Teledyne HPM-2002-OBE Eg = Kg ∆T As/∆x, Eg = arLt273/Th1/2Th-TaAgP, Dual Sensor Operation

loss is only approximately 10% of Es. If ambient changes are small compared to the absolute values of the temperature this loss can approximated as a constant with temperature.

Since the first two losses are essentially constant at high vacuum for a given sensor, we can measure these losses and subtract them from the input power which leaves only the rate of heat transmission through the gas (Eg).

In the viscous flow regime, the Eg loss is directly dependent on the thermal conductivity of the gas (Kg), the surface area of the membrane, the differential temperature and is inversely proportional to distance between the membrane and the lid. It can be written as

Eg = (Kg ∆T As)/∆x

The thermal conductivity of the gas is essentially constant when in viscous flow where the Knudsen number (Kn) is less than 0.01. In the viscous flow regime there is no change in sensor output with pressure since all of the losses are constants with pressure.

In the molecular flow regime where (Kn > 1) the thermal conductivity of the gas becomes directly proportional to the gas pressure as shown below. We can expect then that Eg will be constant at high pressures and directly proportional to the pressure at low pressures. The energy loss, Eg, changes between these two controlling equations as the system passes through the transition region (0.01 < Kn < 1).

Eg = arLt(273/Th)1/2(Th-Ta)AgP

where

ar = accomodation coefficient

Lt = free molecule thermal conductivity Th = temperature of heated membrane Ta = ambient temperature

P = pressure

Ag = surface area of the heated portion of the membrane

For nitrogen at a pressure of 760 Torr and a temperature of 20 °C the mean free path (λ) is less than 1 x 10-

7meters and is inversely proportional to pressure. Since the thermal transfer distance (∆x) is a few micrometers, this sensor will remain in the molecular flow regime at a much higher pressure (10 Torr) than is typical for a thermal vacuum gauge. This extends the linear response part of the output curve up into the 1 Torr range. The nonlinear transition region will extend up to 1000 Torr.

4.4. Dual Sensor Operation

The microprocessor in the control unit continuously monitors the outputs of both the piezoresistive sensor and the Pirani sensor. Figure 4.4 shows representations of the sensors output over the pressure range from 10-5Torr to 10+3 Torr. The microprocessor uses the output of the piezoresistive sensor at high pressures (>32 Torr) and uses the output of the Pirani sensor at low pressures (<8 Torr). In the crossover region, a software averaging algorithm ensures a smooth transition between the two sensors.

HPM-2002-OBEVacuum Gauge Page 30 of 39