ADC Anti-Alias Filter Calculator
Plan analog anti-alias filtering before an ADC by checking Nyquist frequency, signal guard band, alias folding, Butterworth order, interferer attenuation, and ADC LSB-based residual targets.
This is not a generic low-pass calculator. It separates analog filter attenuation from the digital alias frequency that appears after sampling.
Engineering tool
ADC Anti-Alias Filter Calculator
Plan ADC sampling, Nyquist guard band, alias folding, Butterworth order, interferer attenuation, and ADC residual alias targets.
Parameter panel
Result console
- Required Order
- 9
- Raw Order
- 8.276153
- Selected Cutoff
- 21.559 kHz
- Cutoff Range
- 21.559 kHz to 23.208 kHz
- Second-Order Stages
- 4
- First-Order Stage
- Required
- Spec Verification
- Passes
Required order was rounded upward with ceil, not rounded to the nearest integer.
The next lower order does not satisfy the selected specification.
| Actual Passband | 1 dB | Must be <= passband attenuation limit |
|---|---|---|
| Actual Stopband | 65.7609 dB | Must be >= stopband attenuation requirement |
| N-1 Check | Fails | Lower order should not satisfy the same specification |
| Cutoff Range | 21.559 kHz to 23.208 kHz | Derived from Ap and As constraints |
Formula reference
ADC Anti-Alias Formulas
The V1 model targets real-valued sampled ADC signals and analog low-pass filtering before the ADC input.
fN = fs / 2OSR = fs / (2fPB)Guard band = fN - fPBr = fin mod fsfalias = min(r, fs - r)Butterworth order = ceil(log10[(10^(As/10)-1)/(10^(Ap/10)-1)] / [2log10(fst/fp)])Vresidual = Vin x |H|VLSB = VFS / 2^NRequired attenuation = 20log10(Ain / Ares)Variable definitions
- fs
- sampling frequency
- fN
- Nyquist frequency
- fPB
- desired signal passband edge
- fin
- analog input frequency
- Ain
- out-of-band interferer amplitude
- Ares
- allowed residual alias amplitude
ADC Anti-Alias Formula Audit
| Sampling Convention | Real-valued sampled ADC signal. |
|---|---|
| Nyquist Formula | fN = fs / 2. |
| OSR Convention | OSR = fs / (2 fPB), relative to Nyquist minimum rate. |
| Guard Band Definition | Guard band = fN - fPB. |
| Alias Folding Formula | r = fin mod fs; falias = min(r, fs-r). |
| Nyquist Zone Convention | Boundary cases are labeled explicitly. |
| Butterworth Utility | FIL-009 order, response, pole and stage Q utilities are reused. |
| Cutoff Handling | Cutoff range is derived from Ap, As, fp and fst constraints. |
| Residual Formula | Vresidual = Vin x |H|. |
| ADC LSB Convention | VLSB = VFS / 2^N using full-scale span. |
| Required Attenuation | 20log10(Ain / Ares), amplitude criterion. |
| 6.02N+1.76 Boundary | Documented as quantization SNR context, not anti-alias requirement. |
| ADC Input Loading | V1 does not model switched-capacitor acquisition loading. |
Worked Examples
Nyquist
Known: fs = 100 kHz
fN = 50 kHz.
OSR
Known: fs = 100 kHz, fPB = 20 kHz
OSR = 2.5.
Guard band
Known: fN = 50 kHz, fPB = 20 kHz
Guard band = 30 kHz.
Alias 6 kHz
Known: fs = 10 kHz, fin = 6 kHz
Alias = 4 kHz.
Alias 9 kHz
Known: fs = 10 kHz, fin = 9 kHz
Alias = 1 kHz.
Alias 11 kHz
Known: fs = 10 kHz, fin = 11 kHz
Alias = 1 kHz.
Alias 14 kHz
Known: fs = 10 kHz, fin = 14 kHz
Alias = 4 kHz.
Alias 15 kHz
Known: fs = 10 kHz, fin = 15 kHz
Alias = 5 kHz.
Sampling image
Known: fin = integer x fs
Alias = 0 Hz.
Nyquist boundary
Known: fin = fs/2
Alias = fs/2.
Butterworth order
Known: fp = 20 kHz, fst = 50 kHz, Ap = 1 dB, As = 60 dB
Order is rounded upward and verified.
N-1 check
Known: Same specification
The lower order fails the target.
Cutoff verification
Known: Selected cutoff
Passband and stopband constraints are recalculated.
RC at fc
Known: First-order RC
Attenuation = 3.0103 dB.
Butterworth at fc
Known: Any order
Complete response = 3.0103 dB attenuation.
12-bit LSB
Known: VFS = 4.096 V
1 LSB = 1 mV.
0.5 LSB
Known: 12-bit, 4.096 V
Allowed residual = 0.5 mV.
1 V interferer
Known: Allowed residual = 0.5 mV
Required attenuation = 66.0206 dB.
90 kHz interferer
Known: fs = 100 kHz
Alias = 10 kHz.
Frequency units
Known: 1000 Hz and 1 kHz
Equivalent results.
Log sweep
Known: 50 rows
Finite ordered rows with alias locations.
Oversampling
Known: Increase fs with fixed fPB
OSR and guard band increase.
Anti-Alias Filter
The analog filter belongs before the ADC, not after sampling.
Aliasing
Out-of-band analog frequencies can fold into baseband after sampling.
Guard Band
More guard band gives the analog filter room to transition.
Oversampling
Higher fs raises Nyquist and can reduce filter difficulty, at data-rate and power cost.
First-Order RC
A single RC may be insufficient for narrow transition and high attenuation targets.
ADC Loading
SAR ADC input sampling networks can disturb simple RC assumptions.
Resolution
Nominal bits are not ENOB; noise and distortion matter.
Validation
Critical front ends need ADC datasheet review, SPICE, and measurement.
Common Mistakes
Support reference
FAQ
What is an ADC anti-alias filter?
It is an analog low-pass filter placed before the ADC to reduce out-of-band signals before sampling.
Why does an ADC need an anti-alias filter?
Signals above Nyquist can fold into baseband during sampling and cannot generally be removed afterward by ordinary digital filtering.
What is the Nyquist frequency?
Nyquist frequency is half the sampling rate, fN = fs/2.
How do I calculate alias frequency?
For real sampling, take r = fin mod fs, then falias = min(r, fs - r), which lands from 0 to fs/2.
What sampling rate should I use?
The desired signal bandwidth must be below Nyquist, and additional guard band makes analog filtering easier.
What is anti-alias filter guard band?
Guard band is the gap between the signal passband edge and Nyquist frequency.
How do I calculate the required filter order?
Use passband loss, stopband attenuation, and the stopband/passband frequency ratio. Butterworth order is rounded upward with ceil.
How much attenuation is needed at Nyquist?
It depends on interferer amplitude and allowed residual alias error. ADC bit count alone is not enough.
Is a first-order RC filter enough for an ADC?
Sometimes, but demanding transition bands or high attenuation often require higher-order active filters.
How does oversampling reduce filter requirements?
Higher sampling frequency raises Nyquist and usually increases guard band for a fixed signal bandwidth.
Can I remove aliasing with a digital filter after sampling?
Usually no. Once an out-of-band signal has folded into baseband, a digital filter cannot know its original analog frequency.
How does ADC resolution affect anti-alias requirements?
Resolution defines LSB size, but required attenuation also depends on interferer amplitude and acceptable residual error.
Why is 6.02N + 1.76 dB not automatically required filter attenuation?
That expression is ideal quantization SNR for a full-scale sine context, not a universal anti-alias attenuation requirement.
How does ADC input impedance affect the filter?
ADC sampling capacitors and acquisition current can load the filter; check the ADC datasheet input-drive requirements.
What is the difference between ADC resolution and ENOB?
Resolution is nominal code width; ENOB includes real noise, distortion, reference noise, jitter, and front-end limitations.
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Engineering Disclaimer
This calculator uses ideal low-pass, Butterworth, RC and sampling relationships. It does not model ADC acquisition capacitor kickback, op-amp noise, distortion, reference noise, jitter, component tolerance, board parasitics or exact ADC input-drive requirements. Validate critical ADC front ends against the ADC datasheet, SPICE and measurement.