Correlated Magnetics: A Simple Correlation Model

Once correlated magnetics had been invented, a significant effort was undertaken to validate correlated magnetics theory using physical measurements and simulation.  Fig. 1 shows the autocorrelation of two Barker 7 coded signals in the time domain and a simple equation (or model) for calculating their signal strength vs. time offset function, where the equation essentially ignores non-aligning pulses.  Also shown in Fig. 1, is the autocorrelation of two Barker 7 coded magnetic structures in the spatial domain and a similar simple equation (or model for calculating the magnetic force vs. spatial offset function, where the equation essentially ignores non-aligning magnetic sources.

Fig. 1  Signal vs. Magnetic Autocorrelation Models

Fig. 2 depicts the output of the two autocorrelation models. Fig. 3 depicts the output of Ansoft Corporation’s Maxwell 3D Simulation Environment for the autocorrelation of two Barker 7 coded magnetic structures.  The simulated magnets were 1/8” diameter x 1/4” long NIB #42 magnets spaced .01” apart.  Fig. 4 depicts the results of force measurements of two Barker 7 coded magnetic structures. 

The magnets used for the force measurements were 1/8” diameter x 1/4” long NIB #42 magnets spaced .01” apart.  When comparing the output of the normalized simple models depicted in Fig. 2, to the simulated and measured output depicted in Figs. 3 and 4 it is clearly evident that the relative magnitudes are very consistent indicating that the magnetic sources do cancel each other in the spatial domain in a manner similar to how signals cancel each other in the time domain.  Furthermore, the simple model that was used for calculating a magnetic force vs. spatial offset function is a useful and effective tool for quickly assessing force characteristics of correlated magnetic structures.  Further comparisons of two dimensional coded magnetic structures also produced similar results where the simple model, simulation output, and measurement output were very consistent.

Note: This is the principle behind the “Barker-13 Autocorrelation code demonstrator” on our products page. When the trolley is left or right of center it experienced very little magnetic effect; When it is in the exact center the correlation spike caused strong enough attraction to hold it on the track even when held upside down.