A transistor thermostat for DAC voltage references

Frequent contributor Christopher Paul recently provided us with a painstakingly conservatively error-budget-analyzed Design Idea (DI) for a state-of-the-art pursuit of a 16-bit-perfection PWM DAC.

The DI presented below, while shamelessly kibitzing on Chris’ excellent design process and product, should in no way be construed as criticism or even a suggested modification. It is neither. It’s just a voyage into the strange land of ultimate precision.

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In his pursuit of perfect precision, Christopher creatively coped with the limitations of the “art.” Perhaps the most intractable of these limitations in the context of his design was the temperature coefficient of available moderately priced precision voltage references. His choice of the excellent 35xxx family of references, for example, exhibits a temperature coefficient (tempco) of 12 ppm/°C = 0.8 lsb/°C = 55 lsb over 0 to 70°C, reducing this element of conversion precision to only an effective 10.2 bits. 

Since that was more than an order of magnitude worse than other error factors (e.g., DNL, INL, ripple) in Christopher’s simple and elegant (and nice!) design, it got me musing about what possibilities might exist to mediate it. 

Let me candidly admit upfront that my musing was unconstrained by a concern for the practical damage such possibilities might imply towards the simplicity and elegance of the design. This included damage, such as doubling the parts count and vastly increasing the power consumption.

But with those caveats out of the way, here we go.

The obvious possibility that came to mind, of course, was what if we reduced the importance of thermal instability of the reference by the simple (and brute-force) tactic of putting it in a thermostat? Over the years, we’ve seen lots of DIs for using transistors as sensors and heaters (sometimes combining both functions in the same device) for controlling the temperature of single components. Figure 1 illustrates the thermo-mechanics of such a scheme for this application. 

Figure 1 Thermally coupling the transistor sensor/heater to the DAC voltage reference to stabilize its temperature.

A nylon machine screw clamps the heatsink hotspot of a TO-220-packaged transistor (TIP31G) in a cantilever fashion onto the surface of the reference. A foam O-ring provides a modicum of thermal insulation. A dab of thermal grease on the mating surfaces will improve thermal coupling.

Figure 2 shows the electronics of the thermostat. Here’s how that works.

Figure 2 Q1 is a combo heater/sensor for a ±1°C thermostat, nominal setpoint ~70°C. R3 = 37500/(Vref – 0.375).

Q1 is the core of the thermostat. Under the control of gated multivibrator U1, it alternates between a temperature measurement when U1’s “Out” pin is low, and heating when U1’s “Out” pin goes high. Setpoint corresponds to Q1 Vbe = 375 mV as generated by the voltage divider R3/R4, detected by comparator A1, and timed by U1. 

I drew Figure 1 with the R3/R4 divider connected to +5 V, but in practice, this might not be the ideal choice. The thermostat setpoint will change by ~1.6°C per 1% change in Vref, so sub-percentage-point Vref stability is crucial to achieve optimal 16-bit DAC performance. The +5-V supply rail may therefore not be stable enough, and using the thermostatted DAC reference itself would be (much) better.

Any Vref of adequate stability and at least 365 mV may be used by simply setting R3 = 37500/(Vref – 0.375). For the same reason, R3 and R4 should be 1% or better metal film types. The point isn’t setpoint accuracy, which matters little, but stability, which matters much.

Vbe > 375mV indicates Q1 junction temp < setpoint, which gates U1 on. This allows U1 “Out” to transition to +5 V. This turns on driver transistor Q3, supplying ~20 mA to the Q1, Q2 pair. Q2 functions as a basic current regulator, limiting Q1’s heating current to ~0.7 V/1.5 Ω = 470 mA and therefore heating power to 2 W

The feedback loop thus established, Q1 Vbe to A1 to U1 to Q3 to Q1, adjusts the U1 duty cycle from 0 to 95%, and thereby tweaks the heating power to maintain thermostasis. Note that I omitted pinout numbers on A1 to accommodate the possibility that it might be contained in a multifunction chip (e.g., a quad) used elsewhere in the DAC.

Q.E.D. But wait! What are C2 and R2 for? Their reason for being, in general terms, is to be found in “Fixing a fundamental flaw of self-sensing transistor thermostats.”

As “Fixing…” explains, a fundamental limitation on the accuracy of thermostats like Figure 1 is as follows. The junction temperature (Tj) that we can actually measure is only an imperfect approximation of what we’re really interested in: controlling the package temperature (Tc). Figure 3 shows why.

Figure 3 The fatal flaw of Figure 1: the junction temperature is an imperfect approximation of the package temperature.

Because of the nonzero thermal impedance (Rjc) between the transistor junction and the surface of its case, an error term is introduced that’s proportional to that impedance and the heating power:

Terr = Tj – Tc = Rjc*Pj

In the TIP31 datasheet, Rjc is specified in the “Thermal Characteristics” section as 3.125 °C/W. Therefore, as Pj goes from 0 to 2 W, Terr would go from 0 to 6.25 °C. Recalling that the REF35 has a 12 ppm/°C tempco, that would leave us with 12 x 6.25 = 75 ppm = 5 lsb DAC drift. 

That’s 11x better than the 55-lsb tempco error we started with, but it’s still quite a way from true 16-bit accuracy. Can we do even better?

Just like the R11, R12, C2 network in Figure 2 of “Fixing a fundamental flaw of self-sensing transistor thermostats” that adds a Pj proportional Terr correction to the thermostat setpoint, that’s what R2 and C2 do here in this DI. C2 accumulates a ~23 ms average of 0 to 100% heating duty cycle = 0 to 700 mV, and adds through R2 a proportional 0 to 14 mV = 0 to 6.25°C Terr correction to the setpoint for net ±1°C stable thermostasis and < 1 lsb reference instability.

Now Q.E.D!

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

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