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Finished: 20-10-2023


10^5   -   10^-1 Pa    vacuum meter

Whenever one thinks about measuring air pressure, most likely the bourdon gauge comes to mind. We see these everywhere, from welding setups to camping stoves, from fire extinguishers to beer taps... A thin cylinder with a needle and a scale. These are excellent meters when it comes to reliability, and a wide scala of meters is available for whatever pressure you need... except when it comes to vacuum. You can get a meter that measures from 1 bar to 0, but for a better vacuum than about 0.1 bars, the accuracy is very poor. We don't want to know how the exact air pressure, we want to know what order of magnitude our pressure is. Marcello Stefano Pirani, a German physicist, managed to come up with a very clever way on how to do this in 1906. 

From vacuum to voltage...

So... we have a hot wire in a vacuum. It's a two terminal device, that's... huh? Yeah... I know what you're thinking now, we are very spoiled when it comes to sensors nowadays. Usually you buy a device, put a supply voltage on and you receive either a voltage, current or frequency that is proportional to the measured quantity. Or even more convenient, it uses SPI or I2C or whatever and your microcontroller does the heavy lifting. Absolute worst case you're still provided with a datasheet and a circuit you can copy. In this case, however, we're on our own!

Now, there's many ways to get a useful measurement from a hot wire, but I'll only go over how I did it. For the other ones go dig around on Wikipedia. My method is very similar to the one they use back in the days without active  electronics, but automated.

- We know that the heat-transfer of the hot wire is dependent on the air pressure.

- We also know that the temperature of the wire is dependent on the energy put into the wire.

- Since the wire has a resistance, the energy is proportional to either the voltage or current.

- Finally, the resistance is dependent on the temperature of the wire. 

Thus, if we keep the resistance of the hot wire stable by changing the voltage, the voltage across the hot wire is a direct measure for the energy needed to keep the temperature of the wire stable, and indirectly also of the air pressure! The better the vacuum, the less energy you need to keep it hot, the lower the voltage across the wire can be. Get it? No? My phone number and email are under the contact tab. I really want you to understand this before you go build your own meter!

The Wheatstone bridge has two legs, one consists of known R1 and to-be-determined Rx, the other consists of known R2 and variable R3R1, R2, and R3 are highly precise reference resistors where both legs are configured as voltage dividers. In the middle of these legs, a high impedance galvanometer (volt meter/current meter with series resistor) is connected. The goal is simply to alter the value of R3, such that the galvanometer reads 0. Once that's the case, R1/Rx = R2/R3, meaning that if R1, R2, and R3 are known, Rx can be calculated. The voltage may play a small role in the amount the needle of the meter moves left and right, but rather than trying to do a quantitative measurement, the user is trying to minimalize an error. This means that the supply voltage is irrelevant, because a passive element (in this case the resistors) is now the reference! Note that, if the voltage source is AC, the resistances may also be swapped out for capacitors or inductors. (RCL measurement bridge).

Pirani measurement bridge

Now, the Wheatstone bridge shown above is interesting, it is not practical for us... yet. Let's alter the topology around a bit such that we can use it to read out a Pirani gauge instead.

In the left leg, Rx has been replaced by the hot wire Pirani gauge. Regarding that the room temperature (well... the temperature of the gas in the vacuum chamber) is also an important factor in the heat transfer, Rt is a temperature compensating resistor instead of a fixed one. Both resistors in the left leg are the same in order to negate changes in resistance due to temperature. 

The only variable device now, is the voltage of the power supply. By changing V, the current through each branch can be changed. Both R1s may change in resistance a bit due to heat, but since they're the same, the ratio remains the same. The interesting bit is that the resistance of the hot wire will change. The bigger the current through P, the more the wire will heat up, meaning that the resistance of the wire will rise! Rt is chosen such that the resistance is the same as the resistance of at the desired temperature. To take a measurement, V is adjusted such that the galvanometer reads 0, meaning that P = Rt. When the pressure drops, the same voltage will result in a hotter wire as there is less air around to cool the wire off, meaning that V may be turned down a little in order to balance the bridge again! The lower the pressure, the lower V gets in order to keep the bridge in balance. Easy right?

Less boring theory! More practice!

I can see the cogs turning in your brains. "But Mareijn, what if we use a differential amplifier, and make a feedback loop to control the voltage across the bridge". Shush, we go look at that in a minute, but let me first throw you about the most important detail not to overlook when designing your controller. I challenge you to find any resource that gives you a useful value for the temperature of the wire. If you can find a paper stating useful numbers please mail them to me! I've spent hours and hours trying to find a repeatable paper dropping a figure, I couldn't find anything... but what I DID find is a generous (anonymous) donation of a couple Leybold Heraeus 162 02 vacuum meter heads!

I have to be honest, I got completely stuck initially trying to pull this off with a measurement head I got from AliExpress. I got something somewhat working, but the measurement range was poor and after playing a bit too much with the temperature, I ended up burning the filament. I eventually got these Leybold ones and the first thing I did was opening one up to see what's in there.


I thankfully had three, later buying a fourth one for cheap, meaning I could take the risk to permanently accidently kill one in the worst case (thankfully they're all in good condition still). Initially I thought the sensor itself would extend through the blue plastic body, but it quickly turned out that the entire measurement bridge was located inside! Even with temperature compensated resistor and some other convenient goodies. I will tell you beforehand that you will be able to pull this project off with about any measurement head. These meters are not very accurate so the temperature compensation resistor is not THAT important. However, I recommend IF you find this particular model, to get it. It will save you a bit of time. Also try to get one with the appropriate cable for the Hirschmann connector at the back. And uhhhh... do not overpay, you should be able to get one for around  €20-50. It's the wild west out there, people ask stupidly high prices sometimes, don't fall trap to those and be patient! Here's the schematic:

Beautiful! This is about one-to-one to the measurement bridge described previously, but with measurements too! Now, we can see, again, the right leg has two resistors of the same value, 1k0. We also get an extra 100R 10 turn trimmer. This is used to compensate for any manufacturing differences between measurement heads (as these are somewhat disposables). There's a second bigger 10 turn trimmer in the housing as well, this is "optional" regarding it has nothing to do with the measurement bridge itself. It's used as a gain control in the driving circuitry (we will get to that later). But now the interesting bit:

I actually opened up two separate meters, they had slightly different type numbers so I wanted to see the differences, hence the A's and B's. Here we can see that whilst the resistance of the hot wire and the compensating resistors are slightly different, the ratio's are similar. Maybe they decided to use a different manufacturing method? I have no idea, but they seem to be able to be calibrated properly to be used with the same controller, so it doesn't really matter. What we can see is that Leybold wants the wire to heat up to about 1,35 times it's resistance at room temperature. 

Now we need the resistivity of tungsten (assuming the gauge uses a tungsten wire) as a function of the temperature anywhere. We live in an information age, but regarding most of this material is gatekept and behind paywalls, I advice you to go buy the "CRC handbook of chemistry and physics". It is a HUGE table book with all the data you'll ever need within the fields of chemistry and physics. Besides, it's easy to find, not very rare and the older ones are super cheap. I did the measurements at room temperature (293 K), meaning the resistivity of the wire would've been 528 micro-ohm-meter. At a 35% increase, the resistivity should become around 713 micro-ohm-meter, meaning that the temperature of the wire in these Leybold gauges should be somewhere around 380 K, or give or take between 100-120 °C.

For the readers that only skim over my writing for this figure, let me repeat:


Controller design

Now we know how to set up an appropriate measurement bridge. You have the orders of magnitudes for the resistors that will work, the reference resistance should be 1,35 times the value of the resistance of the Pirani measurement head at room temperature, it is also handy to have add a trimmer so that multiple measurement heads can work with the same controller. May you add this feature, be sure to also add a second trimmer in order to calibrate the full range of your meter. 

So probably less interesting but still useful, I'll show you one example for a control system for the bridge. Whenever I will build a second gauge controller (which I certainly will), I will definitely update the schematic and make a less accurate, but a much more economic version of the control system! For now, this one has been proven to work very accurately!

Regarding I made these designs on perfboard, there was never an incentive to digitalize the schematics. I hope these are readable enough, if there's any questions regarding legibility, please contact me. 

The control system works as follows:

The signal from pins 1 and 3 of the sensor (I'm simply following the same numbering as the schematics shown above for the Leybold Pirani bridge) is buffered by buffers A9 and A10, and is then fed into a differential amplifier A8. This amplifier calculates the error (these three elements are the substitute for the galvanometer spoken earlier about). A4 through A7 from a PI-controller. A7 is an amplifying stage, then the output is fed into a proportional amplifier A5, and an integrating amplifier, A6. The output is summed by A4. A3 is used as a rectifier to suppress any positive output from the PI-controller. A1 and A2 and the PNP transistor form a voltage controlled power supply. The desired setpoint is fed into A1. The output of A1 is tied to the transistor, and the emitter voltage is fed into pin 4 of the sensor. The supply voltage for this gauge is therefore negative! A2 buffers this voltage (technically you could measure the voltage directly on the bridge as a sense line. In my configuration I don't make use of it), and feeds it back into A1 through a voltage divider. This means the voltage controlled power supply has both a gain of 3, and can handle larger currents in order to properly heat up the wire in the sensor. Pin 2 of the sensor is tied to ground. The output of A2 is directly proportional to the quality of the vacuum the sensor is measuring. This signal is fed through the trimmer between pins 5 and 6 of the sensor, to A12. The trimmer can therefore be used to calibrate the output voltage such that it is between 0 and 10 volts (of course you can change the gain such that it falls within your desired range). Finally the output of A12 is buffered by A11 for an external connector, whilst the output of A12 is used to drive a 5mA panel meter through a 2k resistor. 

One peculiarity is that sometimes, at startup the controller misbehaves. If the supply voltage on the bridge is 0 volts, then obviously the error between the two legs of the bridge is also 0! Whilst the goal of the controller is to make sure the error is 0, it thinks it's going a good job by not doing anything at all! This is bad, because you're not measuring anything. Thankfully, the hot wire in the measurement head is not 100% thermally insulated from the outside (as it is connected to the two conductors it's powered by) meaning that you will always need a little bit of energy to keep it hot. The supply voltage on the bridge should NEVER be 0! Thus, whenever this is a case, a poke-button was installed into the controller. One can see that at the base of the transistor, a second diode was added with a series resistor. When, with a push button, a negative voltage is supplied through this branch, it slightly opens the transistor, letting a little bit of current flow in order to heat the wire. The error between the branches suddenly is not 0 anymore, and the controller wakes up and starts to actively regulate the temperature of the wire.

Ofcourse, A3 through A7 could be replaced by a single opamp. A9 and A10 can be omitted if the input resistors of A8 are made larger by atleast a factor 10. A2 is not necessary if you do not use a 3 wire system, and A11 can be taken out as well, leaving 4 opamps total. Whilst doing this will reduce accuracy, it would be cheaper and easier to build, so I'll be exploring this idea soon enough once I'll build Pirani meter V2.0!

Error detection

This Pirani meter was built in such a way it could detect it's own mistakes. The control loop shown above is already plenty to do accurate measurements with, but if you want to use it in an automatic safety system it is important to detect whenever a measurement is false. 

There are technically four failure modes:

- The vacuum changes rapidly, meaning the controller can't keep up, resulting in a false measurement.

- The wire burns up, meaning the controller thinks the wire is infinitely hot, thus it brings the supply voltage of the       bridge to 0V.

- The controller refuses to regulate, because it thinks it's doing a good job whilst not outputting a big enough             voltage to heat up the wire

- The wire to the sensor or one of the PCBs comes loose.

The two circuits shown above are used to condition the signals taken from the error amplifier of the control loop. The left circuit simply adds a trimmable voltage to the error signal so the needle of the meter is set to the middle. The right circuit generates a set of error bounds around 0V. Opamps A15 and A16 are used as comparators to check whether the control system falls within these boundaries, and an overcomplicated AND gate combines the signals from the opamps such that whenever one of the bounds is exceeded, a signal turns high (or low after the inverter stage).

To measure whenever the control system outputs a signal close to 0, another comparator is used, measuring against a reference of around 0,4V (the voltage drop over a germanium diode), outputting a high signal whenever the measured vacuum is above a certain threshold. 

For loose connections, an interlock wire is run through every connector in the system. From PCB to PCB, through the cable to the sensor, etc. One end of the line is by definition high, whilst the other end is pulled low with a resistor. This means the line will always measure low whenever one connector is not seated properly, and goes high if everything is properly in place. 

Through these three signals through an AND gate, will result in a signal that is high whenever the meter is functioning properly. If one of these 4 listed criteria goes wrong, the signal turns low. 


The last feature introduced to the meter are setpoints. Whenever a vacuum drops below a certain setpoint, a signal will be pulled high. This can be incredibly useful for turning on your diffusion pump and ion gauge after a certain level of vacuum is reached, or maybe to turn off a high voltage power supply if the chamber is vented and the pressure gets too high. 

In the schematic above, it can be seen two setpoints can be set (IP1 and IP2). These are combined through an AND gate with the signal from the error detection system. Whenever there are no errors and a setpoint are reached, an output signal is put high, if there is an error or the vacuum is too poor, the output signal is turned low (this is accompanied by a two coloured LED on the front panel of the meter). 

In the schematic, B1 is a buffer for a -5,1V reference. B2 inverts and has a controlled gain such that a reference voltage of 10V can be made. B3 and B4 buffer the output of B2, and the signal is sent through two trimmers available at the front panel of the meter. These trimmers are set up as voltage dividers, where the outputs are buffered by B7 and B8 for display on a panel meter. B5 and B6 are used as comparators, comparing the setpoints with the voltage proportional to the vacuum. Extra resistors are added in order to create a little bit of hysteresis (to prevent oscillations at the output signal). The output of the comparators are buffered by a couple transistors. 

Power supply

The power supply I used to power all this is according to the following schematic:

The topology was deliberately kept incredibly simple, using a small signal transistor as an error amplifier between a setpoint and a reference, driving a big TO-3 transistor to dissipate the heat efficiently. The power supply is balanced and can be separately adjusted. In this case everything is fed off -14V and 14V. I do not want to go in depth when it comes to this circuit, there is a MUCH better article on my website about this topology where I explain everything about discrete transistor power supplies! 

Use whatever design you can get your hands on when it comes to the circuitry shown above. Everything was designed such that the power supply itself never acts as a reference. This means the supply does not have to be very stable or clean.

The build

I think the theory and schematics are most interesting. Ofcourse I made my own implementation, and I am happy to show it off for inspiration.

All circuitry was made on perf boards with big edge connectors:

You can probably see the amount of time that had to be sunk into these to build them by hand. Don't worry, I already designed a standardized power supply and interlock board. This cuts the time in half, meaning that most of the prototyping can be done very efficiently in the future! From top to bottom you can see the power supply, the controller + error detector, the setpoint board and finally the interlock board (with a little bodge on the left side).

These edge connectors click into an aluminium chassis with a transformer and pi-filter solidly mounted for the powersupply:

The connections between all connectors are made on the bottom side of the chassis. I already designed a big motherboard PCB rather than an aluminium chassis. I haven't had an excuse to use it yet however...

Here's a cool perspective angle:

The final steps...

The last step of a build like this is to design a scale for the panel meter itself. Regarding the voltage is not linearly proportional with the quality of the vacuum, easiest is to adapt the scale of the meter to the un-linearities of the system itself. I took the almost finished vacuum meter to my job, and went to measure it against a reference vacuum meter. I set the "100%" trimmer to the middle setting, and I used the "0%" trimmer in order to line up the needle perfectly on the outer end of the scale. My coworker came up with the idea to put the controller right next to the screen of the reference vacuum meter and film the process of pulling a vacuum. Since the original scale in the panel meter was linear, a frame-by-frame analysis could be done in order to determine what voltage corresponds with what pressure.

There's many ways to go about this now. you can use a pen and a protractor to draw up a scale, you could design one by hand using a program that preferably uses vectors like Corel, or if you want consistency in your projects, you can design a bit of software to do everything for you:

I printed the finalized scale on a sheet of printer paper, cut it into the right shape with a scalpel and mounted it to the backside of the original aluminium backing plate of the panel meter using spray adhesive. One final calibration later et voilà. One working, home built, Pirani gauge controller!

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