Please enter valid values. All fields are required.
RESULTS
TYPE-1 (Shunt Resonant Start Lattice)
TYPE-2 (Series Resonant Start Lattice)
Input Parameters Specification
LC Pairs No (n)
The target configuration order definition factor representing total alternating filter mesh nodes (Valid dynamic scale: 1 up to 9).
Center Frequency
The operational mid-band geometric resonant baseline channel peak frequency location handling filter waves, specified in MHz.
Passband Bandwidth
The absolute width frame profile size parameter mapping the low-attenuation transmission spectrum width, in MHz.
Impedance / Ripple
The standard source transmission line characteristic load network impedance matching (Ohms) along with passband dB ripple variations.
Practical Operational Examples
Input Benchmark Set
LC Pairs: 3
Center Frequency: 100 MHz
Passband Bandwidth: 10 MHz
Impedance: 50 Ω
Passband Ripple: 0.1 dB
Calculated Element States
• Type-1 L1 Shunt: ~754.21 nH | C1 Shunt: ~3.35 pF
• Type-2 L1 Series: ~8.22 nH | C1 Series: ~308.11 pF
• Alternating matching lattice elements scale down to 9th stage mesh limit.
Filter Response Transfer Function Model
The system maps output transmission response parameters showing low-attenuation passband loops bound between symmetric attenuation roll-off stopbands.
Diagrams & Theory
An LC Bandpass Filter is an electronic network that selectively passes electromagnetic radio signals within a designated frequency spectrum (Passband) while attenuating all signals whose frequencies fall below the lower corner or above the upper corner limits (Stopbands).
Core Structural Attributes:
- Passband Range: The transmission band localized between the lower cut-off point (fL) and higher cut-off point (fH). Signal attenuation within this loop stays inside the designer's specified ripple dB limit.
- The Roll-Off Slopes: Mapped at the outer skirts of the curve, the transition steepness follows a strict attenuation rate (e.g., +20dB/Decade or -20dB/Decade per filter stage), defining how quickly adjacent channel interference is suppressed.
- Type-1 vs Type-2 Ladders: Symmetrical networks can be constructed starting with either shunt resonant pairs or series resonant pairs. This tool computes both multi-stage network arrays concurrently to provide alternative implementation paths.
Formulas & Mathematical Logic
w = 2 * pi * Center Frequency / 1000
wbw = 2 * pi * Passband Bandwidth / 1000
Series L = g * Z / wbw | Series C = 1000 * wbw / (g * Z * w²)
Shunt L = wbw * Z / (g * w²) | Shunt C = 1000 * g / (wbw * Z)
The network transformation loops map alternating element matrix values onto 9 independent cascades utilizing Chebyshev polynomial root distributions matching the ripple loss boundary coefficients.
Step-by-Step Example
Example: LC Pairs (n) = 3, Center Frequency = 100 MHz, Passband Bandwidth = 10 MHz, Impedance = 50 Ohm, Passband Ripple = 0.1 dB.
Step 1: Convert Center Frequency and Bandwidth to radian velocities: w = 2 * pi * 100 / 1000 = 0.628318 rad/ns, and wbw = 2 * pi * 10 / 1000 = 0.062831 rad/ns.
Step 2: Calculate the Chebyshev ripple factor and normalized element values (g-parameters): bt = ln(coth(0.1 / 17.37)) = 5.84, gn = sinh(5.84 / 6) = 1.05. Winding up with g1 = 1.0315, g2 = 1.1474, g3 = 1.0315.
Step 3: Solve the lumped component values for the Series resonant branches: Series L1 = g1 * Z / wbw = 1.0315 * 50 / 0.062831 = 820.61 nH. Series C1 = 1000 * wbw / (g1 * Z * w^2) = 1000 * 0.062831 / (1.0315 * 50 * 0.628318^2) = 308.11 pF.
Step 4: Solve the lumped component values for the Shunt resonant branches: Shunt L1 = wbw * Z / (g1 * w^2) = 0.062831 * 50 / (1.0315 * 0.628318^2) = 7.74 nH. Shunt C1 = 1000 * g1 / (wbw * Z) = 1000 * 1.0315 / (0.062831 * 50) = 328.11 pF.
Result: Type-1 (shunt-start) and Type-2 (series-start) filter ladder component arrays are derived up to the 3rd order mesh limits.
How to Use This Calculator
Enter the target number of alternating filter nodes in the LC Pairs No input field (Minimum 1, Maximum 9).
Input the targeted Center Frequency representing the peak passage band in MHz.
Enter the targeted Passband Bandwidth determining the transmission window width in MHz.
Enter the characteristic line Impedance (typically 50 or 75 Ohms) and desired Ripple in dB.
Click the orange Calculate button to initiate the Chebyshev matrix.
Analyze both Type-1 (Shunt Start) and Type-2 (Series Start) lumped component tables under the Results section.
About This Calculator
Synthesize high-frequency Chebyshev lumped-element ladder filters with professional precision.
The CalcBoy LC Bandpass Filter Calculator computes alternating series and shunt inductor (nH) and capacitor (pF) component arrays for Type-1 and Type-2 Chebyshev ladder networks.
An LC Bandpass Filter is a passive, multi-stage electronic network composed of inductors (L) and capacitors (C) arranged in an alternating ladder configuration. It selectively permits a specified band of radio frequencies (the passband) to pass from the input transmitter port to the output load terminal while blocking and attenuating all frequencies that fall below the lower cutoff edge (fL) or exceed the upper cutoff edge (fH). This capability is absolutely essential in radio receivers, wireless transceivers, and spectrum analyzers to isolate desired channels and suppress out-of-band noise, harmonics, and co-channel interference.
The synthesis of passive lumped-element bandpass filters relies on normalized Chebyshev filter prototypes. By entering the desired filter order (LC Pairs), center frequency, operating bandwidth, port impedance, and passband ripple, this tool calculates the exact required inductances and capacitances. The calculator concurrently outputs both Type-1 (shunt-resonant start) and Type-2 (series-resonant start) topologies, giving RF designers, ham radio operators, and hardware engineers complete flexibility in physical circuit implementation and component sourcing.
Ideal ApplicationRF receiver preselectors, harmonic filter design, satellite transponders, and intermediate frequency (IF) filters.
Key OutputDirect component values for Type-1 (shunt-first) and Type-2 (series-first) ladder topologies.
Crucial PhysicsNormalized Chebyshev transfer polynomials govern the passband attenuation slope and ripple boundaries.
Design RuleAlways select high-Q capacitors and low-loss inductors to minimize filter insertion loss and passband heat generation.
Tip: In high-power transmitter systems, make sure to verify the voltage ratings of the lumped capacitors and core saturation levels of the inductors to prevent non-linear distortion.
Frequently Asked Questions
What physically limits the Spurious-Free Dynamic Range (SFDR) of a receiver?
SFDR is bounded on the low-power end by the thermal noise floor (Minimum Detectable Signal) and on the high-power end by non-linear intermodulation products (principally IMD3, governed by IIP3). It represents the maximum signal range where the system is completely free of unwanted spurious products that rise above the noise floor.
Why does the SFDR formula use a 2/3 factor?
Third-order intermodulation distortion products grow at a rate of 3 dB for every 1 dB increase in input signal power, while fundamental linear signals grow at a rate of 1 dB per 1 dB. Solving for the theoretical point where these two curves meet mathematically derives the 2/3 factor.
What is the difference between SFDR expressed in dBc and dBFS?
SFDR in dBc (decibels relative to the carrier) measures the difference between the carrier signal power and the peak spurious product. SFDR in dBFS (decibels relative to full scale) is standard in digital converters, measuring the range between the converter's full-scale digital limit and the peak spur.
How does reducing the receiver bandwidth affect SFDR?
Reducing the system operating bandwidth lowers the integrated thermal noise floor, which decreases the Minimum Detectable Signal (MDS). A lower MDS directly increases the SFDR because the noise floor drops, leaving a wider window before distortion products become prominent.
Can we use IIP3 specified in Watts directly in this calculator?
Yes. The calculator includes a unit selection dropdown. If Watts (W) is selected, the script internally converts the value to dBm using the standard equation IIP3(dBm) = 10 * log10(Watts * 1000) before performing the SFDR calculation.
How can system designers improve the SFDR of an RF front-end?
Designers can improve SFDR by using high-linearity low-noise amplifiers (LNAs) and mixers with high IIP3 ratings, optimizing stage gain distribution with attenuators, or reducing the receiver bandwidth to lower the thermal noise floor.
Related Radio Frequency Calculators
VSWR and Return Loss CalculatorCheck antenna match and transmission line reflections.
RF Path Loss CalculatorModel free-space signal attenuation across distance boundaries.
Microstrip Line Impedance SolverModel trace dimensions on printed circuit board layouts.
Specific Absorption Rate (SAR) SolverEvaluate biological electromagnetic wave absorption limits.