Mathematical Madness

• My good friend Norm gave me some old flight instruments for the sim which I am slowly modifying for use with computerized inputs. One of the coolest ones was a VOR gauge. This gauge has a full-circle wirewound potentiometer for the course select control. The problem was how to read the course position from this oddball pot.

The problem

• The pot is essentially a modified Wheatstone bridge. That is 4 resistors arranged in a diamond shape. Where a normal Wheatstone has a meter connected across the East/West terminals this pot has nothing. Instead it has a wiper that can travel around the pot. The pot and it's electrical circuit look like this. The pot is the ring around the meters and you can see one of the taps. It's not readily apparent, but the course ring has non-linear divisions.

Idea 1

• My first thought was to connect +5V to the wiper and use the analog to digital converter in a PIC to measure the voltages at the four cardinal taps. My thoughts were that the voltages would give me the wiper position.

• After a bit of study, it became apparent that the calculations required to find the wiper position from these readings would involve superposition theorem to work out the currents in all the branches of the circuit. Furthermore, the exact resistance of each branch needed to be known. This in itself required solving 4 simultaneous equations. This was looking like a serious math problem, and for a math-free zone like me, decidedly not do-able. There had to be a better way. It turns out there is.

Idea 2

• In the real instrument, two signals 90 degrees out of phase are applied across North/South and East/West. The resultant voltage and phase are tapped off the wiper and fed to a mechanical resolver. The voltage and phase of the signal are dependant on the wiper position. The mechanical resolver part meant that this approach was not going to take me anywhere, BUT.
• It got me to thinking about turning my measurement method inside out. I thought that if I applied two 5 Volt signals 90 out of phase I might be able to get something useful from the wiper. If I rotated these voltages 90 degrees and took a set of readings that might do the trick.

• This approach turned out to be even simpler and more effective than I first thought, here's why...

The method

• When you apply the voltages this way, what happens is that you get the 5 volts spread across two quadrants of the pot. One of the other quadrants has ground on both ends. The remaining quadrant has 5 volts on both ends.

• If you apply each voltage configuration in turn and take a voltage reading from the wiper for each configuration, what you will get is this.
• One reading will be 0 volts when the wiper's quadrant has ground on both sides. One reading will be 5 volts. The other two readings will be somewhere between 5 volts and ground depending on the wiper position. Co-relating the 5 volt reading with the configuration that caused it will tell us which quadrant the wiper is on. This is the coarse (not course) position.
• Now if we change the voltage configuration so that one end of this quadrant has ground on it and the other end has 5 volts then read the voltage on the wiper, we will get a voltage which is proportional to the wiper position in the quadrant. For example, If the North tap has 5 volts and the east tap has ground and the voltage on the wiper is 4 volts, then the wiper is 4/5 of the way from 90 towards 0. or 1/5 of the way from 0 to 90. 1/5 of 90 degrees is 18 degrees. Since we are in the 0-90 quadrant our course setting (fine reading) is 18 degrees.
• What affect to the voltages on the other quadrants have on the reading? Well if the source can supply a constant voltage then they don't interact with the reading at all. Given that one end of the quadrant being read is at the full supply voltage and the other end is connected to ground, it is effectively isolated from the other quadrants.
• The best part is that the reading is not dependant on the absolute resistance value of the quadrant. Nor is it dependent on resistance changes over time or due to temperature. As it turned out, there were small differences in the resistance values between the quadrants which looked like complicating the maths and calibrations.

The practical aspects

• The next problem was how to switch a constant voltage source and keep the circuitry as simple as possible. What I needed was a circuit that had 4 outputs that could be switched high(5V) or low(0V) on command of the PIC and which could supply a constant voltage when doing so. I hit on the idea of a stepper motor driver. I have a lot of these chips at hand and they can supply up to 1 Amp from each output. Given that the resistance of the quadrants is around 2K, at 5 volts they will draw only 2.5ma. That will make the stepper chip look near enough like a constant voltage source as the stepper chip can supply 400 times the amount of current required by the quadrants. The stepper chip looks like this...

• The stepper chip has two channels, each with two complementary outputs. It only requires two IO pins to drive this chip. The four states of the inputs can give me all the voltage configurations as shown in the circuits shown earlier.  I bought a bulk quantity of these chips for  about $1.00 each.

Fighting the manufacturer

• The final problem to be solved is the non-linear spacing of the markings on the course ring. Apparently the circuitry used with the original instrumentation was non-linear and the manufacturer made up for it by altering the spacing of the course markers around the wiper ring. This was easy to fix by printing a new set of marks on a label and sticking it on the ring.

Testing

• I've tested my measurement technique on the bench with a linear marked compass ring. The calculations agree with the setting to within a few tenths of a degree. In fact the course setting cannot be read as accurately as the calculations can predict. However when the calculations say that the setting is 135.25 degrees and the setting is a poofteenth (= 1/poofteen) past 135 degrees, that's good enough for me. ;-)

Acknowledgement

• I'd like to thank Gordon my nephew for his mathematical help. I've forgotten half of the maths I learned in college and never used the rest. Gordon is studying mechatronics and is current with the maths as well as some very neat tricks with Excel. His help with mathematical analyses has been invaluable.

Feedback

• If you know of an easier or better way to get the course information from this circular pot, I'd love to hear from you. Even if you just want to discuss or refine this technique, write to me at my hotmail address.