A Review of Passive Waveguide Phase Shifters

As featured in Everything RF

A RF (radio frequency) phase shifter, sometimes know as a phase changer, is a two-port device that varies the phase angle of the transmitted output signal with respect to the input signal. The ideal phase shifter would have very low insertion loss through the device, a near perfect impedance match to the adjoining transmission lines, and an equal signal amplitude with respect to phase change. Following on from these characteristics, a broader bandwidth and a flat phase change verses frequency response are also important. Lastly, depending on the application high power, reciprocity, or a known calibrated phase response are sometimes required.

Phase shifters have a variety of use cases in both test and measurement applications such as phase bridge measurements [1] as well as practical applications such as radar and phased array antennas [2,3].

In the microwave bridge circuit example, the phase shifter us used as a known reference phase change. This allows the unknown phase of the device under test to be measured by comparing how the resulting amplitude from the superposition of both paths. With the advancements, modern vector network analysers (VNAs) phase bridge measurements that are no longer the chosen method to measure the phase. However, VNAs are still very expensive, in the hundreds of thousands of dollars for a full THz band set-up, therefore, a phase bridge measurement allows for a more cost-effective method for measuring an unknown phase change.

Phased arrays employ a technique using phase differences between paths to create an interference pattern in the radiation pattern of an antenna array. this then allows the main beam to be steered electronically without a physical rotation of the whole antenna array. Know as beam steering, it is used in a wide range of applications from military radar and satellite to mobile data networks and smartphones [4].

Depending on the type of transmission line, the internal topology, the requirement for phase shift variability, and if a passive or active device is required, there are a variety of different phase shifter designs present in literature and available off the shelf. The rest of the article is a discussion of the background and different options available for passive waveguide phase shifters.

Passive Phase Shifters

The most basic way to change the phase of the transmitted signal can be shown from the general form of the sinusoidal plane wave, a function dependant of both spatial position and time.

The sinusoidal plane wave describes how, at a constant frequency, a value of a field F(x,t) varies as a sinusoidal function over time t, with respect to its angular frequency w, and space x, with respect to its wave number k. Choosing a specific point in time, the equation shows that by offsetting the position of the wave, you can introduce a phase difference when comparing the original wave and offset wave. Therefore, the theoretically simplest method of creating a phase shifter is by adding additional path length to the transmission line, or the option of different paths of differing lengths.

Another method of introducing a phase shift can also be shown from equation 1 by adjusting the wavenumber k, the angular reciprocal of wavelength and keeping the path length the same. A well-known way to change the wavelength of a free-space electromagnetic (EM) wave comes from Snells’s law of refraction; whereby changing the propagation medium to one with a different refraction index changes the phase velocity and as a result, the wavelength to keep a constant frequency. Figure 1 shows how introducing a different medium in the path of the EM wave induces a phase shift when compared to the same EM wave if this medium was not present [5]. The previous figure was created using Ansys HFSS, a high frequency 3D finite element method electromagnetic simulation software [6].

 

Fig. 1) Shows how changing the refractive index of the medium of propagation decreases the wavelength and decreases the phase velocity of the EM wave. The example shown is an HFSS simulated surface magnitude plot of the E-field at 30GHz in WR28 (WG22) with a block of glass inserted with a dielectric constant of 5.5. The phase shift can also be similarly achieved using the magnetic effect by using toroidal ferrites within the waveguide.

 

 

However, if the EM wave is confined to a boundary such as a RF waveguide, it can offer other ways to vary the wavelength of the propagating wave. A RF waveguide is described as a metallic tube that propagates an EM wave between two locations. The RF waveguide’s size depends on the frequency range required for their application which can range from half a millimetre to nearly a metre in size, some examples are present in figure 2. In the cross-sectional plane of the waveguide, the oscillation of the EM wave is simply described using modes and harmonics. This is especially the case when the cross-sectional shape is rectangular which are generally used within their fundamental frequency range.

 

Fig. 2) A WR6.5 (WG29 cross-section of 1.651 mm) E-plane bend and standard gain horn and a WR2300 (WG00 cross-section 584.2 mm) waveguide to coax calibration adapter.

 

Describing how the EM wave oscillates down the waveguide and how the boundary conditions, provided by the walls, effects the propagation requires further discussion. Using a rectangular RF waveguide within the range of the fundamental frequency mode, the guide wavelength g , the distance between two equal phases along the waveguide and direction of wave propagation, can be defined as the following:

Where c is the speed of light in a vacuum, f is the frequency, and a is the broad dimension of the rectangular waveguide. Unintuitively this means that the guide wavelength is longer than the wavelength if the wave was propagating in free space, therefore the phase velocity is greater than the speed of light. Another consequence is the guide wavelength is also affected by the width of the broad dimension of the waveguide a, so differing sizes of waveguide have different guide wavelengths for the same frequency [3]. This then provides a similar effect to changing the medium at which the wave is propagating in; to keep the frequency constant, the phase velocity must change thereby inducing a phase shift as shown in figure 3.

 

Fig. 3) An HFSS simulated surface magnitude plot of the E-field at 30GHz in waveguide WR28 (WG22) whereby the broad-wall dimension change caused an increase in guide wavelength and phase velocity. Note that this device has an inherent bad match due to the abrupt impedance change, hence the differing maximum E-field amplitude through the waveguide.

 

1. Path length – Two methods are generally used to adjust the path length: by using multiple paths of different lengths or by increasing the physical length of the path. Using the option of multiple paths is a popular method to adjust the paths taken. A novel method to increase the physical length has been reported in [7]. The design takes advantage of the non-contacting top wall of groove-gap waveguide to slide a section of waveguide in a ‘T-U shaped’ section to change path length and therefore the output phase.
2. Dielectric loaded waveguide – A simple method to vary the phase of a section of waveguide is to introduce an object to change an overall relative permittivity of the waveguide. This can be achieved by inserting a dielectric vane into the centre of the waveguide where the E-field is as its maximum. The material that makes up the vane has been chosen to reduce the transmission loss through the phase shifter. The shape of the vane is optimised to achieve a certain return loss performance so that the phase shifter is matched to the connecting waveguide. The simulated example in figure 4 contains a vane that is protruding into the height of the waveguide causing the phase shift seen in the plotted E-field.

Fig. 4) A HFSS simulated vane phase changer showing how a change in vane penetration (PV) changes the phase of E-field at the left-hand port with respect to the right-hand port.

 

Passive Rotary Phase Shifters

One of the most precise types of phase shifters is the rotatory vane phase shifter (RVPS) which is a variable and passive, therefore reciprocal, phase shifter that is varied by rotating a central vane within an EM wave that has been circularly polarised. The RVPS exploits the property that a circular waveguide can propagate two dominant orthogonally polarised modes simultaneously and that any wave, of any angular polarisation, can be resolved into these two orthogonal components.

The design of a RVPS contains five constituent vanes of which perform three separate tasks. The outer four vane’s purpose can be described as two oppositely handed linear to circular waveguide polarisers that convert a linearly polarised wave to circular and then back to linear again. Their main purpose is to introduce a 90° phase shift between two orthogonal components that have been decomposed from the original linear wave angled at 45° to this new basis. This is achieved by inserting a quarter-wavelength dielectric vane that introduces a delay in one of the orthogonal components, the vector component parallel to the vane, with respect to the other vector component normal to the vane. A more in-depth discussion was covered in a previous article [8].

 

Fig. 5) HFSS simulated E-field plot in an RVPS

 

Fig. 6) Measured test data of the relative phase difference of different rotation positions for a Flann RVPS in waveguide WR28 (WG22)

 

Lastly, the purpose of the central vane is to introduce the phase shift of the device by changing the angle of the central vane with respect to the outer two 90° vanes. Individually looking at the central section, it introduces a 180° phase shift between two orthogonal components, which is the same as reversing the direction of the vector component that is parallel to the dielectric vane. Depending on the angle of the original undecomposed field to the normal vector to the vane, this delay rotates the final field vector by twice that original angle. This angle is what causes the phase shift of the RVPS whereby 90° rotation of this central vane leads to a 180° phase shift. Consequently, this converts counterclockwise circular polarisation to clockwise circular polarisation hence the need for the opposite-handed linear to circular waveguide polariser [9]

An equivalent design can be achieved using a magnetic effect inducing the phase shift between the orthogonal components. They use the principle of Faraday rotation, a polarisation rotation caused by an electromagnetic wave travelling through a magnetic field whereby the rotation is proportional to the projection of the magnetic field along the direction of travel. Therefore, much like the RVPS, as described above, this induces a phase shift due to the rotation through the central section, however as it is a magnetic effect it is no longer reciprocal [3].

References:

1. Doyle A. Ellerbruch, “Evaluation of a Microwave Phase Measurement System”‘, Journal of Research of the National Bureau of Standards C, vol. 69C, No.1 Jan-Mar 2965
2. Frank. Gustrau, RF and Microwave Engineering: Fundamentals of Wireless Communications, Wiley,2012
3. David M. Pozar, Microwave Engineering 4th ed. John Wiley & Sons,2011
4. Thomas A. Milligan, Modern Antenna Design 2nd ed. Wiley-IEEE Press, 2005.
5. David J. Griffiths, Introduction to Electrodynamics 4th ed. Pearson, 2013.
6. A. Farahbakhsh, D.Zarifi & M. Mrozowski, ” A gap waveguide-based mechanically reconfigurable phase shifter for high-power Ku-band applications“, Scientific Reports Nature, vol.14, Jul 2024.
7. Ansys Electronic Desktop HFSS Release 2024R2.1, 2024.
8. Peter. Young, (2023, Aug. 11) What are Waveguide Polarizers?, [Online] Flann Microwave/Everything RF. Available: https://www.everythingrf.com/community/what-are-waveguide-polarizers
9. A. G. Fox, “An Adjustable Wave-Guide Phase Changer,” in proceedings of the IRE, vol.35, no.12, pp. 1489-1498, Dec. 1947.