Skip to content
RFrftools.io
Signal

Passive RC/LC Filter Designer

Design passive Butterworth and Chebyshev LC ladder filters up to order 10. Calculate component values for low-pass, high-pass, and band-pass topologies. Free, instant results.

Loading calculator...

Formula

Ck=gkωc⋅Z0,Lk=gk⋅Z0ωcC_k = \frac{g_k}{\omega_c \cdot Z_0},\quad L_k = \frac{g_k \cdot Z_0}{\omega_c}

Reference: Williams & Taylor, Electronic Filter Design Handbook 4th ed.; Zverev, Handbook of Filter Synthesis

g_k— Normalized prototype element value (Butterworth or Chebyshev)
ω_c— Angular cutoff frequency (2πf_c) (rad/s)
Z₀— Characteristic impedance (Ω)
τ— RC time constant (s)
f_c— Cutoff frequency (Hz)
Q— Quality factor
n— Filter order (1–10)

How It Works

The Filter Designer Calculator computes component values for Butterworth and Chebyshev analog filters — essential for anti-aliasing, signal conditioning, and EMI filtering applications. Analog designers, audio engineers, and RF specialists use this to create lowpass, highpass, and bandpass filters with predictable frequency response. Per Williams & Taylor 'Electronic Filter Design Handbook' (4th ed., McGraw-Hill) and Zverev's 'Handbook of Filter Synthesis' (Wiley, 1967), Butterworth filters achieve maximally flat passband with -20N dB/decade rolloff, where N = filter order. Filter design follows ITU-R recommendations for bandpass specifications and IEEE Standard 1241-2010 (IEEE Standard for Terminology and Test Methods for Analog-to-Digital Converters) for anti-aliasing filter requirements. A 5th-order Butterworth provides 100 dB attenuation at 10x cutoff frequency. Chebyshev filters trade passband ripple (0.5-3 dB typical) for steeper rolloff — a 5th-order Chebyshev 0.5 dB achieves same attenuation as 7th-order Butterworth. Per Zverev "Handbook of Filter Synthesis," normalized g-values enable direct component calculation: L = g*R/(2*pi*fc), C = g/(2*pi*fc*R).

Worked Example

Design 3rd-order Butterworth lowpass at 10 kHz for 12-bit ADC anti-aliasing with 50 ohm source/load. Step 1: Normalized g-values for 3rd-order Butterworth: g1=1.0, g2=2.0, g3=1.0. Step 2: Denormalize: C1 = g1/(2*pi*10000*50) = 318 nF. L2 = g2*50/(2*pi*10000) = 1.59 mH. C3 = g3/(2*pi*10000*50) = 318 nF. Step 3: Select standard values: C1=C3=330 nF (E24), L2=1.5 mH. Step 4: Verify: -60 dB at 100 kHz (10x fc) per Butterworth rolloff. Per IEEE 1241, this provides adequate aliasing rejection for 12-bit ADC with fs >= 25 kHz.

Practical Tips

  • ✓Per Williams, use 1% tolerance components for filters requiring < 0.5 dB passband accuracy
  • ✓Simulate in SPICE before building — component parasitics shift actual response from ideal
  • ✓For high-Q bandpass filters (Q > 10), consider active topologies to avoid impractical inductor values
  • ✓Cascade 2nd-order sections for orders > 3 to reduce component sensitivity per Analog Devices MT-210

Common Mistakes

  • ✗Neglecting component tolerances — 5% capacitor tolerance shifts fc by +/-5%; use 1% for critical applications per Williams
  • ✗Failing to account for op-amp bandwidth — GBW must exceed 10x fc for active filter accuracy per TI AN-779
  • ✗Overlooking parasitic inductance — 10 nH lead inductance causes 1% impedance error above 100 kHz

Frequently Asked Questions

Maximally flat passband — no ripple, monotonic rolloff per Butterworth (1930). Transfer function magnitude |H(jw)|^2 = 1/(1+(w/wc)^2N). At cutoff, attenuation is exactly -3.01 dB. Rolloff is -20N dB/decade. Per Zverev, Butterworth minimizes in-band amplitude distortion at cost of slower rolloff vs. Chebyshev.
1st-order: -20 dB/decade, 45 deg phase shift at fc. 2nd-order: -40 dB/decade, 90 deg at fc. Per Williams, 2nd-order provides 60 dB rejection at 30x fc vs. only 30 dB for 1st-order. Use 2nd-order minimum for anti-aliasing; 4th-6th order typical for production systems.
Per Williams: Butterworth for passband flatness (audio, wideband amps) — 0 dB ripple. Chebyshev for sharp cutoff (anti-aliasing, interference rejection) — 0.5 dB ripple achieves equivalent of +2 Butterworth orders. 5th-order 0.5 dB Chebyshev matches 7th-order Butterworth rolloff while using 30% fewer components.
Per Zverev formula: N_Butterworth = log(10^(40/10)-1)/(2*log(fs/fc)). At 2x fc: N = 6.6 -> use 7th order. At 3x fc: N = 4.2 -> use 5th order. Chebyshev 0.5 dB needs N-2 orders less for same rejection. Use the stopband/passband frequency ratio to minimize filter order.
Per Williams: (1) Inductor Q limits passband insertion loss — Q=50 inductor causes 0.1 dB loss per pole. (2) Narrow bandwidth (BW/fc < 10%) requires Q > 10 inductors rarely available in standard values. (3) 5% component tolerance causes +/-0.5 dB passband ripple. (4) Use Monte Carlo analysis — this site's RF filter tool simulates 1000 tolerance combinations.
Yes — cascading Nth-order sections yields N*M total order. Per Sedra & Smith, cascade identical 2nd-order sections for even orders; add 1st-order for odd orders. Total rolloff = -20*(N*M) dB/decade. Cascading simplifies component selection and reduces sensitivity to tolerance variations.

Advanced Simulation Tools

RF Filter Monte Carlo Analysis

Analyse how component tolerances affect your filter's passband ripple and stopband rejection. Run thousands of Monte Carlo trials to get yield and worst-case statistics.

PRO

Shop Components

As an Amazon Associate we earn from qualifying purchases.

Op-Amp IC Assortment

General-purpose and precision operational amplifiers

Amazon →

Function Generator

DDS function generator for signal and filter testing

Amazon →

Related Calculators

General

RC Time Constant

Calculate RC circuit time constant τ, charge time to 63.2% and 99%, and −3dB cutoff frequency. Essential for filter and timing circuit design.

Signal

Nyquist Sampling

Calculate Nyquist sampling rate, oversampling ratio, and aliasing frequency. Verify your ADC sampling meets the Nyquist criterion and determine data rate. Free, instant results.

General

LC Resonance

Calculate the resonant frequency, characteristic impedance, Q factor, and bandwidth of a series or parallel LC tank circuit. Enter inductance, capacitance, and optional series resistance.

Signal

SNR

Calculate signal-to-noise ratio, noise floor, receiver sensitivity, and dynamic range for RF systems. Analyze your signal chain performance. Free, instant results.