How does a Rotman Lens work?

The Rotman Lens has beam ports on one side and array ports on the other, connected through a parallel-plate region (or stripline cavity). Each beam port excites a wavefront that arrives at the array ports with a linear phase gradient, forming a beam at a specific angle. The path lengths from each beam port to each array port are designed so that three focal points produce perfect beams, with remaining beam positions having small phase errors.

Advantage over phase shifters?

Phase shifters produce constant phase shift across frequency, causing the beam to squint (change direction) with frequency. The Rotman Lens provides true time delay: the path length difference is constant, so the beam direction is frequency-independent. This eliminates beam squint across wide bandwidths (octave or more). No active components, no power consumption, no control electronics needed for fixed beam positions.

Automotive radar (77 GHz): multiple simultaneous beams for object detection. EW systems: wideband direction finding. 5G mmWave: fixed multi-beam coverage. Satellite: wideband receive arrays. The Rotman Lens can be fabricated as a planar PCB structure, making it compact and low-cost at mmWave frequencies where the lens dimensions shrink proportionally.

Antenna Technology

Bootlace Lens

A Bootlace Lens (commonly implemented as a Rotman Lens) is a true-time-delay (TTD) beamforming network that produces multiple simultaneous beams from a phased array antenna. It uses a parallel-plate region with beam ports and array ports connected by transmission lines of engineered lengths. Because it provides true time delay rather than phase shift, beam directions are frequency-independent, eliminating beam squint over octave or greater bandwidths.

Category: Antenna Technology

Bandwidth: Octave+

Understanding Bootlace Lenses

The Rotman Lens design specifies three perfect focal points on the beam port contour. Beams excited from these focal points produce zero phase error at the array ports. Intermediate beam positions have small residual phase errors (typically <10°) that are acceptable for most applications. The design parameters include the focal length, scan angle range, and number of beam/array ports.

At mmWave frequencies (77 GHz automotive radar, 28/39 GHz 5G), the Rotman Lens fits on a small PCB. A 16-beam, 16-element lens at 77 GHz measures approximately 30×20 mm. The lens is passive, requiring no power supply or control electronics for its fixed beam set.

Rotman Lens Parameters

Beam squint (phase shifter):
Δθ = arcsin(sinθ₀·f₀/f) − θ₀

Rotman Lens (TTD):
Δθ = 0 (frequency independent)

Phase error at non-focal beams:
Typically <10° across scan range

Beamforming Network Comparison

Network	BW	Squint	Beams	Power
Rotman Lens	Octave+	None	Simultaneous	0 W (passive)
Butler Matrix	10-20%	Moderate	Simultaneous	0 W (passive)
Phase shifters	5-10%	Yes	One at a time	Watts
Digital BF	Wide	None	Simultaneous	High

Common Questions

Frequently Asked Questions

How it works?

Beam ports excite wavefronts through parallel-plate region. Path lengths create linear phase gradient. Three focal points = zero error beams.

vs Phase shifters?

Phase shifters: constant phase = beam squint with frequency. Rotman: true time delay = no squint. Passive, no power.

Applications?

77 GHz auto radar, EW direction finding, 5G mmWave multi-beam, satellite. PCB-fabricated at mmWave.

Related Terms

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Antenna Design

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