On June 12, 2011, the analog EE world misplaced a star when guru James M. Williams died. Jim’s a whole bunch of articles, books, and software notes have been (and proceed to be) a bottomless wellspring of data, inspiration, and the enjoyment of seeing thorny design puzzles handily solved by a grasp, all wrapped up in a pleasant writing model. The design concept introduced right here derives from considered one of his circuits printed on web page 7 of AN45 Measurement and Control Circuit Collection (Diapers and Designs on the Night Shift).

Wow the engineering world together with your distinctive design: Design Concepts Submission Information

In his notice, Jim discusses the enchantment of utilizing transistor V_BE tempco as an affordable temperature sensor, however how in observe, its utility is restricted by unpredictable transistor-to-transistor V_BE variability. He explains how this downside necessitates preliminary sensor transistor calibration (and recalibration if the sensor ever wants substitute), which largely cancels any anticipated comfort and price financial savings. 

Then Jim saves the day with an ingenious resolution.

It seems, says Jim, that though the fixed-current V_BE of a random transistor isn’t usefully predictable, BJT V_BE change with variable-present is very predictable. Particularly, it reliably obeys this easy logarithmic equation…

∆V_BE = Tabs 198µV LOG₁₀(I₁/I₂)

The place Tabs = absolute temperature in ^oKelvin. Due to this fact, when used as a thermometer…

Tabs = ∆V_BE 5050 / LOG₁₀(I₁/I₂) = 5050 ∆V_BE if I₁/I₂ = 10

 Word the cool (and simply remembered) “fifty-fifty” fixed!

Jim applies this relationship within the Determine 1 topology that’s mentioned to place a ten:1 bias present cycle ¹ onto Q2’s diode-connected NPN transistor, synchronously rectify the ensuing 198µVpp / ^oOkay AC waveform, then amplify and offset the ensuing DC to supply a 0 to 10V = 0 to 100^oC, no sensor-transistor-specific calibration required, output.

Determine 1 Jim Williams’s ∆V_BE-based thermometer.

 I’ve used “fifty-fifty” in lots of profitable thermometric purposes and supply a brand new variation on the thought right here in Determine 2’s ^OOkay-degrees-to-microseconds oscillator.

Determine 2 An oscillator that’s an absolute thermometer.

The ∆V_BE present ratio is ready right here by the R3/R4 resistor pair (plus a small contribution from the R1+R2 integrator community) to 16:1. This creates a temperature-proportional ∆V_BE periodic step on A2 pin 7 of: LOG₁₀ (16)/5050 = 238µV/^OOkay at any time when the A1 comparator switches the Q2 FET. I selected the bigger 16 versus 10:1 present ratio to supply a considerably simpler sign for the op-amps to course of, and to cut back the significance of some secondary potential error sources. C2 gives constructive suggestions to make sure the comparator transitions are fast and clear.

The A2 integrator then ramps from the ∆V_BE step again towards A1’s 500mV setpoint as proven in Determine 3, producing symmetrical half-cycle timeouts of length T = 10µs/^OOkay = 3ms at 300^OOkay = 27^OC.

Determine 3 Thermometer oscillator waveforms.

Though as famous within the Willams software, the Q1 sensor transistor itself wants no calibration. Trimmer R1 is offered as one-point compensation primarily for integrator capacitor C1 and Vdd tolerances. As soon as R1 is adjusted, it needn’t be revisited even when Q1 is changed.

The thermometer oscillator’s 0/5V output may be conveniently transformed to a digital temperature readout by normal microcontroller timer {hardware}. At a clock charge of 1MHz, conversion decision over one oscillation half-cycle interval T is 0.1^O.

1. A typo apparently by some means slipped by means of into Jim’s schematic. The resistor pair that’s mentioned to set the ten:1 present ratio and subsequently needs to be in a 9:1 resistance ratio, are in truth 549k/49.9k = 11:1, would set 12:1 currents, and subsequently a scale issue of 214uV/^oOkay; not the said 198uV. I don’t know if a revised version exists that corrects this minor 8% hiccup, nevertheless it’s a easy repair which I’ve taken the freedom to do. Additionally, Q1 is pointless.

Stephen Woodward’s relationship with EDN’s DI column goes again fairly a methods. In all, a complete of 64 submissions have been accepted since his first contribution was printed in 1974.

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