The past weeks I've been quite busy, so I do not have alot of updates so far. Therefore I decided to make a combined blog for weeks 6 and 7 as I did for weeks 2 and 3.
Thoughts on the frequency counter in the LDC1000
I had another look at the resolution limitations of the LDC1000 and came up with a different idea. It is clear that the resolution of the Rp measurement is determined by the membrane displacement, the specifications of the coil and the settings of the Rpmin and Rpmax registers. Because the settings of the Rpmin and Rpmax registers are fixed (there are only 32 values to choose from) it is quite difficult to design a coil that fits exactly between those two limits so that a maximum displacement amplitude of the membrane corresponds to Rpmax-Rpmin and a minimum displacement amplitude (i.e. a membrane that is not moving) corresponds to (Rpmax-Rpmin)/2.
While looking at the graphs in the Webbench tool I noticed that the inductance changed quite a lot too and for these short distances it was also pretty linear. This got me thinking about the possibility of measuring the distance by looking at the inductance instead of Rp.
The datasheet mentions that L is not measured directly, but instead the oscillation frequency of the LC tank is measured with a frequency counter. The advantage of this method is that you can choose the external frequency that is used for the frequency counter. To understand why this is such a big advantage I will first explain the principle of a basic frequency counter.
This means that we can theoretically choose our external frequency so that we achieve an Fcount value of value of 0xFFFFFFF for the maximum distance (membrane is furthest away from the coil) and 0x0000000 for the minimum distance (membrane is closest to the coil). Furthermore the counter is 24-bit, which allows for quite an accurate frequency measurement. However, the practical resolution is limited by the maximum external frequency which is only 8MHz.
So let’s do some calculations. We want to determine what the resolution of this measurement is. The datasheet mentions a 24-bit resolution, but this spec is not entirely representative of the actual inductance resolution.
The sensor frequency can be calculated by:
Choosing the maximum sample rate and maximum external clock frequency we get:
Which corresponds to an inductance of (assuming C=100pF):
The approximate resolution can then be calculated as follows (assuming we have a total variation of 1µH over the entire range):
Which is alot lower than the full 24-bit resolution.
3D printing woes
Anyway, I am currently trying to 3D print some plastic mounts for holding the membrane. I started off by using Sketchup, but whenever I converted the files to .stl, the model became all messed up. I also tried the new 123D software by Autodesk, but it seems to be very limited. In the end I decided to try Inventor which has been great so far.
I plan to make the mounts in various sizes to see the effect of the diameter and the membrane distance on the resolution and sensitivity. Here is an example of a 35mm diameter mount:
The two halves basically fit together to tighten the membrane. Here is a side view to illustrate what I mean:
Inventor also lets you animate an assembly:
The coil will be a PCB coil that is essentially a third circular part, also attached to the mount.
Now this all sounds good in theory, but I’m having a lot of practical problems with the 3D printing. The Ultimaker I’m using seems to have a leak between the aluminum block and the feeding tube. This appears to be quite a common problem, but I haven't been able to solve it yet. I probably won't have acces to a 3D printer in July-August, so I need to get this fixed as soon as possible.
Furthermore I'm not sure if the Ultimaker will be able to print small details like the ridges I made in the two mount halves.
There still alot to be done so I hope I'll be able to finish this in time.