Resonance, Current and Radiated Power
Resonance, Current and Radiated Power
Resonance can make an antenna easier to feed, but it is not an efficiency certificate. Useful radiation depends on accepted power, the complete current distribution, radiation resistance, loss and pattern.
An antenna can be resonant and inefficient, non-resonant and efficient, well matched and lossy, or poorly matched and capable of efficient radiation after low-loss matching. These are different properties and must be evaluated at named reference planes.
Engineering principle: resonance describes an impedance or modal condition. Current distribution determines the field pattern, but current magnitude alone does not establish radiated power. The power balance also needs radiation resistance, loss and accepted power.
1. Resonance Is a Port and Frequency Condition
At a declared antenna port, write the input impedance as:
Zin(f) = Rin(f) + jXin(f)
A common one-port resonance convention identifies a frequency where the input reactance is zero. The remaining resistance can be low, near 50 Ω, very high or dominated by loss. Parallel or anti-resonant modes can also pass through zero reactance while presenting a high resistance. Therefore “resonant” does not mean “50 Ω,” “matched,” “wideband” or “efficient.”
Zero input reactance means that the net reactive behaviour at that port is balanced at that frequency. It does not mean that electric and magnetic energy vanish everywhere around the antenna. The slope of impedance with frequency and the relevant mode determine bandwidth and quality factor. Yaghjian and Best’s primary impedance, bandwidth and Q analysis treats resonance and antiresonance explicitly for general one-port linear antennas.
| Property | Question it answers | What it does not prove |
|---|---|---|
| Resonance | What impedance or modal condition occurs at this frequency and port? | 50 Ω, efficiency, gain or useful pattern |
| Match | How much available power is accepted at this plane? | How accepted power divides between radiation and heat |
| Radiation efficiency | What fraction of accepted power becomes radiation? | Direction of that radiation or mismatch at another plane |
| Current distribution | Where current flows with what magnitude and phase? | Radiated power unless scale, radiation resistance and loss are also known |
| Pattern/directivity | How radiated power is distributed by angle | Absolute radiated power or source match |
2. Current Distribution Creates the Field Pattern
Time-varying charge and current create electromagnetic fields. In the far field, contributions from every part of the structure add vectorially. Position, direction, magnitude and phase determine whether those contributions reinforce or cancel in a given direction.
That is why a current plot is valuable: it exposes the active parts of the complete antenna and helps predict lobes, nulls and unintended radiators. Lawrence Livermore National Laboratory’s Numerical Electromagnetic Code documentation reflects this chain directly: a full-wave model can calculate conductor currents, radiation patterns and near electric and magnetic fields from one declared geometry and excitation.
Current magnitude by itself is insufficient. Equal and opposite currents on closely spaced conductors can produce strong local current with substantial far-field cancellation. Large current through loss resistance can produce heat. A compact tuned circuit can carry high circulating current while having very small radiation resistance.
Useful distinction: a current distribution determines the relative field pattern. The absolute radiated power also needs a calibrated excitation or accepted-power reference and a complete account of loss.
3. Radiation Resistance Connects Port Current to Radiated Power
For an equivalent one-port series model at a fixed frequency, the resistive part can be separated conceptually into radiation and loss:
Rin = Rradiation + Rloss
When both terms are referred to the same port current, radiation efficiency is:
ηrad = Pradiated / Paccepted = Rradiation / (Rradiation + Rloss)
The formula explains why a current reading alone cannot settle efficiency. The same current can correspond to different radiated power when geometry changes the radiation resistance, and to different efficiency when conductor, coil, dielectric, ground or matching losses change.
NIST’s primary reverberation-chamber efficiency study makes the measurement boundary explicit: radiation efficiency relates radiated power to power accepted at the antenna port, while total efficiency also includes mismatch from available power.
4. Match, Accepted Power and Gain Complete the Budget
For a real reference impedance, the mismatch efficiency at a named plane is:
ηmismatch = 1 − |Γ|²
A matching network can improve accepted power by transforming resistance and cancelling reactance. It also has insertion loss and component limits. Its result must be stated at the plane where Γ or SWR is measured.
The power chain is:
available source power
↓ mismatch at the named plane
accepted power
↓ feedline / matching / conductor / dielectric / ground loss
radiated power
↓ angular current distribution
directivity and gain in a stated direction
The current IEEE 145-2025 antenna-definitions standard is the terminology anchor for keeping radiation efficiency, directivity, gain and related quantities separate. Realized gain includes mismatch at its declared reference plane; ordinary gain does not.
A low SWR answers the first part of this chain only. A dummy load can be well matched while converting accepted power to heat. Conversely, a non-resonant radiator can perform efficiently when a low-loss network delivers accepted power to a favourable current distribution.
5. Resonant Structures Can Support Multiple Modes
A wire, loop, folded structure or coupled set of conductors can support more than one current mode. Each mode has its own impedance behaviour and field pattern. Modal frequencies shift with conductor diameter, insulation, feed position, height, ground, loading, coupling and nearby objects.
An open-ended conductor often has a current minimum near its open end, but the installed antenna also needs a return path. Counterpoises, radial systems, a mast and the coax exterior can therefore change the resonances observed at the feedpoint. A closed DC path does not eliminate RF modes; current can form standing-wave distributions around a loop or folded conductor.
Higher-frequency resonances are not simply copies of the lowest mode. Additional phase reversals and current maxima can create extra lobes and nulls. Harmonic or multiband operation may provide a convenient impedance while producing a different elevation or azimuth pattern.
Installation boundary: an analyzer resonance belongs to the complete network connected at its calibration plane. It does not identify which conductor radiates, how much accepted power is lost, or whether the pattern is useful.
6. Return Current and Common Mode Must Be Included
An unbalanced radiator cannot be analysed as one isolated wire. Current returns through intended radials or counterpoises and through coupled conductors in the environment. If the exterior of a coaxial feedline participates, it becomes part of the installed antenna geometry.
In the wanted coaxial mode, current on the centre conductor is accompanied by equal and opposite current on the inner surface of the shield. Additional net current involving the shield exterior and an external return path is a common-mode component. The in-force ITU-R Report SM.2158-3 presents the corresponding differential/common-mode decomposition and the conversion caused by imbalance.
A choke changes the impedance of the exterior-current path. It can alter the feedpoint impedance and apparent resonance because it changes the complete current solution. That does not automatically mean the choke improved or degraded radiation; the current distribution, loss and pattern must be checked.
7. A Measurement Sequence That Separates the Questions
- Declare the port. State whether the reference plane is at the transmitter, tuner, feedline input or antenna feedpoint.
- Measure complex impedance. Record resistance and reactance across frequency, not only the minimum SWR.
- Inspect the installed current distribution. Use a validated model for intended conductors and an RF current probe at several positions on plausible common-mode paths.
- Quantify matching and line loss. Characterise the network under the actual complex load, frequency, power and duty cycle.
- Use a complete efficiency method. Calibrated gain/directivity, full-pattern, Wheeler-cap or reverberation-chamber methods can determine efficiency when their assumptions and uncertainty are satisfied.
- Measure the pattern. A resonance used on another band can have a substantially different angular distribution even when its feed impedance is convenient.
- Repeat after installation changes. Cable routing, choke position, height, ground moisture and nearby conductors can shift both impedance and current.
8. Practical Conclusions
- Resonance is an impedance or modal condition at a declared frequency and port.
- Zero reactance does not imply 50 Ω, high efficiency or a useful pattern.
- Current distribution determines relative pattern, but current magnitude alone does not prove radiated power.
- Radiation resistance and loss resistance connect port current to the power balance.
- Matching controls accepted power and may add loss; it is separate from radiation efficiency.
- Multiple resonant modes can produce different current phase and radiation patterns.
- Return conductors and coax common-mode current belong in the installed antenna model.
- Efficiency, gain and pattern require measurements that go beyond impedance or SWR.
Decision rule: use resonance to describe a feed or modal condition, then follow the accepted power. Measure where current flows, how much becomes heat, how much becomes radiation and where that radiation goes.
Primary Sources and Scope Anchors
- IEEE 145-2025—current antenna terminology for impedance, efficiency, directivity, gain and related quantities.
- Yaghjian and Best, “Impedance, Bandwidth, and Q of Antennas”—primary one-port resonance, antiresonance, impedance and bandwidth analysis.
- NIST, Reverberation Chamber Techniques for Determining the Radiation and Total Efficiency of Antennas—accepted-power and efficiency definitions, methods and uncertainty.
- Lawrence Livermore National Laboratory, Numerical Electromagnetic Code—model scope linking conductor currents, fields and patterns.
- ITU-R Report SM.2158-3—differential/common-mode current decomposition and imbalance.
Mini-FAQ
- Does an antenna need to be resonant to radiate? No. A non-resonant antenna can radiate efficiently when a low-loss matching system delivers accepted power to a useful current distribution.
- Does high antenna current prove high radiated power? No. Radiated power also depends on radiation resistance and the complete current distribution; current through loss or cancelling conductors can produce little useful radiation.
- Does zero reactance mean the antenna is 50 Ω? No. A resonant or anti-resonant input can have low, moderate or high resistance.
- Does a tuner improve radiation efficiency? It can reduce mismatch and increase accepted power, but it cannot remove antenna loss and it adds its own loss. Radiation efficiency must be evaluated separately.
- Why can the pattern change on a higher resonance? Higher modes have different current maxima, minima and phase reversals, so their fields reinforce and cancel in different directions.