4 Analysis and Results

First analyze the sensor orientation and spacing relative to the ring magnet. For this design, a magnet and device according to Table 4-1 and Table 4-2 were assessed in a configuration as illustrated in Figure 3-6.

To perform the analysis, consider a plane located a specified distance (for example, an air gap) away from the radial surface of the magnet. This plane corresponds to the PCB position where the Hall latches are mounted. Depending upon board constraints imposed by the PCB, enclosure, board components, or simply fabrication and assembly tolerances, the device can be offset from directly below the magnet center by some x-offset or y-offset distance as shown in Figure 4-1.

A simulation was conducted of a radial sweep of the ring magnet and the resulting field on the plane below the magnet. Comparing these calculated values to the chosen B_OP and B_RP thresholds of the Hall sensor allowed an estimate of a set of PCB locations that allow the Hall latch to work properly. The analysis looked at 5° intervals around the point directly below the center of the magnet. The resulting region is shown in Figure 4-2. Outside this region, the sensed field is not sufficiently strong to trigger the latches.

The shape and relative size of the simulated region varies with air gap distance (for a given magnet) and the latch trigger thresholds. For this magnet, a typical air gap of 6 mm with ±3 mm tolerance was observed, as indicated in Figure 4-3. The plot in Figure 4-3 shows there is a relatively large region - with respect to the outline of the magnet – which can support the desired sensor and latch behavior, even with loose manufacturing tolerances. However, the area of the region is expected to decrease with increasing air gap between the magnet and device. To gauge how region size varies as a function of air gap distance, Table 4-3 summarizes approximations of the areas for each simulated region, as well as the percentage decrease in the area relative to the area resulting from the 3-mm gap.

Having established that the Hall latch can properly monitor the magnet for the intended orientation and placement, now determine the required bandwidth. Using the mechanical model and the number of magnet poles, estimate the required motor speed and the required Hall sensor bandwidth.

Equation 8 allows calculation of the total number of motor rotations (R_REG) needed to completely open or close a window. Assigning parameter values in the equation based on the ongoing regulator example, a total of 365.7 rotations is calculated.

where

• N_GL = # window lever gear teeth = 32
• N_PG = # pinion gear teeth =7
• N_WW = # worm wheel gear teeth = 80
• N_WG = # worm gear teeth =1

Assigning the values provided in the regulator requirements into Equation 9, calculate the required motor speed, S_M:

Reality check: the speed of the pinion gear that drives the geared lever is (N_GL/N_PG)/T_WIN which gives 4.57/4 = 1.14 revs/s = 68.6 rpm, which aligns with values of some common window motor modules.

Using the computed motor speed in Equation 12, along with magnet pole count and the pulse-to-pole ratio for the device yields the magnet input signal bandwidth . For the TMAG5111 there is 1 pulse-per-pole passing the device. For the TMAG5110 there is 1 pulse on each output per pole pair, thereby halving the required bandwidth

How do the estimated Hall sensor bandwidths compare to readily available devices? Three automotive-grade, low-cost, low-power Hall latches - the TMAG5110-Q1, TMAG5111-Q1, and DRV5015-Q1 - have typical bandwidths of 40 kHz, while a third latch, the DRV5011 supports 30 kHz. So at the previously-determined motor speed, and with practical magnet pole counts, the design is well within the bandwidth of readily-available Hall latches.

Another consideration is the resolution of the window position estimate – based on monitoring the motor revolutions – versus the number of magnet poles. Equation 14 shows the relationship between the system requirements and the number of magnet poles. Table 4-5 shows some numerical results from Equation 14. For the TMAG5111, there are 2 states (1 pulse) per pole passing the device. For the TMAG5110, there are 4 states (2 offset pulses) per pole pair. If considering a dual-planar device, there are 2 states per pole pair for the output corresponding to rotational distance, thereby having half the resolution of the TMAG511x devices.

Table 4-5 shows that the window step resolution is below 1 mm. While the initial design requirements do not have specified a step size, presume the step size is beneath the average user perception. With an average visual perception around 60 Hz, equivalent to a period of 1/60 Hz = 0.016 s, each visual step is 457 mm/4 s × 0.016 = 1.828 mm at a minimum. However, a user reaction time of around 0.17 s is factored in, then a minimum step of 19.4 mm is observed, or a 4-s open-close duration. Therefore; our four-pole magnet resolution of 0.15 mm is well below what is necessary.

Based on these findings, this preliminary design iteration has quite a bit of margin against failure with a relatively large acceptable placement region, sufficiently low bandwidth, and sufficiently low resolution. At this point prototyping can be pursued. However, such margins suggest there is an opportunity to take another high-level look at the system and determine if modifications to gear ratios, motor speeds, or different magnets yields material cost-savings or greater efficiency. For the Hall-effect feedback stage, a smaller magnet can lower cost because magnets with fewer poles are less expensive.