Design and Analysis of a 2.4 GHz, Fifth- Order Chebyshev Microstrip LPF

JOURNAL OF TELECOMMUNICATIONS, VOLUME 21, ISSUE 2, AUGUST 2013

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Design and Analysis of a 2.4 GHz, Fifth-Order Chebyshev Microstrip LPF

Talib Mahmood Ali

AbstractIn this paper, a design of miniature fifth order Chebyshev lowpass filter is presented. The filter consists of Flame

Retardant 4 (FR-4) as a substrate having a thickness of 1.6 mm, loss tangent of 0.027 and relative permittivity of 4.5. The

proposed filter with basic stepped impedance structure, the width and length of low and high characteristic impedance

was calculated based on microstrip analysis. The design was simulated and optimized using CST Microwave Studio. The

best simulated attenuation S11 response was observed at 2.45 GHz with a value of -26.4 dB for 0.01 ripple while the

corresponding Insertion Loss S21 is -0.01dB. The proposed fifth-order filter also has the merits of small circuit area.

Validation of the LPF design was obtained via good agreement between the theoretical analysis and simulation results.

Keywords Microstrip, Chebyshev filter, microwave LPF.

—————————— ——————————

1.Introduction icrowave filters are essential circuits in the wireless communication systems such as wireless LAN and cellular

telephone [1] and they are vital components in a huge variety of other electronic systems[2]. Microwave filters can be divided into two main different types, lumped or distributed. Lumped elements consists of discrete elements, such as inductors and capacitors, while distributed elements uses the lengths and widths of transmission lines to create their inductive or capacitive values. Lumped elements are very small compared to the wavelength, while distributed elements usually are in the order of the wavelength. At high frequencies (10’s of GHz or higher) the wavelength is so short that only distributed elements are possible to practically realize, while at low frequencies lumped elements are used due to the fact that distributed elements becomes too large[3]. There are several divisions in the approach to filter design. A very intuitively satisfying method known as image parameter design was the main approach for many years. In fact, it is still useful and is often included in filter surveys. However, the second division, the insertion loss design method, is simpler to learn

and somewhat more flexible[4].In the insertion

loss method a filter response isdefined by its insertion loss, or power loss ratio, which equal to the power available from the source divided by the power delivered to load PLR.,The insertion loss (IL) in dB is 10 log PLR

)1.(..........)(1

1

load todeliveredPower

source from availablePower

2

load

inc

LR

P

P

P

Observe that this quantity is the reciprocal of

|S12|2 if both load and source are matched. We

know that is an even function of

therefore it can be expressed as a

polynomial in . Thus we can write

)2........()()(

)()(

22

22

NM

M

where M and N are real polynomials in

Substituting this form in (1) gives the

following:

)3.......()(

)(1

2

2

N

MPLR

Thus, for a filter to be physically realizable its

power loss ratio must be of the form in (3).

Notice that specifying the power loss ratio

simultaneously constrains the reflection

coefficient, we now present two practical

filter responses. [5]

M

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Electrical EngineeringDepartment,University o f

Mustansiriyah,Baghdad ,Iraq


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Figure 1. Microstrip geometry and structure.

1.1 Butterworth Filters This filter has the flattest possible pass-band magnitude response. That means all the derivatives of the amplitude with frequency are zero at DC. The Butterworth response is a good compromise between attenuation characteristic and group delay. The group delay of Butterworth filters is reasonably flat but has a rise near the cut off frequency. The step response of these filters exhibits some ringing, which degrades its use for data communications.

1.2 Bessel filter

Due to its linear phase response, this filter has

excellent pulse response (minimal overshoot

and ringing). For a given number of poles, its

magnitude response is not as flat. The Bessel

filter type is very suitable for data

communication systems.

1.3 Chebyshev Filter

The pole positions for the Chebyshev filter lie

on an ellipse, hence the Chebyshev filter is also

called an elliptical filter. The Chebyshev filter

has ripples in the passband and the value of

the ripples is a parameter that is selected as

part of the filter design. Chebyshev filter and

will thus have very poor transient response.

The group delay of the Chebyshev is poor and

these filters should not be used for data

communications or applications where the

group delay is important.Chebyshev Filter

Better rate of attenuation beyond the pass-

band than Butterworth[6]. Chebyshev filters

are more suitable and require less orders than

Butterworth filters do [7], [8].

The selection of the correct filter type is critical to ensure that the filter used satisfies both the transient response requirements and the passband insertion loss and stopband attenuation requirements for the filter. In digital communication applications, the Bit Error Rate (BER) after demodulating is the critical parameter. To reject signals in an adjacent channel intuition suggests the use of a Chebyshev filter. However, computer simulations carried out for a 3rd Generation Mobile Radio system, have shown that the lowest demodulated BER when there is a large unwanted signal in an adjacent channel isobtained with a Bessel type filter response for the Channel filters[9].

2. Stepped-Impedance, Lowpass Filters The stepped-impedance lowpass microstrip filters, which use a cascaded structure of alternating highand low impedance transmission lines. These are much shorter than the associated guidedwavelength, so as to act as semi lumped elements. The high-impedance lines act as series inductors and the low-impedance lines act as shunt capacitors [96].Microstrip consists of a copper track on one side of a printed circuit board, the other side of the board being covered with copper used as a ground plane. The characteristic impedance of such a track commonly 50Ω depends upon the thickness of the board and its permittivity, and the width of the track; the thickness of the copper has only a minor second order effect on the characteristic impedance [10]. The microstrip lines comprise a conducting strip have (width w, thickness t) of conductivity δ, on a substrate of thickness h, relative permittivity εr, on top of an infinite grounded electrode. The strips couples to the ground plane as shown in (figure 1). The characteristic impedance depends mainly upon w/h, [11]

)4.......(12

1

1

2

1

2

1

W

H

rre

)5.....(1for

444.1ln667.0393.1

120

1for 4

8ln

60

H

W

H

W

H

W

W

HZ

H

W

H

Wr

r

o


8

Figure 2. Characteristics impedance of microstrip

line versus w/h and er[11].

Table 1. Normalized Chebyshev element values, 0.5 dB

ripple

0.5 dB ripple

Order g1 g2 g3 g4 g5

5 1.1468 1.3712 1.975 1.3712 1.1468

Table 2Normalized Chebyshev element values, 0.01 dB

ripple

0.01 dB ripple

Order g1 g2 g3 g4 g5

5 0.7563 1.3049 1.5773 1.3049 0.7563

Table 3.The Impedance and frequency scaling of 5th order Chebyshev LPF Filter, 05&0.01 Ripple.

Ripple C1 L2 C3 L4 C5

0.5 dB

2.216 pF

3.994 nH

3.301 pF

3.99 nH

2.216 pF

0.01 dB

0.9827 pF

4.238 nH

2.049 pF

4.238 nH

0.9827 pF

Table 4.The Impedance and frequency scaling of 5th order Chebyshev LPF Filter, 05 and 0.01 ripple.

Z0 Ω T μm W/H H mm W mm e

14 35.56 10.45 1.5 15.680 3.92427

50 35.56 1.85 1.5 2.77 3.33737

106 35.56 0.28 1.5 0.50 2.9788

2.2 Lowpass Prototype Filter and Elements

lowpass prototype filter is in general defined

as the lowpass filter whose element values are

normalized to make the source resistance or

conductance equal to one, denoted by g0 = 1,

and the cutoff angular frequency to be unity,

denoted by wc=1(rad/s) [11].

3. Design procedure of the LPF In general, the design of microstrip lowpass

filters involves the fallowing steps:

Step 1: select an appropriate lowpass

prototype, the choice of the type of response,

including passband ripple and the number of

reactive elements [3], will depend on the

required specifications. The elements value of

5thorder Chebyshev LPF Filter , 05 and 0.01

ripple are shown in table 1 and table (2)

respectively.

Step 2Impedance and frequency scaling. The network needs to be scaled from a source resistance of 1 Ω to R0 The element values of the lowpass prototype filter, which are usually normalized to make a source impedance g0 = 1 Ω and a cutoff frequency wc= 1.0 rad/Sec, are then transformed to the L-C elements for the desired cutoff frequency and the desired source impedance, which is normally 50 Ω for microstrip filters as shown in equations (6) and (7),[12].

Frequency scaling is achieved by using the transformation; wn =w/w0 The Impedance and frequency scaling of 5th order Chebyshev LPF Filter, 05 and 0.01 ripple are shown in table ( 3).

Step 3 design of microstrip lowpass filters is to find an appropriate microstrip realization that approximates the lumped element filter, it is recommended to use a substrate with high permittivity [13]. The typical FR4 PCB with r = 4.5 and H = 1.5mm is used. From Figure 2 the following trace parameters are obtained: e, W, W/H, for high impedance and low impedance 14 Ω and 106 Ω respectively. These values are ablated as shown in table(4).

C =Ln R

2πfc

6

C =Cn

2fcR 7


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Table 6.The length and width of microstrip tracks for 0.01 ripple, Chebyshev LPF Filter.

Section Length (mm) Width (mm)

1 50 2.77124

2 2.0821 15.6796875

3 6.9448 0.50

4 6.7 15.6796875

5 6.9448 0.50

6 2.0821 15.6796875

7 50 2.77124

Table 5.The length and width of microstrip tracks for 0.5 ripple, Chebyshev LPF Filter.

Section Length (mm) Width (mm)

1 50 2.77124

2 4.7 15.6796875

3 6.55 0.50

4 4.3413 15.6796875

5 6.66 0.50

6 4.7 15.6796875

7 50 2.77124

Figure 3. The top view of the layout for the Low Pass Filter on the printed circuit board.

C3

L2

C1

50

line

C5

50

line L4

Determine the microstrip. The equations (4)

&(5) are used to determine the length of

microstrip as shown below:

𝛽ℒ𝒪𝒲 = 𝜀ℒ × 𝜇° × 𝜀° × 2𝜋𝑓𝑐 = 3.9242665 ×

3.3356 × 10−9 × 2𝜋 × 2.45 × 109 =

101.7174548 𝑆−1

𝛽ℋ𝒾ℊ𝒽 = 𝜀ℋ × 𝜇° × 𝜀° × 2𝜋𝑓𝑐

= 2.9788129 × 3.3356

× 10−9 × 2𝜋 × 2.45 × 109

= 88.62199673 𝑆−1

ℓ1 =2𝜋𝔣𝒸 × 𝐶1 × 𝑍ℒ𝒪𝒲

𝛽ℒ𝒪𝒲

=2𝜋 × 2.45 × 109 × 2.216 × 10−12 × 14

101.7174548= 4.6951369 𝓂𝓂

ℓ2 =2𝜋𝔣𝒸 × 𝐿1

𝛽ℋ𝒾ℊ𝒽 × 𝑍ℋ𝒾ℊ𝒽

=2𝜋 × 2.45 × 109 × 3.994 × 10−9

88.62199673 × 106= 6.55 𝓂𝓂

ℓ3 =2𝜋𝔣𝒸 × 𝐶3 × 𝑍ℒ𝒪𝒲

𝛽ℒ𝒪𝒲

=2𝜋 × 2.45 × 109 × 3.301 × 10−12 × 14

101.7174548= 6.994 𝓂𝓂

𝐶1 = 𝐶5 ⟹ ℓ1 =ℓ5 ≅ 4.6951369 𝓂𝓂

𝐿2 = 𝐿4 ⟹ ℓ2 = ℓ3 ≅ 6.55 𝓂𝓂

Repeat calculation for 0.01 dB ripple:

𝐶1 = 𝐶5 ⟹ ℓ1 =ℓ5 ≅ 2.0821 𝓂𝓂

𝐿2 = 𝐿4 ⟹ ℓ2 = ℓ3 ≅ 6.9448 𝓂𝓂

4. Filter Simulation and Results

The electromagnetic simulation software CST Studio was used to simulate the LPF design. Figure 4 detailed the dimensional data of the proposed LPF. A step element (offset)was inserted at the junction between the transmission line sections to make the simulated result more accurate. Figure 5 shows the simulated S11, S12,S21 and S22 results of the proposed Chebyshev Filter LPF, 0.5 ripple, while Figure 4 shows the simulated S11, S12,S21 and S22 results of the proposed Chebyshev Filter LPF, 0.01 ripple. Table (7) illustrates the simulated result at cutoff frequency.


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Table 7.The optimized S-parameters Chebyshev LPF Filter.

Ripple S11 (dB) S12 (dB) S21 (dB) S22 (dB)

0.5 -9.63883 -0.500 -0.500 -9.63883

0.01 -26.437442 -0.00989 -0.00989 -26.43744

5. Conclusion

A compact microstrip fifth-order Chebyshev lowpass filter has been designed, analyzed and, simulated. The optimal design of S-parameters of microstrip filter using a conventional analysis method is a time consuming method therefore, the optimal parameter was obtained by using the CST Studio package to tune and optimize the tracks length and tracks width of the microstrip. The effectiveness of the design has been proven by the results of simulation. The performance is good causing the insertion loss and return loss near with theory. The analysis and design procedures are also presented in this paper. Based on the results that have been obtained from this project, it is proven that the lowpass filter provides better results in term of reducing the size, stopband attenuation and operating frequency. The results carried out after optimizations have shown excellent performance of the propose. For future work it is recommended to design the LPF filter on different substrate with high permittivity with folded line section to reduce the footprint of filter.

REFERENCES

[1] K. C. Lek and K. M. Lum, “Stepped Impedance Key-shaped Resonator for Bandpass and Bandstop Filters Design”, Progress In Electromagnetics Research Symposium Proceedings, KL Malaysia, March 27-30, 2012.

[2] Ian Hunter, “Theory and Design of Microwave

Filters”, The Institution of Engineering and Technology, London, United Kingdom, 2006.

[3] Navita Singh, Dr.Avinash Kumar and Pravesh

Singh, “Low Psss Filter for L- Band Application Using Stepped Impedance Microstrip Lines”, Journal of Engineering Research and Studies JERS/Vol.II/ Issue II/April-June, 2011.

[4] George D. Vendelin, Anthony M. Pavio and Ulrich, “Microwave Circuit Design Using Linear and Nonlinear Techniques”, Second Edition, A John Wiley & Sons, Inc., Publication, 2005.

[5] David M. Pozar, “Microwave Engineering”, John Wiley & Sons, Inc., New York, 1998.

Figure 4. The schematic of LPF using CST Microwave

Design Studio.

Figure 5. The S-parameters Chebyshev, 0.01 ripple LPF.

Figure 6. The S-parameters Chebyshev, 0.5 ripple LPF

filter


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[6] C. J. Kikkert, “RF Electronics” Chapter 7: RF Filters. through AWR Corp, 2009

[7] S. D’Amico, M. Conta, and A. Baschirotto, “A 4.1 mW 79 dB-DR 4th-order source-follower-based continuous-time filter for WLAN receivers,” in IEEE ISSCC Dig. Tech. Papers, Feb. 2006, pp. 352–353.

[8] Shouhei Kousai, Mototsugu Hamada, Rui Ito,

and Tetsuro Itakura, “A 19.7 MHz, fifth-Order Active-RC Chebyshev LPF for Draft IEEE802.11n With Automatic Quality-Factor Tuning Scheme”, IEEE Journal OF Solid-State Circuit, VOL. 42, NO. 11, November 2007,PP. 2326.

[9] Jia-Sheng Hong, M. J. Lancaster, “Microstrip Filters for RF/Microwave Applications”, John Wiley & Sons, Inc, PP 109, 2001.

[10] IAN HICKMAN, “Practical Radio-Frequency

Handbook” Fourth edition, Elsevier Ltd, 2007. [11] Guillermk Gonzalez, “Microwave Transistor

Amplifiers Analysis and Design”, Second Edition, Prentice Hall, PP 145, 1997.

[12] Dr. E.H.Fooks, Dr. R.A. Zakarevicius,

“Microwave Engineering Using Microstrip Circuits”, Prentice Hall, PP 209,1990

[13] S. V. AL-DIN MAKKI, A. AHMADI, S.

MAJIDIFAR, H. SARIRI, Z. RAHMANI, “Sharp Response Microstrip LPF using Folded Stepped Impedance Open Stubs” RADIOENGINEERING, VOL. 22, NO. 1, APRIL 2013, pp. 328.

Design and Analysis of a 2.4 GHz, Fifth- Order Chebyshev Microstrip LPF

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