Thermal techniques in measurement and control circuitry
Circuit design: Applying thermal techniques to measurement and control circuits allows novel solutions to difficult problems, most obviously temperature control.
Designers spend much time combating thermal effects in circuitry. The close relationship between temperature and electronic devices is the source of more design headaches than any other consideration.
Instead of eliminating or compensating for thermal parasitics in circuits, it is possible to use them. In particular, applying thermal techniques to measurement and control circuits allows novel solutions to difficult problems. The most obvious example is temperature control. Familiarity with thermal considerations in temperature control loops permits less obvious, but very useful, thermally based circuits to be built.
Temperature controller (TC)
Figure 15.1 shows a precision temperature controller for a small components oven. When power is applied, the thermistor, a negative TC device, is at a high value. A1 saturates positive. This forces the output for the switching regulator (Linear Technology LT3525A) low, biasing Q1. As the heater warms, the thermistor’s value decreases. When its inputs finally balance, A1 comes out of saturation and the LT3525A pulse width modulates the heater via Q1, completing a feedback path. A1 provides gain and the LT3523A furnishes high efficiency. The 2 kHz pulse width modulated heater power is much faster than the thermal loop’s response, and the oven sees an even, continuous heat flow.
The key to high-performance control is matching the gain bandwidth of A1 to the thermal feedback path. Theoretically, it is a simple to do this with conventional servo-feedback techniques. Practically, the long time constants and uncertain delays inherent in thermal systems present a challenge. The unfortunate relationship between servo systems and oscillators is very apparent in thermal control systems.
The thermal control loop can be very simply modeled as a network of resistors and capacitors. The resistors are equivalent to the thermal resistance and the capacitors equivalent to thermal capacity. In Figure 15.2, the heater, heater-sensor interface, and sensor all have RC factors that contribute to a lumped delay in the ability of a thermal system to respond. To prevent oscillation, A1’s gain bandwidth must be limited to account for this delay. Since high gain bandwidth is desirable for good control, the delays must be minimized. The physical size and electrical resistivity of the heater selected give some element of control over the heater’s time constant. The heater-sensor interface time constant can be minimized by placing the sensor in intimate contact with the heater.
The sensor’s RC product can be minimized by selecting a sensor of small size relative to the capacity of its thermal environment. Clearly, if the wall of an oven is 6-in. thick aluminum, the tiniest sensor available is not an absolute necessity. Conversely, if one is controlling the temperature of a 1/16-in.-thick glass microscope slide, a very small sensor (that is, fast) is needed.
After the thermal time constants relating to the heater and sensor have been minimized, some form of insulation for the system must be chosen. The function of insulation is to keep the loss rate down so the temperature control device can keep up with the losses. For any given system, the higher the ratio between the heater-sensor time constants and the insulation time constants, the better the performance of the control loop.
After these thermal considerations have been attended to, the control loop’s gain bandwidth can be optimized. Figures 15.3A, 15.3B, and 15.3C show the effects of different compensation values at A1. Compensation is trimmed by applying small steps in temperature setpoint and observing the loop response at A1’s output. The 50Ω resistor and switch in the thermistor leg of the bridge furnish a 0.01 C step generator.
Figure 15.3A shows the effects of too much gain bandwidth. The step change forces a damped, ringing response over 50 seconds in duration. The loop is marginally stable. Increasing A1’s gain bandwidth (GBW) will force oscillation.
Figure 15.3B shows what happens when GBW is reduced. Settling is much quicker and more controlled. The waveform is overdamped, indicating that higher GBW is achievable without stability compromises.
Figure 15.3C shows the response for the compensation values given and is a nearly ideal critically damped recovery. Settling occurs within 4 seconds. An oven optimized in this fashion will easily attenuate external temperature shifts by a factor of thousands without overshoots or excessive lags.
Thermally stabilized PIN photodiode signal conditioner
Positive-intrinsic-negative (PIN) photodiodes are frequently employed in a wide range of photometric measurements. The photodiode specified in Figure 15.4 responds linearly to light intensity over a 100 dB range. Digitizing the diode’s linearly amplified output would require an analog-digital (A/D) converter with 17 bits of range. This requirement can be eliminated by logarithmically compressing the diode’s output in the signal conditioning circuitry. Logarithmic amplifiers use the logarithmic relationship between base-emitter voltage (VBE) and collector current in transistors. This characteristic is very temperature sensitive and requires special components and layout considerations to achieve good results. Figure 15.4’s circuit logarithmically signal conditions the photodiode’s output with no special components or layout.
A1 and Q4 convert the diode’s photocurrent to a voltage output with a logarithmic transfer function. A2 provides offsetting and additional gain. A3 and its associated components form a temperature control loop that maintains Q4 at constant temperature (all transistors in this circuit are part of a CA3096 monolithic array).
The 0.033μF value at A3’s compensation pins gives good loop damping if the circuit is built using the array’s transistors in the locations shown. These locations have been selected for optimal control at Q4, the logging transistor. Because of the array die’s small size, response is quick and clean. A full-scale step requires only 250 ms to settle (photo, Figure 15.5) to final value.
To use this circuit, first set the thermal control loop. To do this, ground Q3’s base and set the 2k pot so A3’s negative input voltage is 55mV below its positive input. This places the servo’s setpoint at about 50 C (25 C ambient + 2.2 mV/ C • 25 C rise = 55 mV = 50 C). Unground Q3’s base, and the array will come to temperature. Next, place the photodiode in a completely dark environment and adjust the “dark trim” so A2’s output is 0 V. Finally, apply or electrically simulate (see chart, Figure 15.4) 1 mW of light and set the “full-scale” trim to 10 V out. Once adjusted, this circuit responds logarithmically to light inputs from 10 nW to 1 mW with an accuracy limited by the diode’s 1% error.
50 MHz bandwidth thermal RMS->dc converter
Conversion of ac waveforms to their equivalent dc power value is usually accomplished by rectifying and averaging or by using analog computing methods. Rectification averaging works only for sinusoidal inputs. Analog computing methods are limited to use below 500 kHz. Above this frequency, accuracy degrades beyond the point of usefulness in instrumentation applications. Additionally, crest factors greater than 10 cause significant reading errors.
A way to achieve wide bandwidth and high crest factor performance is to measure the true power value of the waveform directly. The circuit of Figure 15.6 does this by measuring the dc heating power of the input waveform. By using thermal techniques to integrate the input waveform, 50 MHz bandwidth is easily achieved with 2% accuracy.
Additionally, because the thermal integrator’s output is at low frequency, no wideband circuitry is required. The circuit uses standard components and requires no special trimming techniques. It is based on measuring the amount of power required to maintain two similar but thermally decoupled masses at the same temperature. The input is applied to T1, a dual-thermistor bead. The power dissipated in one leg (T1A) of this bead forces the other section (T1B) to shift down in value, unbalancing the bridge formed by the other bead and the 90k resistors.
This imbalance is amplified by the A1-A2-A3 combination. A3’s output is applied to a second thermistor bead, T2. T2A heats, causing T2B to decay in value. As T2B’s resistance drops, the bridge balances. A3’s output adjusts drive to T2A until T1B and T2B have equal values. Under these conditions, the voltage at T2A is equal to the root-mean-square (RMS) value of the circuit’s input. In fact, slight mass imbalances between T1 and T2 contribute a gain error, which is corrected at A4. RC filters at A1 and A2 and the 0.01μF capacitor eliminate possible high frequency error due to capacitive coupling between T1A and T1B. The diode in A3’s output line prevents circuit latch-up.
Figure 15.7 details the recommended thermal arrangement for the thermistors. The Styrofoam block provides an isothermal environment, and coiling the thermistor leads attenuates heat pipe effects to the outside ambient. The 2-in. distance between the devices allows each to have identical thermal conditions without interaction. To calibrate this circuit, apply 10 V dc to the input and adjust the full-scale trim for 10 V out at A4. Accuracy remains within 2% from dc to 50 MHz for inputs of 300 mV to 10 V. Crest factors of 100:1 contribute less than 0.1% additional error, and response time to rated accuracy is 5 sec.
See next page for flowmeter and other discussions and diagrams...
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