H-bridge driver simulation in Simulink - Time & Space Complexity

Time Complexity: H-bridge driver simulation

O(n)

Understanding Time Complexity

We want to understand how the time needed to run an H-bridge driver simulation changes as the simulation details grow.

Specifically, we ask: how does the simulation time grow when we increase the number of steps or signals?

Scenario Under Consideration

Analyze the time complexity of the following Simulink model snippet.

% H-bridge driver simulation steps
for t = 1:simulation_steps
    % Calculate PWM signals
    pwm1 = mod(t, pwm_period) < duty_cycle;
    pwm2 = ~pwm1;
    % Update motor state
    motor_voltage = pwm1 * supply_voltage - pwm2 * supply_voltage;
    motor_current = motor_voltage / motor_resistance;
    % Store results
    voltage_log(t) = motor_voltage;
    current_log(t) = motor_current;
end
    

This code simulates the H-bridge driver by calculating PWM signals and motor responses at each time step.

Identify Repeating Operations

Look for repeated actions in the simulation.

• Primary operation: The loop running through each simulation step.
• How many times: Exactly once per time step, so as many times as simulation_steps.

How Execution Grows With Input

Each additional simulation step adds a fixed amount of work.

Input Size (simulation_steps)	Approx. Operations
10	About 10 times the basic step work
100	About 100 times the basic step work
1000	About 1000 times the basic step work

Pattern observation: The total work grows directly in proportion to the number of simulation steps.

Final Time Complexity

Time Complexity: O(n)

This means the simulation time grows linearly as you increase the number of simulation steps.

Common Mistake

[X] Wrong: "The simulation time grows faster than the number of steps because of complex calculations inside the loop."

[OK] Correct: Each step does a fixed amount of simple calculations, so the total time grows only in direct proportion to the number of steps.

Interview Connect

Understanding how simulation time grows helps you design efficient models and explain performance clearly in real projects.

Self-Check

"What if we added nested loops inside each simulation step to model multiple motors? How would the time complexity change?"