Duty cycle control for motor/LED in Embedded C - Time & Space Complexity

Time Complexity: Duty cycle control for motor/LED

O(1)

Understanding Time Complexity

We want to understand how the time it takes to control the duty cycle changes as we adjust the input size.

Specifically, how does the program's work grow when changing the duty cycle steps?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void setDutyCycle(int dutyCyclePercent) {
    for (int i = 0; i < 100; i++) {
        if (i < dutyCyclePercent) {
            turnOnOutput();
        } else {
            turnOffOutput();
        }
        delayMicroseconds(10);
    }
}
    

This code sets the duty cycle by turning the output on or off in a loop of 100 steps, simulating PWM control.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop running 100 times to set output on/off.
• How many times: Always 100 times, regardless of dutyCyclePercent.

How Execution Grows With Input

The loop always runs 100 times, so the work stays the same no matter the duty cycle value.

Input Size (dutyCyclePercent)	Approx. Operations
10	100 loop steps
50	100 loop steps
90	100 loop steps

Pattern observation: The number of operations does not change with input size; it stays constant.

Final Time Complexity

Time Complexity: O(1)

This means the time to run the code stays the same no matter what duty cycle value you use.

Common Mistake

[X] Wrong: "If I increase the duty cycle percent, the program will take longer to run because it turns on more."

[OK] Correct: The loop always runs 100 times no matter what, so the total steps stay the same. Turning on or off inside the loop doesn't change how many times the loop runs.

Interview Connect

Understanding how loops and input sizes affect time helps you explain how embedded systems keep timing precise and predictable.

Self-Check

"What if the loop ran up to the dutyCyclePercent value instead of always 100? How would the time complexity change?"

Practice

1. What does the duty cycle control in a motor or LED?

easy

A. The percentage of time the device is ON during each cycle

B. The voltage supplied to the device

C. The frequency of the power supply

D. The temperature of the device

Solution

1. Step 1: Understand duty cycle meaning

   The duty cycle is the fraction of one period in which a signal or system is active.

2. Step 2: Relate to motor/LED control

   For motors or LEDs, it controls how long the device is ON in each cycle, affecting speed or brightness.

3. Final Answer:

   The percentage of time the device is ON during each cycle -> Option A

4. Quick Check:

   Duty cycle = ON time percentage [OK]

Hint: Duty cycle means ON time percentage per cycle [OK]

Common Mistakes:

• Confusing duty cycle with voltage
• Thinking it controls frequency
• Assuming it controls temperature

2. Which of the following is the correct way to set a 50% duty cycle using a timer compare register in embedded C?

easy

A. OCR0 = 0; // Full OFF

B. OCR0 = 255; // Full ON

C. OCR0 = 128; // Assuming 8-bit timer with max 255

D. OCR0 = 64; // 25% duty cycle

Solution

1. Step 1: Understand timer resolution

   An 8-bit timer counts from 0 to 255, so max value is 255.

2. Step 2: Calculate 50% duty cycle value

   50% of 255 is approximately 128, so setting OCR0 to 128 sets 50% duty cycle.

3. Final Answer:

   OCR0 = 128; // Assuming 8-bit timer with max 255 -> Option C

4. Quick Check:

   50% of 255 = 128 [OK]

Hint: Half of max timer value sets 50% duty cycle [OK]

Common Mistakes:

• Using max value for 50% duty cycle
• Using zero for 50% duty cycle
• Confusing 25% with 50%

3. Given the code snippet below, what will be the duty cycle percentage set for the LED?

unsigned char duty = 64;
unsigned char max = 255;
float dutyCycle = (duty / (float)max) * 100;

medium

A. 25%

B. 50%

C. 75%

D. 64%

Solution

1. Step 1: Calculate duty/max ratio

   Divide duty (64) by max (255): 64 / 255 ≈ 0.25098.

2. Step 2: Convert ratio to percentage

   Multiply by 100: 0.25098 * 100 ≈ 25.1%.

3. Final Answer:

   25% -> Option A

4. Quick Check:

   (64/255)*100 ≈ 25% [OK]

Hint: Divide duty by max, multiply by 100 for percentage [OK]

Common Mistakes:

• Using integer division without casting
• Confusing duty value with percentage
• Rounding incorrectly

4. Identify the error in the following code that attempts to set a 75% duty cycle on an 8-bit timer:

unsigned char duty = 75;
unsigned char max = 255;
OCR0 = duty / max * 255;

medium

A. OCR0 register cannot be assigned directly

B. Integer division causes duty/max to be zero

C. max value should be 100, not 255

D. Duty cycle calculation is correct

Solution

1. Step 1: Analyze division operation

   Both duty and max are unsigned char, so duty/max does integer division: 75/255 = 0 (integer).

2. Step 2: Effect on OCR0 assignment

   Multiplying 0 by 255 results in 0, so OCR0 is set to 0, not 75% duty cycle.

3. Final Answer:

   Integer division causes duty/max to be zero -> Option B

4. Quick Check:

   Integer division truncates to zero [OK]

Hint: Cast to float before division to avoid zero result [OK]

Common Mistakes:

• Ignoring integer division rules
• Assuming OCR0 cannot be assigned
• Using wrong max value

5. You want to smoothly increase the brightness of an LED from 0% to 100% duty cycle using PWM on an 8-bit timer. Which approach is best to implement this in embedded C?

hard

A. Use a fixed OCR0 value of 128 for half brightness

B. Set OCR0 to 255 once and leave it

C. Toggle the LED pin ON and OFF manually without PWM

D. Use a loop to increment OCR0 from 0 to 255 with a delay between steps

Solution

1. Step 1: Understand smooth brightness control

   Smooth brightness change requires gradually changing the duty cycle from 0 to max.

2. Step 2: Implement gradual PWM change

   Increment OCR0 from 0 to 255 in a loop with delays to create smooth brightness ramp.

3. Final Answer:

   Use a loop to increment OCR0 from 0 to 255 with a delay between steps -> Option D

4. Quick Check:

   Gradual OCR0 change = smooth brightness [OK]

Hint: Increment OCR0 gradually with delay for smooth fade [OK]

Common Mistakes:

• Setting OCR0 once for full brightness only
• Using fixed mid value for all brightness
• Not using PWM for brightness control