PWM generation in Simulink - Time & Space Complexity

Time Complexity: PWM generation in Simulink

O(N)

Understanding Time Complexity

We want to understand how the time needed to generate PWM signals changes as the input size changes.

Specifically, how does the system behave when the number of PWM channels or signal resolution increases?

Scenario Under Consideration

Analyze the time complexity of the following PWM generation setup in Simulink.

% Simulink model snippet for PWM generation
% 1. Compare input signal with carrier waveform
% 2. Generate PWM output based on comparison
% 3. Repeat for each PWM channel

for i = 1:N_channels
  pwm_output(i) = input_signal(i) > carrier_waveform;
end
    

This code compares each input signal with a carrier waveform to create PWM signals for multiple channels.

Identify Repeating Operations

Look at what repeats in this process.

• Primary operation: Comparing input signals to the carrier waveform.
• How many times: Once for each PWM channel, so N times.

How Execution Grows With Input

As the number of PWM channels increases, the number of comparisons grows directly with it.

Input Size (N_channels)	Approx. Operations
10	10 comparisons
100	100 comparisons
1000	1000 comparisons

Pattern observation: The operations increase in a straight line as channels increase.

Final Time Complexity

Time Complexity: O(N)

This means the time to generate PWM signals grows directly with the number of channels.

Common Mistake

[X] Wrong: "The time to generate PWM signals stays the same no matter how many channels there are."

[OK] Correct: Each channel needs its own comparison, so more channels mean more work and more time.

Interview Connect

Understanding how time grows with input size helps you explain system performance clearly and confidently in real projects.

Self-Check

"What if we increased the resolution of the carrier waveform instead of the number of channels? How would the time complexity change?"

Practice

1. What does PWM stand for in Simulink and what is its main purpose?

easy

A. Pulse Wave Measurement; it measures signal frequency.

B. Power Width Management; it manages battery power levels.

C. Pulse Width Modulation; it controls power by switching signals ON and OFF quickly.

D. Pulse Width Memory; it stores signal data.

Solution

1. Step 1: Understand PWM meaning

   PWM stands for Pulse Width Modulation, a method to control power by changing signal ON/OFF times.

2. Step 2: Identify PWM purpose in Simulink

   In Simulink, PWM controls power by switching signals ON and OFF quickly to adjust power delivery.

3. Final Answer:

   Pulse Width Modulation; it controls power by switching signals ON and OFF quickly. -> Option C

4. Quick Check:

   PWM = Pulse Width Modulation controlling power [OK]

Hint: PWM controls power by fast ON/OFF switching [OK]

Common Mistakes:

• Confusing PWM with measuring signals
• Thinking PWM stores data
• Mixing PWM with battery management

2. Which Simulink block is commonly used to generate PWM signals?

easy

A. Pulse Generator block

B. Gain block

C. Integrator block

D. Scope block

Solution

1. Step 1: Recall Simulink blocks for PWM

   The Pulse Generator block is designed to create pulses with adjustable width and frequency.

2. Step 2: Match block to PWM function

   Since PWM requires pulses with specific widths, the Pulse Generator block is the correct choice.

3. Final Answer:

   Pulse Generator block -> Option A

4. Quick Check:

   Pulse Generator block creates PWM pulses [OK]

Hint: Pulse Generator creates PWM signals in Simulink [OK]

Common Mistakes:

• Choosing Gain block which scales signals
• Selecting Integrator block which sums signals
• Picking Scope block which only displays signals

3. Given a Pulse Generator block with Amplitude=5, Period=10, Pulse Width=30%, what is the ON time duration of the PWM signal?

medium

A. 3 seconds

B. 5 seconds

C. 7 seconds

D. 10 seconds

Solution

1. Step 1: Calculate ON time from pulse width and period

   ON time = Pulse Width (%) x Period = 30% x 10 = 0.3 x 10 = 3 seconds.

2. Step 2: Confirm units and values

   Period is in seconds, so ON time is 3 seconds.

3. Final Answer:

   3 seconds -> Option A

4. Quick Check:

   ON time = 30% x 10 = 3 seconds [OK]

Hint: ON time = pulse width % x period [OK]

Common Mistakes:

• Using amplitude instead of period for calculation
• Confusing pulse width percentage with time
• Calculating OFF time instead of ON time

4. You set the Pulse Generator block with Pulse Width = 110%. What will happen during simulation?

medium

A. The block will generate an error and stop simulation.

B. The block will generate a continuous ON signal (always high).

C. The block will generate a continuous OFF signal (always low).

D. The block will ignore the pulse width and use default 50%.

Solution

1. Step 1: Understand pulse width limits

   Pulse Width should be between 0% and 100%. Values above 100% mean the signal is ON all the time.

2. Step 2: Predict simulation behavior

   With 110%, the block treats it as always ON, so the output stays high continuously.

3. Final Answer:

   The block will generate a continuous ON signal (always high). -> Option B

4. Quick Check:

   Pulse Width > 100% means always ON [OK]

Hint: Pulse Width >100% means signal always ON [OK]

Common Mistakes:

• Expecting simulation error for >100% pulse width
• Thinking signal stays OFF
• Assuming default pulse width is used

5. You want to simulate a PWM signal that controls a motor speed with a frequency of 50 Hz and a duty cycle of 40%. How do you set the Pulse Generator block parameters in Simulink?

hard

A. Set Period = 0.02 seconds, Pulse Width = 50%, Amplitude = motor voltage level

B. Set Period = 50 seconds, Pulse Width = 40%, Amplitude = motor voltage level

C. Set Period = 0.04 seconds, Pulse Width = 40%, Amplitude = motor voltage level

D. Set Period = 0.02 seconds, Pulse Width = 40%, Amplitude = motor voltage level

Solution

1. Step 1: Calculate period from frequency

   Period = 1 / Frequency = 1 / 50 = 0.02 seconds.

2. Step 2: Set pulse width and amplitude

   Duty cycle is 40%, so Pulse Width = 40%. Amplitude should match motor voltage level to control speed.

3. Final Answer:

   Set Period = 0.02 seconds, Pulse Width = 40%, Amplitude = motor voltage level -> Option D

4. Quick Check:

   Period = 1/50 = 0.02s, Pulse Width = 40% [OK]

Hint: Period = 1/frequency; set pulse width as duty cycle % [OK]

Common Mistakes:

• Using period equal to frequency value
• Setting wrong pulse width different from duty cycle
• Confusing period units (seconds vs milliseconds)