# Understanding Standing Wave Patterns on Interconnects and Antennas

April 5, 2021

### Key Takeaways

• Reflection of electromagnetic waves with phase matching can lead to a standing wave pattern.

• For an antenna, a standing wave pattern in the antenna is desired, whereas it becomes a source of unwanted radiation on transmission lines.

• Interconnect and antenna designers need to apply careful impedance matching to control standing wave formation.

Standing wave patterns can form on these antenna elements to provide high gain and directivity.

Reflection of electromagnetic waves is a fundamental phenomenon in physical systems, but it may not be desired in your electronics. A standing wave pattern that forms on a conductive element like a transmission line in a PCB can emit strong radiation, which may not be ideal. For an antenna, standing waves are natural and will produce strong radiation at particular frequencies, while they are a nuisance on transmission lines.

When you want to take control of a standing wave pattern, you need to engineer reflection in your interconnects and antennas with impedance control and impedance matching. Depending on the level of impedance mismatch, you can understand the standing wave pattern you would expect to see on your interconnects when driven with a harmonic signal. For a broadband signal like a digital pulse, the result is more complex, but the same concepts can be applied with the right set of PCB design and analysis tools.

## How Reflections Form Standing Wave Patterns

A standing wave can form in many physical systems, and standing waves correspond to resonant frequencies of the system’s eigenmodes in some cases. In electronics, standing waves form when an electromagnetic wave traveling on an interconnect reflects off of an interface with an impedance mismatch.

When the reflected wave and incident wave are perfectly in-phase, a standing wave can form that appears as a stationary sinusoid along the length of the interconnect.

If you look at the electric field along the length of the interconnect containing the standing wave, the electric field looks like a stationary wave. Standing waves can form for a range of frequencies. This means that a single-harmonic AC source can excite a strong standing if there is some reflection at one end of an interconnect. This is shown in the image below:

Standing wave patterns for the fundamental (n = 1) and higher order (n > 1) harmonics.

Here, we need two pieces of information to calculate the standing wave excitation frequencies and to describe the reflection and superposition of waves on the interconnect:

• Reflection coefficient: The reflection coefficient at the interface is used to describe the strength and phase shift a wave experiences as it is reflected from the interface.
• Length of the interconnect or antenna: Once a reflection occurs, the wave will travel back through the length of the structure. A standing wave pattern will only form on an electrically long structure, and the length will determine the allowed standing wave frequencies/wavelengths.
• Wave propagation speed: The wave propagation speed (i.e., the speed of light on the interconnect) will determine the wavelengths of standing waves and thus the specific frequencies that can excite standing waves.

The reflection that occurs at an impedance mismatch can occur on a transmission line, at the interface between a transmission line and an antenna, or within an antenna. Let’s look at each case to better see how these standing wave patterns form.

### Transmission Lines

To treat transmission lines, we need the reflection coefficient that is calculated using the source and load side impedances in our reflecting structure. The diagram below shows the standing wave pattern that might form when a harmonic AC wave reflects off of two general impedances, one at each end of the interconnect. This is a common example in a transmission line, where the load has some specific impedance value and is possibly terminated at its output end. When the transmission line is sufficiently long, the reflection coefficient is defined at the interface in terms of the line’s characteristic impedance and the load impedance.

Reflection coefficient and standing wave pattern formation in an interconnect.

At specific frequencies, the transmission line will support the kind of standing wave patterns shown above. Outside of the line, some power is transmitted to the load, which may experience losses external to the line. This load could be some simple component, an antenna, or a complex circuit. In general, these standing wave patterns are not wanted, as there are large oscillations on the line, producing radiation. These oscillations can also happen on an antenna feedline due to a mismatch between the line and antenna. However, inside an antenna, we have a different situation.

### Antenna Standing Waves

Standing waves do form on an antenna due to the impedance mismatch at the open end of the antenna. There is an impedance mismatch with respect to the air beyond the boundary of the antenna. At specific frequencies, a standing wave pattern can be excited that will correspond to a specific eigenmode of the antenna structure, similar to what happens in a resonator cavity or waveguide. Tailoring modal frequencies is an important task in antenna design and remains a continuous subject of research.

Although antennas have standing waves, one place we don’t want standing waves is in the feedline. A standing wave in the feedline can create interference with other portions of a PCB, so reflection at the input of the antenna needs to be eliminated. This is one reason we use impedance matching networks to set the antenna input impedance and feedline characteristic impedance equal.

## Extract Impedance and S-parameters for Broadband Signals

For broadband signals, we need the S-parameters for the system, as this is the best way to treat reflections. Coherent standing wave patterns like those seen above do not necessarily form unless a specific frequency dominates the signal’s power spectrum. To best understand how broadband signals interact with resonant structures, it’s best to use S-parameters. The best design software can determine impedance and network parameters directly from your layout, allowing you to identify strong reflections and potential for standing waves in your layout.

When you need to predict standing wave patterns, you need quality PCB design and analysis software to help you evaluate your PCB layout. Allegro PCB Designer from Cadence integrates with the S-parameter extraction features in Sigrity Extraction and includes a complete set of PCB design and layout features. You’ll have the industry’s best design tools for building and optimizing your interconnects to control standing waves. You can also use InspectAR to accurately assess and improve PCBs using augmented reality and intuitive interaction. Inspecting, debugging, reworking, and assembling PCBs has never been faster or easier.