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TUNABLE IMPEDANCE TRANSFORMERUSING MULTICONDUCTOR COUPLEDLINES

Jinho Jeong,1 Junghyun Kim,2 and Sanggeun Jeon31 Department of Electronic Engineering, Sogang University, Seoul,Korea; Corresponding author: jjeong@sogang.ac.kr2 School of Electrical Engineering and Computer Science, HanyangUniversity, Ansan, Korea3 School of Electrical Engineering, Korea University, Seoul, Korea

Received 19 June 2011

ABSTRACT: A new tunable impedance transformer is presented usingmulticonductor coupled line of quarter-wave length. The switches are

connected at the ends of the conductor lines in the coupled line, andthey are used to adjust the equivalent capacitance of the line. It leads tothe variation of characteristic impedance of the quarter-wave long line,

resulting in the tunable impedance transformer. The measurementaround 1.9 GHz shows that the characteristic impedance of the

transformer using five-conductor coupled line can be adjusted from 29.5to 56.5 X. VC 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett

54:851–853, 2012; View this article online at wileyonlinelibrary.com.

DOI 10.1002/mop.26690

Key words: coupled line; impedance transformer; microwave;transmission line

1. INTRODUCTION

Impedance transformer is an essential component in microwave

circuits. A quarter-wave long transmission line is one of the

widely used impedance transformers, transforming the load im-

pedance ZL to Z02/ZL, where Z0 is the characteristic impedance of

the line [1]. However, the use of the quarter-wave long imped-

ance transformer is limited to a fixed ratio of impedance transfor-

mation. The tunable impedance transformer can control this ratio,

and thus it can be effectively used to optimize the efficiency of

RF power amplifiers [2] and match the antenna impedance [3].

Several researches have been performed to develop tunable im-

pedance transformers. In Ref. 4, tunable capacitors or varactors

are used in the lumped LC impedance transformer, providing

wide range of impedance transformation with compact size. Dis-

tributed elements are also used in the design of tunable imped-

ance transformer which consists of several quarter-wave long

lines with different characteristic impedances and switches [5].

In this work, a multiconductor coupled line is utilized to

design tunable impedance transformer. Figure 1(a) illustrates the

proposed impedance transformer consisting of quarter-wave long

three-conductor coupled line and switches S1 and S2. The P1

and P2 is input and output port of the impedance transformer,

respectively. The equivalent capacitance per unit length of the

line can be adjusted by turning on and off the switches, which

leads to the variation of the characteristic impedance. It allows

three different characteristic impedances of which values are

well controlled, as there are no analog variable elements such as

varactors. The number of the available characteristic impedances

can be easily increased by using more number of conductor

lines as shown in Figure 1(c) where five-conductor coupled line

Figure 1 (a) Proposed tunable impedance transformer using three-

conductor coupled line. (b) Self and mutual capacitances per unit length

of uniform three-conductor coupled line (cross-sectional view of micro-

strip coupled line). (c) Impedance transformer using five-conductor

coupled line

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 4, April 2012 851

is used to give six different characteristic impedances depending

on the switch on–off states.

2. PROPOSED TUNABLE IMPEDANCE TRANSFORMER

To verify the proposed concept, the three-conductor coupled

line is analyzed according to the on–off condition of switches S1and S2. For the simplicity of analysis, the uniform coupled line

is assumed with identical width and spacing. The self and mu-

tual capacitances per unit length, Cii and Cij, are indicated in

Figure 1(b). The total equivalent capacitance per unit length of

the transmission line between ports P1 and P2 can be varied

depending on the on–off state of the switches. Three states are

considered in the analysis: case A where both S1 and S2 are off,

case B where one of S1 and S2 is on, and case C where both S1and S2 are on.

By applying the equations of coupled lines in Ref. 6 to Fig-

ure 1(b), we can obtain the relations between the currents and

voltages at the ends of each conductor as Iia ¼ jP3

k¼1 YikVkb,

Iib ¼ jP3

k¼1 YikVka, where Yik are admittances, or Y11 ¼ vp(2C12 þ C11), Y12 ¼ Y21 ¼ Y13 ¼ Y31 ¼ �vpC12 (from symme-

try), Y22 ¼ Y33 ¼ vp (C12 þ C22), and Y23 ¼ Y32 ¼ 0 (coupling

between nonadjacent conductors is ignored). A vp is a phase ve-

locity. The capacitance per unit length of the uniform coupled

line satisfies the relation, C11 � C22 � C12 // C22 [6]. Solving

these equations in each case, we can derive the total equivalent

capacitance to ground per unit length as follows: Ceq ¼ 2C22 �C11 for case A, Ceq ¼ C11 þ C12 for case B, and Ceq ¼ C11 þ2C12 for case C. This result demonstrates that the equivalent ca-

pacitance can be adjusted by the switches. In other words, the

switches can tune the characteristic impedance of quarter-wave

long line, accomplishing the function of tunable impedance

transformer.

The number of conductors in the coupled line can be

increased to improve the range of impedance transformation and

obtain more various characteristic impedances. The nonadjacent

conductors do not have much effect on the equivalent capaci-

tance due to weak coupling. In this work, five conductors are

arranged as shown in Figure 1(c) in order to increase the cou-

pling effect and obtain more distinct value of characteristic im-

pedance. It provides six different characteristic impedances

depending on the switch conditions: case A where every switch

is off, case B where only one of S1 and S3 is on, case C where

S1 and S3 are on with S2 off, case D where only S2 is on, case E

where one of S1 and S3 is on with S2 on, and case F where ev-

ery switch is on.

3. MEASUREMENT RESULTS

Based on the analysis of the coupled lines, quarter-wave long

tunable impedance transformers consisting of three and five con-

ductors were designed at a frequency of 1.9 GHz. Full-wave

electromagnetic analysis using method of moment was per-

formed to determine the exact dimension of the coupled lines.

Figure 2 Photograph of three-conductor impedance transformer.

[Color figure can be viewed in the online issue, which is available at

wileyonlinelibrary.com]

Figure 3 Input return loss of the impedance transformer using three-

conductor coupled line: (a) case A (both S1 and S2 are off), (b) case B

(one of S1 and S2 is on) and (c) case C (both S1 and S2 are on). Real

resistor means the resistor with parasitic inductance and capacitance.

[Color figure can be viewed in the online issue, which is available at

wileyonlinelibrary.com]

852 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 4, April 2012 DOI 10.1002/mop

They were fabricated on a 30-mil thick Teflon substrate with

dielectric constant of 4.5. For three-conductor impedance trans-

former, the width and spacing of conductors were 1.0 and 0.07

mm, respectively. The length was 21.8 mm. The dimension of

five-conductor impedance transformer is as follows: width ¼0.4, spacing ¼ 0.07, and length ¼ 21.8 mm. To verify the pro-

posed idea, the real switches were not implemented in the fabri-

cation, since they introduces the parasitic effects. To remove the

parasitic effects, on switches were realized by via hole ground.

(Full-wave analysis was performed including the effect of via

holes.)

For the one-port measurement, the fabricated impedance

transformers were terminated with a resistive load RT as shown

in Figure 2. Figure 2 illustrates the input return loss measure-

ment of the impedance transformer in case C (both S1 and S2are on). The termination resistance RT in each case was deter-

mined to provide the best input return loss at a design fre-

quency. Figure 3(a)–3(c) shows the measured input return loss

of three-conductor impedance transformer terminated with RT ¼62 X in case A, RT ¼ 39 X in case B, and RT ¼ 33 X in case

C. As shown in this figure, the measured input return loss was

good enough at the design frequency in every case. The real

chip resistors used in the fabrication have parasitic inductance

and capacitance, which degrade the input return loss and shift

the center frequency. The simulated input return losses of the

transformer terminated with ideal and real resistors are also

included in the figure. The real resistor in the simulation implies

that the model of the chip resistor provided by the manufacturer

was used for the simulation. The simulation results demonstrate

that the frequency shift in the measurement is due to the para-

sitic effect of the real resistors. The values of RT used in the

measurement are slightly different from the ones in the simula-

tion, since the precise values are not available from the discrete

chip resistors. From this measurement, the characteristic imped-

ance of the line was extracted from the formularffiffiffiffiffiffiffiffiffiffiRTZ0

p, where

Z0 ¼ 50 X as follows: 55.7, 44.2, and 40.6 X for case A, B, and

C, respectively.

The same procedure was taken for five-conductor impedance

transformer. The estimated characteristic impedance was 56.5 Xin case A, 46.8 X in case B, 40.2 X in case C, 37.2 X in case

D, 33.0 X in case E, and 29.5 X in case F, respectively. There-

fore, the five-conductor impedance transformer provides the

wider range and more number of characteristic impedances com-

pared with the three-conductor one. Figure 4 shows the meas-

ured and simulated performance of three-conductor and five-

conductor impedance transformers. The measured values of

characteristic impedances depending on the switch conditions

agree wells with the simulated ones.

4. CONCLUSIONS

In this letter, tunable impedance transformer was presented

using multiconductor coupled lines and switches. The analysis

proves that its characteristic impedance can be controlled by

turning on and off the switches. The measurement showed that

the five-conductor quarter-wave long coupled line allowed high

ratio of characteristic impedance variation, or 56.5/29.5 ¼ 1.9.

The performance such as the range of impedance transformation

can be further improved by using more conductors in the

coupled line and optimizing the spacing and width. The pro-

posed tunable impedance transformer can be effectively used for

the design of various tunable microwave circuits.

ACKNOWLEDGMENTS

This work was supported by the Korea Research Foundation Grant

funded by the Korean Government (MOEHRD, Basic Research

Promotion Fund) (KRF-2008-331-D00439). This work was also

supported by the Sogang University Research Grant of 2010.

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VC 2012 Wiley Periodicals, Inc.

Figure 4 Simulated and measured characteristic impedances of quar-

ter-wave long impedance transformer. (a) Three-conductor coupled line.

(b) Five-conductor coupled line. [Color figure can be viewed in the

online issue, which is available at wileyonlinelibrary.com]

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 4, April 2012 853