Antenna Impedance: Matching, Transformation & Feed Point Theory
Feed point impedance determines how efficiently power moves from your transmitter into the air. Understand complex impedance, reactance cancellation, matching networks, and transformer ratios — with interactive calculators for every common scenario.
Every antenna presents a feed point impedance to your transmission line — a complex quantity expressed as R + jX where R is resistance (the real, power-dissipating part) and X is reactance (the imaginary, energy-storing part). Getting power efficiently from your coax into the antenna requires that these two impedances are conjugate matches: the source resistance equals the load resistance and any reactance in one is cancelled by opposite reactance in the other.
Resistance (R) has two components: radiation resistance (Rrad) representing power radiated as electromagnetic waves, and loss resistance (Rloss) representing heat lost in conductors, poor ground systems, or lossy loading coils. A well-designed antenna maximises Rrad relative to Rloss; this ratio defines antenna efficiency.
Reactance (X) is the result of stored energy — capacitive when the antenna is electrically short, inductive when it is electrically long. At resonance, X = 0 and the impedance is purely resistive, making matching straightforward. Off-resonance, the reactive component must be cancelled or absorbed into a matching network before the transmission line sees a good match.
Resistive component (R)
Sum of radiation resistance and loss resistance. Radiation resistance is where your RF actually goes into the air. Loss resistance robs you of efficiency. Typical half-wave dipole: Rrad ≈ 73 Ω at resonance.
Reactive component (jX)
Positive X = inductive (antenna is too long). Negative X = capacitive (antenna is too short). Reactance causes reflected power and SWR — cancel it with a matching network or trim/lengthen the antenna element.
Complex impedance
Written as Z = R + jX. A dipole at 14 MHz might measure 73 + j0 Ω at resonance, or 52 − j35 Ω if cut 5% short. The magnitude |Z| = √(R² + X²); the phase angle θ = arctan(X/R).
These equations underpin every matching problem. Before reaching for a tuner or matching network, calculate your actual feed point impedance using antenna modelling software or a vector network analyser (VNA) — guessing leads to poorly optimised networks.
Common Feed Point ImpedancesDifferent antenna designs present dramatically different impedances at their feed points. The table below covers the most common configurations operators encounter:
| Antenna Type | Typical Z (Ω) | Notes |
|---|---|---|
| Half-wave dipole (free space) | 73 + j0 | At resonance; near ground changes this significantly |
| Half-wave dipole (½λ above ground) | ~50–70 | Varies with height — convenient 50 Ω match possible |
| Folded dipole | ~292 | 4× standard dipole impedance; needs 4:1 balun |
| End-fed half-wave (EFHW) | 2,000–5,000 | Requires 49:1 or 64:1 transformer |
| Ground plane vertical (¼λ) | 35–50 | Depends on radial count and angle |
| Yagi driven element | 20–30 | Mutual coupling from director reduces Z; often needs 4:1 balun |
| Small magnetic loop | <1 Ω resistive | Very high Q, extreme reactance — series capacitor tunes |
| Long wire (random length) | Highly variable | Depends on electrical length at frequency; tuner required |
| G5RV (at 14 MHz) | ~100 Ω | Varies widely; open-wire feeder handles mismatch |
| Quad loop (full wave) | ~100–130 | Higher than dipole; 2:1 balun brings to 50 Ω |
SWR / Return Loss Calculator
When the antenna's natural feed point impedance does not match your 50 Ω coax, you need a matching network. The correct choice depends on the impedance ratio, frequency, bandwidth requirement, and whether you need galvanic isolation. The principal methods are:
1. L-Network (reactive matching)
The simplest two-element matching network consists of one shunt and one series reactive element — one capacitor and one inductor arranged in an L shape. It transforms between two different resistive impedances and can absorb a feed point reactance into one of its elements. The L-network has a fixed Q determined by the impedance ratio; it is narrow-band but highly efficient when built from low-loss components.
2. Pi and T networks
Pi-networks (capacitor-inductor-capacitor) and T-networks (inductor-capacitor-inductor) allow the Q to be chosen independently of the impedance ratio by introducing a third reactive element. This makes them useful in antenna tuners, where high Q provides harmonic attenuation, or low Q allows broadband operation. Most manual antenna tuners use a Pi or T topology with switched inductors and variable capacitors.
3. Transmission line transformers
Coaxial or wound transmission line transformers provide wideband impedance transformation through their characteristic impedance, not resonance. A quarter-wave matching section of coax transforms impedance as Z0 = √(Zsource × Zload). Wound transmission line transformers (on ferrite or powdered iron cores) achieve ratios of 1:4, 1:9, 1:16, and 1:49 across many MHz of bandwidth — essential for end-fed and folded dipole antennas.
4. Ferrite balun/unun transformers
Current-mode baluns and voltage-mode transformers wound on ferrite toroids achieve impedance ratios determined by the turns ratio squared: Ztransformation ratio = (Nsecondary / Nprimary)². A 1:4 current balun uses a 2:1 turns ratio. The choking impedance provided by the core suppresses common-mode current on the outside of the coax shield — critical at the feed point of dipoles and yagis to prevent pattern distortion and RF in the shack.
L-Network Component Calculator
Dipole not at resonance
A dipole cut slightly short or long presents reactance at the feed point. If the antenna reads 52 − j28 Ω on your VNA, the resistance is close to 50 Ω but the capacitive reactance of 28 Ω will cause SWR of approximately 1.9:1. The correct fix is to lengthen the dipole (reducing negative/capacitive reactance) until X ≈ 0. If mechanical adjustment is impossible, a series inductor of appropriate reactance +j28 Ω in each leg cancels the reactance — but be aware that loss in the inductor reduces efficiency.
End-fed wire mismatch
End-fed half-wave antennas present 2,000–5,000 Ω at the feed point depending on frequency and wire geometry. This extreme impedance requires a high-ratio transformer, typically 49:1 (7-turn primary, 1-turn secondary on a FT-240-43 or equivalent toroid). The 49:1 ratio transforms 2,450 Ω to 50 Ω — close enough that the remaining SWR is acceptable. A small capacitor (around 100–150 pF) across the primary can flatten the SWR across bands.
Yagi low impedance
Parasitic elements in a Yagi mutually couple with the driven element, pulling its feed impedance down from the free-space dipole value of 73 Ω to 20–30 Ω in a typical 3-element design. A folded dipole driven element raises this to 4× — so 25 Ω × 4 = 100 Ω — then a 2:1 balun brings it to 50 Ω. Alternatively, a hairpin or beta match uses a shunt inductor across the low-impedance feed to cancel the capacitive reactance introduced by a slightly shortened driven element, raising the resistive component to 50 Ω.
Antenna tuner limitations
An antenna tuner at the radio end of a long coax run does not "tune the antenna" — it tunes the radio to a matched condition at the tuner's output terminals. High SWR still exists on the coaxial feedline between the tuner and the antenna, and line loss at high SWR can be substantial. The correct approach is to match as close to the feed point as possible, minimising the length of high-SWR line.
Quarter-Wave Coax Transformer
Connect your analyser directly at the antenna feed terminals — before any balun, matching network, or feedline. This gives the true complex impedance Z = R + jX. Record R, X, |Z|, and phase at the operating frequency and at ±5% either side to understand the bandwidth.
If you must measure at the shack end, calculate what the feed point impedance is after transforming through the electrical length of coax. Most VNA software can do this automatically if you input the cable length and velocity factor. The Smith chart display makes this trivially visual — the impedance rotates clockwise as you move toward the source.
EZNEC, 4NEC2, or MMANA-GAL will compute the complex impedance at any feed point in the model. Cross-reference with measured values. Discrepancies reveal real-world effects: soil conductivity, proximity to structures, element sag, or connector losses.
Use the actual measured R and X as inputs to your network calculator — not the theoretical textbook value. A dipole at 7 m above clay soil might present 58 + j12 Ω rather than the free-space 73 + j0 Ω. Matching to the real measurement produces a far better result.
Re-measure with the matching network in circuit. Check SWR, return loss, and transmission loss across the band. A good match should show SWR ≤ 1.5:1 across your intended operating range and no significant reactive residual.
The Smith chart is a conformal mapping of the complex reflection coefficient plane onto a normalised impedance chart. Every point on the chart represents a unique complex impedance value. Circles of constant resistance run from left (R = 0, short circuit) to right (R = ∞, open circuit) with the centre at R = Z₀ (perfect match). Arcs of constant reactance run from the bottom (X = −∞, capacitive) through the real axis (X = 0, resonance) to the top (X = +∞, inductive).
Moving along a lossless transmission line traces a perfect circle centred at the middle of the Smith chart. This makes the chart invaluable for designing stubs and matching networks: rotating clockwise by the electrical length of your feedline shows you exactly what impedance the transmitter sees. Adding a series inductor moves you up an arc of constant resistance. Adding a shunt capacitor moves you across an arc of constant conductance. A matching network design is literally a graphical path from your antenna impedance point back to the centre of the chart.
Software tools like the free SimSmith or the Smith chart display in NanoVNA-saver make this process interactive and highly visual, eliminating the manual graphical construction that made the Smith chart intimidating to earlier generations of radio amateurs.
Baluns, Ununs & Common Mode ImpedanceImpedance matching and common-mode isolation are separate problems that are often confused. A balun (balanced-to-unbalanced) provides a high choking impedance to suppress RF currents flowing on the outside of the coax braid — it is not primarily an impedance transformer, though current baluns simultaneously provide a 1:1 ratio. A unun (unbalanced-to-unbalanced) provides impedance transformation between two unbalanced systems, such as the 9:1 unun used at the feed point of random wire antennas.
Common-mode current on the outside of the coax changes the effective antenna pattern, can cause RF burns, and introduces noise directly into the receiver via the braid. Any feed point imbalance — asymmetric antenna arms, asymmetric surroundings, or reactive ground — drives common-mode current. A high-choking impedance balun (target >1,000 Ω of choking reactance across the operating band) suppresses this current and isolates the transmission line from the antenna.
- 1:1 current balun — feed point of dipoles, yagis; suppresses common-mode, does not transform impedance
- 1:4 voltage balun — folded dipole to 50 Ω coax; transforms 300 Ω to 75 Ω; not a true current balun
- 1:4 current balun — preferred for dipoles near lossy ground; better common-mode suppression than voltage type
- 9:1 unun — random wire, NVIS inverted-L; transforms ~450 Ω to 50 Ω
- 49:1 unun — end-fed half-wave; transforms ~2,450 Ω to 50 Ω
What impedance does a standard half-wave dipole present?
In free space a resonant half-wave dipole presents approximately 73 Ω purely resistive. Near ground the impedance varies with height; at around 0.5λ height it approaches 50–70 Ω and can be a direct match to 50 Ω coax without a balun transformer.
Why does SWR change with height above ground?
Ground reflection alters the mutual impedance of the antenna. As height changes, the amplitude and phase of the reflected wave at the feed point changes, modifying both the resistive and reactive parts of the feed point impedance. This is why models should always include realistic ground.
Does SWR of 2:1 cause significant power loss?
The mismatch itself causes only about 11% reflected power — roughly 0.5 dB. The real problem is increased line loss: high SWR causes standing waves that raise peak voltages and currents in the feedline, increasing I²R losses. With low-loss coax and a short run this is minor; with lossy coax or a long run it compounds rapidly.
What is the difference between Rrad and Rloss?
Radiation resistance is a virtual resistance representing the power actually radiated as RF — increasing it increases effective radiated power. Loss resistance represents heat dissipated in the antenna conductor, loading coil, or poor ground. Efficiency = Rrad / (Rrad + Rloss).
What coax impedance should I use for a quarter-wave transformer?
Calculate the geometric mean of source and load impedances: Z₀ = √(Zsource × Zload). To match 50 Ω to 200 Ω you need Z₀ = √(50 × 200) = 100 Ω coax. Standard options are 50 Ω, 75 Ω, and 93 Ω; for non-standard values you may need to parallel or series combine coaxes.
Can I use an antenna tuner instead of a proper matching network?
Yes, for transmit efficiency — a tuner at the radio provides the radio a matched load. However, any tuner placed at the radio's end of a long, mismatched feedline will have high loss on that feedline. For best efficiency, match as close to the feed point as possible, using a remote ATU or dedicated matching network at the antenna.