Analysis and design of microstrip to balanced stripline transitions

RUZHDI SEFA1, ARIANIT MARAJ

2

1Faculty of Electrical and Computer Engineering, University of Prishtina - Prishtina

2 Faculty of Software Design, Public University of Prizren - Prizren

1&2REPUBLIC OF KOSOVA

ruzhdi.sefa@uni-pr.edu, arianitmaraj@yahoo.com Abstract - A design method for microstrip to balanced stripline transition is presented. The transition is

suitable for application in feeding arrays of double-side printed antennas. The transition is a Chebyshev

taper impedance transformer and the conversion from unbalanced to balanced line relied on a gradual

change of the cross-section of the line. The transmission parameters of an asymmetric line are derived

with a method based on the quasi-TEM wave approximation. Also, in this paper are presented calculated

results for 50 microstrip to 100 balanced stripline and 100 microstrip to 50 balanced stripline

transitions.

Keywords- Microstrip, Balanced stripline, Transformer, TEM mode

1 Introduction Printed dipole radiators have been popular

candidates for phased-array antennas that

contain many elements because of their

suitability for integration with microwave

integrated circuit modules [1]–[3]. Arrays of

double-sided printed strip dipoles fed with

corporate networks of parallel striplines and

backed by conductor planes were developed for

radar and various military applications [4].

Various antenna structures of double-sided

printed strip dipoles connected through balanced

striplines having dual-band and broadband

properties have been reported [5]. These

structures are suitable for low-cost base station

antennas, because they have simple

configuration and can be easily manufactured.

To feed a double-sided printed strip antenna

from a conventional coaxial connector, however,

a transition from unbalanced line to a balanced

line must be used to keep the antenna in a

balanced state. The transition performs

conversion of electromagnetic fields and can be

used as impedance transformer. Moreover, the

transition must be capable of operating over a

large frequency range to be compatible with the

antenna performance.

Impedance transformation and matching are

required in general microwave networks and

antenna arrays to obtain maximum power

transfer between the source and load. In

addition, power often has to be divided between

different network elements. At high

frequencies, these common functions are usually

performed with distributed elements consisting

of sections of transmission lines. The most

commonly used quarter-wave impedance

transformer is shown in Fig. 1. A resistive load

of impedance LZ can to be matched to a network

with input impedance inZ by using a quarter-

wave section of transmission line with

impedance Linc ZZZ . The impedance is

perfectly matched only at the frequency at which

the electrical length of the matching section is

.4/L

Figure 1. Quarter wave transformer

The bandwidth provided by a quarter-wave

transformer may be adequate in many

applications, but there are also situations in

which a much greater bandwidth must be

provided. The bandwidth can be increased by

using cascaded quarter wave transformers [6] as

shown in Fig. 2. Each quarter wave section has

the same electrical length, and by a proper

choice of their characteristic impedances a

variety of pass-band characteristics can be

obtained [7]. The most commonly used multi-

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ISBN: 978-1-61804-005-3 137

section transformers are those with maximally

flat (binominal transformer) and equal-ripple

(Chebyshev transformer) reflection coefficient

characteristics. A typical plot of reflection

coefficient of a two-section quarter-wave

Chebyshev transformer as a function of is

shown in Fig. 2(b).

(a)

(b)

Figure 2(a) Multi-section quarter wave

transformer and (b) Input reflection coefficient

of a two-section quarter wave Chebyshev

transformer

Cascaded quarter-wave impedance

transformers of more than two sections are not

practical due to length constrains. Instead, a

transmission line which has the characteristic

impedance that varies continuously along its

length can be used as a broadband impedance

transformer. The broadband impedance

matching properties of the transformer are

obtained by utilizing a continuous transmission

line taper as shown in Fig. 3(a) with its

characteristic impedance changing smoothly

from LZ to inZ . If the variation of characteristic

impedance along the taper )(xZ is known, the

reflection coefficient can be easily calculated by

considering the taper to be made of a number of

short transmission line sections. Exponential

taper and taper with triangular distribution are

two examples of practical designs [7]. A more

important problem is to determine )(xZ to give

an input reflection coefficient with desired

frequency characteristics. An example of

practical importance is a taper that has its

characteristic impedance tapered along its

length. So that the input reflection coefficient

follows a Chebyshev response in the pass band.

The taper has equal-ripple minor lobes and is an

optimum design as it has the shortest length for a

given minor lobe amplitude.

Figure 3 Tapered transmission line

This paper presents a methodology to design

microstrip to balanced stripline (printed twin-

line) tapered transitions, and use them to

construct feed networks for arrays of double-

sided strip dipoles. The transition is

accomplished by narrowing the width of the

ground plane of microstrip line in tapered

fashion. The cross-section of the microstrip

conductor is then varied to obtain the required

impedance across the taper length. A quasi-TEM

method is used to calculate the transmission

characteristics of an asymmetric and in-

homogenous line. Conductor widths of various

printed microstrip to balanced stripline transition

are calculated and their characteristic impedance

and effective dielectric constant across the

length are presented.

2 Microstrip to balanced stripline

transition A microstrip to balanced stripline transition is

shown in Fig. 4. The transition is performed by

gradually changing the cross-section of the line

from microstrip (unbalance) at the input to the

strips of equal width (balanced) at the output. A

smooth change in cross-section of the line, such

as tapered line, is required so that the net

reflection at the input is arbitrary small [8]. The

transition itself together with the conversion of

electromagnetic field may be used to perform

the transformation of impedance. We use this

important advantage to design practically

convenient double-sided feed networks. These

networks consist of tapered line transitions and

cooperate feed network of balanced striplines.

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ISBN: 978-1-61804-005-3 138

Figure 4. Configuration of a microstrip to

balanced stripline transition.

We design tapered lines such that the input

reflection coefficient follows a Chebyshev

response in the pass band. To synthesize the

impedance taper, the parameters of an

asymmetric transmission line are derived by

using the rectangular boundary division method

[9]. The appropriate dimensions of cross-section

at each position along the taper are found by

assuming that the required taper impedance is

equal to the balanced mode characteristic

impedance of a uniform asymmetric line of that

particular cross-section.

3 Characterization Method A microstrip to balanced stripline transition is

designed as an impedance matching section,

which requires a synthesis procedure to

determine the line profile from the given

impedance profile. The tapered impedance

profile is selected so that the input reflection

coefficient follows a Chebyshev response in the

pass band. However, the tapered line shown in

Fig. 4 is an in-homogeneous line which supports

a non-TEM mode with the propagation constant

varying along its length. This makes the design

procedure very involved. As an approximation,

we start with the impedance profile of a TEM

Chebyshev taper, which can be obtained by

using the standard procedure [6], for given mZ ,

bZ , and desired ripple level. Such an impedance

profile will produce the same reflection

coefficient expressed in terms of electrical

length for any line structures. After the taper

profile is determined, the propagation constant

along the taper profile can be found and be

included in the calculation of the reflection

coefficient. The reflection coefficient obtained

in this way will be an approximation but close to

the starting reflection coefficient. The length of

the taper is determined by the lowest operating

frequency and the maximum reflection

coefficient which is to occur in the pass band.

The shape ratio, hw /1 and , at any position

x along the taper is determined by assuming

that the characteristic impedance of the taper at

that cross-section is equal to the characteristic

impedance of a uniform asymmetric line shown

in Fig. 5. The transmission characteristics of the

asymmetrical line are determined under the

quasi-TEM wave approximation, where the

problem is attributed to the calculation of the

line capacitance. The line capacitance for a

given structure is calculated by utilizing the

rectangular boundary division method [9]. The

structure to be analyzed is placed in a metallic

enclosure for the convenience of analysis, but

the dimensions of the enclosure are chosen large

enough such as the propagation characteristics

of the line are not significantly affected. The

presence of the metallic enclosure enables the

propagation of two fundamental modes (out-of-

phase and in-phase modes). The computation of

a taper performance based on the mode analysis,

however, showed that that spikes on the

reflection coefficient due to the excitation of in-

phase mode appear. In the case of an open

structure, the in-phase mode cannot be defined.

So, a different definition for the propagating

mode based on the balanced condition is used in

calculation.

For a two conductor system of fig. 5, a linear

system of equations can be written as:

2121111 VCVCQ (1a)

2221212 VCVCQ (1b)

where 1Q , 2Q denote the line charge per unit

length and 1V , 2V the line potential of each strip

conductor. The balanced condition is defined as

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ISBN: 978-1-61804-005-3 139

21 QQQ and 21 VVV (2)

Figure 5. Cross-section view of an asymmetrical

transmission line

Substituting Eq. (2) into Eq. (1) and rearranging,

the balanced mode capacitance is obtained as

122211

2122211

2CCC

CCC

V

QCb

(3)

The capacitance values 11C , 22C , and 12C are

obtained from three stationary values of

electrostatic energy corresponding to three

combinations of potentials on conductors and

the energy-capacitance relation give by

j

i j

iij VVCU

2

1

2

12

1 (4)

The balanced characteristic impedance and

effective permittivity are given as

00

1

bb

cCCv

Z (5)

0b

beff

C

C (6)

Where 0bC denotes the balanced mode

capacitance in y=the case where the dielectric

substrate in the structure is replaced by vacuum

and 0v denotes the phase velocity in vacuum.

Two parameters have to be determined from the

knowledge of the characteristic impedance at a

particular cross-section. This leads to a non-

unique solution. However, a profile that

changes smoothly along the taper must be

selected as to gradually perform the conversion

of the electromagnetic field. This is essentially

achieved by a tapered bottom conductor, the

parameters of which may be calculated knowing

the desired impedances of the microstrip and

balanced ends, namely mw2 and bw2 . Here, we

adopt a profile for the bottom conductor,

)/(2 Lxw , which can be expressed as

b

mu

mw

w

L

xwLxw

2

222 lnexp)/( (7)

The profile of the top conductor is then chosen

to achieve the Chebyshev impedance taper

between two impedances. The parameter u in

Eq. (7) is selected such that the obtained top

conductor profile changes smoothly along the

taper. Calculation experience showed that a

value between 2 and 3 will give satisfactory

results.

4 Calculated results The described characterization method was used

to find conductor width profiles of microstrip to

balanced stripline tapered transitions printed on

a substrate of height mmh 8.0 , relative

dielectric constant 2.2r , and conductor

thickness mmt 035.0 . The goal was to design

50 to 100 tapered transitions with reflection

coefficients lower than dB40 over the UMTS

frequency band of .17.2~71.1 GHzGHz Assuming

that the transition would have an average

effective dielectric constant of 2 along the taper

and the lowest operation frequency is GHz6.1 ,

the length of transition was found to be

mmL 90 . For calculation purposes, the

transition was considered as a number of short

transmission lines with uniform cross-sections.

First, the conductor profiles along a 50

microstrip to 100 tapered transition were

determined. For the given substrate, the

conductor widths on the microstrip and balanced

stripline ends were found as mmw 4.21 ,

mmw 0.242 and mmww 2.121 , respectively.

The lower conductor tapered profile was

determined by using equation (7). The width of

upper conductor was then determined such as

the characteristic impedance along transition is

similar to that of Chebyshev impedance taper.

The calculated conductor widths along this

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ISBN: 978-1-61804-005-3 140

transition are shown in Fig. 6(a). Variations of

characteristic impedance and effective dielectric

constant along the transition are shown in Fig.

6(b). Although this is an in-homogenous

transition with variable effective dielectric

constant, the response of input reflection

coefficient is similar to that of a typical

Chebyshev filter as shown in Fig 6(c).

(a)

(b)

(c)

Figure 6 (a) Profile of a 50 microstrip to

100 balanced stripline transition, (b)

Calculated characteristic impedance and

effective permittivity along the taper, (c)

Calculated input reflection coefficient

Next, the conductor profiles along a 100

microstrip to 50 tapered transition were

determined. For the given substrate, the

conductor widths on the microstrip and balanced

stripline ends were found as mmw 66.01 ,

mmw 0.202 and mmww 08.321 ,

respectively. The conductor widths of this

transition were calculated following the same

procedure and are shown in Fig. 7(a).

Variations of characteristic impedance and

effective dielectric constant along the transition

are shown in Fig. 7(b), and the input reflection

coefficient in Fig. 7(c). Again, the calculated

input reflection coefficient resembles that of a

Chebyshev taper.

(a)

(b)

(c)

Figure 7 (a) Profile of 100 microstrip to 50

balanced stripline transition. (b) Calculated

characteristic impedance and effective

permittivity along the taper. (c) Calculated input

reflection coefficient.

5 Conclusion A method to design microstrip to balanced

stripline tapered transitions was presented. Such

transitions are required when feeding balanced

antennas from unbalanced coaxial cables. The

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ISBN: 978-1-61804-005-3 141

transitions were also used as impedance

transformers to design feed networks that can be

used in arrays of double-sided printed strip

dipoles. The geometry of transition was selected

to provide a Chebyshev taper response as this

taper is characterized with smooth variations of

characteristic impedance along the taper that is

suitable for electromagnetic field conversion and

nearly perfect impedance matching over wide

frequency bandwidths. The transition was

accomplished by narrowing the width of the

ground plane of microstrip line in tapered

fashion.

A quasi-TEM method was used to

characterize asymmetric and in-homogenous

transmission lines encountered in design of

microstrip to balanced stripline transitions.

Calculated results for 50 microstrip to 100

balanced stripline and 100 microstrip to 50

balanced stripline tapered transition were

presented and their input reflection coefficients

shown to be similar to that of a TEM Chebyshev

taper.

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1993.

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Schaubert, “Analysis of infinite arrays of printed

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ground plane,” IEEE Trans. Antennas

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[6] Ruzhdi Sefa, Alida Shatri Maraj, Arianit

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conference, ID: 649-290, 2011

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ISBN: 978-1-61804-005-3 142