Analog Filtering#

Analog filters shape the frequency content of a signal before it reaches the converter. The most critical role is anti-aliasing — removing frequency components above the Nyquist limit so they don’t fold back into the signal during sampling. But analog filters also reject interference, limit noise bandwidth, and define the useful frequency range of a signal chain. Filter design is where frequency-domain thinking meets real component constraints.

Anti-Aliasing: The Mandatory Filter#

Before an ADC samples a signal, any energy above half the sampling rate (f_s/2) must be attenuated enough that aliased components fall below the noise floor. This is not optional — aliasing is irreversible. Once aliased components are folded into the signal band, no digital processing can remove them.

How much attenuation is enough? The answer depends on the ADC resolution:

These numbers assume worst-case out-of-band signals at full scale. In practice, the required rejection depends on the actual spectral content — if there’s nothing above Nyquist, no filter is needed. But designing for worst-case is the safe approach.

Filter Order and Rolloff#

A filter’s order determines how steeply it attenuates past its cutoff frequency:

To achieve 80 dB of attenuation one octave above cutoff, a 13th-order filter at -20 dB/decade per order would be required — impractical. Real anti-alias filters are typically 2nd to 4th order, and the transition band between passband and stopband is managed by choosing the sampling rate appropriately.

Filter types trade off passband flatness, transition steepness, and phase behavior:

• Butterworth — Maximally flat passband, moderate rolloff. The default choice when predictable amplitude behavior is needed
• Chebyshev — Steeper rolloff than Butterworth for the same order, but with passband ripple. Useful when transition band is tight
• Bessel — Maximally flat group delay (best transient response), but the gentlest rolloff. Choose when waveform shape matters more than frequency selectivity
• Elliptic (Cauer) — Steepest rolloff for a given order, but with ripple in both passband and stopband. Maximum efficiency when sharp cutoff is the priority

See Filters & Frequency Behavior for analog filter implementation details.

Filter Placement#

Where the anti-alias filter sits in the signal chain matters:

• After the preamp, before the ADC — The standard position. The preamp amplifies the signal (and noise within its bandwidth), then the filter removes out-of-band content before sampling
• At the sensor — Sometimes a simple RC filter at the sensor limits bandwidth early, preventing overload from out-of-band signals (e.g., RF interference on a low-frequency sensor)
• Multiple stages — A first-order filter at the preamp output followed by a steeper filter before the ADC. The first filter prevents slew-rate limiting; the second provides the required stopband rejection

Oversampling as a Strategy#

Instead of building a steep analog anti-alias filter, sample at a much higher rate and use a digital filter to achieve the required selectivity. This is the oversampling approach:

• Sample at N× the required Nyquist rate — This moves the aliasing boundary further from the signal band, relaxing the analog filter requirements
• Digitally filter and decimate — A digital low-pass filter provides the steep cutoff, then the sample rate is reduced (decimated) to the required rate

At 4× oversampling, the analog filter only needs to provide adequate rejection at 4× the signal bandwidth instead of at 1×. At 64× or 128× oversampling (common in delta-sigma ADCs), a simple first-order RC filter is often sufficient.

Tradeoff: Oversampling requires a faster ADC, more digital processing, and more power. But it dramatically simplifies the analog filter and improves overall system performance by pushing the transition band far from the signal.

Tips#

• Use oversampling when practical — it relaxes analog filter requirements significantly
• Place a simple RC filter at the sensor to reject RF interference before it reaches the preamp
• For waveform fidelity (pulse measurements, step response), prefer Bessel filters despite their gentler rolloff

Caveats#

• Component tolerances shift the cutoff — A filter designed for 20 kHz cutoff with 5% resistors and 10% capacitors might actually cut off anywhere from 16 kHz to 25 kHz. Use 1% components for precision filter work
• Op-amp bandwidth limits filter performance — The op-amp’s open-loop gain must be much higher than the filter’s Q at the cutoff frequency. A Sallen-Key filter with Q = 5 using an op-amp with only 20 dB of open-loop gain at cutoff will not behave as designed
• Aliased noise can look like signal — If broadband noise extends above Nyquist, it aliases back into the signal band and raises the noise floor. The anti-alias filter must attenuate noise, not just the desired signal’s harmonics
• Group delay causes waveform distortion — Steep filters (Chebyshev, elliptic) have non-constant group delay near cutoff, which distorts transients. For analyzing pulse shapes or timing, Bessel filters preserve waveform fidelity
• Passive filters have impedance interactions — An RC filter followed by a low-impedance load changes its cutoff frequency. Buffer the filter output or account for the load in the design
• Don’t forget the input — An anti-alias filter at the ADC input doesn’t help if the ADC’s sample-and-hold is exposed to high-frequency signals through other paths (e.g., digital feedthrough on the PCB)

In Practice#

• A signal that shows unexpected low-frequency content after sampling likely has aliased high-frequency components — verify the anti-alias filter is working
• A filter that doesn’t achieve the expected rolloff may have component tolerance issues or op-amp bandwidth limitations
• Ringing on step response indicates a high-Q filter (Chebyshev, elliptic) — switch to Butterworth or Bessel if this is problematic
• A passive RC filter that appears to have the wrong cutoff frequency may be loaded by the next stage’s input impedance