SNOAAA5 April 2024 DRV8220 , FDC1004-Q1 , LDC3114-Q1 , TMAG5131-Q1 , TMAG5173-Q1 , TMAG6180-Q1
Even an approximate analysis for the door handle in the retracted and extended positions is a little more complicated because of air gaps and plastic between the sensor, the outer surface and the user's hand. Some simple calculations - similar to the touch button - but considering the permittivity effects of plastic and air gaps, combined with the parallel plate capacitor equation in Equation 2, can arrive at results that are very close to our experimental results using the demo. To that end, we can specify the thicknesses of the plastic and air gaps for the case of a hand on an extended handle.
The mechanical stack-up (showing widths of air gaps and thicknesses of plastic) is shown in Table 4-1 and Figure 4-20.
Handle Sensor Dimensions | Width = 8cm, Height = 5cm |
---|---|
1. Plastic thickness between door handle sensor and chamber that houses retracted handle | 2mm |
2. Distance between chamber outer surface and door handle outer surface (air gap) | 10mm |
What are the approximate capacitance can we expect with the previous stack-up using the parallel capacitor equation given earlier? Consider a hand gripping the extended handle as shown in Figure 4-21.
Consider that items (1) and (2) in Table 4-1 are really the only distances we need to consider for our capacitor equation. First, item (1) is the 2mm-thick plastic (εr = 5) between the door 8cm by 5cm door handle sensor and the chamber that houses the retracted door handle. The second, item (2) is the 1cm air gap (εr = 1) between the outer surface of the 2mm-thick plastic and the outer surface of the door. When a hand grips the extended handle, the user's fingers can form a ground plane that can be about 1cm from the chamber's outer surface (per item 2 above).
So for our capacitor, one parallel plate can be the sensor, and the other can be the ground plane formed by the user's fingers gripping the door handle. If we make the simplifying assumption the surfaces of the two planes are equal, and our total capacitance can be approximated by a region with two different permittivity, as shown in Figure 4-20.
The total capacitance between the sensor and the users fingers can be approximated as two capacitors in series that have the same plate areas, but different gap lengths and permittivity. The quantities based on our stack-up are based on the plastic [d1 = 2mm, εr1 = 5] and the air gap [d2 = 1cm, εr2 = 1] between the chamber's surface and the user's fingers are summarized in the following equation.
How does this simple calculation compare with results from the demo? Figure 4-22 shows a plot of the demo's FDC1004 output versus time samples with a hand gripping the deployed handle between the 400th and 500th time samples. Before the hand grips the handle, the FDC1004 reports the sensor capacitance is about 1.5pF, which somewhat in agrees with our rough calculations of 1pF. After a hand grips the handle, the reported capacitance settles out to about 2.9pF. While this is not the calculated value, it does reflect the fact the surface of the hand closest to the sensor is around 12mm to 13mm, not the 10mm used in our calculations.