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Triple-Current-Modulation Delta V<sub>BE</sub> Thermometry Cancels Ohmic Error Sources

Delta VBE-based (VBE) thermometry1,2,3,4 is based on this classic bipolar junction I/V/T relationship: For an ideal transistor, the VBE corresponding to ratiometric change in collector current (I2 / I1) is exactly proportional to absolute temperature: VBE = 198.4 µV * °K * LOG10(I2 / I1).

Because cheap, common, and robust small-signal transistors conform closely to the ideal model, circuits that exploit the “PTAT (Proportional to Absolute Temperature) VBE” effect can implement accurate and cost-effective thermometers that need no calibration. As the references illustrate, this handy and cost-effective technique can serve a broad range of applications.

Yet despite the already wide range of applications served by VBE thermometry, its utility and accuracy would be even better if VBE could be made less vulnerable to the effects of ohmic (IR) errors. These errors occur when parasitic resistances (e.g., RW, RE) introduced by interconnecting wiring, connectors, multiplexers, and internal non-ideality of the transistor itself appear in series with the VBE signal. These factors introduce undesired (I2 - I1) * RW IR noise components that are effectively summed with the desired VBE signal. The resulting measurement errors can become unacceptably large if interconnecting wiring is long, especially if multiplexing is used to share VBE signal processing circuitry among many inexpensive remotely located sensors.

This design elaborates on the basic VBE principle by adding a third modulation current level to the usual two (see the figure). “Tri-Current” VBE makes possible the separate sampling, subtraction, and cancellation of IR effects by exploiting the inherent linearity of Ohm’s Law and V = I * R contrasted with the logarithmic and, therefore, extreme nonlinearity of the PTAT response.

The basis of generating the new modulation scheme is the CMOS sequencer circuit, which comprises the 4013 dual flip-flop and 4052 multiplexer. FF1 is connected in an unusual configuration that forces it to implement a non-inverting buffer amplifier function. This amplifier provides the positive feedback required for oscillation, while the “0” and “2” outputs of the multiplexer provide the negative feedback required for timing its ~500-Hz frequency.

Meanwhile FF2 is connected in a conventional divide-by-2 topology. This combination applies stepwise tri-current modulation in a four-step sequence: (I1, I2, I1, I3), consisting of a 250-Hz.

VBE measurement cycle. The values of the modulation currents were carefully chosen so:

1. I1 = ~14.4 µA
2. (I1 + I2)/I1 = 18.94 = 101.2775 = 101 * 100.2775
3. I3 = 2 * I2
4. (I3 + I1)/I1 = 36.89 = 101.5550 = 10(1.2775 + 0.2775) = 101 * 100.2775 * 100.2775

Synchronous demodulation of the resulting ac signal accumulates the (I1 + I2) VBE response as V1 on C1 and the (I1 + I3) response as V2 on C2. The combination of modulation currents means that, when differentially summed (V = 2V1 - V2 = 198.4 µV/K), offset (VC = V - 0.05412 = 0 @ 273 K), and scaled (VO = 504 VC = 0.1 V/ °C) by op amps A1 and A2 and the associated resistor network, the output VO = 0 @ 0°C and 10 V @ 100°C, with an untrimmed accuracy of better than ±1°C.

Achieving this accuracy requires 0.1% resistors (note the “*” on the schematic) and a 2.500-V reference of similar precision. But Q1, by contrast, is any common small-signal, general-purpose NPN transistor such as the venerable 2N2222 or 2N3904.

1. “Transistor Sensor Needs No Compensation,” Jim Williams, EDN, April 25, 1991
2. “Low-Cost Precision Thermometry,” W. Stephen Woodward, Electronic Design, August 21, 1995
3. “Transistor Forms RS-232 Digital Thermometer,” W. Stephen Woodward, EDN, May 9, 1996
4. “VBE-Based Cold-Junction Compensator for Thermocouples,” W. Stephen Woodward, Electronic Design, November 6, 2000

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