Design Optimization of Microstrip Matching Circuits ...

PIERS Proceedings, Stockholm, Sweden, Aug. 12–15, 2013

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Design Optimization of Microstrip Matching Circuits Using a Honey Bee Mating Algorithm Subject to the Transistor’s Potential Performance

C2

Peyman Mahouti, Salih Demirel, and Filiz G¨ une¸s Department of Electronics and Communication Engineering, Yıldız Technical University Istanbul, Turkey

Abstract— In this work, the same Honey Bee Mating Optimization as in [1], this time is applied to design of the input and output microstrip matching circuits to provide the source ZS and load ZL terminations ensuring the selected performance quadrate to the transistor, respectively for the desired performance triplets (Vin , F (f ), GT ) [1, 2]. In this implementation, the populations of ~ and lengths ~` of the input the Queen Candidates and Drones are defined in terms of the widths W and output microstrip matching circuits to determine the fitness values or estrogen values of the bees. Among the female bees probabilistically mating with the drones, the one with the fittest gens or estrogen level will be chosen as the Queen bee, in the other words, the best solution for optimization problem. On the other hand, the multi-objective design optimization procedure of the amplifier is reduced into the single objective design procedures of the input/output matching circuits using Darlington realizations of the quadrate ZS , ZL terminations. It can be concluded that in this work, all the constituents of the HBMO design optimization are defined rigorously and at the output, all the microstrip lengths and widths of the input and output matching circuits are obtained to be printed on a selected dielectric substrate. Finally as a work example the design of a typically ultra-wide band low noise amplifier with NE3512S02 is presented on a substrate of Rogers 4350 (εr = 3.48, h = 1.524 mm, tan δ = 0.003, t = 0.001 mm) within 2–5 GHz satisfying (Vin = 1.5, F = Fmin (f ), GT = 10 dB) triplet using the T type of microstrip matching circuit and verified using the circuit simulator AWR. 1. INTRODUCTION

Honey Bee Mating Optimization (HBMO) is a recent swarm-based optimization algorithm to solve highly nonlinear optimization problems, in which the search algorithm is inspired by the process of honey bee mating in real life where the Queen of the colony is the most important member with the duty of giving birth to the new members of the hive by mating with a series of Drone Bees. In honey bee colonies, female bees that have the most amount of estrogen will be chosen as the Queen Bees. In open literature, HBMO is applied firstly to the optimal reservoir operation by Afshar, Haddad, Marino and Adams [3]. To the best knowledge of the authors, the HBMO algorithm is built as a simple and efficient optimization tool and applied as a first time to determine the Feasible Design Target Space (FDTS) for a front-end microwave amplifier and the resulted numerical solutions are compared with their analytical counterparts [1]. This FDTS covers all the compatible (Input VSWR Vinreq ≥ 1, Noise Figure Freq ≥ Fmin (f ), Gain GT req ≤ GT max , Bandwidth B) quadrates and their corresponding source ZS and Load ZL terminations within the continuous operation (VDS , IDS , f ) parameter domain of the microwave transistor In this work, it is aimed to find the widths and lengths of the microstrip transmission lines of matching circuits. The proposed algorithm will try to find these dimension values for T type matching circuit for input or output of a LNA design. In the next section, matching circuits design with microstrip transmission lines and Darlington theorem will be described. In the Section 3, HBMO algorithm its parameters and its cost function for our optimization problem will be presented. In the last section, an example work for the proposed algorithm is done for an ultra-wide band low noise amplifier. 2. MATCHING CIRCUIT DESIGN

In order to make an ultra-wide application design one of the most hard challenges is to design the matching circuit for the application in order to have the low return loss in input of the structure. Matching circuits are two port structures that change the impedance value of a certain load to the impedance value of the source. Briefly, it is desired that the input impedance of the two port network is equal to the conjugate or to the value of the source impedance. The value of the input impedance can be obtained as follows: Zin =

AZL + B CZL + D

(1)

Progress In Electromagnetics Research Symposium Proceedings, Stockholm, Sweden, Aug. 12-15, 2013 1891

Figure 1: Schematic of a two port matching circuit.

In this work, our two port matching circuit is a T type microstrip matching circuit. The chain (ABCD) parameters of the T type matching circuit can be shown as follow: ¸ · 1 + Z1 Y2 Z3 + Z1 (Y2 Z3 + 1) (2) Y2 1 + Y2 Z3 The optimization problem or the cost function for this work is the difference between the required input impedance value and the values of the T type matching network with 50 ohm termination as the source or load impedance for input or output of the LNA. Cost =

m X

|Rin (fi ) − Rinreq (fi )| + |Xin (fi ) − Xinreq (fi )|

(3)

i

3. HONEY BEE MATING OPTIMIZATION

As it is mentioned before HBMO is a recent swarm-based optimization algorithm to solve highly nonlinear optimization problems, in which the search algorithm is inspired by the process of honey bee mating in real life where the Queen of the colony is the most important member with the duty of giving birth to the new members of the hive by mating with a series of Drone Bees. For our optimization problem these bees will be taken in terms of widths and lengths of a microstrip transmission line. The Queen and Drone Population are defined in terms of the optimization variables respectively as below: · ¸ · ¸ w1Qi , w2Qi , w3Qi w1Dj , w2Dj , w3Dj Qi Dj = (4) l1Qi , l2Qi , l3Qi 2x3 l1Dj , l2Dj , l3Dj 2x3 Furthermore Genetic inheritance belonging of the optimization variables as follows: · W1 , QiGen = L1 , · W1 , DjGen = L1 ,

to each Queen Qi and Drone Dj are expressed in terms

Wi = [wi ]m×1

W2 , W3 L2 , L3 W2 , W3 L2 , L3

¸ (5) ¸

2x3

(6) 2x3

Li = [`i ]m×1 ,

i = 1, 2, 3

(7)

m = 5000 for Queens and m = 100 for each Drone bee as the predefined parameters. The Queen bee and the Drones will take mating flights just as like in [2] in order to create a genetic pool for next generations. The created genetic pool can be simply described as follow: · ¸ W1GP , W2GP , W3GP GP = (8) L1GP , L2GP , L3GP 2x3 WiGP = [wi ]m×1

LiGP = [`i ]m×1

i = 1, 2, 3

(9)

m = 1000+100 NDrs and NDrs ≤ NDrone is the number of the drones each of which had a successful mating flight with the Master Queen Bee. In the proposed HBMO algorithm, gender of all new born members of the colony will be assumed as female, thus each solution can be considered as a potential Master Queen Bee candidate. · ¸ £ ¤ w1Eggi , w2Eggi , w3Eggi Egg population = Egg1 Egg2 . . . EggNEgg Eggi = (10) `1Eggi , `2Eggi , `3Eggi 2x3

PIERS Proceedings, Stockholm, Sweden, Aug. 12–15, 2013

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i = 1, . . . , Negg , which is generated by random selection by crossing over among the corresponding elements of the genetic pool. In the next step, the cost value of each egg will be calculated according to Eq. (3), and the best member of the Bee colony will be taken as the final solution just like it is done in [2]. In the next section, a worked example for our proposed algorithm has been done and its success rate is conformed in AWR. 4. WORKED EXAMPLE

In this section of the work, NE3512S02 had been used as a high technology transistor for our ultra-wide band low noise amplifier. In Figure 2 the designed LNA structure with its microstrip matching circuits are shown. The matching circuits are designed in order to satisfied the required impedance values for Vin = 1.5, F = Fmin (f ) and GT = 10 dB for 3–5 GHz bandwidth.

MLIN ID=TL10 PORT W=3.458 mm P=1 Z=50 Ohm L=8.944 mm MSUB=MSUB1

MLIN ID=TL1 W=0.311 mm L=2.108 mm MSUB=MSUB1

MLIN ID=TL3 W=0.3 mm L=8.417 mm MSUB=MSUB1

MTEE$ ID=TL7 1

MLIN ID=TL4 W=0.3 mm L=16.96 mm MSUB=MSUB1 SUBCKT ID=S1 2 NET="NE3512S02"

MLIN ID=TL6 W=0.4217 mm L=17 mm MSUB=MSUB1

MTEE$ ID=TL8 1

2 3

1

2

3 MLEF ID=TL12 W=0.795 mm L=7.339 mm

MSUB Er=3.48 H=1.524 mm T=0.035 mm Rho=1 Tand=0.003 ErNom=3.48 Name=MSUB1

MLEF ID=TL2 W=15 mm L=0.3 mm

3

MLIN PORT ID=TL11 P=2 W=3.458 mm Z=50 Ohm L=8.944 mm MSUB=MSUB1

MLIN ID=TL9 W=11.61 mm L=4.749 mm MSUB=MSUB1

Figure 2: Schematic of the designed microstrip LNA.

15

DB(GT()) LNA

Graph 1

0

S11 DB(|S(1,1)|) LNA

-5 -10

10

-15 5

-20 -25 -30

0 2

3

4

2

5

3

4

5

Frequency (GHz)

Frequency (GHz)

Figure 3: GT results of the designed microstrip LNA.

5

Figure 4: Return loss results of the designed microstrip LNA.

Noise Figure

4

DB(NF()) LNA

3

2 3.504 GHz 0.5889 dB

1

0 2

3

4

5

Frequency (GHz)

Figure 5: Noise results of the designed microstrip LNA.

As it is seen in previous figures, the proposed algorithm is an effective and successful algorithm for our designed problem. By simply giving the required impedance values for the input and output of the transistor for Vin = 1.5, F = Fmin (f ) and GT = 10 dB for 3–5 GHz the algorithm can easily make the design with microstrip transmission lines.

Progress In Electromagnetics Research Symposium Proceedings, Stockholm, Sweden, Aug. 12-15, 2013 1893 REFERENCES

1. Mahouti, P., F. G¨ une¸s, and S. Demirel, “Honey-bees mating algorithm applied to feasible design target space for a wide-band front-end amplifier,” 2012 IEEE International Conference on Ultra-wideband, 251–255, 2012. 2. G¨ une¸s, F., M. G¨ une¸s, and M. M. Fidan, “Performance characterisation of a microwave transistor,” IEE Proceedings — Circuits, Devices and Systems, Vol. 141, No. 5, 337–344, 1994. 3. Afshar, A., O. B. Haddad, M. A. Marino, and B. J. Adams, “Honey — Bee mating optimization (HBMO) algorithm for optimal reservoir operation,” Journal of the Franklin Institute, Vol. 344, 452–462, 2007.