A Design of a Compact Microwave Diplexer in Microstrip Technology Based on Bandpass Filters Using Stepped Impedance Resonator

Abstract

This paper describes the design of a compact microstrip microwave diplexer based on bandpass filters and a stepped impedance resonator for 4G applications. The diplexer is composed of two band-pass filters (BPF) that operate at 1.8 and 2.5 GHz. Both bandpass filters for the receiver at 1.705-1.895 GHZ and the transmitter at 2.41-2.6 GHZ have a -3dB fractional bandwidth of 10.5 % and 7.6 % respectively. These BPF, suitable for 4G telecommunications, are examined, evaluated, developed, and simulated, yielding theoretically consistent results. With a dielectric permittivity of 4.4 and a thickness of 1.6 mm, FR-4 is employed as a substrate material. The theoretical design and simulation are used to calculate the size and position of the SIR and feed lines. The diplexer has a low insertion loss and a high isolation, and its efficiency is quantitatively analyzed using the HFSS software. This application allows us to swiftly and simply create electrodynamic structures. A diplexer prototype was developed using a typical method of fabricating PCBs, with a structural area of (47.4020x247.063=11711.28 mm²). The obtained simulation results of the proposed circuit are in good agreement with the measurements.

Index Terms
Band-pass filter; Diplexer; High-pass filter; Low-pass filter; Stepped impedance resonators

I. INTRODUCTION

In recent years, new mobile applications that perform bandwidth-intensive activities have emerged in the digital world. Indeed, scientific and technical developments in this field have aided the amazing expansion of wireless communication systems and applications. In this regard, the optimization and utilization of these applications need a large increase in bandwidth. Multiservice and multistandard wireless communication systems are appealing alternatives for maximizing bandwidth utilization. Indeed, the employment of the duplexing feature, which permits two-way communication through a transceiver, is required for the development of a multiservice system.

Many communication systems rely on microwave filters and diplexers for channel selection and signal separation, and the electrical output of these devices is critical to the overall design of the device. Filters must simultaneously have a low insertion loss, a high return loss, and high slope selectivity. Also, these filters should be tiny, cheap, mass-producible, and tune-free. Only a handful of the many possible filter topologies that fulfill one or more of the aforementioned characteristics are appropriate for low-cost mass manufacture.

This could be accomplished by employing two unique bandwidths for transmission and reception, as well as two highly selective filters to differentiate the transmission and reception signals. One filter is centered on the transmission band, while the other is centered on the receive band. Significant transmission signal leakage desensitizes the receiving direction due to the diplexer limited isolation. As a result, the design of this type of circuit is not simple, and it is critical to achieving a diplexer with high isolation and low insertion loss to ensure the system proper operation. Each diplexer combines two filters, with one port connected to the transmitter, another to the receiver, and the third port is used to connect the two filters and the antenna. There are several approaches to designing RF diplexers, but three are the most common:

1. The application of two bandpass filters with dissimilar center frequencies.

2. The use of a bandpass filter on one channel and a notch filter on the other channel to reject the same frequency band.

3. Through the use of two notch filters with distinct center frequencies.

Generally, filters can be developed and manufactured using either distributed or lumped component processes, depending on the application. The implementation of these filters with lumped components,

i. e. inductors and capacitors, at frequencies beyond 500 MHz or 1GHz is extremely difficult since their diameters tend to be equivalent to the signal wavelength, resulting in disseminated effects on the signal. The latter is more efficient than distributed components, which are composed of transmission line segments that are transformation equivalents of the proper inductance and capacitance values. Several methods exist in the literature for converting lumped low-pass and high-pass filters to their equivalent distributed filters. The distribution filter topology may be achieved through the use of a microstrip stub implementation in which the Richard transform is employed to replace the lumped components with transmission lines. Lumped elements make it possible to change a low pass filter into a high-pass filter with the same cutoff point as long as the capacitors and inductors are swapped with each other. The open-circuit and short-circuit transmission lines may be simply interchanged. However, building a series capacitor is more difficult. Also, an open-circuit transmission line may simply be substituted for a short- circuit transmission line, and vice versa. However, constructing a series capacitor is more complicated. One way is to cut the line very short (a few micrometers to a few tens of micrometers), however this presents modeling and implementation challenges that might be overcome using the impedance inversion technique adopted in this paper. Therefore, many aspects influence this technical option, including the desired frequency response, the complexity of the circuit, its size and cost, handling capacity, insertion losses, and isolation. This work is based on planar technology because of its low cost, compact size, and integration capacity. Numerous microstrip diplexers have been proposed in the literature [¹]-[³], [³]-[¹⁰], as well as a variety of methods for increasing electrical efficiency, including (HTS, SAW/BAW, SIW...). In addition, stepped impedance resonators (SIR) are frequently used because they allow control of the spurious response, insertion losses, and resonator size.

This paper investigates the design of a compact microwave diplexer in microstrip technology that is based on bandpass filters using the stepped impedance resonator. This filter can operate at up to 4 GHz, and the diplexer frequency bands will be determined by practical considerations. A practical implementation is achievable, but the issue will be in increasing the frequency and adjusting the selectivity, which will be heavily dependent on manufacturing precision. The purpose of this work is to improve the performance of diplexers in terms of insertion losses and frequency band selectivity by choosing an appropriate dielectric. Before its realization for that we used the FR-4 substrate which has the possibility of use in the range of frequency going from 1 to 4 GHz for the design of our diplexer [¹¹], the diplexer was developed theoretically then modeled and optimized by the HFSS simulation software. To validate our results, measurements were carried out on a vector network analyzer. The diplexer, which may be used for 4G telecommunications reception and transmission, is based on bandpass filters in microstrip technology with the stepped impedance technique:

-A band-pass filter at 1.8 GHz center frequency.

-A band-pass filter at 2.5 GHz center frequency.

The remainder of this paper is summarized as follows. Section 2 provides a quick overview of the employed tools. The suggested approach is described in Section 3. Section 4 summarizes the results, and finally a conclusion is drawn in Section 5.

II. BACKGROUND

A. Quarter-Wave Coupling

A quarter-wave wavelength propagation line can reverse impedance. The placement of the capacitor in series on the mainline microstrip being technologically not possible to achieve, the idea would be to reverse their impedances through two-quarters of waves to the terminals which are placed the parallel inductor (as illustrated in Fig. 1)

Fig. 1
Series capacitor made using a quarter wave line.

the Impedance Z̅_e view has the entry of a line quarter wave of characteristic impedance Z₀ completed by a load impedance Z̅_L is written ${\overline{Z}}_e=\frac{Z_0^2}{Z_L}$ with Z₀=50Ω

The impedance of the capacitor as shown in (1):

(1) $$Z_C=\frac{1}{jC\omega }$$

The impedance of the inductor as shown in (2):

(2) $$Z_L=j\omega L$$

It simply establishes the expression of the capacitor as shown in (3):

(3) $$Z_C=\frac{1}{jC\omega }=\frac{Z_0^2}{jL\omega }\Rightarrow C=\frac{L}{Z_0^2}$$

B. Richard’s transformation

The Richards transformation has been introduced to replace localized elements by short-circuit or open-circuit transmission lines. From transmission lines, low-value passive components such as capacitors and inductors can be realized, provided that the length of the line synthesizing them is of length $l<\frac{\text{λ}}{10}$. A lossless line segment of length l. with characteristic impedance Z₀ terminated by an impedance Z_l has an input impedance as shown in (4) :

(4) $$Z\left(l\right)=Z_0\frac{Z_l+j{Z}_{0}tan\beta l}{Z_0+j{Z}_{l}tan\beta l}$$

Where Z_l is the load impedance and β is the phase constant. If the end of the transmission line is an open-circuit i.e. Z(l) = ∞; then the input impedance of the transmission line can be re-written as shown in (5):

(5) $$Z\left(l\right)=Z_0\frac{1+j\frac{Z_0}{Z_{\mathrm{l}}}tan\beta l}{\frac{Z_0}{Z_{\mathrm{l}}}+jtan\beta l}$$

As Z(l) → ∞ and $\frac{Z_0}{Z_t}\to 0$

Then as shown in (6):

(6) $$Z\left(l\right)=Z_0\frac{1+j\left(0\right)tan\beta l}{\left(0\right)+jtan\beta l}=\frac{Z_0}{jtan\beta l}=-j{Z}_0\cot \beta l$$

Therefore, this line behaves as a value capacitor as shown in (7):

(7) $$\frac{Z_0}{jtan\beta l}=-j{Z}_0\cot \beta l=\frac{-j}{\omega C}$$

$\cot \beta l=\frac{1}{Z_0\omega C}\leftrightarrow tan\beta l=Z_0\omega C$

The value capacitor as shown in (8)

(8) $$C=\frac{tan\beta l}{Z_0\omega }$$

with Z₀ = Z_0C=25 Ω

As a result, a capacitor can be implemented by an open circuit line or a line with a low characteristic impedance Z₀ with respect to the load Z_l.

When a line is terminated in a short circuit. Z_l = 0; then the input impedance of the transmission line can be re-written as shown in (9): As Z(l) → 0

(9) $$Z\left(l\right)=j{Z}_{0}tan\beta l=j\omega L$$

Then this line behaves like an inductor of value as shown in (10) :

(10) $$L=\frac{Z_{0}tan\beta l}{\omega }$$

with Z₀ = Z_0L=90 Ω.

Hence, an inductor can be realized by a short circuit (cc) or Z₀≥Z_l.

III. PROPOSED METHOD

A. Bandpass filter design of center frequency 1.8 GHz using a stepped impedance resonator (SIR):

In modern wireless communication systems, microstrip filters play a critical role in achieving the desired frequency spectrum passage and in rejecting undesired ones. We may develop lowpass, high pass, bandpass, or band-reject filters subject to communication device requirements. bandpass filters are used extensively in microwave systems and antenna design. A bandpass filter has the purpose of passing a band of frequency components concerning their specified lower and higher cutoff frequencies. Microstrip filters can be designed and analyzed using high-frequency software. The design approach depends on their application. Firstly, the filter can be realized for study in lumped components. Due to the impossibility of this approach, we should adapt the design to distributed equivalent circuits to resolve this issue. A variety of techniques are available in the literature for designing and producing microstrip bandpass filters due to their compactness and ease of manufacture. These microstrip filters work well at frequencies ranging from a few MHz to 10 GHz. The filters can be developed using normal low-pass design procedures and subsequently modified to bandpass equivalent circuits to ease the design methodology, or with the combination of two low-pass and high-pass filters. Different structures such as short stubs, open stubs, step impedance resonators, and ring resonators may be included to implement the filter in a microstrip transmission line arrangement. Using these techniques has improved the performance of designed filters and makes them suitable for various applications such as microwave systems, wireless communication systems, antennas, etc. The receiver microstrip band-pass filter (BPF) will be investigated, assessed, built, and simulated utilizing a stepped impedance resonator operating at 1.8 GHz with a 3-dB fractional bandwidth of 10.5 %. The BPF is suitable for 4G telecommunications reception with low frequency at 1.705GHz and high frequency at 1.895GHz. The architecture employs cascaded High Pass structures (HPF) and low pass filters (LPF). The stepped-impedance, 3rd order LPF is used to attenuate the upper stopband, and the stepped-impedance, 3rd order HPF is used to reach the lower stopband. The results of the planned BPF are theoretically consistent. The substrate has a relative dielectric constant ε_r = 4.4 and a substrate thickness h =1.6 mm. The filter configuration has a characteristic impedance of a microstrip line of Z_C = 50Ω, a copper line thickness of T = 0.035 mm, and a loss tangent tan δ =0.02.

A1. Lowpass filter design at frequency 1.895 GHz using a stepped impedance resonator (SIR).

Low pass filters are primarily designed in two stages:

1. The first step is to choose a suitable low pass prototype. The response type, including passband ripple, and the number of reactive elements (filter order) will be determined by the needed parameters. The element values of the low pass prototype filters, which are typically normalized to produce a source impedance g0=1 and a cutoff frequency Ωc = 1, are then changed to the L-C elements with the desired cutoff frequency and source impedance, which is typically 50 ohms for microstrip filters.

2. The next critical step in designing microstrip low pass filters is to select a microstrip realization that closely approximates the lumped element filter. The element values for the low pass prototype with the maximally flat response at L_AR=3.01dB passband ripple factor. The characteristic source/load impedance Z₀=50 is derived from the normalized values gi, i.e. g1, g2, g3, g4 gn. Using the element transformation [¹²], [¹³], the filter is expected to be constructed on a substrate with a dielectric constant of ε_r = 4.4 and a thickness of h=1.6 mm for an angular (normalized) cutoff frequency of Ωc = 1.

The designed lowpass filter, with maximally flat response, has the following specifications:

Maximally flat response.

Passband ripple factor L_AR = 3.01 dB

Cutoff frequency=1.895 GHz.

Frequency of rejection=5.685 GHz.

Relative Dielectric Constant ε_r = 4.4

Height of substrate, h=1.6mm

The loss tangent tan δ=0.02.

The characteristic impedance of source/load Z₀ =50Ω.

The lowest line impedance ZL=Z_0C=25Ω;

The highest line impedance ZH=Z_0L=90Ω.

Ωc = 1.

Insertion loss (S21)≥ 20dB at 5.685 GHz

For proposed design work, to get maximally flat response in passband we assume Butterworth approximation. The first step is to compute the order of filter satisfying the insertion loss specifications at 5.685 GHz. as shown in Fig. 2 show the curves of attenuation versus normalized frequency for maximally flat prototype filter in [¹⁴], it is clear that N=3 is sufficient for at least 20 dB attenuation at 5.685 GHz with ripple level of 3.01 dB in passband. Filter prototype element values for N=1 to N=10 are tabulated as shown in Table I, [¹²].

Fig. 2
the curves of attenuation versus normalized frequency for maximally flat prototype filter.

Table I
Element values table for maximally flat low-pass filter

N	g 1	g 2	g 3	g 4	g 5	g 6	g 7	g 8	g 9	g 10	g 11
1	2.0000	1.0000
2	1.4142	1.4142	1.0000
3	1.0000	2.0000	1.0000	1.0000
4	0.7654	1.8478	1.8478	0.7654	1.0000
5	0.6180	1.6180	2.0000	1.6180	0.6180	1.0000
6	0.5176	1.4142	1.9318	1.9318	1.4142	0.5176	1.0000
7	0.4450	1.2470	1.8019	2.0000	1.8019	1.2470	0.4450	1.0000
8	0.3902	1.1111	1.6629	1.9615	1.9615	1.6629	1.1111	0.3902	1.0000
9	0.3473	1.0000	1.5321	1.8794	2.0000	1.8794	1.5321	1.0000	0.3473	1.0000
10	0.3129	0.9080	1.4142	1.7820	1.9754	1.9754	1.7820	1.4142	0.9080	0.3129	1.0000

As a result as shown in (11):

(11) $$\frac{\omega }{{\omega }_c}-1=\frac{\text{5.685}}{\text{1.895}}-1=2$$

Table I of element values table for the maximally flat low-pass filter in gives element values in [¹²] such as g₁ = g₃=1.0000 g₂=2.0000

From the expressions of L and C given shortly, we will calculate these elements and a choice must be made first to have as the first component either the capacitor in shunt (case 1) or the inductor in series (case 2); for our example, it will be the capacitor in shunt.

So: The low-pass filter’s lumped element circuit can be calculated by (12) and (13):

(12) $$C_n=\frac{g_n}{Z_0{\omega }_c}$$

(13) $$L_n=\frac{Z_0{g}_n}{{\omega }_c}$$

The model is made up of alternating transmission lines with low and high impedance. Low impedance lines indicate the presence of a shunt capacitor, whereas high impedance lines indicate the presence of a series inductor. The impedance characteristics of high impedance (Z_0L) and low impedance (Z_0C) are set to 90 Ω and 25 Ω, respectively. The circuit depicted in Fig. 3 shows a lumped element low-pass filter.

Fig. 3
Low-pass filter.

To determine the capacitor and inductor width and length, we use the filter formulas given in [¹²], [¹³]. The width (W) and and length (l) of the strip conductor are function of its characteristic impedance where a 50 Ω impedance line serving as the source/load. The lines with low impedance act as shunt capacitors, whereas the lines with high impedance act as inductors.

For microstrip line section of 50 Ω, the calculation of A by (14) with Z_C=50Ω, ε_r = 4.4, is as follows:

(14) $$A=\frac{Z_C}{60}{\left[\frac{{\epsilon }_r+1}{2}\right]}^{0.5}+\frac{{\epsilon }_r-1}{{\epsilon }_r+1}\left[0.23+\frac{0.11}{{\epsilon }_r}\right]$$

For $\frac{W}{h}<2$; A > 1.52 calculation of $\frac{W}{h}$ by (15)

(15) $$\frac{W}{h}=\frac{8exp\left(A\right)}{exp\left(2A\right)-2}$$

So: W₀= 3.054mm

Where $\frac{W}{h}>1$ the effective dielectric constant can be found by the following formula as shown in (16):

(16) $${\epsilon }_{re}=\frac{1}{2}\left({\epsilon }_r+1\right)+\frac{1}{2}\left({\epsilon }_r-1\right)\left[{\left(1+12\frac{h}{W}\right)}^{-0.5}\right]$$

So: ε_re0=3.33

For the capacitor:

Calculation of A by (14) with Z_C=Z L=Z_0C=25Ω,ε_r = 4.4

For $\frac{W}{h}>2$; A < 1.52, Calculation of B by (17) and $\frac{W}{h}$ by (18)

(17) $$B=\frac{60{\text{π}}^2}{Z_C\sqrt{{\epsilon }_r}}$$

(18) $$\frac{W}{h}=\frac{2}{\text{π}}[\left(B-1\right)-Ln\left(2B-1\right)+\frac{{\epsilon }_r-1}{2{\epsilon }_r}(Ln\left(B-1\right)+0.39-\frac{0.61}{{\epsilon }_r})]$$

So: W_0C = 8.371mm

Where $\frac{W}{h}>1$ the effective dielectric constant can be found by the following formula as shown in (16):

${\epsilon }_{re}=\frac{1}{2}\left({\epsilon }_r+1\right)+\frac{1}{2}\left({\epsilon }_r-1\right)\left[{\left(1+12\frac{h}{W}\right)}^{-0.5}\right]$

So: ε_reC=3.637

For the inductor :

Calculation of A by (14) with Z_C=ZH=Z_0L=90Ω, ε_r = 4.4

For $\frac{W}{h}>2$; A > 1.52 calculation of $\frac{W}{h}$ by (15)

$\frac{W}{h}=\frac{8\exp \left(A\right)}{\exp \left(2A\right)-2}$

So: W_0L= 0.936mm

where $\frac{W}{h}<1$ the effective dielectric constant can be found by the following formula as shown in (19):

(19) $${\epsilon }_{re}=\frac{1}{2}\left({\epsilon }_r+1\right)+\frac{1}{2}\left({\epsilon }_r-1\right)\left[{\left(1+12\frac{h}{W}\right)}^{-0.5}+0.04{\left(1-\frac{W}{h}\right)}^2\right]$$

So: ε_reL=3.08

The guided wavelength in a micro-strip transmission line can be calculated using equation as shown in (20):

(20) $${\text{λ}}_g=\frac{\text{λ}}{\sqrt{{\epsilon }_{re}}}$$

The physical length of the high impedance line is determined by the equation: Z₀=Z_0L = 90Ω as shown in (10):

$L=\frac{Z_{0}tan\beta l_L}{\omega }\leftrightarrow tan\beta l_L=\frac{{\omega }_L}{Z_0}$

$\beta l_L={\tan }^{-1}\left(\beta l_L\right)$

$l_L={\text{λ}}_{gL}\frac{\beta l_L}{{360}^{\circ }}$

Where λ_gL denotes the guided wavelength in the high impedance line as shown in (21):

(21) $${\text{λ}}_{gL}=\frac{c}{f_c\sqrt{{\epsilon }_{reL}}}$$

Where c is the speed of light in vacuum, and represents f_cthe cutoff frequency. The physical length of the low impedance line is determined by equation Z₀=Z_0C = 25Ω as shown in (8):

$C=\frac{tan\beta l_C}{Z_0\omega }\leftrightarrow tan\beta l_C=Z_0\omega C$

$\beta l_C={\tan }^{-1}\left(\beta l_C\right)$

$l_C={\text{λ}}_{gC}\frac{\beta l_C}{{360}^{\circ }}$

Where λ_gC represents the guided wavelength as shown in (22):

(22) $${\text{λ}}_{gC}=\frac{c}{f_c\sqrt{{\epsilon }_{reC}}}$$

Table II shows the dimension of the Stepped Impedance Low Pass Filter for order three (N=3).

Table II
Microstrip low-pass filter dimensions (N=3).

Dimension	Value
Characteistic impedance in Ohm	Z0 = 50	Z0C = 25	Z0L = 90
Microstrip line width in mm	W0 = 3.054	W0C = 8.371	W0L = 0.936
Effective dielectric constant	εre0 = 3.33	εreC = 3.637	εreL = 3.08
Microstrip line length in mm		lC1 = lC3 = 6.125	lL2 = 12.031

A2. Design high-pass filter at 1.705GHz using a stepped impedance resonator (SIR).

In the previous section, the prototype low-pass filter design was presented for maximally flat transfer function responses. This low-pass filter is normalized such that the resistances of the load and source is 1 Ω and have a cutoff frequency of Ωc = 1. Therefore, to obtain the desired level of frequency and impedance which is normally 50 Ω for microstrip filters, appropriate transformations must be used to measure the values of the prototype filter components.

It will also be necessary to convert the low-pass filter to high-pass filters, using the frequency transformation as shown in (24), (25) below in [¹⁴] and having the new values (L’, C’). Based on the impedance inversion technique discussed earlier in the Background and the implementation of an equivalent parallel inductor preceded by a quarter-wave line and another quarter-wave line at the output instead of a serie capacitor in the design of a high-pass filter. After obtaining the design of a suitable filter in distributed elements, the next main step is to find a suitable implementation.

High-pass filter Specifications:

Maximally flat response.

Passband ripple factor L_AR = 3.01dB Cutoff frequency=1.705GHz.

Frequency of rejection=5.115 GHz

Relative Dielectric Constant ε_r = 4.4

Height of substrate, h=1.6mm

The loss tangent tan δ=0.02.

The characteristic impedance of source/load Z₀ =50Ω.

The highest line impedance ZH=Z_0L=90Ω.

Ωc = 1.

Insertion loss (S21)≥ 20dB at 5.115 GHz.

For the proposed 1.705GHz filter, we use the attenuation versus normalized frequency curves as shown in Fig. 2 in [¹⁴] to establish that N=3 is the appropriate order for the maximally flat filter to give acceptable attenuation of 20dB at 5.115 GHz.

As a result as shown in (23):

(23) $$\frac{\omega }{{\omega }_c}-1=\frac{\text{5.115}}{\text{1.705}}-1=2$$

Table I of the element values for the maximally flat low-pass filter in [¹²] may be used to derive the suggested filter element values, and the coefficients for the filter elements are:

$$g_1=g_3=\text{1.0000}{g}_2=\text{2.0000}$$

The low-pass filter’s lumped element circuit can be calculated by (12) and (13).

As shown in Fig. 4, a low-pass filter can be approximated using a lumped element circuit. The prototype filter transformation using of equations (24),(25) in [¹⁴] will be used to convert all low-pass components to high-pass filters. Table I in [¹²] may be used to convert the values of the components in the maximally flat low-pass filter into the values for the high-pass filter.

Fig. 4
Low-pass filter.

According to [¹⁴], the low-pass prototype shunt capacitors are changed to parallel inductors with element values given by (24):

(24) $$L^{\prime }=\frac{1}{\left({\omega }_c^2\right)\cdot C}$$

The series inductor in the low-pass prototype is transformed to a series capacitor using the element values described by (25):

(25) $$C^{\prime }=\frac{1}{\left({\omega }_c^2\right)\cdot L}$$

The circuit in Fig. 5 has the following frequency-transformed element values determined using the low-pass filter’s previous formulas at 1.705 GHz: Using the inversion equation (3) the serie capacitor of the highpass prototype are converted into the parallel inductor equivalent as illustrated in Fig. 6.

$$C^{\prime }=\frac{L}{Z_0^2}$$

Fig. 5
The high-pass filter circuit.

Fig. 6
Equivalent quarter-wave-coupled high pass filter.

To determine the width and length of inductors, we utilize (10), (14), (15), (16), (19), (20), (21), which are found in [¹²], [¹³]. The dimensions of the stepped impedance high-pass filter for order three are shown in Table III.

Table III
Dimension of microstrip high-pass filter(for N=3)

Dimension	Value
Characteistic impedance in Ohm	Z0 = 50	Z0L = 90
Microstrip line width in mm	W0 = 3.054	W0L = 0.936
Effective dielectric constant	εre0 = 3.33	εreL = 3.08
Microstrip line length in mm	λg/4 = 24.11	${l^{\prime }}_{L_1}={l^{\prime }}_{L_3}=\text{8.092}$	lL2 = 4.323

B. Design of the bandpass filter of center frequency 2.5 GHz using a stepped impedance resonator (SIR)

The transmitter microstrip band-pass filter (BPF) will be investigated, evaluated, developed, and simulated utilizing a stepped impedance resonator operating at 2.5 GHz with a 3-dB fractional bandwidth of 7.6 %. With a low frequency of 2.41 GHz and a high frequency of 2.6 GHz, the BPF is appropriate for 4G telecommunications transmission applications. The architecture employs cascading high-pass structures (HPF) and low-pass filters (LPF). The upper stopband is attenuated using the stepped-impedance third order LPF, and the lower stopband is reached using the stepped-impedance third order HPF. The intended BPF produces theoretically consistent outputs. The substrate relative dielectric constant is ε_r = 4.4, and the length of the substrate is h =1.6mm. The filter configuration has a characteristic impedance of Z_C =50Ω, a copper line thickness of T = 0.035mm, and a loss tangent tan δ =0.02.

To design this band-pass filter, we use the same approach as previously described; we begin by designing a lowpass filter at 2.6 GHz using a stepped impedance resonator, and then a high-pass filter at 2.41 GHz.

B1. Design of the lowpass filter at 2.6 GHz using a stepped impedance resonator (SIR).

We use the same procedure as previously indicated.

Lowpass Filter Specifications:

Maximally flat response.

Filter order 3.

Passband ripple factor L_AR = 3.01dB

Cutoff frequency=2.6 GHz.

Frequency of rejection=7.8 GHz

Relative Dielectric Constant ε_r = 4.4

Height of substrate, h=1.6mm

The loss tangent tan δ=0.02.

The characteristic impedance of source/load Z₀ =50Ω.

The lowest line impedance ZL=Z_0C=25 Ω

The highest line impedance ZH=Z_0L=90Ω.

Ωc = 1.

Insertion loss (S21) ≥ 20dB at 7.8 GHz

We apply (8), (10), (14), (15), (16), (17), (18), (19), (20), (21), (22) as in [¹²], [¹³] to compute the width and length of capacitors and inductors. Table IV shows the dimensions of the Stepped Impedance third order Low Pass Filter.

Table IV
Dimensions of the microstrip low-pass filter of order three (N=3).

Dimension	Value
Characteistic impedance in Ohm	Z0 = 50	Z0C = 25	Z0L = 90
Microstrip line width in mm	W0 = 3.054	W0C = 8.371	W0L = 0.936
Effective dielectric constant	εre0 = 3.33	εreC = 3.637	εreL = 3.08
Microstrip line length in mm		lC1 = lC3 = 4.464	lL2 = 8.769

B2. Design the high-pass filter at 2.41 GHz using a stepped impedance resonator (SIR).

We follow the same procedure as indicated before. Highpass Filter Specifications:

Filter order 3.

Maximally flat response.

Passband ripple factor L_AR = 3.01dB

Cutoff frequency=2.41 GHz.

Frequency of rejection=7.23 GHz

Relative Dielectric Constant ε_r = 4.4

Height of substrate, h=1.6mm

The loss tangent tan δ=0.02.

The characteristic impedance of source/load Z₀ =50Ω.

The highest line impedance ZH=Z_0L=90Ω.

Ωc = 1.

Insertion loss (S21) ≥ 20dB at 7.23 GHz

The equations (10), (14), (15), (16), (19), (20), (21) as in [¹²], [¹³] may be used to determine the width and length of inductors. Table V shows the dimensions of the stepped impedance third order high-pass Filter.

Table V
Dimension of microstrip high-pass filter(for N=3)

Dimension	Value
Characteristic impedance in Ohm	Z0 = 50	Z0L = 90
Microstrip line width in mm	W0 = 3.054	W0L = 0.936
Effective dielectric constant	εre0 = 3.33	εL = 3.08
Microstrip line length in mm	λg/4 = 17.055	${l^{\prime }}_{L_1}={l^{\prime }}_{L_3}=\text{5.725}$	lL23.059

IV. RESULTS AND DISCUSSION

A. Design

This paper analyzes a microstrip diplexer based on bandpass filters consisting of low pass and high pass filters with stepped impedance resonators using the HFSS program. Both devices make use of the widely available FR-4 substrate material, which has a dielectric permittivity of ε_r = 4.4, a tan δ=0.02, and a thickness h=1.6 mm. The diplexer layout, shown in in Fig. 7, begins with the setup of the two filters, each with a different operating band and coupled by microstrip transmission lines to build a single circuit with one input, two bandpass filters, and two outputs.

Fig. 7
Diplexer layout.

A1. The receiver microstrip band-pass filter

The low-pass filter model, developed using the HFSS program, is illustrated in in Fig. 8. It is consists of alternating low and high impedance transmission line transmission lines. The S parameter dependency on the frequency of the simulated filter is shown in in Fig. 9.

Fig. 8
Structure of the proposed low-pass filter with HFSS.

Fig. 9
the Simulated frequency response of the proposed low-pass filter with HFSS.

The obtained results indicate that the low-frequency passband has a minimum loss of 0.7 dB. The operating band is 2.33. The reflection coefficient over the passband starts at about 3.47 dB at the cutoff frequency of 2.33 GHz and remains below 12.5 dB over the entire passband as seen in in Fig. 9

The configuration of the high-pass filter model created by the HFSS software is depicted in Fig. 10. Fig. 11 shows the S parameter in terms of the simulated filter frequency. According to the obtained results(see Fig. 11 below), the filter has limited passband losses of approximately 0.9 dB. The width of the high-frequency passband is 2.44 GHz, and there is significant suppression of electromagnetic waves at the low-frequency rejection band frequencies. The cutoff frequency is 1.56 GHz, the passband reflection coefficient S₁₁ starts at about 3.85 dB at the cutoff frequency and remains below 14 dB over the entire passband.

Fig. 10
Structure of the proposed high-pass filter with HFSS.

Fig. 11
the Simulated frequency response of the proposed high-pass filter with HFSS.

A2. The transmitter microstrip band-pass filter

Fig. 12 depicts the HFSS-created low-pass filter model, which utilizes transmission lines with alternating low and high impedance to achieve its low-pass filtering effect. Fig. 13 depicts the relationship between the S parameter and the simulated filter frequency.

Fig. 12
Structure of the designed low-pass filter in HFSS.

Fig. 13
Simulated frequency response of the designed low-pass filter using HFSS.

According to the obtained results, the minimum loss in the low-frequency passband is 0.7 dB. The operational band is 3 GHz. As seen in Fig. 13, the reflection coefficient throughout the passband begins at around 3.41 dB at the cutoff frequency of 3 GHz and continues below 12.5 dB throughout the passband. Fig. 14 depicts the configuration of the HFSS program’s high-pass filter model, while Fig. 15 depicts a graph demonstrating the dependency of the S parameter on the frequency of the simulated filter.

Fig. 14
Structure of the proposed high-pass filter with HFSS.

Fig. 15
The frequency response of the suggested high-pass filter using HFSS.

As per the results reported in Fig. 15, the width of the high-frequency passband is about 1.86 GHz, with minimal passband losses of around 0.9 dB. At the low-frequency rejection band frequencies, significant suppression of electromagnetic radiation is noticed. The cutoff frequency is 2.14 GHz. The reflection coefficient over the passband starts at about 3.90 dB at the cutoff frequency and remains below 14 dB over the entire passband.

B. Design of diplexer

The constructed filters are merged into a single structure containing a diplexer (Fig. 8, Fig. 10, Fig. 12, Fig. 14). Its working band is created by each filter, namely the low-pass and high-pass filters. in Fig. 16 and in Fig. 17 show the structure of the proposed diplexer and the numerical simulation results respectively.

Fig. 16
Structure of the proposed diplexer with HFSS.

Fig. 17
The Simulated frequency response of the proposed diplexer with HFSS :S₁₁,S₂₁,S₃₁.

Based on the current numerical simulation results, the diplexer has two operating frequency bands of 280 MHz and 210 MHz with fractional bandwidth of about 15.6 % and 8.4 % for the R(x) and T(x) bands respectively as shown in Fig. 17. The two bands, obtained by the receiver and the transmitter microstrip band-pass filters, operate at 1.8 GHz and 2.5 GHz respectively. Within both bands, the reflection coefficient S₁₁ exceeds 12.02 dB.

The receiving bands has transmission and reflection coefficients of 2.75 dB and 17.29 dB, respectively, whereas the transmitting band has transmission and reflection coefficients of 4.15 dB and 12.02 dB, respectively.

B1. Optimization and Modification with HFSS

For the design of a microwave circuit, the simulation tool is very helpful and essential. In general, the design is simulated to ensure that the results meet the design aim.

Otherwise, fine-tune and re-simulate to get as near to the design objective as possible. The values of the reflection coefficient (S11) and the transition factor inside the passband of the proposed diplexer transmit filter at 2.5 GHz center frequency are about 12.02 dB and 4.15 dB, respectively. This is more than we expected from the simulation results, as the desired transmission coefficient within the passband is at least 4.15 dB. This may be due to transmission line microstrip discontinuities, which are never straight or uniform and include discontinuities such as changes in direction, width, and intersections. Here we try to refine the tuning by adjusting the length of the LPF inductor l_L2 =5mm. Table VI reports the dimensions of the suggested optimized diplexer, and Fig. 18 and Fig. 19 depict the structure and dimensions of the proposed optimum diplexer, with the blue squares representing the short circuits. Fig. 20 shows the results of the diplexer numerical simulation.

Table VI
Dimensions of Optimized Diplexer

Diplexer	Receiver BPF (Rx)		Transmitter BPF (Tx)
Dimensions	LPF	HPF	LPF	HPF
Microstrip line width in mm	W0 − 3.054 ; W0L − 0.936 ; W0L = 8.371
Characteristic impedance in Ohm	Z0 = 50 ; Z0L = 90 ; Z0C = 25 ;
Effective dielectric constant	εre0 = 3.33 ; εreL = 3.08 ; εreC = 3.637
Microstrip line lengh in mm	lC1 = lC3 = 6.125	λg/4 = 24.11	lC1 = lC3 = 4.464	λg/4 = 17.055
	lL2 = 12.031	${l^{\prime }}_{L_1}={l^{\prime }}_{L_3}=\text{8.092}$	lL2 = 5	${l^{\prime }}_{L_1}={l^{\prime }}_{L_3}=\text{5.725}$
		lL2 = 4.323		lL2 = 3.059

Fig. 18
Structure of the proposed optimized diplexer with HFSS.

Fig. 19
Dimensions of optimized diplexer.

According to the numerical simulation results, the diplexer has two operational bands, one provided by the receiver microstrip filter band-pass operating at 1.8 GHz and the other by the transmitter microstrip band-pass filter working at 2.5 GHz. The two working bands have bandwidths of 280 MHz, and 390 MHz, respectively, with a reflection coefficient S11 that exceeds 15.5 dB inside both bands. Additionally, the receiving filter transmission and reflection coefficients are 2.69 dB and 19.20 dB, respectively, while the transmitting bandpass filter coefficients are 2.81 dB and 15.5 dB, respectively.

As illustrated in Fig. 20, the fractional bandwidths of both bands (R(x): 280 MHz and T(x): 390 MHz) are about 15.5 % and 15.6 %, respectively. Fig. 21 depicts simulated isolation between the transmitter and receiver S23 that is greater than 13.08 dB.

Fig. 20
The Simulated frequency response of the proposed optimized diplexer with HFSS :S₁₁,S₂₁,S₃₁.

Fig. 21
The Simulated frequency response of the proposed optimized diplexer with HFSS :S₂₃.

It should be noted that the diplexer simulation method is further complicated by the fact that each filter is separated when joining the microstrip lines in a specific arrangement. This implies that the feed line configuration will need to be optimized further, which will require a certain number of iterations. To evaluate the suggested diplexer performance, a prototype with a total area of (47.4020×247.063=11711.28 mm²) was developed. To make short circuits, it is necessary to use plated holes (vias). The experimental results were obtained using the Agilent Technologies E5071C network analyzer which operates in the 300 kHz to 20 GHz frequency range.

The proposed optimized diplexer is shown in Fig. 22, with the 4G telecommunications reception BPF on the right and the 4G telecommunications transmission BPF on the left. The three ports 1, 2, and 3 represent the antenna input, the transmit filter output, and the output of the receive filter, respectively.

Fig. 22
Photograph of the proposed optimized diplexer.

The diplexer measured results are given in Fig. 23, Fig. 24, Fig. 25, with measured isolation between the two channels of around 17 dB. The rejection of the receiver microstrip bandpass filter at a low band signal is about 18.53 dB, whereas the rejection of the transmitter microstrip bandpass filter at a high band signal is approximately 16.53 dB. Insertion losses measured at lower and higher bands are about 2.7 and 2.8 dB, respectively. The first operating band is 270 MHz, while the second is 400 MHz, resulting in fractional bandwidths of approximately 15 % and 16.8 %, respectively. Comparisons of the simulated and measured S-parameters are given in Fig. 26, Fig. 27, Fig. 28, where there is a good agreement with a minor difference between simulation and measurement.

Fig. 23
The measured frequency response of the Rx filter of optimized diplexer S₃₁,S₁₁.

Fig. 24
The measured frequency response of the Tx filter of optimized diplexer S₂₁,S₁₁..

Fig. 25
The measured isolation between the two channels S₂₃

Fig. 26
Comparison between the simulated and the measured results of the proposed optimized diplexer S₃₁,S₁₁.

Fig. 27
Comparison between the simulated and the measured results of the proposed optimized diplexer S₂₁,S₁₁.

Fig. 28
Comparison between the simulated and the measured isolation of the proposed optimized diplexer: S₂₃

Table VII shows simulation and measurement results of the diplexer.

Table VII
Simulation and Measurement Results of The Diplexer

Parameter	Simulation Results		Measured Results
	RX	TX	RX	TX
Frequency GHz	1.8	2.5	1.8	2.5
Bandwidth [MHz]	280	390	270	400
Insertion loss [dB]	2.69	2.81	2.7	2.8
Return loss [dB]	19.19	15.54	18.53	16.53
Isolation [dB]	16.75	13.07	17.81	16.51

V. CONCLUSION

This paper examines the design and analysis of a compact and highly manufacturable microstrip diplexer appropriate to modern multi-service communication systems. The underlined diplexer acts as a frequency separator by splitting the working band into two subchannels defined by the bandwidth of the microstrip filters. A prototype was created via simulation experiments and then quantified using a vector network analyzer. According to the measured data which are closely correlated to the HFSS simulation results, the two working bands operate at 270 MHz and 400 MHz respectively, with a reflection coefficient (S11) larger than 16 dB in both passbands. In addition to meeting the required criteria, the designed circuit has a low insertion and return loss on both channels, with a transmission coefficient of about 2.7 dB in both frequency ranges. Furthermore, the obtained results show that, at R(x) and T(x), the reflection coefficient is larger than 16 dB and the isolation between the two channels is more than 17 dB.

• FUNDING STATEMENT
  This work was supported by Directorate General for Scientific Research and Technological Development (DGRSDT).

ACKNOWLEDGMENTS

The authors would like to thank the telecommunications and digital signal processing laboratory and Djillali Liabes University for their support.

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Publication Dates

• Publication in this collection
  06 June 2022
• Date of issue
  June 2022

History

• Received
  30 July 2021
• Reviewed
  05 Aug 2021
• Accepted
  24 Mar 2022