Design of lange coupler for MIC and MMIC technology using complementary deformed omega structure

Design of Lange Coupler for MIC and MMICTechnology Using Complementary DeformedOmega Structure

R. K. Mishra,1 G. Arun Kumar,2 D. Mishra,3 D. R. Poddar4

1 Department of Electronics Science, Behrampur University, Bhanja Bihar, Orissa2 SAMEER Kolkata Centre, Kolkata, West Bengal3 Department of Electronics and Telecommunication Engineering, VSSUT, Burla, Orissa4 Department of Electronics and Telecommunications, Jadavpur University, Kolkata, West Bengal

Received 31 March 2011; accepted 9 June 2011

ABSTRACT: A novel design for a 3 dB Lange coupler based on complementary deformed

omega structure (CDOS) is proposed. Observations, from parametric study for the CDOS

based Lange coupler, are provided to aid in the design process. A functional linked artificial

neural network has been used to determine the dimensions of the CDOS. Electromagnetic

simulations have been validated with experimental results obtained from fabricated proto-

types. VC 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE 22:85–92, 2012.

Keywords: coupling; deformed omega structure; even and odd mode; functional link neural net-

work; Lange coupler

I. INTRODUCTION

Many innovative RF components and wireless systems

[1–6] are evolving to meet the rapid growth of the tele-

communication market. Due to constraints on floor space

of components and devices, circuit miniaturization is fast

becoming an essential part of wireless systems design.

Compact designs are being explored to make passive com-

ponents small and efficient. Couplers form an important

part of components in communication systems. Many a

times tight coupling is essential in the design of mixers,

balanced amplifiers, etc [7]. Space constraints restrict the

use of readily available 3 dB couplers such as branch line

couplers [8, 9] and rat race couplers [10, 11]. For a single

parallel line coupler, the spacing between the coupled

lines reduces with increasing coupling coefficient. There-

fore, in design of components like broadside coupled

lines [12, 13], reentrant couplers [14, 15], tandem couplers

[16, 17], etc, tight coupling techniques suffer from narrow

coupling gaps, long coupling lengths, etc. The tolerance

limitation of in-house fabrication process available in

many laboratories prohibits use of such tight coupling

techniques in compact design, because after a certain

point (when the spacing becomes very narrow) the fabri-

cation becomes unrealizable. To avoid this, extra parallel

lines are usually added to the coupler structure using

bonded wires for tighter coupling with wider spacing

between the lines. The extra lines technique also has some

difficulties. By skillfully folding the lines and rearranging

the ports, the difficulties in wire bonding the lines are

resolved, and the resulting coupler is called Lange coupler

(LC). LC [18] has advantages of smaller size and large

bandwidth [19, 20]. This coupler also suffers from narrow

line widths and coupling gaps. The amount of coupling can

be increased by increasing the number of fingers but this

decreases the line width of the fingers. It puts inconvenient

mechanical fabrication constraints due to strict etching tol-

erances for designing LC. Moreover, the increase in cou-

pling after a certain number of fingers beyond which use of

additional fingers is of no benefit. This article presents the

design of realizable LC using complementary deformed

omega structure (CDOS) for 3 dB coupling.

II. COMPENSATED LC

As discussed, the LC is a parallel line coupler. Parallel-

coupled microstrip lines exhibit poor directivity [21] due

to the inequality of even- and odd-mode wave phase

velocities [22, 23] since microstrip is an inhomogeneous

medium. The techniques to avoid problem of unequal

phase velocities in parallel-coupled microstrip lines can be

divided into two main classes: lumped and distributed

Correspondence to: R. K. Mishra; e-mail: [email protected].

VC 2011 Wiley Periodicals, Inc.

DOI 10.1002/mmce.20587Published online 1 December 2011 in Wiley Online Library

(wileyonlinelibrary.com).

85

compensation approaches. In the lumped compensation

approach [24–26], external reactive components are con-

nected between or shunted with the parallel coupled-lines’

ports. Major disadvantages of the technique are the para-

sitic of lumped components and difficulty in layout [24,

25]. The distributed approach involves modification of the

parallel-coupled line structure [27, 28], dielectric layer

[29], or ground plane [30] to reduce the difference in

phase velocities of both modes. No external components

or extra space are needed for this approach. Absence of

closed-form design equations is its main disadvantage,

because of which the design depends on the electromag-

netic (EM) simulation stage, which need more effort and

heavy computing time.

This work uses deformed omega slots on the ground

plane for the compensation, thus avoiding the disadvant-

age of lumped elements. The deformed omega structure

(DOS) consists of a semicircular ring with two tangential

strips (or tails) at both ends of the ring as shown in Fig-

ure 1a. Etched out on the ground plane (Fig. 1b), it

forms a resonant structure. The equivalent circuit (EQ)

of the structure at the reference plane is shown in Figure

1c. The inductance in the series arm of the T network

and the shunt capacitance in the shunt arm are due to the

interaction of the microstrip line with the structure and

the parallel resonant structure is due the resonant behav-

ior of the DOS.

III. PARAMETRIC STUDY ON CDOS COMPENSATED LC

To develop a behavioral model, it is essential to know the

effects of different parameters of the CDOS on character-

istics of the compensated LC. The effect of the width,

radius (and tail length), and gap between the structures

are discussed below. The EM simulations, for parameter-

ization, have been done on a 10 mil substrate of dielectric

constant 2.2. To get an idea on how width, radius (tail

length), and gap between the structures affect the charac-

teristics, EM simulations on CDOS of different dimen-

sions had been performed. In the simulations, the refer-

ence plane has been shifted to the A–A0 (refer Fig. 1b).

From these EM simulations, it is observed that the DOS

in ground plane results in considerable variation in the

values of the inductance of the line and the resonant

capacitance of the structure. The inductance of the micro-

strip line depends on the length of the tail (and the ring

radius) of deformed omega while the capacitance to the

ground is dependent on the width of the ring and the strip.

The gap between two DOS s affects the coupling of fields

between them and changes the resonant frequency of the

structures. Hence, proper dimensions of the CDOS need

to be determined for inductive compensation. As Artificial

Neural Network (ANN) is known to be efficient in func-

tion approximation for nonlinear relationships, and is

extensively used in the RF and Microwave domain [31],

this work uses it in the absence of closed form design

equations for CDOS.

IV. FUNCTIONAL LINKED ARTIFICIAL NEURALNETWORK (FLANN)

Usually, a feed-forward type Artificial Neural Network

follows a pyramidal structure, that is, number of hidden

neurons is more than output neurons but less than the

input neurons. For LC, most of available design proce-

dures rely on the even and odd mode impedances of the

coupler as well as the terminating impedance. The etching

of the deformed omega slots on the ground plane changes

the first two for specified terminating impedance. A sim-

plified design of the deformed omega slot uses equal

strip-width for the omega tail and the semicircle (i.e., wt

¼ ws ¼ w) and the radius of the semicircle is equal to the

length of the tail (i.e., rs ¼ lt ¼ L). Therefore, the output

of the network shall give L, w, and g (gap between the

two slots). These outputs shall be obtained for given even

mode impedance (Z0e), odd mode impedance (Z0o), and

center of frequency (fc). It makes number of input equal

to number of outputs, which can sometimes create prob-

lems of training with limited number of data. In fact, due

to EM simulations for data generation, the number of data

will be limited. To reduce such problems, the number of

inputs can be increased. A nonlinear mapping between the

inputs and outputs is being established through the ANN.

Each output can be considered as a product of many sin-

gle variable functions, where the variables are the inputs

for the network. Each such single variable can either be

expanded as a polynomial or as a Fourier series. If one of

the inputs is X, then let us assume that the function is

approximated as a second degree (in fact it can be of any

degree, but for convenience it is considered second

degree) polynomial. Similarly, the function can also be

Figure 1 (a) Physical layout of the DOS. (b) Dimensions of the structure rad ¼ 0.9 mm, w ¼ 0.5 mm, and s ¼ 0.3 mm. (c) EQ of the DOS.

86 Mishra et al.

International Journal of RF and Microwave Computer-Aided Engineering/Vol. 22, No. 1, January 2012

expanded in Fourier series as sums of sine and cosine

terms. Therefore, it can be said that the output of the net-

work depends on X, X2, sin (X), and cos (X). These are

expanded inputs of X. The first and second terms repre-

sent polynomial expansion while the third and fourth

terms represent Fourier series expansion. Thus, there will

be a four fold increase in the input, excluding of course

the bias. Then, the training with limited number of data

becomes less problematic. This ANN, in which the inputs

are expanded functionally, is termed as FLANN [32] and

its architecture, used in this work, is shown in Figure 2.

The FLANN operates exactly like a feed forward neural

network well established in literature. For determination

of the dimensions of the CDOS for given even mode and

odd mode impedances and center frequency of operation,

a FLANN is used in this work.

V. CDOS EMBEDDED LC DESIGN PROCEDURE

Conventional design, of a LC with 50-Ohm port imped-

ance, starts with the calculation of the odd and even mode

impedances for given number of fingers. The odd and

even mode impedances are then used for realization of the

physical dimensions. Odd and even mode impedances, for

the coupler with k fingers (k is even) having terminating

impedance Z0 and coupling coefficient C, are calculated

[19] using eqs. (1)–(3). Once, the Z0e and Z0o are

obtained, standard procedures are followed [33, 34] to

obtain the dimensions of the coupled lines.

Z0o ¼ Z01� C

1þ C

� �12 ðk � 1Þð1þ qÞðCþ qÞ þ ðk � 1Þð1� CÞ (1)

Z0e ¼ Z0oðCþ qÞ

ðk � 1Þð1� CÞ (2)

q ¼ C2 þ ð1� C2Þðk � 1Þ2� �1

2

(3)

Z0, Z0O, Z0E, C, and k represent respectively the terminat-

ing impedance, odd mode impedance, even mode impedance,

voltage-coupling coefficient, and the number of fingers.

However, this procedure is not useful for CDOS em-

bedded LC. In such case, for a given CDOS the Z0e and

Z0o can be obtained from EQ simulation. In this work, the

following procedure is followed. First, a 3D EM simulator

is used to obtain the S-Parameters of the conventional LC.

Then these S-Parameters are exported to a circuit simula-

tor (Agilent ADS) as the S-Parameters of an inductively

coupled coupler, for which the EQ model proposed by

Frye et al. [35] is shown in Figure 3a. The even mode

and odd mode analysis is performed on the EQ to obtain

the odd and even mode impedances using eqs. (4)–(7).

Z0e ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiLð1þ KLÞCð1� KCÞ

sKL ¼ M

L(4)

Z0o ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiLð1� KLÞCð1þ KCÞ

sKC ¼ Cg

Cp þ Cg

(5)

Z0 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiZ0e:Z0o

p(6)

C ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZ0e � Z0oZ0e þ Z0o

r(7)

where L, C, m, KL, KC, Cg, and Cp are respectively the

self inductance, self capacitance, mutual inductance, cou-

pling factors, capacitance between the adjacent strips and

capacitance between the strip and ground.

Then, the S-parameters at each of the four-ports for

the circuit are calculated using the electric and magnetic

walls about the symmetric planes P1 and P2 shown in

Figure 3a. For the two symmetric planes, the following

four cases are considered at each port for determining the

S-parameters.

• Case 1: P1 is magnetic wall and P2 is magnetic wall

and reflection coefficient is C1.• Case 2: P1 is magnetic wall and P2 is electric wall and

the reflection coefficient is C2.• Case 3: P1 is electric wall and P2 is magnetic wall and

the reflection coefficient is C3.

Figure 2 Schematic representation of the FLANN for CDOS dimensions.

CDOS Based Lange Coupler for MIC and MMIC 87

International Journal of RF and Microwave Computer-Aided Engineering DOI 10.1002/mmce

• Case 4: P1 is electric wall and P2 is electric wall and

the reflection coefficient is C4.

The calculation of the reflection coefficient for these

four combinations of electric and magnetic walls is done

using eq. (8). The admittance YL is obtained by applying

the electric and magnetic walls and Y0 is the terminating

admittance of the coupler.

C ¼ Y0 � YLY0 þ YL

(8)

Superposition of the four reflection coefficients (C1,C2, C3, and C4) in the manner given in eqs. (9)–(12) pro-

vides the S-parameters for the coupler.

S11 ¼ ðC1 þ C2 þ C3 þ C4Þ4

(9)

S21 ¼ ðC1 � C2 þ C3 � C4Þ4

(10)

S31 ¼ ðC1 þ C2 � C3 � C4Þ4

(11)

S41 ¼ ðC1 � C2 � C3 þ C4Þ4

(12)

These S-parameters are compared with those obtained

from the EM simulation. If the mismatch between the EM

simulated S-parameters and the circuit simulated S-param-

eters are intolerable, the values of circuit elements are

adjusted iteratively, until acceptable matching.

In the next stage, the EM simulation is done for a LC with

CDOS embedded in its ground plane. In this simulation, the

dimension of the LC remains same as that for the uncompen-

sated one described above. Therefore, in the EQ the value of

the elements corresponding to the LC are kept the same as

those for the uncompensated coupler. However, the additional

elements due to CDOS, as shown in Figure 3b, are unknown.

Their values are changed iteratively following the above

method till the matching between the S-Parameters obtained

from EM simulation and circuit simulation match reasonably.

Then the Z0e and Z0o for the CDOS embedded LC are

obtained. These values along with the center frequency of

operation form the basis of input for the FLANN and the

dimensions of the CDOS form the FLANN’s output. An algo-

rithm for developing a CAD model for CDOS embedded LC,

based on the above procedure, is given below.

Algorithm 1: EM simulation of conventional LC

1. Read required coupling coefficient (C) and port im-

pedance (Z0) and number of fingers (k).2. Read the substrate thickness (h) and dielectric con-

stant (er).3. Read the smallest realizable width of the coupler (wr)

and fingers.

4. Read the smallest realizable gap (Gr) between the

coupled lines and fingers.

5. Determine Z0e and Z0o using eqs. (1)–(3) and store

them as vector Z0 ¼ [Z0e Z0o].6. Use [33, 34] to determine the width of the coupled

lines and fingers (wc) and the gap (Gc) between them.

7. If wc �wr and Gc � Gr

W ¼ wc

G ¼ Gc

else

W ¼ wr

G ¼ Gr

endif

8. (a) Invoke the EM simulator engine.

(b) Export C, Z0, k, h, er, W, and G to the simulator

and run it.

9. Import the S-Parameters from the EM simulator and

store them in a vector SEM ¼ [S11em S21em S31em].10. Close the EM simulator engine.

11. End

Algorithm 2: Determine EQ of conventional LC

1. Fix a fitness tolerance value [.2. Form 20 random position vectors containing values of

elements for EQ of the coupler Pi ¼ [Li, Cpi, Cgi, kLi]i ¼ 1, 2, …, 20.

3. Invoke the circuit simulator.

Figure 3 EQs for (a) conventional LC and (b) the coupler with CDOS loading.

88 Mishra et al.


4. Simulate a coupled line given by an EQ depicted in

Figure 3a.

5. Use eqs. (9)–(12) to determine the S-parameters and

store them in a vector Sck ¼ [S11ck S21ck S31ck].6. Determine the fitness value.

F ¼ 1

3

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS11em � S11ckð Þ2þS21em � S21ckð Þ2þS31em � S31ckð Þ2

0@

1A

vuuut

7. If [> F, thenupdate Pi using an algorithm like PSO or GA

else

P ¼ Pi

end

8. Store the optimized values P ¼ [L, Cp, Cg, kL].9. End.

Algorithm 3: FLANN Development Procedure

1. Import h, er, W, and G from algorithm 1.

2. Read L, w, and g for the CDOS.

3. Read number of required groups of data N.4. Initialize n ¼ 1

5. While n < N.a. Invoke EM simulator.

b. Export h, er, W, G, fc, L, w, and g to it and simulate.

c. Import the S-Parameters from the EM simulator and

store them in a vector SEMn ¼ [S11emn S21emn

S31emn].

d. Close EM simulator.

e. Invoke circuit simulator.

f. Simulate a coupled line given by an EQ depicted in

Figure 4b.

g. Export P obtained in algorithm 2 to it.

h. Use the procedure described in algorithm 2 for

obtaining circuit parameters for the CDOS, while

keeping P constant.

i. Close the circuit simulator.

j. Use eqs. (4)–(7) to determine Z0e and Z0o.

k. Append Z0e, Z20e, cos (Z0e), sin (Z0e), Z0o, Z

20o, cos

(Z0o), sin (Z0o), and fc, fc2, cos (fc), and sin (fc) as

input and L, w, and g as output for the FLANN to a

data file.

6. Train the FLANN with an error tolerance of better than

10–3.

VI. RESULTS AND DISCUSSIONS

The objective of prototype design has been to obtain 3 dB

coupling from a 10 mil substrate with a dielectric constant of

2.2 in the X-band. Due to limited fabrication facilities avail-

able in the laboratory, the length and width of the conven-

tional coupler were fixed to be 4.2 and 0.1 mm, respectively,

with six fingers having gaps of 0.1 mm. This conventional

coupler gave a coupling coefficient of 4.08 dB for 50 Ohm

terminating impedance. Then the algorithms described above

were used to obtain the data for the FLANN. While imple-

menting the algorithms, only the dimensions of CDOS had

been varied, while that of the LC on the top of the substrate

was kept constant. The S-parameters obtained from the EM

simulation were sent to ADS circuit simulator software. The

ADS simulator has a built in coupled line model and using

the coupled line model and the odd and even mode impedan-

ces were optimized by comparing the S-parameters. While

implementing the algorithms, it was observed from the EQs

for CDOS embedded LC that the increase in the inductance

of microstrip line increases not only the self-inductance of

the fingers of the coupler but also the mutual inductances.

The testing data are shown in Table I.

The FLANN had 13 input neurons, 7 hidden neurons

and 3 output neurons. The activation function for the hidden

neurons was tan h (.) and that for the output neurons are lin-

ear, since the output are continuous. From calculations, it

had been found that for 3 dB coupling with 50-ohm termi-

nating impedance, the odd and even-mode impedances

should be 243.3 and 82.5 Ohms, respectively, at 10 GHz

center frequency. Using these values in the FLANN, length

of strip (and radius of the ring), width of the strip and the

ring and gap between the two structures were found to be

Figure 4 (a) Top side of the fabricated LC with DOS embedded in the ground plane and (b) bottom side. [Color figure can be viewed

in the online issue, which is available at wileyonlinelibrary.com.]



0.9, 0.5, and 0.3 mm. The Figure 4 shows the top and the

bottom sides of the fabricated prototype. Top side of the cir-

cuit has been gold plated for bonding of wires between the

fingers of the coupler. The measurements on the fabricated

prototype were done using E8363B vector network analyzer.

The EQ, EM simulated (EM) and measured (Meas) S pa-

rameters are shown, respectively, in Figure 5 and 6. A return

loss of 10 dB or better throughout the band is observed in

Figure 5. It suggests good matching at the input port. Isola-

tion of 15 dB or more is also observed in this figure for all

the three cases (EQ, EM, and Meas). The EM shows 20 dB

or better isolation, but EQ and Meas show that isolation is

between 15 and 20 dB. Coupling of 3 dB or better between

port 1 and 3 is evident in Figure 6, irrespective of EQ, EM,

or Meas. The amplitude and phase difference between

through and coupled ports for the EQ, EM simulation and

measurement results are shown in Figure 7. A phase differ-

ence of 90� between through and coupled ports is evident

from this figure. The deviations of experimental results from

the simulated results may be due to the PCB fabrication tol-

erances as well as numerical approximations used in the

simulating packages. The dimensions of the fabricated LC

are width of the fingers is 80 microns, gap between the fin-

gers is 120 microns, and due to the variation in the width

and gap between the fingers, the amplitude imbalance in the

fabricated prototype is higher than the simulated results.

TABLE I Testing Data Obtained from ADS Simulation

155 34 12.25 0.5 0.1 0.3

160 32 11.75 0.5 0.2 0.3

159 32 12 0.5 0.3 0.3

153 31 11.5 0.6 0.1 0.3

145 30 11.5 0.6 0.2 0.3

151 29 11.25 0.6 0.3 0.3

163 29 11.25 0.6 0.4 0.3

147 31 11.25 0.7 0.1 0.3

158 30 11 0.7 0.2 0.3

143 28 11 0.7 0.3 0.3

136 26 11 0.7 0.4 0.3

166 27 10.75 0.7 0.5 0.3

142 30 10.75 0.8 0.1 0.3

153 27 10.25 0.8 0.2 0.3

153 27 10.25 0.8 0.3 0.3

154 26 10.25 0.8 0.4 0.3

171 27 10.25 0.8 0.5 0.3

149 29 10.25 0.9 0.1 0.3

146 28 10 0.9 0.2 0.3

159 27 9.75 0.9 0.3 0.3

164 27 9.75 0.9 0.4 0.3

173 27 10.25 0.9 0.5 0.3

152 33 12.25 0.5 0.1 0.2

148 32 12 0.5 0.2 0.2

151 31 12 0.5 0.3 0.2

148 32 11.75 0.6 0.1 0.2

152 31 11.5 0.6 0.2 0.2

160 30 11.25 0.6 0.3 0.2

163 29 11.25 0.6 0.4 0.2

151 32 11.25 0.7 0.1 0.2

155 30 11 0.7 0.2 0.2

162 28 10.75 0.7 0.3 0.2

166 28 10.75 0.7 0.4 0.2

173 27 10.75 0.7 0.5 0.2

149 30 10.75 0.8 0.1 0.2

154 29 10.5 0.8 0.2 0.2

162 28 10.5 0.8 0.3 0.2

168 28 10.5 0.8 0.4 0.2

174 27 10.5 0.8 0.5 0.2

149 28 10.25 0.9 0.1 0.2

152 28 9.75 0.9 0.2 0.2

152 28 9.75 0.9 0.3 0.2

163 27 9.75 0.9 0.4 0.2

179 27 10 0.9 0.5 0.2

150 33 12 0.5 0.1 0.1

155 32 12 0.5 0.2 0.1

152 31 12 0.5 0.3 0.1

160 30 11.75 0.5 0.4 0.1

147 32 11.75 0.6 0.1 0.1

151 30 11.5 0.6 0.2 0.1

155 30 11.25 0.6 0.3 0.1

158 29 11.25 0.6 0.4 0.1

165 28 11.25 0.6 0.5 0.1

150 30 11.25 0.7 0.1 0.1

147 29 11 0.7 0.2 0.1

161 28 10.75 0.7 0.3 0.1

165 28 10.75 0.7 0.4 0.1

173 27 10.75 0.7 0.5 0.1

152 30 10.75 0.8 0.1 0.1

150 29 10.5 0.8 0.2 0.1

157 29 10.5 0.8 0.3 0.1

157 27 10.5 0.8 0.4 0.1

176 27 10.5 0.8 0.5 0.1

154 30 10.25 0.9 0.1 0.1

159 29 9.75 0.9 0.2 0.1

163 28 9.75 0.9 0.3 0.1

167 28 10 0.9 0.4 0.1

170 27 10 0.9 0.5 0.1

Figure 5 Return Loss and Isolation of the CDOS embedded

LC. [Color figure can be viewed in the online issue, which is

available at wileyonlinelibrary.com.]

Figure 6 Through and coupled port of the CDOS embedded

LC. [Color figure can be viewed in the online issue, which is

available at wileyonlinelibrary.com.]

90 Mishra et al.


VII. CONCLUSION

Usually, metamaterial couplers [36, 37] are fabricated on

thick substrates because they ensure that the dimensions of

the couplers, that is, width of the fingers and gap between

the fingers are within the fabrication limits. For high fre-

quency applications, thick substrates are not mostly avoided.

Many applications require the MIC and MMIC substrate

thickness to be thin. With thin substrate the dimensions of

the coupler diminish making fabrication a difficult task. As

a remedy to this problem, a CDOS is proposed to be em-

bedded in the ground plane of a LC for inductance compen-

sation to increase the coupling. An added advantage with

the proposed structure is the gain in floor space, since the

depth of semicircle and the tails have same orientation.

In the absence of closed form design formulae for

CDOS, a FLANN has been suggested for use. A prototype

has been designed using the FLANN. The measured and

simulated results are closely matching validating the pro-

posed model, and FLANN model. The proposed structure is

compact and finds applications in mixer and balanced ampli-

fiers with relaxed PCB tolerances to obtain tight coupling.

ACKNOWLEDGMENTS

The authors thank the Director, Sameer, Group Head, Circuits

and Systems Division and MIC division for providing facili-

ties for bonding and measurement. Prof. D. R. Poddar also

thanks AICTE (Govt. of India) for awarding him the Emeritus

Professorship under which this work has been done.

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BIOGRAPHIES

Rabindra Kishore Mishra is a pro-

fessor in the Electronic Science Depart-

ment of the Berhampur University.

After obtaining a PhD in microstrip

antenna and arrays on ferrite substrate

from Sambalpur University, he spent 12

years with Berhampur University as a

Lecturer. He then joined Sambalpur

University as the Reader in Electronics. He joined Berhampur

University as a Professor in 2007. He has researched exten-

sively in the areas of planar antennas and applications of soft-

computing techniques to analysis and design of planar anten-

nas. He had visited the University of Birmingham as a British

Commonwealth Fellow during 1999–2000. He has supervised

10 doctoral theses. He has published two monographs and

over 150 learned articles in journals of repute and proceedings

of conferences, seminars etc. These publications have earned

the IETE Sir J. C. Bose best application paper award (1999)

and Shri Hari Ohm Ashram Prerit Hariballabha Das Chunilal

Research Endowment Award (2000), Samanta Chandra

Sekhar Award in Engineering and Technology (2008), which

is the highest award by the Govt. of Orissa. Professor Mishra

is a Senior Member of the IEEE and Life Member of the IETE

and the ISTE. He had chaired a sessions and special session of

many conferences. He had organized short courses related to

applications of Artificial Neural Network in the fields of

Microwave Technology and Antennas. He is a reviewer for

the IEEE Transactions on Antennas and Propagation.

Dipak Ranjan Poddar is a Professor

and Emeritus Fellow in the Depart-

ment of Electronics and Telecommuni-

cation Engineering in Jadavpur Univer-

sity. He has supervised 20 PhD theses.

He has more than 150 publications in

various National/International journals

and conference. He is also currently

the chairman of mm wave committee. He has successfully

carried out a number of scientific projects in various areas in

microwave engineering. He serves as reviewer of IEEE and

other reputed journals. He has chaired several technical ses-

sions in International conferences and symposia. His areas of

research include EMI/EMC, fractal antennas, computational

electromagnetic, microwave metamaterial, and application of

soft computing techniques in engineering. He is a senior

member of IEEE. He is a fellow of IE and IETE.

G. Arun Kumar was born in Hyder-

abad, in 1982. He received M. E.

Tel. E. degree from Jadavpur Univer-

sity. He is currently working toward

the PhD degree in optimization of

Metamaterials. Since 2006, he has

been with SAMEER Kolkata centre

as Scientist, where he has been

involved in the design and development of millimeter

wave nonlinear circuits. His research interests and activ-

ities include simulation, modeling, and measurement of

millimeter wave devices and systems, design optimization

of metamaterials based microwave devices.

D. Mishra is presently working as a

Reader in the department of Electron-

ics and Telecommunications Engineer-

ing, VSS University of Technology,

Burla, Sambalpur, Odisha, India. He

received the BE degree in Electronics

and Communications Engineering

from University of Mysore, India, M.

Tech. degree in Electronics (Microwave Engineering) from

IT, Banaras Hindu University, India and PhD degree from

Jadavpur University, Kolkata. He is the author and coauthor

of 15 papers published in International journals and Confer-

ence Proceedings. He has guided thesis for 10 PG students.

His research area includes Microstrip Antenna, Metamateri-

als and Computational Electromagnetics.

92 Mishra et al.


Documents

Design of lange coupler for MIC and MMIC technology using complementary deformed omega structure