Abstract
For Hall plates, the ratio of signal over thermal noise is determined by material properties, thickness, layout geometry, magnetic field, and the electric power at which the plate is operated. For traditional Hall plates with four contacts, the optimum choice is a symmetrical device with medium-sized contacts. This paper shows that the signal-to-noise-ratio (SNR) can be further increased by up to 90% for Hall plates with more than four contacts. Supply currents flow through several pairs of contacts, while a signal conditioning circuit taps output voltages at all pairs of contacts and sums them up. We compute the total thermal noise of the sum of correlated noise voltages and relate it to the total magnetic sensitivity. We also prove that for electrically linear devices a spinning current scheme cancels out zero point errors (offset errors) in a strict sense. All our investigations use the definite resistance matrix of multi-port Hall plates. We develop an analytical theory based on recent advances in the theory of Hall plates, and then we compute the integrals and matrices numerically for symmetrical Hall plates with six to 40 contacts. We also present measurements in accordance with our theory.
Highlights
In this work we look for ways about how to get less noisy signals from Hall plates
A more common method is the spinning current scheme, which greatly reduces the zero-point error of the Hall plate, and simultaneously it cancels out 1/f-noise, too [2] [3]. Note that all these operating modes allow for a detection of static and low frequency magnetic fields even though the Hall plate is electrically operated at elevated frequencies
We have shown by calculation that under a given supply voltage and current drain a regular multi-port Hall plate can achieve up to 90% better signal-to-noise ratio (SNR) than classical Hall plates with four contacts
Summary
In this work we look for ways about how to get less noisy signals from Hall plates. On the one hand we want to maximize the output signal per milli-Tesla of impressed magnetic field; on the other hand we want to minimize the noise in the signal while keeping the power consumption of the Hall plate constant. For maximum SNR the Hall plate should be symmetric with medium-sized contacts That means, it should have identical input and output resistance and the average potential of both output contacts should be half of the supply voltage; i.e. the common mode potential of the differential output signal should be exactly in the center between both supply potentials. Hall plates with more than eight contacts were used in spinning current schemes studied by Munter [10] [11] Still he used only single pairs of output contacts in each phase (single input current, single output voltage). Appendix A computes the resistances of the equivalent network for multi-port Hall plates at zero magnetic field It shows the particular type of Toeplitz symmetry in their conductance matrix. Appendix F shows an algorithm to optimize currents and weighing coefficients from circuits of Section 6
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