A feeding network with chebyshev distribution for designing low sidelobe level antenna arrays

VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 16-21

A Feeding Network with Chebyshev Distribution

for Designing Low Sidelobe Level Antenna Arrays

Tang The Toan¹, Nguyen Minh Tran², Truong Vu Bang Giang^2,*

¹University of Hai Duong

²VNU University of Engineering and Technology, Hanoi, Vietnam

Abstract

This paper proposes a feeding network to gain low sidelobe levels for microstrip linear antenna arrays. The

procedure to design a feeding network using Chebyshev weighting method will be proposed and presented. As

ademonstration, a feeding network for 8×1 elements linear array with Chebyshev distribution weights (preset

sidelobelevel of -25 dB) has been designed. The unequal T-junction power dividers have been applied in

designing the feedingnetwork to guarantee the output powers the same as Chebyshev weights. The obtained

results of the amplitudes ateach output port have been validated with theory data. The phases of output signals

are almost equal at all ports. Thearray factor of simulated excitation coefficients has been given and compared

with that from theory. It is observedthat the sidelobe level can be reduced to -22 dB. The proposed feeding

network, therefore, can be a good candidatefor constructing a low sidelobe level linear antenna arrays.

Received 24 January 2017; Accepted 27 February 2017

Keywords: Feeding network, Chebyshev distribution, Lowsidelobe.

1. Introduction^*

weighting method is the most effective and

efficient one.

In the recent years, microstrip antennas are

commonly used in modern wireless systems

due to possessing a number of advantages such

as light weight, low cost, easy fabrication and

integration into PCB circuits. However, they

still have limitations, among which low gain is

one of these drawbacks. Though this can be

alleviated by combining single patches into

arrays, it will generate high sidelobe level

(SLL) that wastes the energy in undesirable

directions and can be interfered by other

signals. Therefore, designing arrays with low

SLL has always captured a great attention of

designers and researchers. Among several ways

to reduce SLL of the array antenna, amplitude

There are some common amplitude

weighting methods, which are Binomial,

Chebyshev, and Taylor [1]. Of three methods,

Binomial can help eliminate minor lobes and

have no sidelobes, but it is not preferable for

large arrays due to high variations in weights

[2]. Taylor produces a pattern whose inner

minor lobes are maintained at constant level [2].

Whereas Dolph- Tschebyshev (Chebyshev)

array provides optimum beamwidth for a

specified SLL [1, 2]. Among three methods,

Chebyshev arrays can provide better directivity

with lower SLL [3]. These methods are used

mostly in digital beamforming, but occasionally

used directly in antenna design. In microstrip

antenna arrays, the amplitude weight

distributions can be obtained by designing a

_______

^*Corresponding author. E-mail.: [email protected]

https://doi.org/10.25073/2588-1086/vnucsce.157

16

T.T. Toan et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 16-21

17

feeding network that has powers at output ports

proportional to the coefficients of the above

distributions.

distribution in [12, 13]. This array could

provide a low SLL of -22 dB in E-plane, but it

was about -14 dB in H-plane.

In the literature, there are several publications

involved the study and design of feeding network

with amplitude weight tappers. A number of

series feeding networks have been proposed in

[3-9]. The design of feeding network for an

aperture coupled microstrips antenna array with

low sidelobe and backlobe has been studied in [4].

Though the feed designed for 25×1 aperture

linear array can help to acquire low SLL (-20.9

dB), the authors did not mention the distribution

to be used. In [5, 6], two novel feeding networks

were designed for 5×1 elements linear arrays.

Sidelobe suppression (-16 dB in [5], and -20 dB in

[6]) has been given by using Dolph Chebyshev

power distribution. Sidelobe reduction to -20 dB

has also been obtained by using Chebyshev

amplitude weight feeding network in [7]. Several

Chebyshev feeding networks for 8×1 linear

arrays have been presented in [8-10]. However,

those proposals are difficult to fabricate due to the

complex structure of the feed (2-3 layers) that

may cause high fabrication tolerance.

In this work, a feeding network with

Chebyshev distribution (only one layer) for

designing low SLL microstrip antenna arrays

will be proposed. The step by step in design

process will be presented. A Chebyshev feeding

network for a 8×1 linear antenna array with

preset SLL of -25 dB has been designed as a

demonstration of the procedure. In order to get

the output power at each port proportional to

Chebyshev weights, unequal T junction power

dividers have been used. The obtained results

indicate that the amplitude of output signal at

each port is proportional to the coefficient of

the Chebyshev weights. The phases of signals

at each port are also in phase with each other.

The array factor of simulated excitation

coefficients has been given and compared with

that from theory. It is observed that the sidelobe

level can be reduced to -22 dB.

2. Dolph-chebyshev’sdistribution

Corporate feed networks for the

performance of low SLL have also been

introduced in [10-13]. The work in [11]

presented a feed network based on Binomial

weight distribution and Wilkinson power

dividers with circular polarization for vehicular

communications. However, the SLL was only

reduced to -18 dB as the effect of complex

structure of the feed and resistors in Wilkinson

power dividers. A. Wahid has proposed a 8×4

Chebyshev

tapered

distribution,

a

well-known amplitude weight method, can help

to set SLL to a specified value. This work can

be done by mapping the array factor to

Chebyshev polynomial [13]. The array factor

(AF) of a linear array as given in [14] is written

as:

( )

푁−1

푛=0

푁−1

푢_푛푒^{푗훽푑푛cos 휃}

(푧 −

( )

퐴퐹 휃 =

∑

=

푛=0

푒^푗휓^푛)(1)

planar

J

array

with

Dolph-Tchebysheff

Table 1. Chebyshev amplitude weights for 8×1 linear array

with the inter-element spacing = 0.5휆 (SLL = -25 dB)

Element No. (푛)

1

2

3

4

1

5

1

6

7

8

Normalized

amplitude (푢_푛)

0.378 0.584 0.842

0.842 0.584 0.378

Amplitude

distribution (dB)

-11.7 -9.82 -8.32 - 7.49 -7.49 -8.32 -9.82 -11.7

p

T.T. Toan et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 16-21

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where: 푢_푛is amplitude weight excited at

each port, 훽 is the wave number, 푑 is the

element spacing, 휃 is scanning angle, 휓_푛=

훽푑푛cos(휃).

A Chebyshev polynomial 푇_푚(푥) of 푚^푡ℎ

order and an independent variable 푥 is an

orthogonal polynomial and can be represented

by:

푇_푚(푥) =

cos(푚cos⁻¹푥)

−1 ≤ 푥 ≤ 1

|푥| > 1

−1

{

(2)

cosh(푚cosh 푥)

It can be observed that when −1 ≤ 푥 ≤ 1,

Figure 1. Normalized radiation pattern of 8×1 linear

array with SLL suppressed to -25 dB

(element spacing = 0.5휆).

these polynomials oscillate as a cosine function.

However, outside that range, they quickly rise

or decrease as the cosh function. Assuming that

the maximum SLL is 1.0, it will equal to the

height of the ripples of the Chebyshev

polynomial as−1 ≤ 푥 ≤ 1. An 푁 element array

corresponds to a Chebyshev polynomial of

order 푁 − 1. The main lobe of the array factor

can be mapped to the peak value of the

Chebyshev polynomial by the equation below:

3. Feedingnetworkdesign

3.1. T-junction power divider

As the weight coefficients have been

defined, the next step is to design a feeding

network that has amplitude outputs proportional

to the obtained weights. In order to do that,

unequal T-junction dividers have been used in

this work. A typical unequal T-junction power

divider is shown in Figure 2.

푇_푁−1(푥_푚푏) = 10^푠/20

(3)

where: s is the SLL (in dB), 푥_푚푏is the

position of main lobe.

Then, setting (3) equal to (2) results in the

main lobe at:

−1

푠/20

(10

푥_푚푏= cosh [^cosh

⁾] (4)

푁−1

Next, zeros of the polynomial are mapped

to NULLs of the array factor followed by the

equation:

푥_푛= cos[^{휋(푛−0.5)}] = 푥_푚푏cos (^휓₂^푛) (5)

푁−1

Figure 2. An unequal T-junction power divider.

By using the expression 푧_푘= 푒^푗휓푘, the

weights 푢_푘can be found by substituting phases

and 푥_푚푏to the AF. As a demonstration, the

Chebyshev amplitude weights for 8×1 linear

array with preset SLL of -25 dB are calculated

and given in the Table 1. Figure 1 gives the

normalized radiation pattern of 8×1 linear array

with Chebyshev weights (SLL reduced to -25

dB) assuming that isotropic elements are used.

Assuming that the input voltage is 푉₀, and

the transmission line used is lossless, the

relationship between input and output power

will be:

푃_표푢푡= 푃 + 푃₂= 푃

(6)

1

푖푛

where: 푃 = _2푍², 푃 = ², 푃₂= ². The

푉

0

푖푛

1

2푍

2

0

1

relation between two outputs and the input can

be given by:

T.T. Toan et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 16-21

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푃 = 푎푃

푃₂= (1 − 푎)푃

weights of Chebyshev distribution. After that,

the divider, 퐷₂is mirrored at the center of the

divider 퐷₁to get the full feeding network. Each

port has been designed with uniform spacing to

ensure that the output signals are in phase. The

simulation results of this feed will be given

specifically in the next section.

1

푖푛

(7)

0 < 푎 < 1

푖푛

Solving the above equations, the

impedances at each output port of the divider

can be obtained as

푍₁= ^푍

0

푎

(8)

푍

0

푍₂=

1−푎

Therefore, if the output powers are given,

the impedance at each output port of the divider

will be easily determined. In order to facilitate

the simulation and futher division, it is

necessary to transfer the impedance at each

output port back to input impedance. Therefore,

the 휆/4 transformer, which defines the resonant

frequency of the feed, is used to transfer the

impedance (푍₁, 푍₂) to the input impedance,

while maintaining the expected output powers.

4. Simulationresults and discussions

The proposed feeding network has been

simulated in CST Microwave Studio. Some

simulated results have been exported and

compared with the theory. Figure 4 presents the

simulation results of S-parameters of the

feeding network (detailed data are summarized

in Table 1).

3.2. Chebyshevfeeding network

Based on the Chebyshev weights and T-

junction power divider design method, the

feeding network for 8×1 linear array has been

designed on Rogers RT/Duroid 5870tm

substrate (thickness of 1.575 mm and the

permitivity of 2.33) as given in Figure 3.

Figure 4. The simulated S-parameters

of the feeding network.

As can be seen from Figure 4 and Table 1,

the simulated amplitudes obtained at each port

are uniform in pairs (푆₂₁= 푆₉₁= −13.72 dB,

푆₃₁= 푆₈₁= −11.27 dB, 푆₄₁= 푆₇₁= −10.58

dB, and 푆₅₁= 푆₆₁= −9.1 dB), which are

similar to the characteristic of Chebyshev

weights as presented in Table 1. The simulated

amplitudes of output signals have also been

compared to the calculated weights from theory

as shown in Figure 6. It is clear that the

simulated and measured lines are quite uniform.

The discrepancy between two lines is caused by

the losses of the transimission line, which are

not considered in theory.

Figure 3. The proposed Chebyshev

feeding network.

It is observed that the Chebyshev

coefficients are symmetrical at the center.

Therefore, with even number of elements, an

equal T-junction power divider, 퐷₁, has been

designed to ensure that two sides are identical.

The combination of dividers, 퐷₂, is calculated

and designed in order to match the first four

T.T. Toan et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 16-21

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Table 2. Simulated S-parameters of the proposed feeding network at 5.25 GHz

S-parameter

푆₂₁

푆₃₁

푆₄₁푆₅₁푆₆₁푆₇₁푆₈₁푆₉₁

Value (dB) -13.72 -11.27 -10.58 -9.12 -9.12 -10.58 -11.27 -13.72

u

f

Figure 7. Comparison between the normalized

radiation pattern of simulated and theoretical

antenna arrays.

Figure 5. Comparison of amplitude

distribution between simulation (solid line)

and theory (dotted line).

5. Conclusions

In this paper, a Chebyshev distribution

based feeding network for designing low SLL

microstrip antenna arrays has been proposed.

The detailed design procedure and calculation

have been presented. A feeding network for

8×1 linear antenna array with Chebyshev

weigths (preset SLL of -25 dB) has been

designed and simulated as a demonstration. The

results show that the output power at each port

is proportional to the weights generated using

Chebyshev weighting distribution method as

required in Table 1. The phases are also in

phase at all ports. This feeding network can be

used to construct a linear array antenna, which

has sidelobe level suppressed to -22 dB.

In the theory [1], Chebyshev weighting

method only impacts the amplitude but the

phase of the output signals. Therefore, in order

to ensure that the simulated results meet well

with the theory, the phase should be in phase at

all output ports of the feeding network. As can

be seen in Figure 7, the phases at all ports are

equal to each other. The simulated normalized

radiation pattern has been compared to that of

theory as shown in Figure 8. It is clear that the

linear array with simulated excitation

coefficients has the SLL of -22 dB. Therefore,

the proposed feeding network is appropriate to

be combined in the 8×1 linear array to have

SLL preset at -22 dB.

Acknowledgements

This work has been partly supported by

Vietnam National University, Hanoi (VNU),

under project No. QG. 16.27.

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