### The Light-Bulb Pirani Gage Project

Pirani Gage Information:  http://en.wikipedia.org/wiki/Pirani_gauge

Background.
The principle is that the resistance of metals increases at higher temperatures and a heated wire suspended in a gas will lose heat by conduction and convection in proportion to the number of gas molecules present; the heat loss is thus proportinal to pressure. One of the best ways to measure the heat loss is to measure the voltage required to maintain the filament at a fixed temperature. The wire has a positive coefficient of temperature and, given the value of resistance at ambient temperature, one can calculate the resistance of the wire at a chosen elevated temperature. If a Wheatstone Bridge is configured so that a reference resistor, in value equal to the resistance that the filament will reach at an elevated temperature, is paired with the sensor filament, the bridge will be out of balance at ambient temperature since these resistances are not equal (as are the insensitive resistors in the other bridge leg - as shown in the schematic). If this imbalance is used to control a voltage applied to the Wheatstone bridge, an increased voltage will heat the filament and its resistance will increase, while the reference resistor (far less temperature sensitive) remains stable. The bridge and feedback circuit stabilize when the filament resistance reaches the value of the paired reference; this assumes that the other leg of the bridge uses equal value resistors as shown in the schematic. The voltage being applied to the bridge at balance at atmospheric pressure becomes the "ATM" calibration point. As the pressure surronding the filament is reduced, less heat is lost than at atmospheric pressure, and less voltage is needed by the bridge circuit to maintain the filament at the correct resistance (and temperature); the bridge excitation voltage is then an indication of the pressure, the voltage decreasing with decreasing pressure.

The elevated filament temperature can be selected  so that the filament is hot enough to burn off any contaminants that may reach it, but not incandescent. In all cases the filament will be this temperature and will be robust and avoid burnout. The filaments of the best gages are often formed of platinum wire alloys, but tungsten, in the form of a light bulb filament makes a nice sensor as well.

This is a simple single-element sensor that utilizes the tungsten filament of the GE "Indicator-6" 6W/120V lamp as a sensor of vacuum. This lamp has good balance of characteristics for this application; the 120V, low wattage lamp filament can operate in the <20V range at the modest filament temperatures used without much power consumption. To make the sensor, the aluminum screw base is cut off with fine wirecutters exposing the base of the glass envelope as shown. There is some resin that will need to be scraped away. There is a small central tubular stem of heat sealed glass visible at the center. This is where the lamp envelope was evacuated and/or backfilled. A diamond or tungsten scribe can be used to score the stem and it can then be snapped off (as shown), allowing the interior of the lamp and filament to communicate with the "outside" environment; the opened bulb needs to be mounted inside the vacuum system and the leads connected to "feedthroughs" that connect to the measuring circuit externally. From Wikipedia - Temperature Coefficient:

The temperature coefficient is the relative change of a physical property when the temperature is changed by 1 K.

In the following formula, let R be the physical property to be measured and T be the temperature at which the property is measured. T0 is the reference temperature, and ΔT is the difference between T and T0. Finally, α is the (linear) temperature coefficient. Given these definitions, the physical property is: $\operatorname{R}(T) = \operatorname{R}(T_0)(1 + \alpha\Delta T)$

Here α has the dimensions of an inverse temperature (1/K or K−1). This equation is linear with respect to temperature.

Sample Calculations
The GE Indicator-6 lamp used had a resistance of 200 ohms at 20C.
Tungsten has a temperature coefficient of resistivity of 0.0046/K
For an elevation of +100C the calculation is: R(T) = 200Ω(1+0.0046*100) = 200Ω (1.46) = 292Ω (at 120C, assuming 20C initial)
A 294Ω 1% resistor was selected as the closest value for the bridge (R8 in the schematic).

Description of Bridge Operation
The Wheatstone Bridge is the R8-R9 pair for one leg and R6-R7 pair for the fixed reference legs. The junction of these bridge pairs is compared by the amplifier IC1a, and the error signal when R8≠R9 drives the transistor Q1 to provide the bias to the bridge array. The error amplifier output will go positive when the (-)input is below the (+)input - this is inverting operation. When first turned on the sensor leg of the bridge is the 200Ω filament paired with the 294Ω so the (-) input is low, therefore the opamp output will be high, driving the transistor Q1 "ON" and increased voltage is applied to the bridge legs. The voltage at the junction of R6-R7 will in all cases be half the applied bridge drive, and the junction at the R8-R9 junction will equal this value when the increased voltage has heated the filament and caused it's resistance to reach 294Ω (equal to R8). The voltage driving the bridge is the output, and a sample of it can be scaled to (for example) 10V at atm pressure by RV1 adjustment; this could also be done with a recorder "span"  or scaling adjustment. If the pressure surrounding the sensor filament drops from ATM, less voltage is required to maintain the sensor filament at 294Ω so in this case the bridge excitation is a lower voltage, yielding a lower output voltage - output proportional to pressure.

Schematic of the Light-Bulb Pirani circuit:

Spreadsheet: data of the Light-Bulb Pirani Gage (OpenOffice Spreadsheet)
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Spreadsheet: data of the Light-Bulb Pirani Gage (Excel Spreadsheet)