Non-dispersive tunable reflection phaseshifter based on non-Foster circuits

Fei Gao, Fushun Zhang, Jiang Long, Minu Jacob andDaniel Sievenpiper

ELECT

A new non-dispersive tunable reflection phase shifter is introducedbased on the artificial magnetic conductor (AMC) loaded with non-Foster circuits (NFCs). An AMC structure circuit model is extractedand the possibility of mitigating its intrinsic strong dispersion is dis-cussed by loading it with both negative capacitance and negativeinductance. The NFC is designed to produce the negative capacitanceand inductance based on highly accurate, scalable measurement-basedmodels, and co-simulated with a realistic model of the AMC. Thenumerical results are in good agreement with the analysis and showa nearly flat reflection phase from 450 to 600 MHz. This flat reflectionphase can further be tuned by tuning the loaded inductance from 30 to50 nH. This investigation paves the way towards a dispersion-lessreflection phase shifter design.

Introduction: The ability to control and to tune the phase of reflectedelectromagnetic (EM) waves can lead to many intriguing and promisingapplications. Compared to a meal surface, the high-impedance surfaceor artificial magnetic conductor (AMC) has the property that image cur-rents do not suffer any phase reversal over a limited bandwidth [1]. Thisproperty has been widely used in antenna systems to enhance antennaradiation patterns [1], to miniaturise antennas [2] and to increase thegain [3] as well as the bandwidth [4]. In addition, many applicationsare related to the reflection phase, such as EM wave absorbers [5],reflectarray antennas [6], beam forming and beam scanning antennas[7]. In most of these applications, non-dispersive reflection phasecontrol is desirable. However, all of the existing phase controlling struc-tures, such as the AMC, are strongly dispersive, resulting in the reflec-tion phase of the AMC structure being 0° at only a single frequencypoint. Tunable components such as varactors incorporated into thesemetasurfaces enable one to adjust the reflection phase over a limited fre-quency band, and have been used in active beam scanning in reflectar-rays [8]. Nonetheless, their strong dispersive characteristics have provento be the main challenge in developing wideband reflectarrays [9].

No paper, to our knowledge, has been published so far to demonstratenon-dispersive reflection phase control, although some work has beenconducted to widen the operating bandwidth of AMCs, which isdefined based on the application, and typically is the frequency bandwithin which the reflection phase shifts between ±90° [10, 11].Unfortunately, the reflection phase still shows significant variationover the operating frequency band.

In this Letter, we present an approach to develop a non-dispersivephase shifter based on non-Foster circuits (NFCs). The proposed struc-ture is based on the high-impedance surface without vias. An NFC for aparallel negative inductance and negative capacitance has beendesigned. An AMC model with loss is co-simulated loaded by theNFC, and the stability of the entire structure is discussed and verifiedby transient simulations.

Design: The proposed metasurface arises from the high-impedancesurface which is comprised of periodic subwavelength unit cells [12].The unit cell is marked in red or black dashed rectangle, which consistsof a copper patch on the top of the substrate and a small gap, as shown inFig. 1a. Conventionally, the unit cell in the black dashed rectangle isused in simulation for convenience. The periodicity is 70 mm and theNIC is loaded across the gap. For a horizontally polarised normally in-cident wave, we only need to analyse a single unit cell with two oppositeperfect electric boundaries and two opposite perfect magnetic bound-aries on the vertical walls of the simulator volume. These boundary con-ditions constitute a transmission electron microscopy waveguide with aunit cell as the termination. The concentrated electrical field across thegap due to the incident wave appears as a capacitance and the reflectiondelay through the substrate provides an inductance due to the backsideground [2, 12]. Hence we can obtain the equivalent circuit model shownin Fig. 1b.

To mitigate the strong dispersion, we load the conventional AMCwith a negative inductance and negative capacitance in parallel, asshown in Fig. 1b. By properly adjusting the size of the AMC structureto change its intrinsic inductance and capacitance, it is found that the

RONICS LETTERS 23rd October 2014 Vol. 5

loaded reactance can meet the conditions of stability proposed byUgarte-Munoz et al. [13]. Assuming a lossless surface, Fig. 2 showsthe required reactance for different broadband reflection phases basedon the AMC with dimensions of g = 5 mm and h = 22 mm, fromwhich the intrinsic capacitance and inductance are C0 = 3.2 pF andL0 = 26.5 nH, respectively. The loaded reactance meets the stabilityconditions of |C| <C0 and |L| > L0 [13].

70 mm

gcopper patch

NIC

a

b

+ –

air

substrate h

–L–C

L0

PECPEC

C0

Fig. 1 NFCs loaded AMC

a Configuration of presented structureb Circuit approach representation of unit cell and parallel LC equivalent model

–27

–30

–33

–36

load

ed in

duct

ance

, nH

–39

–42

6

4

2

0

load

ed c

apac

itanc

e, p

F

–2

–4

100 200 300 400 500 600frequency, MHz

a b

c = –3 pF

700 100 200 300 400 500 600frequency, MHz

700

f = –90f = –45f = 0f = +45f = +90

f = –90f = –45f = 0f = +45f = +90

L = –3 nH

Fig. 2 Loaded NFCs value with variation of reflection phase

a Loaded inductance with capacitance fixed at −3 pFb Loaded capacitance with inductance fixed at −30 nH

Results: A floating short-circuit stable configuration of Linvill’s NICcircuit is implemented with a low-noise NPN silicon bipolar transistor(Avago AT41511) on a standard 1.5 mm-thick PCB board [14–16].All of the components were considered based on Modelithic. Thedesigned NIC circuit is shown in Fig. 3, where L4 and C3 are the loadedcomponents; P1 and P2 are the output ports connected to the metallicpatches shown in Fig. 1; and the infinite periodic model in the high-frequency structure simulator is used. It is expected that the loadedreactance is inverted across the output ports. The stability of the realdesign is verified by the transient simulation in the Advanced DesignSystem (ADS) with the acquisition frequency beyond 5 GHz, which isthe one of the best approaches to verify stability among the numericalmethods based on the experience of the NIC circuit measurement [17,18]. As is expected, the whole system is stable.

As shown in Fig. 2, the proposed structure is very sensitive to theloaded capacitance, so it is better to tune the structure by the loadedinductance. Fig. 4 plots the reflection phase when the loaded inductanceis tuned from 30 to 50 nH with steps of 2 nH. The loaded capacitance isfixed at 2.6 pF. The discrepancies between the loaded values and syn-thesised one are expected due to the consideration of the measurement-based model in the PCB design in which parasitics and dispersion areinvolved. A tunable nearly flat reflection phase is obtained from 450to 600 MHz. At lower and higher frequencies, the reflection phase con-verges to 180°/−180° again. The ±90° bandwidth is from 183 to745 MHz, about 120%. Comparing the ±90° bandwidth limitation2πμrh/λ for the passive high-impedance surface which is 23% at500 MHz [9], the bandwidth amelioration due to an increase of effectiveinductance and a decrease of effective capacitance means the increase ofthe effective permeability during the desired frequencies. The stability isalso verified with the transient simulation mentioned above.

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IC

R1 = R4 = 200 W

R2 = R5 = 45 kW

R3 = R6 = 100 W

R7 = R8 = 200 W

C4 = C5 = 5 pF

C6 = C7 = 2000 pF

C9 = C10 = 300 pF

L2 = L3 = 500 nH

Wt/1 = Wt/4 = 50 mil

Wt/12 = Wt/15 = 100 mil

Wt/13 = Wt/14 = 40 mil

Wt/15 = Wt/16 = 100 mil

Lt/1 = Lt/4 = 100 mil

Lt/12 = Lt/15 = 100 mil

Lt/13 = Lt/14 = 140 mil

Lt/15 = Lt/16 = 200 mil

C8 = 2000 pF

L1 = 400 nH

C1 = 20 pF

C2 = 50 pF

SRC3

L1

R4

R5C6

TL16

TL9

R7

TL10

L2

TL4TL3

TL11

TL5R8

R3TL12

TL13

BJT1

C5

C10C9

C4L3

TL6

C1

C2

TL2TL1TL15 R2

R1

C7

TL8

TL7

TL14

C3

L4

R6

BJT2

C8

Vdc = 9 V

Fig. 3 Floating two-port NIC circuit for tunable AMC

C3 and L4 are loaded componentsLumped components are simulated based on ModelithicResistors are from KOA, inductors from MUR and capacitors from JDI

180150

12090

6030

0

–30

–60

–90

–120

refle

ctio

n ph

ase,

deg

–150

–180450 500 550

frequency, MHz600

Fig. 4 Tunable nearly flat reflection phase when sweeping loaded inductancewith capacitance fixed

Conclusion: In this Letter, we have introduced a technique to mitigatethe strong dispersive problem of the reflection phase in a high-impedance surface. To properly design an NIC circuit, a circuit modelof a loaded structure was firstly extracted to discuss the possibility ofa wideband reflection phase shifter. A practical NIC circuit was thendesigned and the numerical co-simulation with a realistic AMC structureshows a tunable reflection phase between 450 and 600 MHz, whichagrees with our analysis. Throughout this Letter, circuit size has notbeen considered, but chip processing can make it easy to integrate thistechnique to smaller structures. Contrary to the traditional passiveAMC design, this method needs a structure with a larger capacitanceso that the required NFCs can be easily achieved with a practical,stable design. Finally, the stability is verified using a transient simulationin ADS. The stable structure can provide a nearly flat tunable reflectionphase within ±90°, for a broadband operating bandwidth of 28% from450 to 600 MHz.

© The Institution of Engineering and Technology 20146 August 2014doi: 10.1049/el.2014.2863One or more of the Figures in this Letter are available in colour online.

ELECTRONICS LETTERS 23r

Fei Gao and Fushun Zhang (Science and Technology on Antenna andMicrowave Laboratory, Xidian University, Xi’an 710071, Shaanxi,People’s Republic of China)E-mail: saltfeig@eng.ucsd.edu

Jiang Long, Minu Jacob and Daniel Sievenpiper (Department ofElectrical and Computer Engineering, University of California at SanDiego, La Jolla, CA 92093-0407, USA)

Fei Gao: Also with the Department of Electrical and ComputerEngineering, University of California at San Diego, La Jolla, USA

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