Short Stub Calculator
Calculate the input reactance, susceptance, and equivalent L/C values of a short-circuited transmission-line stub.
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Math
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Enter parameters and click Calculate to view results
Formula & Theory
X_in = Z₀ · tan(betal) | B_in = -1 / X_in | betal = 2pi(l/lambda)This formula is used to calculate antenna parameters for short stub calculator.
Overview
This short stub calculator (also called a shorted stub calculator or stub reactance calculator) computes the input reactance, susceptance, and equivalent lumped inductance or capacitance presented by a short-circuited transmission-line stub at a given electrical length and frequency. It's a core tool for impedance matching network design, resonant filter design, and RF bias-feed circuits, letting you find the exact stub length needed to synthesize a target reactance without a discrete inductor or capacitor.
Input Guide
Enter Characteristic Impedance (Z₀) exactly as shown on the calculator. Confirm every unit, selected option, and decimal position before calculating so the short stub result matches the intended transmission lines design case.
Output Guide
The output section reports Electrical Length, Input Behavior, Input Reactance (X_in), Input Susceptance (B_in), Behavior Type for the values you entered. Use these values as design targets, then compare them with available space, component limits, feed system behavior, installation environment, and measured performance before finalizing the design.
How This Calculator Works
The Short Stub applies X_in = Z₀ · tan(betal) | B_in = -1 / X_in | betal = 2pi(l/lambda) to the entered values. Calculate the input reactance, susceptance, and equivalent L/C values of a short-circuited transmission-line stub. Use the result as a first-pass transmission lines target, then validate it against losses, tolerances, mounting, nearby conductors, feed-line effects, and measurement conditions.
Design Notes
A shorted stub behaves as a reactive element whose sign and magnitude cycle continuously with electrical length. From 0° to 90° it looks inductive (X_in = Z₀·tan(betal) > 0), it passes through an open-circuit parallel resonance at exactly 90° — a quarter-wave shorted stub calculator result that shows infinite reactance, the basis of quarter-wave RF chokes and DC bias-feed stubs — then swings capacitive from 90° to 180°, and returns to a dead short at 180°, where a half-wave shorted stub reproduces the short at its input and the whole cycle repeats. This periodicity is what makes shorted stubs so valuable in RF and microwave design: picking the right electrical length lets you synthesize almost any reactance value using nothing but a length of transmission line and a short circuit, which matters most at microwave frequencies where discrete lumped inductors and capacitors become physically impractical or behave unpredictably.
Build and Tuning Notes
Shorted stubs are generally preferred over open-circuited stubs in real matching network builds because a short circuit is a well-defined, low-loss termination, while an open end radiates slightly and is sensitive to fringing capacitance from the cut edge — making shorted stubs the more repeatable, lower-loss choice in microstrip and stripline layouts. This calculator assumes a lossless transmission line; real-world stubs have finite Q from conductor and dielectric loss, so the sharp infinite reactance predicted exactly at 90° will in practice be a large but finite value, and the equivalent L/C figures shown here won't capture frequency-dependent loss (ESR). When converting the electrical length into a physical stub length for construction, divide by the transmission line's velocity factor (typically 0.66–0.85 for coax or microstrip, not the free-space value of 1.0) — skipping this step is the most common reason a built stub ends up too long and resonates lower in frequency than designed.
Inputs used by this calculator
- Characteristic Impedance (Z₀) — use ohms.
- Electrical Length (theta = betal) — use °.
- Operating Frequency (f) — use MHz.
Frequently Asked Questions
What does a short stub calculator compute?
It calculates the input reactance and susceptance seen at the feed end of a short-circuited transmission-line stub, along with the equivalent lumped inductor or capacitor value that would present the same reactance at your chosen operating frequency.
Why does a quarter-wave shorted stub behave like an open circuit?
A shorted transmission line transforms its termination impedance based on its electrical length, and at exactly a quarter wavelength the tangent function in the input reactance formula goes to infinity — so a dead short at the far end appears as an open circuit (parallel resonance) at the input. This property is widely used in RF chokes that block signal while still passing DC bias current.
When should I use a shorted stub instead of an open stub?
Shorted stubs are usually preferred in practical builds because a short circuit is a cleaner, more predictable termination than an open end, which suffers from fringing-field capacitance and minor radiation loss at the cut edge. Open stubs are chosen instead when a physical short isn't convenient to implement, such as certain via-free microstrip layouts.
How do I find the physical length of a shorted stub from its electrical length?
Divide the electrical length (as a fraction of a wavelength) by the transmission line's velocity factor to get the physical length — using the free-space wavelength instead of the velocity-factor-adjusted length is the most common error and produces a stub that's too long and resonates below the target frequency.
Why can measured stub reactance differ from the calculated value?
This calculator assumes an ideal, lossless transmission line, but real stubs have conductor and dielectric losses that round off the sharp resonances predicted by the ideal tangent function, especially near the quarter- and half-wave points. Manufacturing tolerances and nearby coupling can also shift the effective electrical length slightly away from the design value.
Alex Warren
B.Sc. in Electrical & Electronic Engineering (EEE)
Alex specialises in antenna design and wave propagation. His expertise helps ensure these calculators present practical RF concepts, useful design estimates, and clear engineering guidance for students, HAM operators, and wireless professionals.