Improved Performance of Radial Elliptical Low Pass Filter for ISM Band Tanushree and Anjini Kumar Tiwary Department of Electronics and Communication Engineering, Birla Institute of Technology, Mesra, Ranchi, Jharkhand, India tanu_bcet@yahoo.com, aktiwary@bitmesra.ac.in

Abstract: A novel elliptic function low pass filter (LPF) with a wide rejection bandwidth and a sharp roll-off skirt characteristic using microstrip radial stub (RS) is proposed. The proposed LPF is investigated based on a proper ideal lumped equivalent model circuit. An elliptic function sixth order LPF of dimension 0.505 λg × 0.217 λg (where λg is the guided wavelength at the cutoff frequency) is fabricated and tested for performance conformation. The fabricated LPF with 3 dB cutoff frequency of 2.4 GHz demonstrate an excellent out-of-band performance with more than 10 dB rejection from 3 GHz to 15 GHz. The measured results demonstrate good agreement between design, simulation and measurement.

I. INTRODUCTION Low pass filters (LPFs) are widely used in military RADAR receiver systems and modern wireless communication systems to suppress unwanted signals such as harmonics and spurious signals. A good LPF is needed to suppress the mixed frequency elements and leakages of radio frequency and local oscillator frequency from the mixer. LPFs are commonly used to feed direct current bias to active components. Wide stopband and sharp attenuation in the stopband are important for LPF to improve the linearity and signal over noise ratio especially in the high data rate and wideband communication systems. Numerous methods are reported in the literature for the improvement in the performance of a planar microwave LPF. Conventional LPFs, such as stepped impedance, open-stub and semi-lumped element filters, can only provide gradual cutoff frequency response and have narrow stopband [1]. By increasing the number of sections of the LPF, the rejection characteristic can be improved. However, increasing the number of sections will increase the physical dimension of the filter. Several techniques for the LPF designs have been reported to cope with this problem. Compact LPFs [2-6] are reported in the literature by using several techniques e.g. using spiral compact microstrip resonant cells (SCMRCs), diamond-shaped resonator and closed loop stepped impedance (CLSI), U-shape resonators and electromagnetic band gap ground plane etc. A compact elliptic function LPF with ultra wide band [7] is introduced by combining in cascade a microstrip stepped impedance resonator using interdigital capacitor and an admittance inverter. A compact elliptic function LPF [8] using microstrip stepped impedance hairpin resonators and their equivalent circuit models are developed. A novel elliptic function LPF [9-10] is presented, which consists of a dumb-bell-shaped defected ground structure (DB-DGS), a spiral-shaped defected ground structure (SP-DGS) and a broadened microstrip line. An elliptic function low pass microstrip filter are designed with defected ground structures to achieve wide stop band [11]. A novel application of shunt open-stubs at the feed points of a center fed coupled line [12] hairpin resonator is presented for the design of compact LPF with very wide stopband. An elliptic response stepped impedance LPF with a sharp bandpass and reduced size is designed which is based on the use of the double-sided MIC technology [13]. A novel slit-loaded tapered compact microstrip resonator cell is proposed to design a class of elliptic function compact low pass filter with sharp skirt characteristics [14]. A novel transmission line configuration is proposed to design a LPF with sharp cutoff frequency response and wide rejection bandwidth and is realised by cascading

microstrip coupled line hairpin unit, semi circle defected ground structures and semi circle stepped impedance shunt stubs [15]. In this paper, a new compact LPF is designed based on the concept of radial stub (RS). A RS provides excellent roll-off, ultra wide stopband and compact size simultaneously. The RS is in common use in both hybrid and monolithic structures. When very low impedance levels are required, the behaviour of the conventional stub degrades as a result of the excitation of the higher order modes. The RS on the contrary provides a low impedance level at a well specified insertion point in a wide frequency band [16]. Here, in this paper, the design of a sixth order elliptic function LPF for cutoff frequency fc of 2.4 GHz is described. The method is based on introduction of radial stubs in suitable positions in the structure. The proposed filter provides a wide stopband. The passband insertion loss is below 0.2 dB upto 2 GHz.

II. DESING OF WIDE STOPBAND ELLIPTIC LOW PASS FILTERE A conventional sixth order elliptical LPF shown in Figure 1 is designed having a cutoff frequency fc of 2.4 GHz. It is needed to find L-C element values of passive elements shown in Figure 1. The element values for this elliptic function low pass prototype filter with passband ripple LAr = 0.1 dB, minimum stopband attenuation LAs = 43 dB and normalized frequency Ws

= 1.1580 are [1] g0 =g7=1.0000, g1=0.7751=gL1, g2=1.1631=gL2, ,2 20.2870 Cg g= = 3 31.2832 Lg g= = , 4 41.0565 Lg g= = ,

,4 40.5315 Cg g= = ,

5 51.1809 Lg g= = , 6 61.0293 Cg g= = . The L-C element values,which is scaled to Z0 and fC,

can be determined as given in [1]. 1

2i O LiC

L Z gfp

= (1)

1 12i Ci

C O

C gf Zp

= (2)

Calculated element values are given in Table I.

Table I: L-C Element values of desired design. L1 L2 L3 C2 L5 L4 C6 C4

2.5700 nH 3.9565 nH 4.2547 nH 0.3806 pF 3.9155 nH 3.5031 nH 1.3652 pF 0.7049 pF

Fig. 1: Elliptical function lumped element LPF

Since, lumped element equivalent of a radial stub (RS) is the series combination of an inductor and a capacitor. Replacing the series combination of inductor and capacitor as shown by dotted lines in Fig. 1 by RS. These RS are used to generate two finite frequency attenuation poles at 3.2 GHz and 4.15 GHz respectively.

14 4

1 3.202pf GHz

L Cp= = 2

2 2

1 4.152pf GHz

L Cp= =

The role of RS is that it introduces an attenuation pole in the frequency in which it is designed and provides a wide stopband. The inductance L and capacitance C of the RS can be mathematically [17] represented as

120 2.8 10 i

o

rhr

Lc

p

q

æ ö-ç ÷

è ø= (3)

2

240o effr

Chc

q ep

= (4)

here, c is the speed of light, ℰ eff is the effective permittivity, θ is the angle of the RS, ro is the outer radius of the RS and ri (≈ ro/10) is the inner radius of the RS. Based on the calculated values of inductance and capacitance, the dimensions of the radial stub are obtained by using equations 3 and 4 and are as follows

2 9.34Or mm= 2 53q =

4 11.70Or mm= 4 58q = The Rogers RO 5880 with the dielectric constant of ℰ r = 2.2 and a thickness of h=1.57 mm is chosen as the microstrip substrate to realize the LPF. For the design of high impedance and low impedance line Z0L = 140 Ω and Z0C = 20 Ω are taken. Design Equation (5 & 6) can be used to find physical lengths of high and low impedance lines [1] with respect to the desired element values.

( ) 1sin 2

2gL C i

Li COL

f Ll fZ

lp

p- æ ö

= ç ÷è ø

(5)

( ) ( )1sin 22

gC CCi C OC i

fl f Z C

lp

p-= (6)

Table II lists all relevant microstrip design parameters calculated using the microstrip design equations.

Table II: Microstrip design parameters of desired elliptic low pass filter.

1 4.27Ll mm= 2 6.53Ll mm=

3 7.25Ll mm=

2 1.61Cl mm=

5 6.63Ll mm=

4 5.89Ll mm=

6 5.96Cl mm=

4 3.01Cl mm=

λgC (fc)=88 mm λgL (fc) = 95.7 mm

Since, some unwanted reactance/susceptance arises at the junction of the microstrip line elements. So, correction in the line length equations (lL5 and lC6) is done using [1] equations 7 and 8.

( ) ( )5 6

522 sin tanL C

C OL OCgL C gC C

l lf L Z Zf f

p pp

l l

æ ö æ ö= +ç ÷ ç ÷ç ÷ ç ÷

è ø è ø (7)

( ) ( )6 5

621 12 sin tanC L

COC gC C OL gL C

l lf CZ f Z f

p pp

l l

æ ö æ ö= +ç ÷ ç ÷ç ÷ ç ÷

è ø è ø (8)

The corrected lengths are lL5 = 6.16 mm and lC6 = 5.49 mm. The sixth order elliptic low pass lumped filter is shown in Fig. 1.

III. MICROSTRIP STRUCTURES The microstrip equivalent of Fig. 1 is shown in Fig. 2. All the design and simulation procedures are carried out using Ansoft HFSS software.

Fig. 2. Conventional elliptical LPF (CE-LPF)

The simulated result of the conventional elliptical LPF using HFSS and ADS software are shown in Fig. 3 and 4 respectively. The simulated results of Fig. 3 and 4 shows that the 3 dB cutoff frequency is at 2.83/2.70 GHz and two attenuation poles are observed at frequencies 3.71/3.2 and 4.81/4.15 GHz respectively. The stopband gets disturbed at a frequency of 8.81 GHz due to its harmonics.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

-50

-40

-30

-20

-10

0

S 11 ,

S 21 (d

B)

Freq (GHz)

S11

S21

Fig. 3. Simulated frequency response of CE- LPF Fig. 4. Simulation result of the Lumped equivalent of LPF

In order to shift the 3 dB cutoff frequency from 2.83 to 2.4 GHz, inductances L1 and L5 should be increased by shifting two RS towards each other by keeping the total inductive length L as constant. RS 2 is shifted right by 2.23 mm and RS 4 is shifted left by 2.12 mm, as shown in Fig. 5 and its simulated result is shown in Fig. 6. The simulated result of the

conventional structure and the Modified conventional elliptical LPF (MCE-LPF) shows a cut off frequency of 2.4 GHz with harmonics at 9 GHz in out-of-band.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

-60

-50

-40

-30

-20

-10

0

S 11 ,

S 21 (d

B)

Freq (GHz)

S11

S21

Fig. 5. Modified conventional elliptical LPF Fig. 6. Simulated frequency response of MCE-LPF

Incorporation of any radial stub in the conventional elliptical filter can change the cutoff frequency, if it is placed other than the position marked by either A or B in Fig. 2 and is shown in Fig.7. The reason behind the proper positioning of radial stub is that the inductance values of L1 and L5 should not be lesser than the values of the conventional LPF. A radial stub RS 7 having dimension ro = 4.37 mm and angle = 20° is chosen to suppress the harmonic in MCE-LPF and is placed at position B of Fig. 2. This radial stub RS 7 improves the harmonic at the cost of peak generated at 6.91 GHz. So, further studies are carried out, as shown in Table III, to improve the out-of-band rejection by designing the radial stub RS 7 at different frequencies. Table 1 shows that when inductance of the additional radial stub is increased , the S21 peak decreases (in magnitude). Keeping inductance constant and then on increasing the capacitance, the S21 peak increases (in magnitude). Finally, a radial stub (RS 7) is designed for 8 GHz whose radius is ro7 = 4.97 mm and angle = 40°, as shown in Fig. 7. A higher value of angle for RS 7 is not chosen so as to keep the design a bit simple and spacious. The simulated result in Fig. 8 shows that two peaks occur at frequencies 10.55 and 13.11 GHz which disturbs the rejection bandwidth. So, in order to widen the stopband, another radial stub (RS 8) is designed for 12.5 GHz with radius ro8 = 3.18 mm and angle = 90° and is placed at position A shown in Fig. 9.

Table III. Parametric study of RS 7 Freq (in GHz)

Angle (in deg)

Radius (in mm)

S21 peak (in dB)

At Freq (in GHz)

Lrad (in nH)

Crad (in pF)

9.1 20 4.37 -10.12 6.91 10.1736 0.0301 9.1 40 4.37 -11.24 6.41 5.0868 0.0601

8.8 40 4.52 -10.43 6.31 5.0868 0.0643 8.6 40 4.63 -13.24 6.31 5.0868 0.0673 8.4 40 4.74 -13.98 6.21 5.0868 0.0706 8.2 40 4.85 -12.74 6.21 5.0868 0.0741 8.0 40 4.97 -14.63 6.11 5.0868 0.0778

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

-50

-40

-30

-20

-10

0

S 11 ,

S 21 (d

B)

Freq (GHz)

S11

S21

Fig. 7. Single radial loaded LPF (SRL-LPF) Fig. 8. Simulated frequency response

of SRL-LPF

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

-60

-50

-40

-30

-20

-10

0

S 11 ,

S 21 (d

B)

Freq (GHz)

S11

S21

Fig. 9. Double radial loaded LPF (DRL-LPF) Fig. 10. Simulated frequency response

of DRL-LPF The simulated result in Fig. 10 of DRL-LPF shows an acceptable return loss and the insertion loss approaching to -15 dB. The structure is having 3 dB cutoff frequency at 2.44 GHz. The lumped equivalent circuit of the structure is shown in Fig. 11.

Fig. 11. Lumped equivalent circuit of DRL-LPF

An improved performance is observed when the 50 Ω output line is offered an offset of 2.42 mm while optimizing from -5.58 to 5.58 mm offset and is shown in Fig.12. For an offset s = 2.42 mm, cutoff frequency of 2.4 GHz is observed with 20 dB rejection bandwidth ranging from 3.6 GHz to 15 GHz i.e. 11.4 GHz and minimum attenuation 2 dB as shown in Fig. 14. The size of the proposed low pass filter structure, as shown in Fig. 12, is 46.17 x 19.81 mm2.

Fig. 12. Proposed low pass filter

The proposed LPF is fabricated and is shown in Fig. 13. The proposed LPF is measured using PNA series Vector Network Analyzer. The Measured result and the simulated result are shown in Fig. 14. The measured result of the fabricated radial elliptical low pass filter is having a cutoff frequency of 2.35 GHz, stopband rejection in the range of 3 to 15 GHz with more than 10 dB rejection. Although the simulation result shows 20 dB rejection for 3.6 GHz to 15 GHz, some discrepancies in the experimental results may be attributed to the manufacturing tolerances and the variation in material characteristics of the sample supplied.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

-50

-40

-30

-20

-10

0S 11

, S 21

(dB)

Freq (GHz)

sim S11

sim S21

exp S11

exp S21

Fig. 13. Fabricated proposed LPF Fig. 14. Simulated and experimental results of the proposed filter Also, the fabricated structure is tested by inverting the port connections. Fig. 15 shows the comparison between the two measured results with normal connection of ports and with inverted ports. It is observed that the 3 dB cutoff frequency is same for both configurations. The stopband does not show any significant difference.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15-50

-40

-30

-20

-10

0

S 11 ,

S 21 (d

B)

Freq (GHz)

exp LPF S11

exp LPF S21

exp inv LPF S11

exp inv LPF S21

Fig. 15. Experimental results of the proposed filter with normal port connection and with

inverted port connection

IV. CONCLUSION A new radial elliptical LPF is designed for cutoff frequency of 2.4 GHz, i.e., ISM band. The stopband rejection can be tuned by the use of radial stubs. The filter size (area) is constant throughout the paper. The performance of the filter is almost similar for normal connection of ports and with inverted ports. Measured results are in good agreement with the simulated results.

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