SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

defined to be in the direction of the thumb; flux in this direction is taken to be positive. Since this
report adopts the motor (load) sign convention, this will be defined as the direction of positive
current and the terminal into which the current is flowing is the positive terminal. In reference to
Figure 2.8, positive current is that which flows into terminal A and the magnetic axis of the loop
is into the page, thus positive flux will be of the same polarity as the B external field (all magnetic
quantities in this report share the same polarity conventions).
The B field shown is into the page. If an external force Fapplied is applied to the rod and pulls it to
the right, the area of the loop in the B field will increase which will in turn increase the flux
linkage. By Lenz’s law and the right hand rule, a current will flow in the circuit in the
counterclockwise direction, producing a flux which points out of the page. Current flow in this
direction creates a potential across the resistor such that terminal A is more positive than terminal
B; since A is defined as the positive terminal, this shows that an increase in flux linkage
generates a positive EMF. Therefore, it is best to define Faraday’s law according to the motor
(load) sign convention, Equation (2.5).
d
g(
t)
(2.5)
dt
To summarize the convention, if the thumb of the right hand points in the direction of the
magnetic axis, then the fingers will wrap in the direction that (positive) current must flow in order
to produce positive flux along the magnetic axis. When the flux linkage of the coil increases, the
EMF produced will be of positive polarity and have a magnitude given by Equation (2.5).
Finally, this ideal coil can be modeled electrically as shown in Figure 2.9. Note that although the
circuit has thus far acted as a generator, we have selected the motor sign convention; therefore,
the voltage polarity and current direction are correct.
Figure 2.9 – Electrical model of ideal coil shunted by an external resistance.
Given this convention, the EMF induced in the apparatus of Figure 2.8 can be calculated as
follows. Since this is a one-turn coil, N=1 and the flux linkage is simply equal to the flux through
the loop as shown by Equation (2.6).
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