothes dryer, oven, and aquarium heater, to name a few. The version in Figure 1 preserves the best features of the old bang-bang: low cost, simplicity, and efficiency combined with setpoint stability.

Q₁ serves as a temperature sensor via the ­2-mV/°C temperature dependence of its V_BE. In combination with R₁ and R₂, Q₁ forms a standard V_BE multiplier. Q₁'s collector-emitter voltage, V₁, equals V_BE(R₁+R₂)/R_1A, where R_1A is the part of R₁'s resistance element between the 5V supply and the wiper. Thus, by adjusting R_1A over the range 0 to R₁ at any chosen Q₁ temperature, you can set V₁ virtually anywhere at V_BE to 5V.

Because the R₁ adjustment covers such a wide range, it is almost impossible to set a precise temperature using R₁ by itself. You thus need R₂ to fine-tune V₂, the voltage at the adjust terminal of VR, over the range 0.95 to 1.0 times V₁. By properly adjusting R₁ and R₂, you can set V₂ to equal 1.24V, the internal bandgap-reference voltage of the LM385 shunt-regulator chip VR, when Q₁ is at the desired setpoint temperature. Once you establish this setting, VR conducts (thereby turning on the optically isolated solid-state relay, SSR, and applying power to the heater) whenever V₂ rises above 1.24V, as it does if Q₁ cools below setpoint temperature.

When Q₁ warms back up to setpoint, however, V₂ falls below 1.24V and VR ceases conduction, turning off SSR and the heater. You can add hysteresis, which is sometimes useful if too-frequent cycling of the heater is undesirable, by using R₄ according to the formula T_H=4.4 mega-ohms/R₄, where T_H is the temperature hysteresis. For 2°C hysteresis, for example, R₄ equates to 2.7 mega-ohms. Setpoint stability is excellent if you use good trimmers for R₁ and R₂. In practice, the dominant cause of any temperature variation is likely to be drift in the 5V supply. The setpoint has approximately 0.2°C/% dependence on supply drift. (DI #2113)

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