Previous Blog talked a little about using filtering to reduce noise. With position sensors, a lot of applications place them in the loop of a control system. I'm not a control-loop engineer, just had a smattering of exposure enough to know that although noise is important so is the phase. Actually, in a control system you can refer to the stability of the loop by either a phase margin or a gain margin. The critical points are when gain=0db and phase equals -180°. So, your phase margin is how many degrees above -180 that you are when gain declines to 0db. Similarly, gain margin is how much below 0db you are when the phase hits -180°. So it happens just like you see in life, if the gain is too high, the system oscillates. And, of course, you know that despite how terribly the control system is designed, it's the phase shift of the sensor that is causing problems.
Now we're in a familiar place for displacement sensors--right up against the laws of physics. This time the trade-off is noise versus phase. You want the noise to be as low as possible (or, for the customer, lower than physical laws allow ;-), but still have plenty of phase margin. Add to this the fact that eddy-current displacement sensors do have a carrier frequency, and the fun begins. This carrier frequency is the drive signal to the senor that creates the magnetic field that interacts with the target. And, of course, you guess it, that frequency can't just be anything so it's easily placed way out of the band of interest. Distance information is extracted from the carrier (I'll talk about that in a later blog) and the residual carrier has to be removed, or it pretty much dominates your resolution. So we have to filter it out. It ain't going away on its own. Admittedly there are schemes to extract information from the carrier that double the frequency of the residual, however they have other problems (remember, backs up against the laws of physics?).
Most of our products try to limit themselves to two poles of filtering. For every pole in the filter, the amplitude declines by 6 db per octave (20db per decade) and the phase declines by 45° at the pole frequency. It seems to be common sense to put as many poles as possible to kill the residual carrier (and high frequency noise). However, then you have a problem with phase. Having 4 poles does not cause a filter to oscillate, however, in a control system, this translates to -45 x 4 or -180° of phase shift at the pole frequency, so, to be stable, the system would have to have less than 0db (or less than a gain of 1) at that frequency. Of course, this also assumes that the rest of the control system has no phase shift...HA!
Just for laughs, lets look at some typical numbers. You have a system with a bandwidth of 50khz, the carrier frequency is 1 Mhz (I'll talk about carrier frequencies and targets at a later blog), so....your carrier is one decade and one octave higher than the bandwidth. With a two pole filter, the 1 Mhz carrier will be -40 + -12 or -52 db. Reversing the conversion, this gives you a resolution of 1 part in 400. Hardly spectacular. Now take that four pole filter. -80 + -24 or -104 db and now resolution is one part in 160,000. Much better. But--Whoa!--what about that phase shift! With four poles we are already at -180° at the cutoff frequency.
Now's the time we can begin to play games. Not all of the four poles have to be at the same frequency, nor does the filter transfer function have to be smooth in the passband, you can play games with inductors, you can extend out the bandwidth and have the user control the phase in the bandwidth of interest.
Again, no easy answer.