Automated Design of Optimized Tunable Matching Networksin the UHF band

Cesar Sanchez-Perez, Jesus de Mingo, Paloma Garcıa-Ducar, Pedro L. CarroAragon Institute for Engineering Research (I3A), Universidad de Zaragoza, 50018 Spain

e-mail:{ cesarsp,mingo,paloma,plcarro}@unizar.es

Abstract— In this paper a new methodology to design op-timized digitally-controlled tunable matching networks (TMN)is presented. Conceiving the TMN as a concatenation of basicswitching cells, an optimization of the parameters can be carriedout using a genetic algorithm. This method minimizes thenumber of switching elements as well as ensures a near-optimumperformance. We will present the design of a generic 300-800MHz 7-cell TMN with 60% coverage and a specific 3-cell designbased on an antenna characterization.

Index Terms— Tunable matching network, impedance match-ing, reconfigurable, antenna tuning, genetic algorithm, optimiza-tion.

I. INTRODUCTION

Impedance matching circuits are essential to maximizepower transfer in RF and microwave devices. Theory andtechniques for the design and optimization of broadband andhighly efficient fixed matching networks are well-known [1].However, recent development of reconfigurable wireless so-lutions which try to reuse components in transmission andreception and operate with different signals and frequencybands are demanding the use of efficient tunable impedancematching networks (TMNs) [2].

The design, optimization and automation of TMNs presentsnew challenges regarding fixed matching networks, speciallydue to the existence of multiple different states or configu-rations which can essentially be seen as a set of differentcircuits. Although most of RF circuit simulators (ADS, AWRMicrowave Office) have tools to simulate these kind of circuits,the process of automation and specially optimization can resulttedious due to the multi-state nature of the circuit [3]. More-over, the definition of the optimization goals in simulationsoftware turns into a complex process and the optimizationalgorithms performance may be poor in many occasions.

In order to solve these problems, we propose a novelautomated process of design and optimization of digitally-controlled TMNs. Our proposal starts from the definition of abasic switching cells. The TMN is built as a concatenation ofthese basic switching cells. To consider that the TMN designis finished, it will be necessary that the network fulfils theproposed goals. The construction and optimization process iscarried out with Matlab but verified with AWR MicrowaveOffice. A finite set of possible reactive elements, based oncommercial values, is considered as candidate, and a geneticalgorithm is used in the optimization process of these values.This technique ensures the minimum TMN for the desired

Y1

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SW0

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Zn

SWn

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...

Fig. 1. Schematic example of cell concatenation for the constructionof TMNs.

performance, that is, the TMN with less number of cellsbut meeting the target. In this work, PIN diodes are used asswitching elements, although the process would be extensibleto other switching elements like RF MEMS switches [4].On the other hand, attending to the application (generic orspecific), different goals can be defined. To illustrate this, wewill present two UHF TMN examples: a broadband genericpurpose TMN design in the 300-800 MHz band, based on 7-cells and with a coverage above 60% in all the bandwidth,and a specific purpose 3-cell 425-525 MHz TMN designed tocover a specific region of the Smith chart which correspondsto an antenna input impedance variation pattern.

II. DESIGN AND OPTIMIZATION PROCESS

A. Design

A basic cell element is firstly defined. This has to be asimple structure, but versatile enough to be able to generatemore complex networks. Since we are focusing on UHF appli-cations, the basic cell element will consist of reactive lumpedelements, capacitors and inductors, and switches which willprovide the reconfigurability. With these requirements, theauthors think the best choice is to use a simple two-elementL-section as basic cell with the switch included in the shuntedbranch, in series with the reactive component. The basic cellscomposing a TMN can be seen in Fig. 1. The use of realmodels for reactive components is fundamental to have anaccurate prediction of losses in the TMN. For this reason,we are using the same models as AWR Microwave Officefor ATC capacitors and Coilcraft inductors for our Matlabsimulations. A set of 42 possible capacitance commercialvalues ranging from 0.1 pF to 101 pF are employed. Anotherset of 42 inductance commercial values ranging from 1 nH to100 nH are also employed. Additionally to these 84 reactive

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components, two special situations are also considered: shortcircuit and open circuit, as possible virtual components. Thereason to include these two options arises from the flexibilitythey can contribute to. The location of the switching elementsin the basic cell can be seen in Fig.1.

Hence, a basic cell elements will have two different states,and generalizing to a TMN with 𝑁 cells, the number ofdifferent states will be 2𝑁 . To introduce real switch modelsinto the simulations, scattering parameters measured at thedesired bias point are employed. In this work we propose theuse of silicon-glass PIN diodes from M/A-COM (0171-015).

Finally, to have a totally accurate representation of thecircuits which will be constructed, the effect of transmissionlines is also taken into account. The circuits will be builton low-cost FR4 substrate (𝜖𝑟 = 4.5, tan 𝛿 = 0.03). Thegeneration of the final TMN will be carried out by means of theconcatenation of the basic cell elements previously describedas it can be seen in Fig. 1.

B. Optimization

The optimization process of the reactive components isperformed using a standard genetic algorithm (GA). The mostimportant aspect in the GA is the definition of the fitnessfunction. This definition will depend on the target design(generic or specific) as well as the desired bandwidth. Fora broadband generic TMN design, the fitness function will tryto maximize the Smith chart coverage computed at differentfrequency bins and defined as the region of the Smith chartwhose associated values of return losses (RL) and transducerpower gain (TPG) are better than a certain thresholds. Thedefinition of RL and TPG in dB, assuming a source matchedimpedance, are as follows

RL = 20 log

(𝑆11 +

𝑆12𝑆21Γ𝐿

1− 𝑆22Γ𝐿

)(1)

TPG = 10 log

( ∣𝑆21∣2(1− ∣Γ𝐿∣2)∣1− 𝑆22Γ𝐿∣2

)(2)

where 𝑆𝑖𝑗 are the scattering matrix of the TMN and Γ𝐿 theload reflection coefficient. In the case of a specific design, thefitness function definition may be different, but basically thesame can be applied but just in the desired region or specificpoints in the Smith chart. This will be discussed in detail withthe example design. The GA solution will result in the valuesof the TMN reactive components.

III. PROTOTYPE EXAMPLES AND RESULTS

A picture of the two prototypes constructed is shown inFig. 3. The features and performance measurements will beexplained in this section.

A. Generic 300-800 MHz TMN design

A generic broadband design of a TMN covering a 300-800MHz is proposed. The optimization goal is the Smith chartcoverage defined as the percentage of impedances which fulfila determined criteria for RL and TPG. The definition of these

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Cov

erag

e [%

], R

L<−

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Fig. 2. Coverage for the 7-cell generic TMN.

thresholds is not easy, but we consider that −10 dB for RL anda value around −1.5 or −2 dB for TPG is adequate [3]. Lowervalues of TPG are not considered since they can degrade theoverall efficiency.

Since it is a broadband design, the coverage at differentfrequency points is evaluated. In this case we have usedthree frequency points, in the center and the extremes ofthe desired bandwidth. Each point is weighted equally in thefitness function in order to get a uniform coverage in theentire bandwidth. To get the size (number of elements) ofthe network, the optimization algorithm is run for differentsizes. Then, we evaluate the evolution of the coverage withthe number of elements. The trend observed is the following:initially an ascent curve is seen but it tends to saturate aswe increase the number of cells. It is also clear that if thenumber of cells is indefinitely increased, the coverage curvewill begin to drop, since the losses of the network will degradethe performance, and adding a new cell will not improvethe coverage. Based on this, we consider 7 cells as a goodnumber since simulations predict a coverage above 60% inthe entire bandwidth. Increasing the number of cells does notsignificantly improve the coverage while adds complexity.

The picture of the prototype can be seen in Fig 3(a). Ad-ditionally, a comparison between the simulated and measuredcoverage can be seen in Fig. 2. In this graphic, two differentrepresentations corresponding to a TPG better than −1.5 dBand −2 dB have been presented. The agreement between thesimulation and measurements is very good. If we focus on the−1.5 dB limit, it can be seen as the coverage is higher than50% for the bandwidth 300-800 MHz, reaching almost a 70%in the 400-700 MHz. Relaxing the TPG conditions, for −2dB, a coverage higher than 60% is observed in the entire 300-800 MHz bandwidth and around 75% in the center. Finally,an example of the distribution of TPG and return losses at500 MHz is represented in Fig.4. There, it can be seen as theTPG better than −2 dB covers a great part of the Smith chart,

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(a) Generic 7-cell TMN (b) Specific 3-cell TMN

Fig. 3. Constructed prototypes.

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Fig. 4. Measured TPG and RL for the 7-cell TMN at 500 MHz.

almost up to a VSWR of 10. Return losses better than −10dB can also be observed in a great region of the Smith chart.

B. Specific 425-525 MHz TMN design

A specific TMN design covering 425-525 MHz band is alsoproposed. In this situation, the main goal is not to cover all theSmith chart as previously, but to focus on a specific region.This region is defined in base of a previous research on theantenna input impedance variation of a slot antenna in the425−525 MHz [5]. A representation of the observed variationcan be seen in Fig. 5. Watching this picture it is clear thatthe design of a TMN can be simplified regarding to a genericdesign, since it is not necessary a whole coverage of the Smithchart.

In this situation the fitness function is defined as themaximization of the expected value of the TPG in the Smithchart region in which the antenna input impedance is going totake values. We perform optimization simulations for differentnetwork sizes and after this process, it is obtained that a 3-cell TMN offers a good trade-off in terms of good expectedTPG and network complexity. The picture of the prototypecan be seen in Fig. 3(b). The optimization process leads to thefollowing values in the network: {short, 43 nH, short, 10 pF,12 pF, 43 nH}. In Fig. 6, a comparison between the simulatedand measured TPG at 425 MHz can be observed. There is avery good agreement between both, and it can be observed asthe region of interest is covered with TPG better than −1 dB.

IV. CONCLUSION

In this paper, a new method for the design and optimizationof TMN has been presented. To illustrate it, two prototypes,

Fig. 5. Antenna input impedance characterization.

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Fig. 6. Simulated and measured TPG at 425 MHz.

one of them a generic 7-cell 300-800 MHz TMN and a specific3-cell 425-525 MHz TMN were constructed. Coverage valuesabove 60% have been observed for the generic TMN in theentire bandwidth. In the specific design, a good coverage inthe target region with values of TPG better than −1 dB canbe seen. This method automates the design process as well asensures a minimum number of switching elements for a givengoal.

ACKNOWLEDGEMENT

This work has been funded by the Spanish Government(Project TEC2011-29126-C03-03 from MICINN and FEDER),an FPI grant to the first author (BES-2009-016494).

REFERENCES

[1] R. Fano, “Theoretical limitations on the broadband matching of arbitraryimpedances,” Journal of the Franklin Institute, vol. 249, no. 1, pp. 57 –83, 1950.

[2] R. B. Whatley, Z. Zhou, and K. L. Melde, “Reconfigurable RF impedancetuner for match control in broadband wireless devices,” IEEE Trans.Antennas Propagat., vol. 54, no. 2, pp. 470–478, Feb. 2006.

[3] C. Hoarau, N. Corrao, J. D. Arnould, P. Ferrari, and P. Xavier, “CompleteDesign and Measurement Methodology for a Tunable RF Impedance-Matching Network,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 11,pp. 2620–2627, Nov. 2008.

[4] T. Vaha-Heikkila, J. Varis, J. Tuovinen, and G. M. Rebeiz, “A reconfig-urable 6-20 GHz RF MEMS impedance tuner,” in Proc. IEEE MTT-SInternational Microwave Symposium Digest, vol. 2, Jun. 2004, pp. 729–732 Vol.2.

[5] P. L. Carro, J. de Mingo, and P. Garcia-Ducar, “Characterization ofimpedance variations in antennas for tetra terminals,” in Proc. IEEE 72ndVehicular Technology Conf. Fall (VTC 2010-Fall), 2010, pp. 1–5.

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