1. Microstrip Reflectarrays Myths and Realities JINA Conference David M. Pozar ECE Department University of Massachusetts Amherst USA

2. Outline Introduction: Examples
Types of reflectarrays and reflectarray elements:
Basic reflectarray elements
Polarization twist reflectarrays
Myths and Realities:
How do microstrip reflectarrays radiate ?
Variable size or stub-terminated patch – which is better ?
Modeling: single element or infinite array ?
Is reflectarray bandwidth limited by time delay ?
Do proximity-coupled patches increase bandwidth ?
Does element gain affect reflectarray gain ?
How should amplifiers be used in a reflectarray ?

3. Introduction to Microstrip Reflectarrays
A flat array of microstrip patches or dipoles
Excitation with an illuminating feed antenna
Reflection phase from each element controlled for a planar phase front
Flat aperture offers mechanical advantages
Losses due to spillover, amplitude taper, dielectric, metalization, phase errors
Bandwidth limited by time delay variation and element response
Amplifiers and phase shifters can be integrated into reflectarray structure z
feed
Geometry of a basic microstrip reflectarray
r, d

4. Example of a 28 GHz Microstrip Reflectarray (using variable size patches)
Reference: D. M. Pozar, S. D. Targonski, and H. D. Syrigos, “Design of Millimeter Wave Microstrip Reflectarrays”, IEEE Trans. Antennas and Propagation. vol. 45, pp , February 1997.

5. Patterns of 28 GHz Reflectarray
28 GHz, 6” square aperture, 784 elements (variable size patches), 25 degree scan angle,
corrugated conical horn feed, G=31 dB, 51% aperture efficiency

6. Example of a Shaped Beam Reflectarray
Reference:
D. M. Pozar, S. D. Targonski, and R. Pokuls,
"A Shaped Beam Microstrip Patch Reflectarray", IEEE Trans. on Antennas and Propagation, vol. 47, pp , July 1999.

7. Pattern Data for the Shaped Beam Reflectarray
Measured copolar pattern contours at GHz. The desired coverage area (at G=23 dB) is shown by the dashed polygonal (black) contour.

8. Basic Types of Reflectarray Elements
patch with variable resonant length
patch with microstrip stub of variable length
patch with coaxial stub of variable length L

9. Polarization Twist Reflectarrays
horizontally polarized reflected field
Polarization twist is due only to scattering from patches (not GP), with phase controlled by delay lines.
Cross-pol will occur due to specular reflection from GP, but this field is not collimated by the patches
reflectarray with polarization twist elements
vertically polarized incident field
feed
This technique can also be applied to circular polarization.

10. Polarization Twist Reflectarray Elements
polarization twist using two-port aperture coupled patch
polarization twist using two one-port aperture coupled patches (limited to broadside beam due to grating lobes) L
Similar designs can be made with probe-fed patches.

11. Reflection Phase from Aperture Coupled Polarization Twist Reflectarray vs. Connecting Line Length (infinite array)
L=1.81 cm, W=1.6 cm, εra=2.33, d=0.159 cm, εra=2.2, a=5.8 cm, b=2.9 cm, SL=0.67 cm, SW=0.1 cm

12. Example: Polarization Twist Reflectarray Patterns (calculated)
24x24 two-port aperture coupled patch elements. Patch length = patch width = 1.68 cm. Antenna substrate thickness = cm, dielectric constant = Feed substrate thickness = 0.08 cm, dielectric constant = Grid spacings = 2.9 cm. Slot length = 0.79, slot widths = 0.1 cm, centered below patch. f = 5.2 GHz. Gain = 31.2 dB

13. Some Myths and Realities Concerning Microstrip Reflectarrays
How do microstrip reflectarrays radiate ?
Variable size or stub-terminated patch – which is better ?
Reflectarray modeling: single element or infinite array ?
Is reflectarray bandwidth limited by time delay variations ?
Do proximity-coupled patches increase reflectarray bandwidth ?
Does element gain affect reflectarray gain ?
How should amplifiers be used in a reflectarray ?

14. How do Microstrip Reflectarrays Radiate ?
Myth:
Radiation pattern is due to fields scattered by patches.
Reality:
Total radiation field consists of two components: specular reflection from grounded dielectric substrate, and the field re-radiated by patches. This has an impact on the proper modeling of reflectarrays, as well as the proper design of active reflectarrays.
Reflectarray Plane Wave Reflection Coefficients:
specular reflection due to grounded dielectric substrate
note: no cross polarization
scattering from microstrip patches
note: potential cross polarization
total reflection from reflectarray

15. Phasor Diagrams of Reflectarray Reflection Coefficients (lossless infinite array)
Reflection coefficient of substrate
Reflection coefficient of patch
Total reflection coefficient
f = 5.2 GHz, a = b = 2.9 cm, r = 2.33, d = cm, W = 1.9 cm, tan = 0 ,  = 
varying patch length, no polarization twist

16. Example: Reflection Coefficients for a Polarization Twist Reflectarray with Various Terminations / Interconnections
Reflection
Coefficient
Conjugate
Matched
Open
Circuited
40 degree
Line
140 degree
Two-port aperture coupled patches with orthogonal feed slots and an interconnecting microstrip line. Patch length = patch width = 0.74 cm, grid spacings = 2.4 cm, slot length = 0.42 cm, slot width = 0.04 cm. Antenna substrate thickness = cm, dielectric constant = Feed substrate thickness = cm, dielectric constant = 10.2.

17. Reflectarray Elements Stub Terminated Patches vs Variable Size Patches
Myth:
Stub-terminated elements are better (more efficient reflectors) than variable size patches because they are not detuned.
Reality:
Both stub-terminated and variable size patches are detuned – this is the mechanism for controlling the reflection phase. Also, the incident field in both cases is totally reflected (except for dissipative losses). However, reflectarrays using stub terminations suffer from increased loss, increased cross-pol (due to bends), and a non-linear dependence of reflection phase vs. stub length. There is no difference in etching tolerances for the two cases. L
Reference: D. M. Pozar, “Trimming Stubs for Microstrip Feed Networks and Patch Antennas,” IEEE Antennas and Propagation Society Newsletter, Vol. 29, pp , December 1987.

18. Change in Resonant Frequency vs. Stub Length (single patch)
L = 1.8 cm, W = 1.6 cm, r = 2.33, d = cm, Wf = cm (100 ohm), θi = θ0 =30°

19. Reflection Phase from Microstrip Patch vs. Patch Length
W = 1.6 cm, r = 2.33, d = cm, a = b = 2.9 cm, θi = θ0 =0°, phase ref. at ground plane

20. Reflection Phase from Microstrip Patch vs. Stub Length (infinite array)
L = 1.81 cm, W = 1.6 cm, r = 2.33, d = cm, a = b = 2.9 cm, θi = θ0 =0°

21. Reflectarray Analysis and Modeling
Myth:
A reflectarray can be modeled (and designed) by considering reflection from patch elements in isolation.
Reality:
As discussed above, both the specular reflection from the grounded dielectric substrate and the fields radiated by the patches must be considered. Because the reflection of a plane wave from an infinite substrate is another plane wave, the fields from the patches must also be a plane wave in order to apply superposition. Thus an infinite array model is best for determining the total reflection phase of a given patch. This model also includes mutual coupling, a factor that seems to be important. Also included is the important effect of incidence angle, which is generally not included in most commercial CAD simulations or waveguide simulator models.

22. Reflectarray Design and Analysis Procedure
Using an infinite array analysis, compute reflection phase of elements vs length (patch length, stub length, etc). Include incidence angle for best results.
Determine required size (length, stub, etc) for each element in reflectarray
Analysis:
For each element in array, compute reflection phase using infinite array analysis.
Compute patch fields using element factor, amplitude and phase of field from feed, and reflection phase from Step 1.
Compute specular contribution from grounded substrate in each unit cell of array using physical optics, with amplitude and phase of field from feed.
Add over all elements to compute pattern, gain, efficiency of finite array (array factor for a finite number of patches, with finite substrate size)
Reference:
D. M. Pozar, S. D. Targonski, and H. D. Syrigos, “Design of Millimeter Wave Microstrip Reflectarrays”, IEEE Trans. Antennas and Propagation. vol. 45, pp , February 1997

23. Problems with a Finite Array Approach (element-by-element)
Very large number of elements (~400 to ~4000, or more)
Elements vary in size (for reflectarrays using variable size patches or slots)
Element sizes are not known at beginning of design procedure
Brute force modeling not the best approach

24. Is Reflectarray Bandwidth Limited by Time-Delay Variations ?
Myth:
Reflectarray bandwidth is controlled by the reflection phase vs. frequency response of the element, and the limitation introduced by non-constant path delays over the surface of the reflector.
Reality:
Except for very large apertures and/or low f/D, the dominant factor limiting reflectarray bandwidth is generally the element frequency response. Techniques such as segmented reflectarray panels, or two-port patches with time-delay lines, which may compensate for non-constant time delay, are only useful for very large reflectarrays.

25. Reflectarray Bandwidth Limitation due to Non-constant Path Delay Across the Aperture (for a phase error of 180° at the edge of the aperture)
Reference: D. M. Pozar, “On the Bandwidth of Reflectarrays”, Electronics Letters, vol. 39, pp , October 2003.

26. Calculated Gain for Polarization-Twist Reflectarrays Using Two-Port Aperture Coupled Patches (with either time delay lines or phase shift lines)
Nominal design frequency = 9.95 GHz. Antenna substrate thickness = 1.6 mm, dielectric constant = 2.2. Feed substrate thickness = 0.8 mm, dielectric constant = 2.2. Patches are 8.34 mm square, on a square grid with spacings of 18 mm. Coupling slots are 5.2 mm long, 1.0 mm wide. Both reflectarray apertures are circular; the smaller has 376 patches, while the larger has 1340 patches.

27. Do Proximity-Coupled Patches Increase Reflectarray Bandwidth?
Myth:
Using wideband proximity-coupled patch elements with variable length stubs improves reflectarray bandwidth.
Reality:
The feeding method of patch elements with stubs does not directly affect reflectarray bandwidth. For single (non-stacked) elements bandwidth is controlled by substrate thickness and dielectric constant. Stacking elements is best way to improve reflectarray bandwidth.
(Proximity coupling serves to impedance match a microstrip element on a thick substrate to the feed line impedance, but does not provide improved bandwidth by itself.)
Reference:
J. A. Encinar and J. A. Zornoza, “Broadband Design of Three-Layer Printed Reflectarrays”, IEEE Transactions on Antennas and Propagation, July 2003.

28. Calculated Gain of a Reflectarray Using Variable Size Patches (no feed lines) Compared to Measured Results with Proximity Coupled Patches
Substrate thickness = 2.0 mm, dielectric constant = 4.6, Nx = 30, Ny = 24, dx = 1.33 cm, dy = 1.25 cm, f = 35 cm, θo = 27°.
References:
Chang and Y. C. Wei, “Proximity-Coupled Microstrip Reflectarrays”, IEEE Trans. Antennas and Propagation, vol. 52, pp , Feb
D. M. Pozar, “Comments on ‘Proximity-Coupled Microstrip Reflectarrays’”, IEEE Trans. Antennas and Propagation, to appear.

29. Does Element Gain Affect Reflectarray Gain ?
Myth:
Increasing the gain of the reflectarray elements (e.g. with a PBG structure) will increase the gain of the reflectarray
Reality:
For even small reflectarrays, gain is dictated by the array factor - the element factor has minimal effect. Employing PBG apertures in the ground plane will not increase reflectarray gain.

30. Example – Gain of Reflectarray with or without PBG Apertures in Ground Plane
7x7 array of variable size square patches, substrate thickness = cm, dielectric constant = 2.33, grid spacing = 1.8 cm, feed height = 15 cm.
Reference claims a 2.5 dB increase in gain with PBG ground plane.
Reference: K. M. Shum, Q. Xue, C. H. Chan, and K. M. Luk, “Investigation of microstrip reflectarray using a photonic bandgap structure”, Microwave and optical Technology Letters, vol. 28, pp , Jan. 2001

31. How Should Amplifiers be Used in a Reflectarray ?
Myth:
Amplifiers can be inserted into the reflection path of any reflectarray.
Reality:
Because of the specular and scattered components of the total field radiated by a reflectarray, amplifiers are best used with polarization twist reflectarrays.
no twist, no amplifiers
no twist, with amplifiers (voltage gain A)
polarization twist with amplifiers (voltage gain A)

32. (non-polarization twist)
Reflection Coefficient Phasor Diagrams for Reflectarray with Amplifiers
(non-polarization twist)
Reflection coefficient of substrate
Reflection coefficient of patch
Total reflection coefficient
Note 26 degree phase error with amplifiers relative to assumed design without amplifiers
f = 5.2 GHz, a = b = 2.9 cm, r = 2.33, d = cm, L = cm, W = 1.9 cm, tan = 0 ,  = 

33. Reflection Phase (no twist) vs Patch Size with and without Amplifiers
Note reduced phase range caused by amplifiers in patch reflection path. Main effect is increased phase error, degrading patterns, but with little effect on gain.
W = 1.6 cm, r = 2.33, d = cm, a = b = 2.9 cm, θi = θ0 =0°, phase ref. at ground plane

34. Thank you for your attention
Conclusions
Reflectarrays offer a number of interesting features for antenna design
The successful analysis and design of reflectarrays requires a thorough understanding of electromagnetics and antenna theory – thinking is more important than computing !
Problems remain in the analysis of reflectarrays, and in bandwidth improvement
Thank you for your attention