# How to calculate max permanent flux linkage and rotor angle over which back emf is constant for a BLDC?

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### Accepted Answer

Andrew Reibold
on 8 Mar 2024

To simulate a BLDC motor control circuit in MATLAB, you'll need to understand and calculate certain parameters. The maximum flux linkage and the rotor angle over which back EMF is constant are critical for modeling. Here's how you can approach these calculations:

Maximum Flux Linkage (λ_max):

The maximum flux linkage in a BLDC motor can be calculated using the rated voltage and the rated speed. The formula is:

λ_max=V_rated / ω_rated

Where V_rated is the rated voltage and ω_rated is the rated speed in rad/s.

Rotor Angle Over Which Back EMF is Constant:

The rotor angle over which the back EMF is constant is typically considered to be 120 electrical degrees for a 3-phase BLDC motor. If you have a different number of phases, the electrical degrees over which the back EMF is constant would be 360deg/number of phases

Here's a MATLAB code snippet to help you calculate these values:

% Given parameters from the datasheet

rated_voltage = 24; % Example rated voltage in volts

rated_speed = 3000; % Example rated speed in RPM

number_of_poles = 4; % Example number of poles

number_of_phases = 3; % Example number of phases

% Convert rated speed to rad/s

omega_rated = 2 * pi * rated_speed / 60;

% Calculate maximum flux linkage

lambda_max = rated_voltage / omega_rated;

% Calculate rotor angle over which back EMF is constant

electrical_degrees_per_phase = 360 / number_of_phases;

angle_back_EMF_constant = electrical_degrees_per_phase;

% Display results

fprintf('Maximum Flux Linkage: %.4f Vs/rad\n', lambda_max);

fprintf('Rotor Angle Over Which Back EMF is Constant: %.2f degrees\n', angle_back_EMF_constant);

You need to substitute your actual data values for rated_voltage, rated_speed, number_of_poles, and number_of_phases in the code.

These values will help you set up your BLDC motor model in MATLAB with the appropriate parameters.

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