Fixing a fundamental flaw of self-sensing transistor thermostats

Miniature self-sensing transistor thermostats use a single transistor (BJT or FET) to serve as both a temperature sensor and stabilizing heater. These transistor thermostats are (when well designed) an effective, efficient, and inexpensive way to maintain a constant temperature for individual components (sensors, precision references, oscillators, etc.), incubation of sensitive biological cultures, and performance of other small and critical thermal control functions. But they all suffer from a common flaw that can seriously impact temperature stability.

Figure 1 illustrates the problem.

Figure 1 The self-sensed thermostat transistor thermal model: (Tj – Tc) = Rjc Pj.

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The signature design goal of the self-sensing transistor thermostat is to maintain an accurately stable case temperature Tc. This is what matters because what we really want to thermostat is usually not the transistor junction itself but is instead something interesting that we’ve connected to the transistor case. The thermostat starts out by using the properties of the transistor to perform a measurement of junction temperature (Tj). This measurement is then used as the input to a heating feedback loop that controls and continuously adjusts junction heating power (Pj) to hold a stable junction temperature and thereby indirectly maintain a constant case temperature. We hope…

But the trouble with this model is that Tj and Tc aren’t necessarily equal. They’re separated by the non-zero junction/case thermal impedance (Rjc), which creates a temperature differential (Terror) proportional to Pj such that:

Terr = Tj – Tc = Rjc Pj.

So how big a problem is this? Since the magnitude of the error is proportional to Rjc, the answer needs a consultation with the datasheet of the thermometer transistor—Figure 2’s IRF510 for example: https://www.vishay.com/docs/91015/irf510.pdf.

The relevant number is found in the device datasheet “ABSOLUTE MAXIMUM RATINGS” table as the “Linear derating factor” which in this case equals 0.29 W/oC. This is the effective reciprocal of Rjc, so for the IRF510:

Rjc = 1 / 0.29 W/oC = 3.45 oC/W.

Figure 2 MOSFET thermostat incorporating (Rjc Pj) temperature error correction.

Figure 2’s half-wave heater control circuit can supply maximum current-limited junction heating power of:

Pj(max) = 24 Vrms x 0.7 V / R7 / 2 = 16.8 W.

The resulting Tj – Tc differential error could therefore be as bad as:

Terr(max) = Rjc Pj(max) = 3.45 * 16.8 W = 58oC.

Yikes! This seems to make nonsense of any hope for accurate thermostasis.

However, a simple error-cancellation workaround is possible. Because the Tj – Tc error is proportional to Pj, which in turn is proportional to the current sensed by R7, we can add a positive-feedback offset to the setpoint temperature equal to Rjc Pj to generate a new, corrected junction temperature setpoint of:

Tj’ = Tj + Rjc Pj.

Then:

Tc = Tj’ – Rjc Pj = Tj + Rjc Pj – Rjc Pj = Tj,

Tc = Tj.

Problem solved! This is exactly the gimmick shown in the positive-feedback three component network shaded in blue in Figure 2. Here’s how its R11 and R12 were calculated.

Current sensing 0.5 Ω R7 develops:

VR7 = 0.5 / 24 Vrms = 21 mV * Pj,

= 21 mV * Terr / Rjc = 6 mV * Terr,

therefore Terr = VR7 / 6 mV.

The R11 R12 attenuate VR7to yield the signal applied to Q3’s emitter:

VQ3 = VR7 R12 / (R11 + R12) = VR7 / 3,

= 2 mV * Terr.

In this way Q3 effectively compensates Tj by one degree for every degree of Terr thus forcing Tc = Tj, thus fixing fundamental flaw.

C2 imposes a 1 second RC time-constant on this positive feedback, which is about an order of magnitude slower than the rate of junction temperature response to changes in Pj. This suppresses the oscillation that positive feedback is famously known to provoke.

Stephen Woodward’s relationship with EDN’s DI column goes back quite a long way. Nearly 100 submissions have been accepted since his first contribution back in 1974.

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Fixing a fundamental flaw of self-sensing transistor thermostats

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