Switched-Capacitor Filter Cutoff
fc = fclk / ratio
Quick answer
This calculator solves fc = f_clk / ratio for Filter Cutoff. With Clock Frequency 2.2 kHz, Clock-to-Cutoff Ratio 0.5, the result is 4.4 kHz. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Switched-capacitor filters use a clock signal to sample charge packets on capacitors, effectively implementing resistors whose value is R_eq = 1/(C × fclk). The filter cutoff frequency is set by the clock frequency divided by a fixed ratio determined by the IC design (commonly 50:1 or 100:1). This allows precise frequency tuning by simply changing the clock frequency, without changing any component values. Switched-capacitor filters are used in anti-aliasing, data acquisition, and telecommunications where tunable or precise filter frequencies are needed.
Variables
- fc — Filter cutoff frequency (Hz)
- f_clk — Clock frequency (Hz)
- ratio — Clock-to-cutoff frequency ratio (e.g., 50, 100)
Practical Notes
Common clock-to-cutoff ratios: MAX291/MAX292 use 100:1, LTC1062 uses 100:1, MF10 uses 50:1 or 100:1 (selectable). The clock frequency must be much higher than the signal frequency to avoid clock feedthrough artifacts. An external RC filter after the switched-cap filter removes clock feedthrough. Accuracy of the cutoff frequency depends on clock accuracy, typically ±0.2% with a crystal oscillator.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| fc | Filter Cutoff | Hz | Hz, kHz, MHz, GHz |
| fclk | Clock Frequency | Hz | Hz, kHz, MHz, GHz |
| ratio | Clock-to-Cutoff Ratio | — | — |
Step by step
- 1. What you know: Clock Frequency 2.2 kHz, Clock-to-Cutoff Ratio 0.5
- 2. The relation: fc = f_clk / ratio
- 3. Substitute: fclk = 2.2 kHz, ratio = 0.5
- 4. Result: Filter Cutoff = 4.4 kHz
Worked examples
Minimum range
Given: Clock Frequency 11 Hz, Clock-to-Cutoff Ratio 0.025
Result: Filter Cutoff = 0.44 kHz
Low range
Given: Clock Frequency 110 Hz, Clock-to-Cutoff Ratio 0.25
Result: Filter Cutoff = 0.44 kHz
Typical
Given: Clock Frequency 2.2 kHz, Clock-to-Cutoff Ratio 0.5
Result: Filter Cutoff = 4.4 kHz
High range
Given: Clock Frequency 44 kHz, Clock-to-Cutoff Ratio 0.8
Result: Filter Cutoff = 55 kHz
Maximum range
Given: Clock Frequency 0.44 MHz, Clock-to-Cutoff Ratio 8
Result: Filter Cutoff = 55 kHz
Solving for each variable
Solve for Filter Cutoff
Clock Frequency 11 Hz, Clock-to-Cutoff Ratio 0.025 → 0.44 kHz
Solve for Clock Frequency
Filter Cutoff 5 Hz, Clock-to-Cutoff Ratio 0.025 → 0.125 Hz
Solve for Clock-to-Cutoff Ratio
Filter Cutoff 5 Hz, Clock Frequency 11 Hz → 2.2
How Filter Cutoff changes with Clock Frequency
| Clock Frequency (input) | Filter Cutoff (result) |
|---|---|
| 0.22 kHz | 0.44 kHz |
| 0.55 kHz | 1.1 kHz |
| 1.1 kHz | 2.2 kHz |
| 1.65 kHz | 3.3 kHz |
| 2.2 kHz | 4.4 kHz |
| 3.3 kHz | 6.6 kHz |
| 4.4 kHz | 8.8 kHz |
| 8.8 kHz | 17.6 kHz |
| 15.4 kHz | 30.8 kHz |
| 22 kHz | 44 kHz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 4400 |
| kHz | 4.4 |
| MHz | 0.0044 |
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<p><a href="https://vbatpower.com/formulas/switched-cap-filter/">Switched-Capacitor Filter Cutoff</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Switched-Capacitor Filter Cutoff?
Use fc = f_clk / ratio. With Clock Frequency 2.2 kHz, Clock-to-Cutoff Ratio 0.5, Filter Cutoff works out to 4.4 kHz.
What is the formula for Switched-Capacitor Filter Cutoff?
The formula is fc = f_clk / ratio. Switched-capacitor filters use a clock signal to sample charge packets on capacitors, effectively implementing resistors whose value is R_eq = 1/(C × fclk).
How do you find Clock Frequency when you know the other values?
Rearrange for Clock Frequency: with Filter Cutoff 5 Hz, Clock-to-Cutoff Ratio 0.025, Clock Frequency is 0.125 Hz.
How do you find Clock-to-Cutoff Ratio when you know the other values?
Rearrange for Clock-to-Cutoff Ratio: with Filter Cutoff 5 Hz, Clock Frequency 11 Hz, Clock-to-Cutoff Ratio is 2.2.
What units does Switched-Capacitor Filter Cutoff use?
Filter Cutoff is shown in Hz, kHz, MHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Filters formulas →Need more features?
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