PWM frequency and duty cycle relationship in Raspberry Pi - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

PWM Duty Cycle Calculation Output

What is the output of this Python code that calculates the duty cycle percentage for a PWM signal?

Raspberry Pi

frequency = 1000  # 1 kHz
period = 1 / frequency  # seconds
pulse_width = 0.00025  # 250 microseconds

duty_cycle = (pulse_width / period) * 100
print(f"Duty cycle: {duty_cycle:.1f}%")

A Duty cycle: 250.0%

B Duty cycle: 2.5%

C Duty cycle: 0.25%

D Duty cycle: 25.0%

💡 Hint

Duty cycle is pulse width divided by period times 100.

The period is 1/1000 = 0.001 seconds. The pulse width is 0.00025 seconds. So duty cycle = (0.00025 / 0.001) * 100 = 25%.

🧠 Conceptual

intermediate

Effect of Increasing PWM Frequency on Duty Cycle

If you keep the pulse width constant but increase the PWM frequency, what happens to the duty cycle?

A Duty cycle decreases because the period gets shorter.

B Duty cycle stays the same because pulse width is constant.

C Duty cycle increases because the period gets longer.

D Duty cycle becomes zero because frequency is too high.

💡 Hint

Duty cycle = pulse width / period. What happens to period when frequency increases?

Increasing frequency makes the period shorter. Since pulse width is constant, duty cycle = pulse width / smaller period, so duty cycle increases.

🔧 Debug

advanced

Identify the Error in PWM Duty Cycle Calculation

What error does this code raise when calculating PWM duty cycle?

Raspberry Pi

frequency = 0
period = 1 / frequency
pulse_width = 0.0005

duty_cycle = (pulse_width / period) * 100
print(f"Duty cycle: {duty_cycle}%")

A ZeroDivisionError

B TypeError

C NameError

D No error, prints duty cycle

💡 Hint

What happens if you divide by zero in Python?

frequency is zero, so 1 / frequency causes ZeroDivisionError.

📝 Syntax

advanced

Syntax Error in PWM Duty Cycle Code

Which option contains a syntax error in the PWM duty cycle calculation?

Raspberry Pi

frequency = 500
period = 1 / frequency
pulse_width = 0.0005
duty_cycle = (pulse_width / period) * 100
print(f"Duty cycle: {duty_cycle}%")

A duty_cycle = pulse_width / period * 100

B duty_cycle = pulse_width / (period * 100

C duty_cycle = (pulse_width / period) * 100

D 001 * )doirep / htdiw_eslup( = elcyc_ytud

💡 Hint

Check for missing parentheses.

Option B is missing a closing parenthesis, causing a SyntaxError.

🚀 Application

expert

Calculate PWM Frequency from Duty Cycle and Pulse Width

Given a PWM signal with a pulse width of 0.0001 seconds and a duty cycle of 10%, what is the PWM frequency?

A 10,000 Hz

B 1,000,000 Hz

C 1000 Hz

D 100 Hz

💡 Hint

Use formula: duty cycle = pulse width / period * 100, then find frequency = 1 / period.

Duty cycle = 10% = 0.1, pulse width = 0.0001 s. So period = pulse width / duty cycle = 0.0001 / 0.1 = 0.001 s. Frequency = 1 / 0.001 = 1000 Hz. But 1000 Hz is option C, check carefully. Actually, 0.0001 / period = 0.1 → period = 0.0001 / 0.1 = 0.001 s → frequency = 1 / 0.001 = 1000 Hz. So correct answer is A.