Self-heated Darlington transistor pair comprises new air flow sensor

Texas Instruments LM10

Among the many methods available for air flow detection, self-heated thermal flow sensors are simple, cheap, rugged, and sensitive. They rely on the relationship between airspeed (VF) and thermal impedance (ZT = °C/W) of a heated sensor as shown in the empirical thermal impedance formula below. It quantitatively relates junction temperature rise, power dissipation, and air flow speed for a self-heated 2N4401 transistor in the traditional TO-92 package:

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ZJ = junction-to-case thermal impedance = 44 °C/W
SC = still-air case-to-ambient conductivity = 6.4 mW/°C
KT = “King’s Law” thermal diffusion constant = 0.75 mW/°C√fpm
VF = air flow in ft/min

Figure 1 shows junction temperature vs air flow predicted by the above expression for transistor power dissipation of 320 mW and air flow speed from zero (stagnant air) to 1000 fpm (~11 mph). Note that sensitivity is good even for very slow air speeds, e.g., the 50 fpm (~1/2 mph) point indicated.

TO-92 junction temperature rise versus air speed.
Figure 1. TO-92 junction temperature rise versus air speed.

Figure 2 shows how to translate Figure 1’s math into a practical circuit, using to advantage what’s often thought of as a disadvantage of the classic Darlington topology.

The flowrate sensor circuit.
Figure 2. The flowrate sensor circuit.

Q1 plays the role of Figure 1’s self-heated sensor, and its tempco converts junction temperature into voltage at –1.5 mV/°C. The LM10 200 mV reference A1 regulates Q1 current to 0.2 V/R3 = 67 mA and thereby Q1’s power dissipation to a constant 67 mA × 4.8 V = 20 mW. The resulting junction temperature delta, as shown by Figure 1, provides the airspeed readout as it falls from 64 °C at 0 fpm, to 25 °C at 1000 fpm, with a corresponding rise in junction voltage due to Q1’s VBE tempco, from 0.654 V @ 0 fpm to 0.713 V @ 1000 fpm.

Of course, these numbers are relative to ambient temperature and their accurate interpretation therefore depends on accurate compensation for changes in ambient. That’s where the Darlington connection and its “disadvantage” come in.

Since its invention by Sidney Darlington in 1953, the Darlington pair has been a popular topology because of the advantage provided by the cascaded current gains of the two transistors multiplying together. Meanwhile, and usually thought of as a disadvantage of the Darlington, is that the “on voltages” (e.g., VBE) of the pair unavoidably sum together. This Design Idea, by contrast, makes that bad thing into a good thing.

Both VBE1 and VBE2 contain temperature-dependent components proportional to self-heating (which is sensitive to airspeed) and to ambient temperature (which isn’t). But, because Q2’s power dissipation is so very small (~1 mW), its corresponding self-heating is << 1 °C and can therefore be safely ignored, making VBE2 accurately dependent only on ambient temperature and not airspeed.

Thus, the signal at Q2’s base is a reference that the R1-R2 voltage divider inputs to comparator A2, that tracks and cancels the effects of ambient temperature change on Q1. The R1/R2 ratio accommodates the higher –2 mV/°C tempco of Q2 versus Q1’s –1.5 mV/°C (which results from the Darlington current gain and Q2’s consequent 150x lower collector current) making A2’s differential comparison independent of ambient temperature and influenced only by airspeed.

Note that Q1’s net junction temperature (rise + ambient) remains below the 2N4401’s max rated 150 °C in ambient temperatures as hot as 70 °C, even in zero air flow.

Bias resistor R4 provides a voltage offset that cancels Q2’s lower VBE and sets the air flow threshold setpoint. The 220k shown sets a 50 fpm setpoint, but different flow rates can be selected with a simple change to R4; higher R4 = higher flowrate setpoint.

Figure 2’s Darlington-based circuit is robust and energy-efficient. Its total power draw is less than 400 mW.

Materials on the topic

  1. Datasheet Texas Instruments LM10
  2. Datasheet ON Semiconductor 2N4401


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