Stub Matching
A stub is simply a short section of transmission line, with one end connected to the main feedline and the other end either open-circuited or short-circuited. Despite its simple construction, a stub can act as an inductor, a capacitor, a bandpass filter, a band-stop filter, or an impedance transformer — all determined entirely by its electrical length and termination. Stub matching is one of the most elegant tools in RF design, requiring no additional components beyond a piece of coaxial cable or open-wire line.
A shunt stub (shown connected at the antenna feedpoint for simplicity) presents a specific reactance to the transmission line, canceling the reactive component of the load impedance. Short-circuit stubs and open-circuit stubs behave oppositely for the same length.
View LargerWhat a Stub Is and How It Works
A stub is a transmission line terminated in either an open circuit or a short circuit. These terminations are purely reactive — they store energy but absorb none. An open circuit presents infinite impedance at DC but reflects all RF energy back with the same polarity; a short circuit presents zero impedance and reflects all RF energy back with reversed polarity.
When these reflected waves travel back to the stub's input port, they create a specific input impedance at that port. The impedance depends on the stub's electrical length (in degrees), its characteristic impedance Z₀, and whether it is terminated as an open or short circuit. The key feature is that this input impedance is purely reactive — it contains no real (resistive) component — which makes stubs ideal for canceling unwanted reactance in a circuit without affecting the resistive component.
A stub is connected in shunt (parallel) with the main transmission line at a specific point. From the main line's perspective, the stub simply adds a reactive element in parallel — just like connecting a capacitor or inductor across the line at that point. By choosing the correct stub type (SC or OC) and length, you can add any specific inductive or capacitive reactance you need at that point.
Stub Impedance vs. Electrical Length
The input impedance of a short-circuit (SC) stub of electrical length θ and characteristic impedance Z₀:
The corresponding reactance: XSC = Z₀ tan(θ)
- 0° < θ < 90°: X is positive (inductive) — stub acts as an inductor
- θ = 90°: X → ∞ (open circuit) — stub presents infinite impedance
- 90° < θ < 180°: X is negative (capacitive) — stub acts as a capacitor
- θ = 180°: X = 0 (short circuit) — stub presents zero impedance
The input impedance of an open-circuit (OC) stub of electrical length θ:
The corresponding reactance: XOC = −Z₀/tan(θ)
- 0° < θ < 90°: X is negative (capacitive) — stub acts as a capacitor
- θ → 0°: X → −∞ (open circuit) — stub presents infinite impedance
- 90° < θ < 180°: X is positive (inductive) — stub acts as an inductor
- θ = 90°: X = 0 (short circuit) — stub presents zero impedance
Notice the complementary behavior: for the same electrical length, SC and OC stubs produce opposite reactances.
Short-Circuit vs. Open-Circuit Stubs
Both types are used in practice, with different practical advantages:
Short-circuit stubs are created by connecting the center conductor to the outer conductor at the stub's far end with a short wire or jumper. They are physically compact for a given reactance (the inductive range covers the shortest stub lengths), but the short-circuit connection must be made with a reliable, weatherproof electrical contact. They are sensitive to the quality of the short-circuit connection, particularly at UHF where even a millimeter of extra wire at the termination has significant electrical length.
Open-circuit stubs simply leave the far end of the cable unconnected. At HF, this is reliable — the open-circuit capacitance of the cable end is negligible. At VHF and above, radiation from the open-circuited end and the capacitance of the conductor end can slightly alter the effective electrical length. A small capacitance cap or no connector at all is acceptable at HF; at VHF/UHF, the capacitance of even an SO-239 chassis socket at the stub end needs to be accounted for.
| Electrical Length | SC Stub Behavior | OC Stub Behavior |
|---|---|---|
| 0° (very short) | Short circuit (Z → 0) | Open circuit (Z → ∞) |
| Less than 90° | Inductive (positive X) | Capacitive (negative X) |
| Exactly 90° | Open circuit (Z → ∞) | Short circuit (Z = 0) |
| Between 90° and 180° | Capacitive (negative X) | Inductive (positive X) |
| Exactly 180° | Short circuit (Z → 0) | Open circuit (Z → ∞) |
Using a Stub to Match an Antenna
Single-stub matching is a classic technique for matching an antenna to a transmission line. The procedure works in two steps:
Step 1: Find the point on the transmission line (measured from the antenna feedpoint) where the real part of the admittance (1/impedance) equals 1/Z₀ (the line admittance). At this point, the impedance consists of Z₀ in parallel with a pure reactance.
Step 2: Add a stub at that point with a reactance equal and opposite to the reactance at that point. The stub cancels the reactive component, leaving only Z₀ = 50 ohms — a perfect match.
This two-step procedure is most easily done with a Smith Chart or a VNA, and is covered in more detail in Module 16 (Filters and Impedance Matching). For the purposes of this lesson, a simpler and more common amateur radio application of stubs is the direct use of a stub at the antenna feedpoint to cancel the reactive component of the feedpoint impedance:
Your antenna analyzer shows the 20-meter dipole feedpoint at 14.2 MHz as Z = 50 − j35 ohms. The resistive part is already 50 ohms. You only need to cancel the −j35 ohm capacitive reactance.
Required: a shunt stub that presents +j35 ohms (inductive reactance) at 14.2 MHz.
Using a short-circuit stub of 50-ohm coax (VF = 0.66):
XSC = Z₀ tan(θ) = +35 → tan(θ) = 35/50 = 0.700 → θ = arctan(0.700) = 34.99° ≈ 35°
Physical length = (35/360) × (300/14.2) × 0.66 = 0.0972 × 21.13 × 0.66 = 1.356 m = 4.45 ft
Connect a 4.45-foot stub of RG-213 (short-circuited at its far end) in parallel with the feedpoint. The stub adds +j35 ohms, canceling the −j35 ohms from the antenna, leaving a pure 50-ohm resistive impedance. SWR becomes 1:1.
In practice, you trim the stub length while monitoring the SWR until the SWR is minimized, then permanently secure the stub at that length.
Stub Length Calculator
Stub Length Calculator
Enter the stub type, the reactance you want the stub to present (positive = inductive, negative = capacitive), the stub cable's characteristic impedance and velocity factor, and the frequency. The calculator returns the required stub length.
Stubs as Harmonic Traps and Filters
Stubs are also widely used as harmonic traps — filters that block specific frequencies from passing through a feedline. This application uses the fact that a quarter-wave stub short-circuits a signal at the design frequency.
SC stub, quarter-wave long at frequency f₁: Presents zero impedance (short circuit) in shunt with the main line at f₁. Any signal at f₁ is shorted to ground — effectively completely reflected. Signals at other frequencies see the stub's off-resonance impedance (not zero) and pass through with less attenuation.
OC stub, quarter-wave long at frequency f₁: Presents zero impedance in shunt at f₁ (as derived from the open-circuit stub properties in lesson M13D). Also functions as a short circuit at that frequency.
A practical application: if your HF transmitter on 14.2 MHz has a strong second harmonic at 28.4 MHz that exceeds regulatory limits, you can insert a stub trap on the feedline at 28.4 MHz to suppress it. An SC stub, quarter-wave long at 28.4 MHz, will present near-zero impedance in shunt at 28.4 MHz, shorting the harmonic current to ground and preventing it from reaching the antenna.
SC stub, quarter-wave at 28.4 MHz:
Physical length = (300 / 28.4) × 0.66 / 4 = 10.56 × 0.66 / 4 = 1.742 m = 5.71 ft = 68.5 in
Connect a 68.5-inch stub of RG-213 (short-circuited at the far end) in parallel with the feedline. At 28.4 MHz, this stub presents near-zero shunt impedance, reflecting the harmonic back toward the transmitter. At 14.2 MHz, the stub is a quarter-wave at the half frequency — it presents near-infinite impedance (no effect on the 14.2 MHz signal).
Note: the stub's quarter-wave design frequency is the second harmonic (28.4 MHz), which also means it is approximately a half-wave at the fundamental (14.2 MHz) where it presents low impedance again. In practice, add a short-circuit stub that is a quarter-wave at the harmonic and check that it does not introduce excessive loss at the fundamental — this depends on the exact frequency relationship.
Practical Construction and Adjustment
Building a stub from coaxial cable requires only a piece of cable of the appropriate length and a connector to mount it in parallel with the feedline. Here is the practical procedure:
- Calculate the stub length using the calculator above (or by hand), using the velocity factor of your specific cable. Remember to measure the velocity factor of the actual cable if it is unmarked.
- Cut the stub slightly longer than calculated — perhaps 5–10% longer. You can always trim it shorter but cannot make it longer.
- Prepare the far end: for an SC stub, connect center conductor to outer conductor with a short wire or solder bridge. For an OC stub, simply leave the end open (cap it to keep moisture out).
- Connect the stub's input end in parallel with the main feedline, using a T-connector or a coaxial junction box.
- Connect your antenna analyzer or SWR meter and sweep the frequency.
- For a harmonic trap: sweep at the harmonic frequency and observe the SWR peak (which indicates the stub is creating a short circuit at that frequency). Trim the stub slightly if the trap frequency is off.
- For a reactance cancellation stub: sweep at the antenna's operating frequency and observe the SWR minimum. Trim the stub to find the lowest SWR.
- Weatherproof all connections with self-amalgamating tape if installed outdoors.
Test Your Knowledge
Answer the questions below to check your understanding. Every answer can be found in the lesson above.