Open Stub Calculator

The Open Stub Calculator helps RF engineers, microwave engineers, PCB designers, communication system developers, researchers, and students calculate the electrical behaviour of an open-circuited transmission line stub. By entering the characteristic impedance, electrical length, operating frequency, and transmission line velocity factor, the calculator determines the input reactance, equivalent inductance or capacitance, physical stub length, guided wavelength, and transmission line behaviour. Open stubs are widely used for impedance matching, RF tuning, harmonic suppression, microwave filters, antenna matching networks, RF amplifiers, microwave circuits, stripline, microstrip, coaxial transmission lines, and high-frequency PCB design operating from HF through millimetre-wave frequencies.

Enter Characteristic Impedance (Z₀), Electrical Length (θ), Frequency (f), Velocity Factor (VF) exactly in the units shown by this open stub. Check the operating band, unit prefix, and decimal position before calculating; these are the inputs used by the formula.

• Characteristic Impedance (Z₀) — use Ω.
• Electrical Length (θ) — use °.
• Frequency (f) — use MHz.
• Velocity Factor (VF).

The results describe the calculated open stub values for the inputs you entered. Check each value against the available space, selected components, feed system, and operating conditions before making a final design decision.

The Open Stub uses Z_in = -j Z₀ cot(βl) | X_in = -Z₀ / tan(θ) | C_eq = -1 / (ω X_in) | L_eq = X_in / ω. Supply Characteristic Impedance (Z₀) (Ω), Electrical Length (θ) (°), Frequency (f) (MHz), Velocity Factor (VF) in the displayed units, then use the calculated values as the first engineering target for this transmission lines design or analysis.

This calculator is based on the transmission line equations for a lossless open-circuited stub. The input impedance of an open stub is given by Zin = -jZ₀cot(βl), where Z₀ is the characteristic impedance, β is the phase constant, and l is the physical length of the transmission line. Since the impedance is purely reactive for an ideal lossless stub, the calculator evaluates the input reactance using Xin = -Z₀ ÷ tan(θ), where θ represents the electrical length in degrees. The electrical length determines whether the stub behaves like an equivalent capacitor or an equivalent inductor. When the reactance is negative, the open stub behaves capacitively and the equivalent capacitance is calculated using Ceq = -1 ÷ (ωXin), where ω = 2πf is the angular frequency. When the reactance is positive, the stub behaves inductively and the equivalent inductance is calculated using Leq = Xin ÷ ω. The calculator also converts the electrical length into a practical physical length using the guided wavelength of the transmission line. Guided wavelength is determined from λg = (c × VF) ÷ f, where c is the speed of light and VF is the transmission line velocity factor. The physical stub length is then calculated using l = (θ ÷ 360°) × λg. At approximately 90° electrical length the open stub transforms into a virtual short circuit and behaves as a series resonator, while at approximately 180° electrical length it behaves as an open circuit with parallel resonance. These relationships form the theoretical foundation of RF impedance transformation, microwave matching networks, distributed reactive components, and transmission line filter design.

Use the calculated physical stub length as the initial design value when building microstrip, stripline, coaxial, or waveguide matching networks. Accurate impedance transformation requires precise knowledge of substrate dielectric constant, conductor dimensions, velocity factor, and manufacturing tolerances because small dimensional errors become significant at microwave frequencies. During prototype testing, verify input impedance, return loss (S11), VSWR, resonance frequency, insertion loss, and phase response using a calibrated vector network analyser (VNA). Keep stub junctions short, minimise discontinuities, and avoid unnecessary bends to reduce parasitic inductance and capacitance. Practical circuits are also influenced by conductor loss, dielectric loss, radiation, connector transitions, and fabrication tolerances. Electromagnetic simulation using Keysight ADS, CST Studio Suite, Ansys HFSS, FEKO, Sonnet, or AWR Microwave Office is recommended to optimise impedance matching, filter response, and distributed circuit performance before manufacturing.