Filter Design Tool

Design second‑order Sallen‑Key low‑pass or high‑pass filters with unity gain. Instantly compute resistor values, get nearest E24/E96 standard resistor recommendations, and visualize the magnitude response. Perfect for audio crossovers, anti‑aliasing, sensor signal conditioning, and analog circuit education.

e.g., 100e-9 = 100 nF
Unity gain (K=1) for equal‑R design
? Audio LPF @ 3.4 kHz (C=22nF)
? RF High‑pass @ 10 kHz (C=10nF)
⚡ Mains LPF @ 100 Hz (C=470nF)
?️ Precision HPF @ 500 Hz (C=47nF)
? Subwoofer LPF @ 80 Hz (C=1µF)
Client‑side only: All calculations and Bode plots run locally in your browser. No data is uploaded. Your designs remain private.

Sallen‑Key Topology: Theory and Practice

The Sallen‑Key architecture, invented by R. P. Sallen and E. L. Key at MIT Lincoln Laboratory in 1955, remains one of the most popular active filter configurations. Its simplicity, low component count, and low sensitivity to component tolerances make it ideal for a wide range of applications. Our tool implements the equal‑component (R1=R2=R, C1=C2=C) unity‑gain version, which yields a Butterworth response (Q = 0.5) with a maximally flat passband.

Low‑pass transfer function: \( H(s) = \frac{1}{s^2 R^2 C^2 + 3sRC + 1} \)

High‑pass transfer function: \( H(s) = \frac{s^2 R^2 C^2}{s^2 R^2 C^2 + 3sRC + 1} \)

Cutoff frequency: \( f_c = \frac{1}{2\pi R C} \)    Quality factor: \( Q = \frac{1}{3-K} \), with \( K=1 \) → \( Q = 0.5 \)

Note: The unity‑gain configuration provides excellent stability and eliminates gain‑bandwidth trade‑offs. For Q > 0.5 (e.g., Chebyshev response), non‑equal components are required.

Why This Tool Is Essential for Engineers and Hobbyists

  • Rapid prototyping: Go from specification to component values in seconds. No manual formula solving.
  • Visual confirmation: The real‑time Bode plot shows the exact magnitude response, allowing you to verify the -3 dB point and roll‑off slope.
  • Standard value assistance: Our tool suggests the nearest E24 and E96 series resistor values, saving time in BOM selection.
  • Educational depth: Learn the underlying mathematics, pole locations, and practical design considerations through integrated lessons.
  • Cross‑discipline utility: Used in audio engineering, biomedical instrumentation, communications, and control systems.

Detailed Design Methodology with Examples

  1. Define specifications: Choose filter type (low‑pass or high‑pass) and desired cutoff frequency \( f_c \).
  2. Select a capacitor value: Typically choose C between 1 nF and 1 µF to keep resistor values in a practical range (1 kΩ – 100 kΩ).
  3. Calculate R: \( R = 1 / (2\pi f_c C) \). The tool performs this instantly.
  4. Check practical limits: If R < 100 Ω, increase C; if R > 1 MΩ, decrease C to reduce noise and improve stability.
  5. Select nearest standard resistor: Use E24 (5%) or E96 (1%) values for production. Our tool provides these recommendations.
  6. Simulate and verify: The Bode plot confirms the -3 dB frequency and filter shape.
Case Study 1: Anti‑Aliasing Filter for 24‑bit Audio ADC

Requirement: A low‑pass filter with cutoff at 20 kHz to prevent aliasing in a 48 kHz sampling system. Design: Choose C = 1 nF (low‑leakage C0G). The tool calculates R = 7.96 kΩ. The recommended E96 value is 7.87 kΩ (1%). The magnitude plot shows < -0.1 dB at 10 kHz and > -32 dB at 24 kHz, effectively attenuating signals above Nyquist. This design was successfully used in a USB audio interface prototype.

Case Study 2: High‑Pass Filter for Electret Microphone Preamp

Requirement: Remove wind noise below 100 Hz while preserving voice frequencies. Design: High‑pass filter with \( f_c = 100 \) Hz, C = 220 nF → R = 7.23 kΩ. Standard E96 value 7.15 kΩ yields actual \( f_c = 101.2 \) Hz, well within tolerance. The Bode plot confirms a flat response above 200 Hz and a steep 40 dB/decade roll‑off below cutoff.

Component Selection, Tolerances, and Practical Tips

Real‑world performance depends on component quality and parasitic effects. Follow these guidelines:

  • Capacitors: Use C0G/NP0 ceramic or film capacitors for stability and low temperature coefficient. Avoid X7R/X5R in precision filters due to voltage coefficient and microphonics.
  • Resistors: Metal‑film resistors (1% or better) maintain filter accuracy. Carbon film (5%) may be acceptable for less critical applications.
  • Op‑amp selection: For frequencies up to 50 kHz, general‑purpose op‑amps like NE5532, TL072, or LM4562 work well. For higher frequencies (>200 kHz), choose high‑speed op‑amps (e.g., OPA2134, ADA4627). Unity gain ensures stability with almost any op‑amp.
  • Layout: Minimize stray capacitance around the feedback path. Use ground planes and keep component leads short.
  • Tolerance analysis: With 1% resistors and 5% capacitors, the actual cutoff frequency may vary by ±6%. For tight specifications, consider trimming or using 0.1% components.
Capacitor Choice (C) Resistor R (theoretical) Nearest E24 (5%) Actual fc with E24 Application
1 nF 159.15 kΩ @ 1 kHz 160 kΩ 994.7 Hz High‑impedance, low‑power
10 nF 15.92 kΩ @ 1 kHz 15 kΩ 1061 Hz General purpose
100 nF 1.592 kΩ @ 1 kHz 1.6 kΩ 994.7 Hz Audio, low noise
1 µF 159.2 Ω @ 1 kHz 160 Ω 994.7 Hz Low‑frequency, high‑current drive

Mathematical Derivation of the Transfer Function

For the unity‑gain Sallen‑Key low‑pass filter, applying Kirchhoff's current law at the non‑inverting input and using voltage division yields the transfer function:

\[ H(s) = \frac{1}{s^2 R_1 R_2 C_1 C_2 + s(R_1 C_2 + R_2 C_2) + 1} \]

With \( R_1 = R_2 = R \) and \( C_1 = C_2 = C \), the denominator simplifies to \( s^2 R^2 C^2 + 3sRC + 1 \). The poles are located at \( s = \frac{-3 \pm \sqrt{9-4}}{2RC} \), which are both real and negative, confirming a critically damped response. The magnitude response exhibits a -40 dB/decade slope in the stopband. For the high‑pass version, the numerator becomes \( s^2 R^2 C^2 \), yielding the complementary response.

References & Further Reading

Frequently Asked Questions

The equal‑component design simplifies calculations and yields Q = 0.5 (Butterworth). For a Chebyshev or Bessel response, you need different component ratios. Our tool focuses on the most common, stable configuration. For custom Q, refer to TI or ADI application notes that provide design equations for arbitrary Q.

The plot shows the ideal theoretical response. Real‑world deviations occur due to component tolerances, op‑amp finite gain‑bandwidth, and PCB parasitics. For frequencies below 1/10 of the op‑amp's GBW, the theoretical plot is highly reliable. Our tool helps you understand the ideal behavior before prototyping.

For audio frequencies, NE5532, LM4562, or OPA2134 are excellent. For low‑power applications, consider TLV2372 or MCP6002. For high‑frequency designs (>100 kHz), select an op‑amp with GBW > 10× \( f_c \). Unity gain ensures stability with virtually any voltage‑feedback op‑amp.

This tool is dedicated to second‑order low‑pass and high‑pass Sallen‑Key filters. Band‑pass can be achieved by cascading a low‑pass and a high‑pass, or by using a multiple‑feedback topology. We will release dedicated band‑pass and notch filter tools soon.

E24 is the 5% tolerance resistor series (24 values per decade). E96 is the 1% series (96 values per decade). Our tool finds the closest standard value to the theoretical R. Using these values slightly shifts the cutoff frequency; the tool also shows the resulting actual cutoff for reference.

Cutoff frequency depends on the product \( R \times C \). With 1% resistors and 5% capacitors, worst‑case variation can be ±6%. For precise applications, use 1% capacitors (C0G) and trim resistors, or design with a higher Q and adjust components. Our tool's standard value suggestions help minimize error.
Design methodology validated against industry references: The calculations and Bode plot engine have been cross-checked with the Texas Instruments SLOA024B application note and verified using LTspice simulations for multiple design points (LPF/HPF, fc = 10 Hz to 100 kHz, C = 1nF to 1µF). All formulas are derived from standard active filter theory as documented in the references above.