Thermal techniques in measurement and control circuitry


Low-flow rate thermal flowmeter

Figure 15.8 shows a liquid flowmeter schematic. Courtesy: “Analog Circuit Design Volume 2,” Newnes PressMeasuring low flow rates in fluids presents difficulties. “Paddle wheel” and hinged vane type transducers have low and inaccurate outputs at low flow rates. If small diameter tubing is required, as in medical or biochemical work, such transduction techniques also become mechanically impractical. Figure 15.8 shows a thermally based flowmeter with high accuracy at rates as low as 1 mL/min and a frequency output that is a linear function of flow rate.

Figure 15.9 provides details about a flowmeter transducer. Courtesy: “Analog Circuit Design Volume 2,” Newnes PressThis design measures the differential temperature between two sensors (Figure 15.9). One sensor, T1, located before the heater resistor, assumes the fluid’s temperature before it is heated by the resistor. The second sensor, T2, picks up the temperature rise induced into the fluid by the resistor’s heating. The sensor’s difference signal appears at A1’s output. A2 amplifies this difference with a time constant set by the 10MΩ adjustment. Figure 15.10 shows A2’s output versus flow rate.

Figure 15.10 provides flowmeter response data. Courtesy: “Analog Circuit Design Volume 2,” Newnes PressThe function has an inverse relationship. A3 and A4 linearize this relationship, while simultaneously providing a frequency output (Figure 15.10). A3 functions as an integrator, which is biased from the LT1004 and the 383k input resistor. Its output is compared to A2’s output at A4. Large inputs from A2 force the integrator to run for a long time before A4 can go high, turning on Q1 and resetting A3. For small inputs from A2, A3 does not have to integrate very long before resetting action occurs. Thus, the configuration oscillates at a frequency that is inversely proportional to A2’s output voltage. Since this voltage is inversely related to flow rate, the oscillation frequency linearly corresponds to flow rate.

Several thermal considerations are important in this circuit. The amount of power dissipated into the stream should be constant to maintain calibration. Ideally, the best way to do this is to measure the VI product at the heater resistor and construct a control loop to maintain constant wattage dissipation. However, if the resistor specified is used, its drift with temperature is small enough to assume constant dissipation with a fixed voltage drive.

Additionally, the fluid’s specific heat will affect calibration. The curves shown are for distilled water. To calibrate this circuit, set a flow rate of 10 mL/min and adjust the flow calibration trim for 10 Hz output. The response time adjustment is convenient for filtering flow aberrations due to mechanical limitations in the pump driving the system.

Thermally based anemometer (air flowmeter)

Figure 15.11 shows another thermally based flowmeter, but this design is used to measure air or gas flow. It works by measuring the energy required to maintain a heated resistance wire at constant temperature. The positive temperature coefficient of a small lamp, in combination with its ready availability, makes it a good sensor. A type 328 lamp is modified for this circuit by removing its glass envelope. The lamp is placed in a bridge monitored by A1. A1’s output is current amplified by Q1 and fed back to drive the bridge. The capacitors and 220Ω resistor ensure stability. The 2k resistor furnishes start-up. When power is applied, the lamp is at a low resistance, and Q1’s emitter tries to come full on.

Figure 15.11 shows a thermal anemometer. Courtesy: “Analog Circuit Design Volume 2,” Newnes Press

As current flows through the lamp, its temperature quickly rises, forcing its resistance to increase. This action increases A1’s negative input potential. Q1’s emitter voltage decreases, and the circuit finds a stable operating point. To keep the bridge balanced, A1 acts to force the lamp’s resistance, hence its temperature, constant. The 10k-2k bridge values have been chosen so that the lamp operates just below the incandescence point. This high temperature minimizes the effects of ambient temperature shifts on circuit operation. Under these conditions, the only physical parameter that can significantly influence the lamp’s temperature is a change in dissipation characteristic. Air flow moving by the lamp provides this change. Moving air by the lamp tends to cool it, and A1 increases Q1’s output to maintain the lamp’s temperature. The voltage at Q1’s emitter is nonlinearly, but predictably, related to air flow by the lamp. A2, A3, and the array transistors form a circuit that squares and amplifies Q1’s emitter voltage to give a linear, calibrated output versus air flow rate.

To use this circuit, place the lamp in the air flow so that its filament is a 90 deg angle to the flow. Next, either shut off the air flow or shield the lamp from it, and adjust the zero flow potentiometer for a circuit output of 0 V. Then, expose the lamp to air flow of 1000 ft/min and trim the full flow potentiometer for 10 V output. Repeat these adjustments until both points are fixed. With this procedure completed, the air flowmeter is accurate within 3% over the entire 0-1000 ft/min range.

Low distortion, thermally stabilized Wien bridge oscillator

Figure 15.12 shows a low-distortion sinewave oscillator. Courtesy: “Analog Circuit Design Volume 2,” Newnes PressThe positive temperature coefficient of lamp filaments is employed in a modern adaptation of a classic circuit in Figure 15.12. In any oscillator it is necessary to control the gain as well as the phase shift at the frequency of interest. If gain is too low, oscillation will not occur. Conversely, too much gain will cause saturation limiting. Figure 15.12 uses a variable Wien bridge to provide frequency tuning from 20 Hz to 20 kHz.

Figure 15.13 shows oscillator waveforms. Courtesy: “Analog Circuit Design Volume 2,” Newnes PressGain control comes from the positive temperature coefficient of the lamp. When power is applied, the lamp is at a low resistance value, gain is high, and oscillation amplitude builds. As amplitude builds, the lamp current increases, heating occurs, and its resistance goes up. This causes a reduction in amplifier gain, and the circuit finds a stable operating point. The lamp’s gain-regulating behavior is flat within 0.25 dB over the 20 Hz-20 kHz range of the circuit. The smooth, limiting nature of the lamp’s operation, in combination with its simplicity, gives good results.

Trace A, Figure 15.13 shows circuit output at 10 kHz. Harmonic distortion is shown in Trace B and is below 0.003%. The trace shows that most of the distortion is due to second harmonic content, and some crossover disturbance is noticeable. The low resistance values in the Wien network and the 3.8nV√Hz noise specification of the LT1037 eliminate amplifier noise as an error term.

Figure 15.14 charts oscillator distortion versus frequency. Courtesy: “Analog Circuit Design Volume 2,” Newnes PressAt low frequencies, the thermal time constant of the small normal mode lamp begins to introduce distortion levels above 0.01%. This is due to “hunting” as the oscillator’s frequency approaches the lamp thermal time constant. This effect can be eliminated, at the expense of reduced output amplitude and longer amplitude settling time, by switching to the low frequency, low distortion mode. The four large lamps give a longer thermal time constant and distortion is reduced. Figure 15.14 plots distortion versus frequency for the circuit.

This information, used with permission, is based on chapter 15 in “Analog Circuit Design, Volume 2,” published by the Newnes Press imprint of Elsevier Science & Technology Books. Edited by Bob Dobkin and the late Jim Williams, the new volume, “Analog Circuit Design, Volume 2, Immersion in the Black Art of Analog Design,” extends the reach of the first volume, at 1250 pages, covering many analog circuit design techniques.

- By Jim Williams, long-time staff scientist, Linear Technology Corp. He passed away June 12, 2011, according to the company. Edited by Mark T. Hoske, content manager CFE Media, Control Engineering, and Plant Engineering, mhoske(at)

Key concepts

Those designing circuits, instead of battling thermal properties, can apply thermal techniques to measurement and control circuits, helping to resolve challenges, particularly with temperature control.

Consider this

Could these analog circuit design tips help those you know designing instrumentation?

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At, search “Thermal techniques in measurement” to read more advice, see references, and see additional figures. 

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