Switched Capacitor Filters: Clock, Aliasing, Parts

Switched capacitor filters use a clock to simulate resistors, and that clock directly sets the filter’s cutoff frequency, but it also creates aliasing and clock feedthrough that you must handle with external components. You enter the clock frequency and the capacitor ratio (or choose a standard filter IC), and the calculator below gives you the cutoff frequency and the minimum external RC values needed to suppress aliasing and clock noise.

Formula

The cutoff frequency of a basic switched capacitor filter is given by:

f_c = f_clk / (C1/C2)

Where:

• f_clk = clock frequency (Hz, but the calculator uses kHz)
• C1/C2 = ratio of the switched capacitor to the integrating capacitor (dimensionless)
• f_c = cutoff frequency (Hz, or kHz in the calculator)

For a first-order low-pass filter, the –3 dB point is exactly that. For higher-order filters made from cascaded sections, each section’s ratio may differ, but the same clock-to-cutoff relationship holds for each stage.

Worked Example

Using the default values: f_clk = 100 kHz, C1/C2 = 10.

Step 1: Divide the clock frequency by the capacitor ratio:

f_c = 100 kHz / 10 = 10 kHz

Step 2: The Nyquist frequency is half the clock:

f_nyq = 100 kHz / 2 = 50 kHz

Step 3: A typical rule of thumb for the input RC anti-alias filter is to set its corner at about 10× the cutoff (or at least below the clock frequency). The calculator uses a simple time constant of 10 clock periods:

R*C = 10 / 100,000 = 100 µs

So the calculator returns f_c = 10.000 kHz, f_nyq = 50.000 kHz, and R*C = 100.00 µs.

How Switched Capacitor Filters Work

A switched capacitor filter replaces a physical resistor with a capacitor that is alternately charged and discharged by two non-overlapping clock phases. The average current flowing through the switched capacitor is proportional to the clock frequency and the capacitance, so it behaves like a resistor of value:

R_eq = 1 / (f_clk × C_sw)

This equivalent resistance, combined with an integrating capacitor, sets the time constant of the filter. Because the resistance is set by a clock and a capacitor ratio, the cutoff frequency tracks the clock exactly. That is the main advantage: you can tune the filter by changing the clock frequency, without changing any external resistors.

Most practical switched capacitor filters are sold as ICs (like the classic MF10 or LTC1068) that contain several second-order sections. You set the clock frequency and choose a few external resistors to set the Q and gain, but the cutoff is always a fixed ratio of the clock.

Aliasing and Clock Feedthrough

Because the filter samples the input signal at the clock rate, any signal component above half the clock frequency (the Nyquist frequency) will alias down into the passband. For example, if your clock is 100 kHz and your input has a 60 kHz noise component, that noise will appear at 40 kHz in the output, which may be inside your passband if the cutoff is 10 kHz.

To prevent this, you must add a simple RC low-pass filter at the input of the switched capacitor filter. The corner frequency of that RC should be set below the clock frequency, but above the desired cutoff. A common rule is to set the RC corner at about 10× the cutoff frequency, or at least below f_clk/2. The calculator’s output “Min input RC” gives a time constant equal to 10 clock periods, which is a safe starting point.

Clock feedthrough is a different issue: the clock signal can couple into the output through parasitic capacitances. This appears as small spikes at the clock frequency. You can reduce it with a simple RC low-pass filter at the output, with a corner just above the cutoff. The same time constant rule works.

Choosing External Components

For a typical switched capacitor filter IC, you need:

• Clock source: a TTL or CMOS square wave, usually 50% duty cycle. The clock frequency determines the cutoff, so use a stable oscillator if accuracy matters.
• Input RC anti-alias filter: a resistor and capacitor in series to ground, with a corner below the clock frequency. Use the calculator’s value as a starting point.
• Output RC filter: optional but recommended to smooth the clock feedthrough. A simple RC with corner at about 10× cutoff works.
• Power supply decoupling: 0.1 µF ceramic capacitors close to each power pin, plus a 10 µF tantalum or electrolytic for low-frequency noise.
• External resistors for Q and gain: if your filter IC allows programming Q, those resistors set the sharpness of the response. They do not affect the cutoff frequency.

Always check the datasheet of your specific IC for the exact pin connections and recommended component values. The calculator gives a general rule, but the datasheet may specify a different minimum RC.

Common Mistakes and Misconceptions

One common mistake is forgetting that the input signal must be band-limited before the switched capacitor filter. If you feed a signal with high-frequency noise directly, the noise aliases and ruins the output. Another mistake is using a clock that is too low relative to the cutoff: the ratio must be at least 2, but in practice you want a ratio of 10 or more so that the anti-alias filter can be simple.

A frequent misconception is that the clock frequency must be much higher than the cutoff. That is true, but the exact ratio depends on the filter order and the required stopband attenuation. For a first-order filter, a ratio of 10 gives about 20 dB of rejection at the clock frequency, which is often enough. For higher-order filters, the ratio can be lower because the filter itself attenuates the aliased components.

Another error is using a clock with excessive jitter. Jitter on the clock translates to noise in the cutoff frequency and can cause sidebands in the output. Use a clean square wave source, not a noisy microcontroller pin without buffering.

Practical Design Tips

When designing a circuit with a switched capacitor filter, follow these steps:

1. Determine the desired cutoff frequency and the available clock frequencies.
2. Choose a capacitor ratio (or a filter IC) that gives a clock-to-cutoff ratio of at least 10. If you have flexibility, use a higher ratio to simplify the anti-alias filter.
3. Calculate the input RC time constant using the rule of thumb (10 clock periods). Choose R and C values that are practical (e.g., 1 kΩ and 0.1 µF for a 10 kHz cutoff with a 100 kHz clock).
4. Add an output RC filter with a corner at about 10× the cutoff to suppress clock feedthrough.
5. Decouple the power supply with 0.1 µF capacitors close to the IC.
6. Test the circuit with a square wave input to check for aliasing: if you see unexpected frequencies, increase the input RC or lower the clock frequency.

Remember that the switched capacitor filter is a sampled system, so it is not a continuous-time filter. The output holds the last sampled value between clock edges, which creates a slight staircase effect. For most audio and control applications, this is negligible if the clock is much higher than the cutoff.

Alternatives to Switched Capacitor Filters

If aliasing or clock noise is a problem, you might consider:

• Continuous-time active filters: use resistors and capacitors, no clock, so no aliasing. But tuning requires variable resistors or capacitors.
• Digital filters: sample the signal with an ADC, filter in software, and output with a DAC. They offer precise control but require more power and complexity.
• Discrete-time analog filters (e.g., charge-domain): similar to switched capacitor but with different trade-offs.

Switched capacitor filters are ideal when you need a tunable filter that is accurate and stable, such as in audio equalizers, anti-aliasing for data converters, or tone decoding. They are not ideal when the clock noise is unacceptable, such as in very low-noise audio paths.

Frequently Asked Questions

Q: Can I use a switched capacitor filter without an input RC filter?
A: Technically yes, but you will get aliasing if the input contains frequencies above half the clock. Even if your signal is clean, noise from the environment will alias. Always add a simple RC low-pass at the input.

Q: What is the minimum clock-to-cutoff ratio I should use?
A: The absolute minimum is 2 (because of Nyquist), but in practice you need at least 10 to make the anti-alias filter simple and to keep clock feedthrough low. For higher-order filters, you can sometimes use a ratio of 5, but 10 is a safe default.

Q: How do I choose the RC values for the anti-alias filter?
A: Use the calculator’s output for the time constant, then pick a resistor value (e.g., 1 kΩ to 10 kΩ) and compute the capacitor. For a 100 kHz clock, the calculator gives 100 µs, so with 10 kΩ you need 10 nF. That is a good starting point.

Q: Does the clock frequency affect the filter’s Q or gain?
A: No, the Q and gain are set by external resistors, not the clock. The clock only sets the cutoff frequency. That is the main advantage of switched capacitor filters.

Q: Can I use a microcontroller’s PWM output as the clock?
A: Yes, but the PWM must be a stable square wave at the desired frequency. Avoid using a PWM with a variable duty cycle or jitter, as that will cause noise. A timer output is usually fine.

Q: Why does my output have spikes at the clock frequency?
A: That is clock feedthrough. Add an RC low-pass filter at the output with a corner at about 10× the cutoff. Also ensure proper grounding and decoupling.

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in fclk | Clock frequency | kHz | 100 | 0.1 | 10000
in ratio | Capacitor ratio (C1/C2) | - | 10 | 1 | 1000
out fc | Cutoff frequency | kHz | fclk / ratio | 3
out fnyq | Nyquist frequency | kHz | fclk / 2 | 3
out rmin | Min input RC (R*C) | us | (1 / (fclk * 1000)) * 1e6 * 10 | 2