Signal Parameters¶

Parameters¶

Voltage Multiplier\(I_0\): Constant that multiplies the voltage of all the signals, thereby changing the total magnitude of the field. Increases the radius of the 3-D field parametrized in time.
Frequency\(f\): How fast the field rotates, in rotations per second (Hz).
Z-Phase\(\zeta\): The degree (0-360) at which the z-component of the signal is the largest. Determines the direction of microwheel translation. e.g. at a Z-Phase of 0, the Z-Signal is in phase with the left (negative) X-coil. This results in the wheel rolling up (positive y direction).
Camber Angle\(\theta\): The angle measured between the positive z-axis and the rotating field. Determines the “tilt” of the wheel and field.
Z-Coefficient\(C\): A calculated coefficient which multiplies the z-coil signal in order to account for a possible difference in distance to the sample. To determine the z-coefficient for your setup, see calibration.

Equations¶

For reference, these are the final forms of the equations used to generate three signals that always resolve to a perfect circle in parametrized space. If you’re curious about the derivation, please email me at czimmermann@mines.edu!

\[ \begin{align}\begin{aligned}\omega = 2 \pi f\\I_x = I_0[ \sin(\zeta) \cos(\omega t) - \sin(\theta) \cos(\zeta) \sin(\omega t)]\\I_y = -I_0[ \cos(\zeta) \cos(\omega t) + \sin(\theta) \sin(\zeta) \sin(\omega t)]\\I_z = C * I_0 \cos(\theta)\sin(\omega t)\end{aligned}\end{align} \]

Calibration¶

For the signal parameters to work properly and make intuitive sense during control, calibration is necessary. Two simple calibrations are required for two parameters: Voltage Multiplier, to enable a 1 multiplier to equal 1 Amp output; and Z-Coefficient, to ensure that the magnetic field is of equal magnitude throughout its entire rotation (circular). If it is not necessary to have a completely accurate field, it is okay to leave this coefficient at 1. This will probably allow for slightly faster translation as the average field magnitude would be slightly higher, though the camber angle would be incorrect.

Voltage Multiplier¶

In the calibration section, toggle the mode to “Calibration”. The app will now simply output three 20 Hz sin waves, each 90 degrees out of phase with the other.
Adjust the physical dials on the amplifier channels so each wave has a peak amplitude matching the voltage value listed in “Calibration X-Voltage Ampl.”.
Now when the app tells the coils to output an amplitude of 1.5 A, the coils will actually adjust to that value. You can confirm this in the Live Signal Plot.

Note

Calibration mode can also be used to determine which coils are hooked up to which amplifier, by setting one or more “Calibration Voltage Amplitudes” to zero.

Z- Coefficient¶

This coefficient multiplies the Z-Coil signal to account for the difference in field caused by the z coil due to either: 1) a shorter distance to the sample, and/or 2) using only 1 Z-Coil. This coefficient enables the actual magnetic field to be constant magnitude, or “circular”. Another way to think of this constant: “For every amp supplied to the xy coils, z-coefficient amps in the z coils creates the same magnetic field magnitude.”

In the calibration section, toggle the mode to “Calibration”. The app will now simply output three 20 Hz sin waves, each 90 degrees out of phase with the other.
Change the “Calibration Z-Voltage Ampl.” to 0. Ensure that this corresponds to your z-coils and there is no current being supplied to them using a voltmeter. The x and y amplitudes should be 1.
Use a Gauss meter to measure the peak magnetic field caused by the xy coils at the sample location. Take three measurements and average them.
Do the same as step three, but with the z-coil amplitude being 1 and the xy amplitudes being 0. Take three measurements and average them.
Use this equation to determine the z-coefficient. \(C = \frac{xyfield}{zfield}\)
Now that this coefficient has been calculated, enter it in the settings window to save it between application restarts.