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AN857

Brushless DC Motor Control Made Easy

Microchip Technology 

AN857

Before we try the commutation code with our motor, lets

consider what happens when a voltage is applied to a

DC motor. A greatly simplified electrical model of a DC

motor is shown in Figure 5.

FIGURE 5:

DC MOTOR EQUIVALENT

CIRCUIT

R

L

BEMF

Motor

When the rotor is stationary, the only resistance to cur-

rent flow is the impedance of the electromagnetic coils.

The impedance is comprised of the parasitic resistance

of the copper in the windings, and the parasitic induc-

tance of the windings themselves. The resistance and

inductance are very small by design, so start-up cur-

rents would be very large, if not limited.

When the motor is spinning, the permanent magnet

rotor moving past the stator coils induces an electrical

potential in the coils called Back Electromotive Force,

or BEMF. BEMF is directly proportional to the motor

speed and is determined from the motor voltage con-

stant KV.

EQUATION 1:

RPM = KV x Volts

BEMF = RPM / KV

In an ideal motor, R and L are zero, and the motor will

spin at a rate such that the BEMF exactly equals the

applied voltage.

The current that a motor draws is directly proportional

to the torque load on the motor shaft. Motor current is

determined from the motor torque constant KT.

EQUATION 2:

Torque = KT x Amps

An interesting fact about KT and KV is that their product

is the same for all motors. Volts and Amps are

expressed in MKS units, so if we also express KT in

MKS units, that is N-M/Rad/Sec, then the product of KV

and KT is 1.

EQUATION 3:

KV * KT = 1

This is not surprising when you consider that the units

of the product are [1/(V*A)]*[(N*M)*(Rad/Sec)], which

is the same as mechanical power divided by electrical

power.

If voltage were to be applied to an ideal motor from an

ideal voltage source, it would draw an infinite amount of

current and accelerate instantly to the speed dictated

by the applied voltage and KV. Of course no motor is

ideal, and the start-up current will be limited by the par-

asitic resistance and inductance of the motor windings,

as well as the current capacity of the power source.

Two detrimental effects of unlimited start-up current

and voltage are excessive torque and excessive cur-

rent. Excessive torque can cause gears to strip, shaft

couplings to slip, and other undesirable mechanical

problems. Excessive current can cause driver

MOSFETS to blow out and circuitry to burn.

We can minimize the effects of excessive current and

torque by limiting the applied voltage at start-up with

Pulse-Width Modulation (PWM). Pulse-Width Modula-

tion is effective and fairly simple to do. Two things to

consider with PWM are, the MOSFET losses due to

switching, and the effect that the PWM rate has on the

motor. Higher PWM frequencies mean higher switching

losses, but too low of a PWM frequency will mean that

the current to the motor will be a series of high current

pulses instead of the desired average of the voltage

waveform. Averaging is easier to attain at lower fre-

quencies if the parasitic motor inductance is relatively

high, but high inductance is an undesirable motor char-

acteristic. The ideal frequency is dependent on the

characteristics of your motor and power switches. For

this application, the PWM frequency will be approxi-

mately 10 kHz.

DS00857B-page 6

 2002-2011 Microchip Technology Inc.

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