analogWrite() and PWM output in Arduino - Time & Space Complexity

Time Complexity: analogWrite() and PWM output

O(n)

Understanding Time Complexity

We want to understand how long it takes for the Arduino to run code using analogWrite() for PWM output.

Specifically, how does the time change when we call analogWrite() multiple times?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

for (int i = 0; i < n; i++) {
  analogWrite(9, i);  // Set PWM on pin 9
}
    

This code sets PWM output on pin 9 repeatedly, increasing the value each time.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop running analogWrite() calls.
• How many times: The loop runs n times, calling analogWrite() once each time.

How Execution Grows With Input

Each time we increase n, the number of analogWrite() calls grows the same way.

Input Size (n)	Approx. Operations
10	10 analogWrite() calls
100	100 analogWrite() calls
1000	1000 analogWrite() calls

Pattern observation: The total work grows directly with n. Double n, double the calls.

Final Time Complexity

Time Complexity: O(n)

This means the time to run the code grows in a straight line as you increase the number of analogWrite() calls.

Common Mistake

[X] Wrong: "analogWrite() runs instantly, so the loop time does not depend on n."

[OK] Correct: Each analogWrite() call takes some time to set the PWM signal, so more calls mean more total time.

Interview Connect

Knowing how repeated hardware calls like analogWrite() scale helps you write efficient Arduino code and explain your reasoning clearly.

Self-Check

"What if we replaced the for-loop with a nested loop calling analogWrite() multiple times per iteration? How would the time complexity change?"

Practice

1. What does the analogWrite() function do on an Arduino board?

easy

A. It sets a digital pin to HIGH or LOW.

B. It reads the voltage from an analog sensor.

C. It outputs a PWM signal to simulate an analog voltage on a digital pin.

D. It measures the frequency of a signal on a pin.

Solution

1. Step 1: Understand the purpose of analogWrite()

   The analogWrite() function does not output a true analog voltage but uses PWM (Pulse Width Modulation) to simulate varying voltage levels on digital pins.

2. Step 2: Compare options with function behavior

   It outputs a PWM signal to simulate an analog voltage on a digital pin. correctly describes this behavior. Options A, B, and D describe other functions or actions unrelated to analogWrite().

3. Final Answer:

   It outputs a PWM signal to simulate an analog voltage on a digital pin. -> Option C

4. Quick Check:

   analogWrite() = PWM output [OK]

Hint: Remember: analogWrite() controls brightness/speed via PWM [OK]

Common Mistakes:

• Confusing analogWrite() with analogRead()
• Thinking analogWrite() outputs true analog voltage
• Assuming analogWrite() sets pin HIGH or LOW directly

2. Which of the following is the correct syntax to set pin 9 to half brightness using analogWrite()?

easy

A. analogWrite(9, 512);

B. analogWrite(9, 0);

C. analogWrite(9, 255);

D. analogWrite(9, 127);

Solution

1. Step 1: Understand the value range for analogWrite()

   The analogWrite() function accepts values from 0 to 255, where 0 is off and 255 is full brightness.

2. Step 2: Calculate half brightness value

   Half brightness is about half of 255, which is approximately 127. A uses 512 (out of range), B uses 0 (off), C uses 255 (full brightness), so D is correct.

3. Final Answer:

   analogWrite(9, 127); -> Option D

4. Quick Check:

   Half brightness ≈ 127 [OK]

Hint: Use values between 0-255; half is about 127 [OK]

Common Mistakes:

• Using values above 255 (like 512)
• Confusing digitalWrite() with analogWrite()
• Using full brightness value instead of half

3. What will be the effect of the following code snippet on an LED connected to pin 6?

void setup() {
  pinMode(6, OUTPUT);
}

void loop() {
  analogWrite(6, 0);
  delay(1000);
  analogWrite(6, 255);
  delay(1000);
}

medium

A. The LED will blink on and off every second.

B. The LED will stay dimly lit.

C. The LED will stay fully on.

D. The LED will flicker rapidly.

Solution

1. Step 1: Analyze analogWrite values and delays

   The code sets pin 6 to 0 (off) for 1 second, then to 255 (full brightness) for 1 second, repeatedly.

2. Step 2: Understand LED behavior

   When the pin is 0, the LED is off; when 255, it is fully on. The delays cause the LED to stay in each state for 1 second, making it blink on and off every second.

3. Final Answer:

   The LED will blink on and off every second. -> Option A

4. Quick Check:

   0 and 255 with delays = blink [OK]

Hint: 0 means off, 255 means full on; delays cause blinking [OK]

Common Mistakes:

• Thinking analogWrite(0) dims LED instead of off
• Ignoring delay effects on LED timing
• Assuming LED flickers rapidly without delay

4. Identify the error in this code snippet intended to fade an LED on pin 10:

void setup() {
  pinMode(10, OUTPUT);
}

void loop() {
  for (int i = 0; i <= 255; i++) {
    analogWrite(10, i);
    delay(10);
  }
  for (int i = 255; i >= 0; i--) {
    analogWrite(10, i);
    delay(10);
  }
}

medium

A. The code will work correctly and fade the LED in and out.

B. The for loop variable i should be declared outside the loop.

C. The pin 10 is not set as OUTPUT.

D. analogWrite() cannot be used with pin 10.

Solution

1. Step 1: Check pinMode setup

   Pin 10 is correctly set as OUTPUT in setup().

2. Step 2: Analyze the for loops and analogWrite usage

   The loops increase and then decrease the PWM value from 0 to 255 and back, with delays to create a smooth fade effect. This is a common and correct pattern.

3. Final Answer:

   The code will work correctly and fade the LED in and out. -> Option A

4. Quick Check:

   For loops with analogWrite create fade [OK]

Hint: For fading, increase then decrease PWM values smoothly [OK]

Common Mistakes:

• Forgetting to set pinMode to OUTPUT
• Thinking analogWrite can't be used on pin 10
• Misunderstanding loop variable scope

5. You want to control the speed of a DC motor using PWM on pin 3. Which code snippet correctly sets the motor speed to 60% power?

hard

A. analogWrite(3, 60); // 60 is the percentage value

B. analogWrite(3, 153); // 60% of 255 is about 153

C. analogWrite(3, 0.6); // decimal value for 60%

D. analogWrite(3, 255); // full power always

Solution

1. Step 1: Convert percentage to PWM value

   60% of the maximum PWM value 255 is 0.6 x 255 = 153.

2. Step 2: Check the analogWrite parameter

   analogWrite() requires an integer between 0 and 255. analogWrite(3, 153); // 60% of 255 is about 153 uses 153, which is correct. analogWrite(3, 60); // 60 is the percentage value uses 60 which is too low, C uses a decimal which is invalid, and D sets full power.

3. Final Answer:

   analogWrite(3, 153); // 60% of 255 is about 153 -> Option B

4. Quick Check:

   60% x 255 = 153 [OK]

Hint: Multiply percentage by 255 for PWM value [OK]

Common Mistakes:

• Passing percentage directly instead of scaled value
• Using decimal numbers instead of integers
• Always setting full power without scaling