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Design and Optimization of Microstrip Hairpin-Line Bandpass Filter using DOE Methodology

Tanvi Singh, Jesseena Chacko, Neha Sebastian, Roshni Thoppilan, Ashwini Kotrashetti and Sudhakar Mande

Department of Electronics and Telecommunication Engineering Don Bosco Institute of Technology

Mumbai, India

AbstractThis paper proposes a novel methodology for the optimization of Hairpin-Line bandpass filter. The proposed methodology is based on well-known Plackett-Burman Design of Experiment technique. First, a five section hairpin resonator is designed to operate at a center frequency of 2.4GHz with a bandwidth of 300MHz using Genesys software. Plackett-Burman Design of Experiment methodology is then applied to this filter for further optimization. Implementation of proposed approach shows 61% improvement in return loss and 15% improvement in insertion loss of the filter as compared to the filter designed using Genesys software.

Keywords-bandpass filter; hairpin resonator; Plackett-Burman

I. INTRODUCTION The use of microstrip in the design of microwave

components and integrated circuits has gained tremendous popularity in the last few decades because microstrip can operate in a wide range of frequencies. Microstrip is a good candidate for filter design due to its advantages of low cost, compact size, light weight, planar structure and easy integration with other components on a single circuit board [1].

Microstrip band pass filters are essential high frequency components in microwave communication systems. Modern systems require microstrip bandpass filters with improved performance for out-of-band and in-band responses, reduced size, high rejection and low insertion loss [1]. Bandpass filters are used as frequency selective devices in many RF and microwave applications. A design of a microstrip hairpin bandpass filter with centre frequency of 2.4GHz is proposed in this paper. This frequency is useful for wireless LAN application and operates in the ISM band (Industrial, Scientific and Medical). The contribution of this paper is to provide a design of hairpin-line bandpass filter using DOE Methodologies and to discuss its characteristics as they pertain to filter implementation. In section II we discuss the microstrip filter design methodology, followed by the simulation technique and result in section III. In section IV we present the optimization using DOE following which section V depicts the testing of PCB.

II. DESIGN METHODOLOGY

A. Design Equations To design a coupled band pass filter a low pass filter

prototype is selected. For better rejection a five order filter is selected. The designed topology is converted into bandpass using standard transformation equations [2]. Further lumped sections are converted into distributed elements using Richard's transformation and Kurodas criteria. The required coupling co-efficient is found using the equation (1) [3]:

K= flfh

f0 (1)

For basic conventional bandpass filter design, J-inverter concept is used to convert from low-pass filter to bandpass filter after obtaining the low pass prototype element values. Inverters have the ability to shift impedance or admittance levels depending on the choice of K or J parameters. Making use of these inverters enables us to convert a filter circuit to an equivalent form that would be more convenient for implementation with microwave structures [4]. The inverter constants are found using equations (2) (3) & (4):

ZoJ1 =K2g1 (2)

ZoJn = K2gn1gn (3)

ZoJn+1 = K2gngn+1 (4)

where g1,g2,g3.....gn are coefficients of Chebyshev filter design and J1,Jn,Jn+1 are the characteristic admittances of J-inverters and Zo is the characteristic impedance of the terminating lines [4]. From the obtained results the even and odd impedances can be found using equations (5) & (6):

Z0e = Zo[1+JZo (JZo)2] (5)

Z0o = Zo[1+JZo (JZo)2] (6)

2012 International Conference on Communication, Information & Computing Technology (ICCICT), Oct. 19-20, Mumbai, India

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To maintain the compact dimensions of the filter a hairpin line structure is adopted [4]. They are conceptually obtained by folding the resonators of parallel-coupled, half-wavelength resonator filters into a U shape [5]. This type of U shape resonator is the called hairpin resonator which is as shown in Fig.1. The coupling between the resonator sections in the hairpin topology is mainly inductive [2]. The external quality factor is computed using (7) and (8) and coupling coefficients, which determine the space required between adjacent hairpins, is computed using (9). The external quality factors of the resonators at the input and output are given by Qe1 and Qen as in (7) and (8) [4].

Qe1 = gog1FBW

(7)

Qen = gngn+1FBW

(8)

Mi,i+1 = FBWgi gi+1 (9)

Figure 1. Layout of a Hairpin-Line Bandpass Filter

The filter is designed to have a tapped line input and

output that is configured for characteristic impedance that matches the terminating impedance Zo = 50 ohms. The tapping location is denoted by t (10) as shown in Fig.1. The input and output resonators are slightly shortened to compensate for the effect of the tapping line and the adjacent coupled resonator.

The length of the tapped input of the hairpin filter is given as:

t = 2L

sin-1 2Zo Zr

Qe (10)

In which Zr is the characteristic impedance of the hairpin line, Zo is the terminating impedance, and L is about go/4 long. The characteristic impedances and dimensions of the coupled lines can thus be attained [4].

B. Design Specifications The filter is required to radiate at a centre frequency of

2.4GHz with a bandwidth of 300MHz. The acceptable insertion loss & passband ripple is 1dB and 0.5dB respectively. A fifth order hairpin-line filter is to be implemented on an FR4 substrate having dielectric constant 4.4.

III. SIMULATION The Genesys simulation software is used to simulate the

schematic of the microstrip hairpin filter [6]. The corresponding response is obtained after feeding in the desired specifications. A return loss (S11) of -42.5 dB and an insertion loss (S21) of -2.5dB is obtained at 2.4 GHz. The simulation results are as shown in Fig.2.

Figure 2. Simulated Return loss and Insertion loss Response of Bandpass

Filter

IV. OPTIMIZATION USING PLACKETT-BURMAN DOE Plackett-Burman Design of Experiment (PB-DOE)

methodology is widely used to investigate the impact of input factor on the response of a system with minimum number of experimental runs. For example, to investigate the impact of N input parameters, N+1 experimental runs are required. PB-DOE methodology uses concept of orthogonal arrays in which dot product of any two columns is zero. Table I shows the PB-DOE matrix for 7 factor using 8 runs. P1-P7 indicates input factors while Y indicates response of the system and R1- R8 indicates experimental run. In Table I, + indicates high level value of input factor while indicates low level value of the input factor. In this work, we have taken high value of a factor as +10% of the nominal value and low value as -10% of the nominal value.

List of input factors along with their nominal values are shown in Table II. In order to find the impact of the input parameters on the output response, eight simulation experimental runs are performed as per PB-DOE matrix and the corresponding response is obtained as given in Table III.


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In this work, we have considered insertion loss and return loss as the response parameters.

To find impact of input parameters on the response, Sum of Squares (SS) due to each input parameter is calculated using equations from (11) to (13). Once SS due to each input factor is obtained, then (14) is used to find the effect each input parameter has on the output response that is, return loss and insertion loss.

SSP1 = P1 P12 (11)

P1 = Y1+Y4+Y6+Y74 (12)

P1 = Y2+Y3+Y5+Y84 (13)

% variation due to P1 = SS(P1)

SSP1+SSP2++SS(P7) (14)

TABLE I. PLACKETT-BURMAN DOE ORTHOGONAL MATRIX

Seven parameters were chosen for optimization on observing a desirable effect in the simulated response on varying them by fixed amount as given in Table II.

The effect for a factor is always described as the change in the response in going from the low level of that factor to the high level. A negative sign means that going from low level to high level for a factor decreases the response. A positive sign

means that going from the low level to the high level increases the response.

For the optimization of the designed filter, the factors which affect the filter response the great are selected and the required calculations are performed using the above given formulae as shown for best possible result.

TABLE II. THE PARAMETERS CHOSEN FOR OPTIMIZATION

In Table III, YA and YB mean the following:

YA = Insertion loss YB = Return loss

The chosen parameters are shown on the hairpin layout in Fig.3.

Figure 3. Pictorial Representation of Parameters Chosen

P R

P1 P

2 P

3 P

4 P

5 P

6 P

7 YA YB

R1 + + + - + - - Y1 Y

1

R2 - + + + - + - Y2 Y

2

R3 - - + + + - + Y3 Y

3

R4 + - - + + + - Y4 Y

4

R5 - + - - + + + Y5 Y

5

R6 + - + - - + + Y6 Y

6

R7 + + - + - - + Y7 Y

7

R8 - - - - - - - Y8 Y

8

PARAMETERS NAME

NOTATION

ORIGINALVALUES (mm)

P1 Length of the coupling leg (1st & 4th) LC1 13.679

P2 Length of the coupling leg (2nd & 3rd) LC2 13.501

P3 Tap length 1 LTap1 8.991

P4 Tap length 2 LTap2 1.191

P5 Spacing between the hairpins (1st & 2nd,4th & 5th)

SC1 0.804

P6 Spacing between the hairpins (2nd & 3rd ,3rd & 4th)

SC2 1.382

P7 Spacing between two legs of a hairpin SC3 1.891


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TABLE III. CALCULATED VALUES

Table IV gives the effect of 10% variation of each chosen parameter on the return loss and insertion loss. The variations which produce a desirable effect are retained for the final design.

The optimized values for the new design are:

P1= 13.779mm P2= 13.501mm P3= 8.891mm P4= 1.291mm P5= 0.704mm P6= 1.282mm P7= 1.891mm

The effect each parameter has on the desired response parameter is given in Table IV.

TABLE IV. IMPACT OF VARIOUS PARAMETERS ON INSERTION LOSS AND RETURN LOSS

The designed hairpin-line filter was simulated again by

using Genesys software by replacing the original values of the seven parameters chosen by the new optimized values as given in Table V. for obtaining the best possible results.

The optimized design of the filter provides the following improved values of the return loss and insertion loss as compared to the previously obtained values for the same as observed in the simulated graph Fig.4. Return loss = -61.092 dB Insertion loss = -2.286 dB Centre frequency fC = 2392.5MHz

V. TESTING Both the optimized and the nonoptimized filter designs are

implemented on an FR4 substrate with a relative dielectric constant (r) of 4.4 as shown in Fig.5 and Fig.6.

The variations in the dimensions of the optimized filter as compared to the designed filter are as shown in Table V. The dimensions of the filter are, length= 65mm and width= 23mm, without the patches.

The fabricated filter is tested and measured on a network analyser. The optimized filter response and the Genesys results are compared. The response from the optimized filter is better than the nonoptimized filter response.

The graphs in Fig.7 and Fig.8 show the improvement in return loss and insertion loss of optimized filter compared to the nonoptimized filter. The bandwidth of both the filters are approximately in agreement. Some further tuning needs to be performed to achieve an improved return loss and insertion loss.

P R

P1 P2 P3 P4 P5 P6 P7 YA YB

R1 13.779 13.601 9.091 1.091 0.904 1.282 1.791 2.419 29.716

R2 13.579 13.601 9.091 1.291 0.704 1.482 1.791 2.48 32.552

R3 13.579 13.401 9.091 1.291 0.904 1.282 1.991 2.496 26.698

R4 13.779 13.401 8.891 1.291 0.904 1.482 1.791 2.589 39.913

R5 13.579 13.601 8.891 1.091 0.904 1.482 1.991 2.59 29.091

R6 13.779 13.401 9.091 1.091 0.704 1.482 1.991 2.486 33.491

R7 13.779 13.601 8.891 1.291 0.704 1.282 1.991 2.293 48.071

R8 13.579 13.401 8.891 1.091 0.704 1.282 1.791 2.268 37.576

Impact YA(Insertion loss) YB (Return loss)

Impact of P1 0.513% 23.44%

Impact of P2 0.397% 0.106%

Impact of P3 2.438% 38.07%

Impact of P4 1.103% 11.308%

Impact of P5 39.32% 25.33%

Impact of P6 54.77% 1.785%

Impact of P7 1.4% 0.223%


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TABLE V. COMPARISON BETWEEN THE ORIGINAL AND OPTIMIZED VALUES

Figure 4. Optimized Hairpin Filter Response

Figure 5. Etched Hairpin Microstrip Bandpass Filter

Figure 6. Etched Optimized Hairpin Microstrip Bandpass Filter

The test results are as summarized in Table VI.

TABLE VI. FINAL VALUES

PARAMETERS NAME NOTATION

ORIGINALVALUES

(mm)

OPTIMIZED VALUES

(mm)

P1 Length of the coupling leg (1st & 4th)

LC1 13.679 13.779

P2 Length of the coupling leg (2nd & 3rd)

LC2 13.501 13.501

P3 Tap length 1 LTap1 8.991 8.891

P4 Tap length 2 LTap2 1.191 1.291

P5

Spacing between the hairpins (1st & 2nd,4th & 5th)

SC1 0.804 0.704

P6

Spacing between the hairpins (2nd & 3rd ,3rd & 4th)

SC2 1.382 1.282

P7

Spacing between two legs of a hairpin

SC3 1.891 1.891

TYPE OF FILTER

Return loss ( dB )

Insertion loss ( dB )

Hairpin bandpass filter

-17.61

-1.6

Optimized bandpass hairpin filter

-28.4

-1.35


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Figure 7. Return Loss of Optimized and NonOptimized Microstrip Hairpin

Bandpass Filter

Figure 8. Insertion Loss of Optimized and NonOptimized Microstrip Hairpin

Bandpass Filter

VI. CONCLUSION Two hairpin-line bandpass filters are presented in this

paper; simulated using Genesys simulation software and one of them is optimized by using Plackett-Burman Methodology. Both filters have been successfully designed, simulated, implemented and tested at 2.4GHz frequency with a bandwidth of 300MHz at the desired specifications. A comparison between the optimized and the nonoptimized filter is made with respect to both the simulated and tested results. By the optimization technique, 7 critical parameters of the hairpin design are identified and the effect of each parameter on the insertion loss and return loss of the filter is calculated manually by inserting 10% variation with respect to the original designed value. It is observed that the spacing between each hairpin has significant effect on insertion loss as well as return loss, whereas resonator length and tapping point

has significant effect on return loss only. The dimension values are chosen accordingly and the observed responses have a better insertion loss and return loss with a percentage improvement of 15.62% and 61.27% respectively.

ACKNOWLEGDEMENT We wish to express our gratitude to the management of

Don Bosco Institute Of Technology for providing the necessary resources and facilities.

REFERENCES [1] Thomas M. Weller, Edge-Coupled Coplanar Waveguide Bandpass

Filter Design, IEEE Trans. Microwave Theory and Techniques, vol. 48, NO. 12, Dec. 2000.

[2] Kamaljeet Singh et al., Coupled Microstrip Filters: Simple Methodologies for Improved Characteristics, Communication Systems Group., ISRO Satellite Center, Bangalore, India.

[3] G.L Matthaei, L.Young and E.M.T Jones, Microwave Filters, Impedance-Matching Networks, and Coupling structures, Artech House, Dedham, MA, 1980.

[4] J. S. Hong and M. J. Lancaster, Microstrip Filters for RF/Microwave Applications, New York, John Wiley and Sons, Inc, 2001.

[5] Cristal, E. G. and S. Frankel, Hairpin-line and hybrid hairpin line half-wave parallel-coupled line filters, IEEE Trans. Microwave Theory Tech vol. 20, no. 11, pp. 719 728, 1972.

[6] Pozar, D. M. Microwave Engg. John Wiley, 2000. [7] Joseph S. Wong, Microstrip Tapped Filter Design, IEEE Trans, vol.

MTT-27, No. 1, January 1979, pp. 4450. [8] Agilent Technologies, Inc. information. Available:

http //www.agilent.com [9] M. Abdipour et al., Design and Simulation of Microstrip Bandpass

Filter, presented at the International Conference on Signal, Image Processing and Applications, IACSIT Press, Singapore, 2011.

[10] H. Adam et al., X-band Miniaturized Wideband Bandpass Filter Utilizing Multilayered Microstrip Hair-pin Resonator, Centre of Excellence for Wireless and Photonic Networks, Department of Computer and Communication Systems Engineering, Faculty of Engineering University, Putra Malaysia 43400 UPM Serdang Selangor, Malaysia, 2009


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