PWM Resolution (Bits)
bits = log2(fclk / fpwm)
Quick answer
This calculator solves bits = log₂(f_clk / f_PWM) for Resolution (bits). With Timer Clock 10 MHz, PWM Frequency 100 kHz, the result is 6.644. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The resolution of a timer-based PWM output is determined by the ratio of the timer clock frequency to the desired PWM frequency. The timer counts from 0 to (fclk/fpwm − 1), giving fclk/fpwm distinct duty cycle steps. The resolution in bits is the base-2 logarithm of this count. Higher timer clock frequencies or lower PWM frequencies give more resolution. For example, a 72 MHz timer generating a 20 kHz PWM has 72M/20k = 3600 steps ≈ 11.8 bits of resolution.
Variables
- bits — PWM duty cycle resolution in bits
- f_clk — Timer clock frequency (Hz)
- f_PWM — PWM output frequency (Hz)
Practical Notes
Common applications: LED dimming requires 10-12 bits for smooth visual perception. Motor control typically needs 8-12 bits. Audio-class PWM (class D amplifiers) requires 12-16 bits. If the calculated resolution is insufficient, options include: increasing the timer clock, decreasing the PWM frequency, or using dithering to achieve fractional bit resolution. Some microcontrollers offer high-resolution PWM timers (e.g., STM32 HRTIM at 4.6 GHz equivalent) for precisely controlled duty cycles.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| bits | Resolution (bits) | — | — |
| fclk | Timer Clock | MHz | Hz, kHz, MHz, GHz |
| fpwm | PWM Frequency | kHz | Hz, kHz, MHz, GHz |
Step by step
- 1. What you know: Timer Clock 10 MHz, PWM Frequency 100 kHz
- 2. The relation: bits = log₂(f_clk / f_PWM)
- 3. Substitute: fclk = 10 MHz, fpwm = 100 kHz
- 4. Result: Resolution (bits) = 6.644
Worked examples
Minimum range
Given: Timer Clock 100 kHz, PWM Frequency 100 Hz
Result: Resolution (bits) = 9.966
Low range
Given: Timer Clock 1 MHz, PWM Frequency 1 kHz
Result: Resolution (bits) = 9.966
Typical
Given: Timer Clock 10 MHz, PWM Frequency 100 kHz
Result: Resolution (bits) = 6.644
High range
Given: Timer Clock 100 MHz, PWM Frequency 0.5 MHz
Result: Resolution (bits) = 7.644
Maximum range
Given: Timer Clock 1 GHz, PWM Frequency 5 MHz
Result: Resolution (bits) = 7.644
Solving for each variable
Solve for Resolution (bits)
Timer Clock 100 kHz, PWM Frequency 100 Hz → 9.966
Solve for Timer Clock
Resolution (bits) 0.025, PWM Frequency 100 Hz → 101.7 Hz
Solve for PWM Frequency
Resolution (bits) 0.025, Timer Clock 100 kHz → 98.28 kHz
How Resolution (bits) changes with Timer Clock
| Timer Clock (input) | Resolution (bits) (result) |
|---|---|
| 1 MHz | 3.322 |
| 2.5 MHz | 4.644 |
| 5 MHz | 5.644 |
| 7.5 MHz | 6.229 |
| 10 MHz | 6.644 |
| 15 MHz | 7.229 |
| 20 MHz | 7.644 |
| 40 MHz | 8.644 |
| 70 MHz | 9.451 |
| 100 MHz | 9.966 |
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<p><a href="https://vbatpower.com/formulas/pwm-resolution-bits/">PWM Resolution (Bits)</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate PWM Resolution (Bits)?
Use bits = log₂(f_clk / f_PWM). With Timer Clock 10 MHz, PWM Frequency 100 kHz, Resolution (bits) works out to 6.644.
What is the formula for PWM Resolution (Bits)?
The formula is bits = log₂(f_clk / f_PWM). The resolution of a timer-based PWM output is determined by the ratio of the timer clock frequency to the desired PWM frequency.
How do you find Timer Clock when you know the other values?
Rearrange for Timer Clock: with Resolution (bits) 0.025, PWM Frequency 100 Hz, Timer Clock is 101.7 Hz.
How do you find PWM Frequency when you know the other values?
Rearrange for PWM Frequency: with Resolution (bits) 0.025, Timer Clock 100 kHz, PWM Frequency is 98.28 kHz.
Related Concepts
All Timing & Oscillators formulas →Need more features?
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