A New Method Of Designing Electrical Impedance Matching Network . - JESTR

JestrJOURNAL OFJournal of Engineering Science and Technology Review 7 (1) (2014) 71 – 75Engineering Science andTechnology Reviewwww.jestr.orgResearch ArticleA New Method of Designing Electrical Impedance Matching Network for PiezoelectricUltrasound TransducerJianfei An * and Shuangxi ZhangDept. of Modern Physics, University of Science and Technology of China, Hefei, Anhui – ChinaReceived 10 October 2013; Accepted 22 January 2014AbstractA new method that is based on genetic algorithm (GA) is developed to design electrical impedance matching network forbroadband piezoelectric ultrasound transducer. The new method can both optimize the topology of the matching networkand perform optimization on the components at the same time. Results of classical algorithms are referenced to reducethe number of candidate topologies and greatly simplify the calculation process. Some calculation strategies, such aselitist strategy and clearing niche method, are adopted during optimization to make sure that the algorithm canconvergence to global optimal result. Simulation results show that the new method has advantages over designingcomplex impedance matching network.Keywords: transduce, impedance matching1. IntroductionPiezoelectric transducers have been widely applied indifferent fields [1][2]. Most of traditional piezoelectrictransducers are narrowband which can only produce largescale vibration within a narrow range of resonant frequency.However more and more applications need transducers towork within rather wide range. Similar to narrowbandtransducers, the equivalent impedance of broadbandtransducers is capacitive too. In most cases, the excitationsource and the transducer are impedance mismatched. If noelectrical impedance matching network (EIMN) is adopted,the power reflected from the transducer will reduce theefficiency of the source and, as the condition worsens, evencause permanent damage to components. For narrowbandpiezoelectric transducer, a suitable inductance would beenough in EIMN. As for a broadband piezoelectrictransducer (BPT), however, methods of designing EIMN areusually complicated and hard to understand.Some successful methods [3][4] of designing EIMN havebeen developed, but it is still meaningful to find a new waythat is easy to realize in practice and has good performanceat the same time. In this paper, a brief review about methodsof designing EIMN is made first. Second, a method based ongenetic algorithm (GA) developed in this paper is describedin detail. Third, simulation results of several examples aregiven to confirm the effectiveness of the method. Last, thispaper is summarized briefly.A general purpose of designing EIMN is to make thesignal’s energy transfer from source to load as much aspossible within a broad frequency range. It is realized bymeans of inserting a lossless two ports matching networkbetween the source and the load as is shown in Fig. 1.* E-mail address: ajf@mail.ustc.edu.cnISSN: 1791-2377 2014 Kavala Institute of Technology. All rights reserved.SourceMatchingNetworkZLZqFig. 1. The matching network is inserted between the source and loadThe performance of EIMN in Fig. 1 can be evaluated by aparameter called transducer power gain (TPG) which isdefined by Eq.(1).TPG 4 RQ RL( RQ RL ) 2 ( X Q X L ) 2(1)In Equation (1), ZL RL jXL and ZQ RQ jXQ. ZQ isthe impedance seen from ZL to the matching network.Through simple calculation, the value of TPG is between 0and 1. A common purpose of the matching network is tomake theTPG as big as possible within a specifiedfrequency range.There are mainly two types of broadband impedancematching methods: analytical method and CAD method. Theanalytical method started from Bode’s theoretical researchabout impedance matching [5]. Fano developed Bode’stheory and solved matching problem of any kind of load in amore general way Fano and Youla reconsidered this problemand made a progress[6][7]. Although analytical method can

Jianfei An and Shuangxi Zhang/Journal of Engineering Science and Technology Review 7 (1) (2014) 71 – 75solve any impedance matching problem if the analyticalform of the load is known, the method is very complicated.Besides, for most of the time, the analytical form of the loadis unknown. These shortcomings limit the theory’s practicein engineering.In order to overcome the limitations of analytical theory,Carlin first developed the CAD method, namely realfrequency technique (RFT), for solving single matchingproblem [4]. Yarman proposed simplified real frequencytechnique (SRFT) [8]. Both RFT and SRFT have beenwidely adopted in designing broadband EIMN [9][10].Dedbeu has pointed out that an EIMN that have resonantunits might have better performance than an EIMN of LCladder structure, but it is not mentioned that how manyresonant units are needed and the locations of the resonantunits in network are determined by a little arbitrary tionInitial Ybiggest fitnessNelder-meadsimplex methodA different CAD method is recursive stochasticequalization (RSE) method [12]. Based on a topologyimposed first, TPG is obtained as the objective functionwhich has a function relationship with frequency and theimpedance of the matching network. However, it is difficultto decide what kind of topology is appropriate especiallywhen the topology of EIMN is complex.From the above discussion, it can be concluded thatEIMN synthesized by current typical methods still mighthave room for improvement. This paper puts forward to amethod based on GA. This method can find the optimaltopology as well as the values of the componentsautomatically within a set of predefined topology. Thedefinition of the set is very important to the success of thealgorithm and is selected based on the experiences of onents tationElitismNew culationnichingStoppingConditions?NYReturn biggestfitnessFinal matchingnetworkFig. 2 Overview of the new method based on GAto have ladder-like structure that is shown in Fig 3. Thetypes of Z1, Z2, Zn could be one of the four optionswhich are L, C, parallel LC and serial LC and they aredetermined automatically by the algorithm.The reason why the ladder-like structure is chosen is thatit has been proved to be effective for most EIMN problemsand some popular methods are based on this structure [5][6].Another reason is that it can assure that most of the newnetworks generated by the algorithm are valid and can beeasily evaluated which can reduce the computation time.The number of branches in the structure is pre-specified,but it is not determined arbitrarily. The way the number ischosen is based on the conclusion that, for a specified load,if a matching network with LC ladder structure is applied,there will be a critical number of the branches. When thenumber of branches is less than the critical value, the morebranches are, the better the performance of the EIMN is, andwhen it outnumbers the value, the performance is nearlyinvariable or even declines as the number increases. Thecritical number of branches of the LC ladder structure is2. Design of Broadband EIMN Based On GA2.1 Overview of the algorithmThe idea of the GA-based method presented here is to find away that not only both the network topology and the valuesof components can be optimized but also a lot of computingresources are not necessary so that the algorithm can run ona laptop. To reduce the computing resources and make surethe performance is good at the same time, prior experiencesof classical methods are referenced to limit the number ofthe candidate topologies.The calcullation process of the method is shown in Fig. 2The topology optimization and the optimization ofcomponents are separated. Binary-coded GA is adopted toevolve the topology and real-coded GA is followed todetermine the values of components and the TPG of thetopology.To improve the ratio of validity of new topology andreduce computation time, the matching network is assumed72

Jianfei An and Shuangxi Zhang/Journal of Engineering Science and Technology Review 7 (1) (2014) 71 – 75specified to be the number of Zn in our algorithm. In part 3,an example will be used to prove that it is a feasible idea.the global optimal solution of the multimodal fitnessfunction.In a practical transducer excitation circuit, a pulsetransformer is needed. The effect of the transformer is:changing voltage, transforming impedance and blocking DC.In this method, the parameter of the transformer isdetermined by means of finding the optimal sourceresistance Rg . The relation between Rg and real sourceresistance Rg is : Rg n2 Rg. The parameter n is realizedby a transformer.ACZlRg(a).ACZl(b)Fig. 3 (a)Ttype of matching network,and(b)πtype of matching network2.2 Topology optimization methodIn the algorithm, the matching network topologies arebinary-encoded. Each branch is represented using two binarybits which is shown below.011011The fitness function we use here is shown in Eq. (2) inwhich TPG (ω) is shown in Eq. (1).fitness min(TPG (ω ))n2Rg n RgWhen GA is applied to optimize a multimodal function,it tends to converge to the local optimal values. To overcomethis shortcoming, a clearing niching method is adopted [15].In this method, the distance between two individuals isdefined first which is the Euclidean distance in ouralgorithm. The capacity of a niche is defined which meansthat within the predefined range of an individual, only alimited number of individuals that have bigger fitness thanothers are effective, while other individuals’ fitness arecleared to zero.TPG is also used as the fitness of RCGA. When thealgorithm finishes evolution, the genes in the chromosomethat has the biggest fitness is assigned to the components ofthe specified topology.Another shortcoming of GA is that the efficiency willdecrease dramatically and be difficult to achieve the optimalsolution when the algorithm is close to the optimal value. Inorder to overcome this problem, a local optimizationalgorithm called the Nelder–Mead simplex algorithm(NMSA) [16] is adopted as a complement to RCGA.001Vg3. Simulation and TestIn this part, a typical example is presented to prove theeffectiveness of the algorithm.(2)3.1 EIMN of a piezoelectric ultrasound transducerEach topology of the initial population is createdrandomly and the population size we use here is 120.Parents are selected by tournament [13] in threerandomly-chosen individuals.Uniform crossover [13] is used as crossover operator bywhich each gene of new individual is randomly chosen intwo parents.The probability of mutation [13] we use here is 0.1.The evolution will stop when the generation exceeds themaximum value g max or a fitness value is bigger than aC123pL14mC240pL25.8mC30.2nL35.4mC4235pspecified figure.The new individual generated in each generation isdifferent from all individuals in the population. Elitiststrategy [13] is adopted that the individual with the bestfitness in current generation will be reproduced to the nextgeneration directly.R128492.3 Values optimization methodR21684R3298Fig. 4. Electro-mechanical equivalent circuit of a multi-resonantbroadband piezoelectric ultrasound transducerTo calculate the fitness of a topology, the components of thetopology need to be determined first. A real-coded geneticalgorithm (RCGA) [14] is adopted to perform optimizationon the values of components. Although based on the sametheory, some operators in RCGA are different from those inBCGA. A niching method [15] and the elitist strategy areadopted in combination to make sure the algorithm can findIn this part, a broadband EIMN of a piezoelectrictransducer is designed. Although the algorithm can beimplemented directly with the measured data of thetransducer, the analytical form of the impedance is still73