Phantom-powered solid-state linear airflow sensor
Self-heated Darlingtion transistor pair linearly senses airflow using just two wires for both power in and signal out.
Suppose we take a common TO-92 transistor and heat it to a constant temperature differential above ambient. The power input required to keep it there will be determined by its thermal impedance ZT relative to the surrounding air. This suggests it might be handy for air flow measurement. Maybe even moreso if it needed only a simple two-wire connection for both (phantom) power supply from, and signal delivery to, the supporting electronics.
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Please see the Related content listings below for a more detailed treatment of the subject. Figure 1 graphs the resulting power vs air speed relationship. Unfortunately, it’s badly bent.
Figure 1 This graph logs power dissipated vs air speed of a TO92 held at a constant 31oC above ambient. Pw = 31/ZT.
Figure 2 shows a practical thermostat circuit to achieve and maintain the delta-T while outputting a signal predictably related to Pw. It utilizes a Darlington sensor transistor pair (Q1 and Q2) to compensate for ambient temperature and convert the resulting nonlinear Pw curve into a linearized airflow readout. Its current mode, phantom-power output is compatible and convenient for the long cable runs often seen in airflow measurement applications.
Figure 2 This circuit implements a phantom-powered Darlington anemometer with a 40-140 mA current mode output. Adjust R10 to calibrate 40 mA (zero fpm), and R11 to calibrate 140 mA (250 fpm). The adjustments interact so some iteration may be necessary. Sorry ‘bout that.
Q1 serves as the self-heated sensor with Q2 providing ambient temperature compensation. Opamp A2 runs a feedback loop that forces a constant Vbe differential between Q1 and Q2. This establishes a constant 31oC temperature differential between Q1 and ambient. It does this (with the help of Darlington current gain) by forcing Q1’s current draw (I) through R3 to drive Q1’s power dissipation (Pw) to follow the Figure 1 curve of heat-vs-air flow.
Okay so far. But how does compensation for Figure 1’s nonlinearity happen? Well, happily the function of Q1’s Pw vs collector current I isn’t linear either. In fact Pw = 5vI – I2R3. That quadratic I2 term is the key. It creates the lovely linearizing curve shown in Figure 3.
Figure 3 This graph logs Q1 power dissipation vs collector current. Pw = 5vI – I2R3.
The 2nd-order curvature of fig. 3 irons out (most of) the bend in Figure 1 and results in a linear 33 to 125 mA current draw over the 0 to 250 fpm flow rate range. Although the match isn’t perfect, when converted to the 40 to 140 mA by opamp A1 and output transistor Q4, the realized output is a calibrated readout of air speed that differs from ideal by less than +/- 5% from 0 to 250 fpm, as shown in Figure 4.
Figure 4 This graph logs anemometer output vs airspeed. FPM = 2.5(Iout – 40mA).
Note that most (~90%) of the output current is actually drawn by inverted regulator U1 as it maintains a constant 5v across the (thirsty) thermal transistors. All that’s left for A2 and Q4 is to conduct several mA of shim current to establish and maintain calibration, which barely gets Q4 warm. U1, however, can be called on to dissipate about three quarters of a watt and thus should be bundled in a TO220 or similar package.
Stephen Woodward‘s relationship with EDN’s DI column goes back quite a long way. Over 200 submissions have been accepted since his first contribution back in 1974. They have included best Design Idea of the year in 1974 and 2001.
Related Content
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- Linearized portable anemometer with thermostated Darlington pair
- Nonlinearities of Darlington airflow sensor and VFC compensate each other
- Improve thermal airflow sensor PSRR with just two resistors
- A groovy apparatus for calibrating miniature high sensitivity anemometers
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