Compact Microstrip Low-pass Filter with Wide Stop-band Using P-Shaped Resonator

This paper, a compact low-pass filter (LPF) with an Elliptic function response using P-shaped resonators is presented. The LPF with simple structure results in the low insertion loss less than 0.1 dB and high return loss better than 20 dB, in the passband. The proposed filter with a -3 dB cutoff frequency of 2.61 GHz is fabricated and measured. The measured results show that the proposed LPF has significant advantages such as a wide stopband from 2.9 GHz to 17.3 GHz with the suppression level better than -20 dB, and it has an acceptable sharp frequency response in the transition band. The measurement results are in good agreement with the simulation results. Keywords— Low Pass Filter (LPF), Microstrip, P Shaped, Stop-band

stop-band and sharp roll-off.
In this paper, a compact microstrip low-pass filter with a wide stop-band using P-shaped resonators is presented that result in low insertion loss and high return loss in the pass-band.The proposed filter has simple shape and achieves good performance in the stop-band region, pass-band and transition band.

II. FILTER DESIGN
The design process of the proposed filter is as follows: i-Design of an Elliptic function resonator to achieve sharp cutoff response.
ii-Provide an LC model of the proposed P-shaped resonator in order to optimize the resonator.
iii-Design of the proposed filter that include the combination of the proposed resonator with suppressing cells.

A. Design of Elliptic Function Resonator
A prototype Elliptic-function low-pass resonator with desired cutoff frequency is selected, and the values of the circuit's elements are calculated [6], as shown in Figure 1.The characteristic impedances for microstrip lines with width 0.2 and 0.3 and 0.8 mm are 136 Ω and 117 Ω and 74 Ω, respectively.The resonator creates two transmission zeros at 3.3 GHz and 3.9 GHz with corresponding attenuation levels of -55 dB and -54 dB, respectively, where return loss in the pass-band is 30 dB.By increasing the width of W1 from 0.3 mm to 0.7 mm as shown in Figure 4 (a), decreasing d2 from 4 mm to 2 mm as shown in Figure 4 (b) and decreasing R1 from 2.5 mm to 1.5 mm as shown in Figure 4 (c), the transmission zeros move away from the lower frequencies.Therefore, the location of the transmission zeros can be controlled by tuning the values of W1, d2 and R1.
With the increment of d3 from 6mm to 6.5mm with a step of 0.25mm, the attenuation level in the stop-band region is increased from 3.2GHz to 4 GHz.Also, the effect of increment of G1 is similar to the effect of the increment of d3.The effect of variation of d3 and G1 on the frequency response of the resonator is shown in Figure 4(d).But with increment of w2 from 0.2mm to 0.6mm with step of 0.2mm, the attenuation level in the stop-band region is decreased, as shown in Figure 4(e).Therefore, the dimensions of these parameters are optimized using optimization tools in the ADS software, which uses the local gradient optimization process.By considering the open-end radial stubs as a unit, which is shown in Figure 6; the capacitance of the radial stub can be obtained through one port -parameter using ( 1) and ( 2) [7].
)) ( ( 2 where Zin can be calculated as: For the straight stub, the equivalent capacitance can be directly obtained as (3) when the effective electrical length is less than a quarter-wave length [7]: where β, Ls and Zs represent the propagation constant, length of the straight stub and impedance of the straight stub, respectively.The other parameters of the accurate LC model of the proposed resonator are obtained from [6]: where, Li and Ci represent the inductance and capacitance of the transmission line, respectively, Z0 represent source impedance, fc is cutoff frequency and g0 and gi represent either the inductance of a series inductor or the capacitance of a shunt capacitor.
Therefore, in the first step, the LC model of the elliptic function resonator with desired characteristics is designed.The parameters of the LC model of the proposed resonator are obtained from Equations ( 4) and (5).Then after obtaining LC values, in order to improve the accuracy of the response, the LC values are optimized by tuning tool in the ADS software, which uses the local gradient optimization process.The LC value of the proposed LPF is shown in Table .1.
The optimized dimensions of the proposed P-shaped layout are: d1= 10 mm, W1= 0.3 mm, d3 = 6.5 mm, W2= 0.2 mm, W3= 0.8 mm, R1=2.2 mm, G1= 0.7 mm.The physical lengths of the high-and low-impedance lines may be found by [6]: where, l Li and l ci represent the dimension's inductance and capacitance of the transmission line, Z 0 represent source impedance, ωc is cutoff frequency, λ gL and λ gc represent guided wavelengths (mm) for inductance and capacitance, respectively.

C. Design of the Proposed Filter
To reach wide stop-band with good suppression of the harmonics in the stop-band region, a multiple resonator with different dimensions is used.In first step, two P-shaped units are added to the proposed resonator, as shown in Figure 7 (a).As shown in Figure 7(c), by increasing d3 from 6mm to 10mm, the transmission zeros are moved to the lower frequency (with considering the proposed LC model in Figure 5, by increasing d3, the capacitance of Cr and inductance of L3 are increased) .When w3 is decreased from 0.8mm to 0.2mm as shown in Figure 7(d), the transmission zeroes are moved to the lower frequency (with considering the proposed LC model in Figure 5, by decreasing w3, the inductance of L3 is increased).The proposed structure does not have wide stop-band.To obtain a LPF with better stop bandwidth and attenuation level, third resonator is added to the structure of Figure 7(a).Each of P-shaped units adds a transmission zero, at about 11 GHz that can guarantee the harmonics rejection in higher frequencies than 9 GHz, as shown in Figure 8.The layout of the proposed LPF consists of six P-shaped units, as illustrated in Figure 9    As shown in Figure 9(c), when w4 is decreased from 0.8mm to 0.2mm, the transmission zeroes are moved to the lower frequency.Therefore, the location of transmission zeros in the stop-band can be easily controlled by the variation of dimensions of the proposed filter parameters.

III. MEASUREMENTS AND RESULTS
The proposed LPF has been fabricated on a RT/Duroid 5880 substrate with a relative dielectric constant εr = 2.2, thickness h = 20 mil and loss tangent of 0.0009.The photograph of the fabricated filter is shown in Figure 10.The Simulations and measurements are performed using ADS software and HP 8757A network analyzer, respectively.The simulated and measured results are shown in Figure 11.A metallic cover is normally required for most microstrip circuit applications, such as filters.The presence of conducting top and side walls will affect both the characteristic impedance and the effective dielectric constant.In practice, a rule of thumb may be applied in the filter design to reduce the effect of cover: the height up to the cover should be more than 8 times and the distance to walls more than 5 times the substrate thickness.For more accurate design, the effect of cover, including the housing loss, can be taken into account by using full-wave EM simulation [6].The filter has a -3 dB cutoff frequency equal to 2.61 GHz and insertion loss less than 0.1dB in the pass-band from DC to 2 GHz.The return loss is better than 21 dB in the pass-band.The insertion loss has the suppression level better than -20 dB from 2.9 up to 17.3 GHz that obtains a wide stop-band.
The return loss in the stop-band region is very close to 0 dB.The size of the LPF is only 22×10 mm 2 .
Table 2 summarizes the performance of some other works.In this Table : The roll off rate ζ is used to evaluate the roll off sharpness where a higher ζ represents a sharper roll off, which is defined as below [8]: where αmax is the -20 dB attenuation point; αmin is the -3 dB attenuation point; fs is the -20 dB stop-band frequency; and fc is the -3 dB cutoff frequency.The Relative stop-band bandwidth (RSB) is given by [8][9], where a higher RSB represents a wider stop-band region: The suppression factor (SF) is based on the stop-band suppression.A higher suppression degree in the stop-band leads to a greater SF.For instance, if the stop-band bandwidth is calculated under -20 dB restriction, then the SF is considered as 2. The normalized circuit size (NCS) is given by [8], which a lower NCS represents a smaller circuit size:  (10) This is applied to measure the degree of miniaturization of diverse filters, where λg is the guided wavelength at -3 dB cutoff frequency.The architecture factor (AF) can be recognized as the circuit complexity factor, which is signed as 1 when the design is 2D and as 2 when the design is 3D.Finally, the figure of merit (FOM) is defined as below [8] and with the above discussion a higher FOM represents a better high-performance LPF:

Fig. 1 .
Fig. 1.The LC model of prototype Elliptic function low-pass resonator To realize the Elliptic resonator, a P-shaped microstrip layout is proposed, as shown in Figure 2. In this layout, to realize the Elliptic function LC circuit, the high impedance lines with width of W1 and W2 are equivalent to inductance and the semicircle open-stubs are equivalent to capacitor.The coupling capacitance, between the semicircle open-end stubs, is ignored in this realization because the gap distance is large.

Fig. 2 .
Fig. 2. The proposed resonatorThe S-parameters of the P-shaped resonator are compared with the LC equivalent circuit frequency response, as shown in Figure3.It can be seen clearly that the cutoff frequency of the proposed resonator is adjusted to 2.6 GHz with an Elliptic response.

Fig. 3 .
Fig. 3.The frequency response of the prototype filter

Fig. 4 .Fig. 5 .
Fig. 4. (a) The S12 parameter of the proposed resonator as a function of W1 (b) The S12 parameter of the proposed resonator as a function of d2 (c) The S12 parameter of the Proposed resonator as a function of R1 (d) The S12 parameter of the proposed resonator as a function ofd3 and G1 (e) The S12 parameter of the proposed resonator as a function of W2

Figure 7 (
b) shows that the resonator 2 creates TZ3 and TZ4 in the stop-band region.On the other hand the stop bandwidth with -17dB attenuation level up to 9 GHz is created.

Fig. 8 .
Fig. 8.The effect of adding a new P-shaped unit to the proposed cascaded P-shaped resonator.

Fig. 9 .
Fig. 9. (a) The proposed filter (b) The S12 parameter of the proposed filter (c) The S12 parameter of the proposed resonator as a function of w4.

Fig. 11 .
Fig. 11.The measured and simulated S-parameters of the fabricated LPF.

TABLE I .
LC VALUES OF THE PROPOSED FILTER.

TABLE II .
PERFORMANCE COMPARISON WITH OTHER WORKS.
As seen from the table, the proposed LPF exhibits highest figure of merit (6988) among the other