Implementation of a compact diplexer based on a modified T-shaped step-impedance resonator (MTSIR) for 5G networks

Abstract

In this paper, a microstrip diplexer with a very compact size is presented for 5G networks. The proposed diplexer operates at 3.5 GHz and 4.2 GHz, which fall within the 5G extended C-band (3.3–4.2 GHz) allocation, showing potential for next generation wireless applications. The design of this diplexer utilizes two similar filters with different sizes. In designing the filters, T-shaped resonators, meandered lines, and coupled lines are used to form a novel structure called the modified T-shaped step-impedance resonator (MTSIR). The proposed diplexer employs two modified T-shaped step-impedance resonators (MTSIRs) to achieve compact size, low insertion loss, and high isolation in the 5G extended C-band, while maintaining a very low frequency ratio of 1.2. The proposed diplexer operates at a frequency of 3.5 GHz with an insertion loss of 0.5 dB. The second channel of the diplexer operates at a frequency of 4.2 GHz with an insertion loss of 0.8 dB. The designed diplexer features a very compact size of 18.2 mm × 10.9 mm, corresponding to a normalized size of 0.16 λg × 0.28 λg.

Introduction

Filters play a fundamental role in many microwave applications and are used for splitting or combining different frequencies. Emerging applications in wireless communications continue to challenge microwave/RF filters with stringent requirements, demanding higher performance, smaller size, lighter weight, and lower cost^1–3. Diplexers combine two filters, usually low-pass with band-pass or two band-pass filters. Diplexers are crucial components in RF and microwave systems, enabling the separation or combination of signals at different frequency bands. They play a key role in applications such as wireless communication, satellite systems, and radar, allowing efficient use of the electromagnetic spectrum while minimizing interference^4,5.

In general, recent techniques for designing diplexers use resonators^6–9, open stubs¹⁰, defected ground structures (DGS)¹¹, varactors¹², lumped elements¹³, and step impedance resonators (SIRs)⁵. For example, the diplexer proposed in⁵ demonstrates the potential of SIR-based resonators combined with UIR components to achieve compact structures with high isolation and low insertion loss. In contrast, our work employs a modified T-shaped step-impedance resonator (MTSIR), which provides a different balance of performance by focusing on miniaturization and low insertion loss in the 5G extended C-band.

In¹⁴, a band-pass to band-pass diplexer is presented, utilizing a dual-mode structure. This diplexer operates at two frequencies. Transmission zeros are employed in the circuit to enhance isolation performance. The relative bandwidths of the passbands in this circuit are 25% and 20%. Coupled transmission lines are used in this work; however, the insertion loss is rather high. In¹⁵, a dual-band filter and a diplexer are presented using open-loop resonators. The main resonator of this circuit consists of a capacitor, a resistor, and a variable capacitor. To achieve a diplexer, two similar bandpass filters with different sizes can be utilized. The calculated insertion losses are 1.4 dB and 2.3 dB, which are not very favorable. One advantage of this circuit is its appropriate stopband performance, achieving a rejection below − 20 dB around operating frequency. In the circuit presented in¹⁶, a DGS (defected ground structure) is utilized, which reduces the circuit size. The initial structure of the resonator, modified into a T-shape, provides a transmission zero at the frequency of 3.5 GHz, which is crucial for the design of this diplexer. In¹⁷, a diplexer with two outputs and one input is utilized, incorporating a via (ground connection) structure. In this structure, changing the voltage across the varactor diode alters the main frequency of the circuit. In¹⁸, a 6-channel diplexer is designed, utilizing both open-circuit and short-circuit stubs simultaneously to achieve an optimal response. A multiplexer consisting of one low-pass channel and four band-pass channels is introduced in¹⁹, in which the low-pass filter utilizes a step-impedance structure. In²⁰, the authors designed a diplexer using a combination of low-pass and band-pass filters. The design employs coupled lines and resonators.

Although several diplexer designs have been reported, many suffer from drawbacks such as large physical size, high insertion loss, limited stopband suppression, or insufficient channel isolation. Additionally, few designs have effectively combined compactness with low-loss performance in the C-band range relevant to 5G systems. To address these limitations, this paper presents a novel and compact microstrip diplexer based on a proposed modified T-shaped step-impedance resonator (MTSIR). The T-shaped resonators are commonly used in microwave circuits, and depending on their geometry they can operate as low-pass, band-stop, or as band-pass resonators. In this paper, we introduce a modified T-shaped step impedance resonator that uses step impedance loading, coupled line sections, and meandered paths to improve performance and reduce size. Figure 1 presents a direct comparison between the proposed resonator and a typical band pass T-shaped resonator. The results show that the proposed design provides a smaller physical size, a more controlled passband response, and improved suppression of unwanted frequencies. These improvements demonstrate the significant advantages of the proposed resonator for compact filters used in the C-band diplexers.

Fig. 1.

Comparison of the proposed band-pass MTSIR with typical band-pass T-shaped resonators. The (a) layout and (b) simulated responses of the typical band-pass T-shaped resonators are compared with (c) layout and (d) simulated responses of the proposed band-pass MTSIR resonator. The proposed MTSIR demonstrates stronger stopband rejection, a sharper and more controlled passband, and a significantly smaller physical size compared to the typical band-pass T-shaped resonator.

The proposed design achieves low insertion losses, high isolation, strong stopband performance, and low frequency ratio all within a significantly miniaturized footprint, showing potential for next generation wireless applications.

Filter design and evolution

First filter design

To design the target band-pass filter, an air gap was initially used. Therefore, an initial structure is presented to create a gap between the input and output. The initial structure of this air gap resonator, its response, and its equivalent circuit are shown in Fig. 2a–c. Based on the response, it is observed that there is no clear resonance to produce a passband with acceptable losses.

Fig. 2.

(a) Physical layout of Resonator1, showing the air gap structure between Port 1 and Port 2. (b) Equivalent lumped-element circuit model representing the resonator as a series of inductors and a central capacitor. (c) Simulated S-parameters of Resonator1, indicating the absence of a defined passband and poor resonance characteristics across the frequency range of 0–10 GHz. The values of inductors and capacitor in the equivalent circuit model of Resonator1 is L_a = 0.5 nH and C_a = 0.05 pF, respectively.

To increase the capacitance of the line and achieve better resonance in the circuit, the air gap needs to be reduced. For this purpose, an additional line has been placed beneath the initial air gap, which has formed Resonator2. The structure of the Resonator2, its response, and its equivalent circuit are shown in Fig. 3a–c. Based on the response, it can be observed that the attenuation level in the S₂₁​ plot has improved by approximately 10 dB, which is highly significant for reducing insertion and return losses.

Fig. 3.

(a) Physical layout of Resonator2, formed by introducing an additional lower line beneath the air gap to enhance capacitive coupling. (b) Equivalent circuit model consisting of multiple inductors and capacitors that represent the improved coupling and resonance behavior. (c) Simulated S-parameters showing enhanced transmission (S₂₁) compared to Resonator1, with improved attenuation performance across the 0–10 GHz range. The values of inductors and capacitors in the equivalent circuit model of Resonator2 is L_a = 0.3 nH and C_a = C_b = 0.05 pF, respectively.

In the previous design, there was only one resonance in the system, which resulted in an inadequate response. To improve the system, multiple transmission zeros must be introduced. For this purpose, an additional line was added to the circuit, creating a transmission zero at 4.2 GHz, forming Resonator3. However, further zeros still need to be added to the system. Figure 4a,b illustrate the layout and equivalent circuit of Resonator3, respectively. Figure 4c shows the simulated S-parameters of Resonator3, indicating the presence of a transmission zero near 4.2 GHz, which improves the rejection band.

Fig. 4.

(a) Physical structure of Resonator3, formed by adding a vertical stub to the previous configuration, resulting in a modified T-shaped geometry. (b) Equivalent circuit model consisting of multiple inductors and capacitors that represent the improved coupling and resonance behavior. (c) Simulated S-parameters showing the introduction of a transmission zero near 4.2 GHz and improved rejection band around 0–3.5 GHz, indicating enhanced selectivity and resonance performance for filter applications. The values of inductors and capacitors in the equivalent circuit model of Resonator3 are: L_a = 8.5 nH, C_a = C_b = 0.16 pF, and C_c = 0.15 pF respectively.

To further improve the circuit, the length of this line can be increased, which shifts the operating frequency to 4.3 GHz. However, the insertion loss of this configuration is 0.8 dB, which is relatively high. This adjustment resulted in Resonator4, whose structure and frequency response are shown in Fig. 5a,b.

Fig. 5.

(a) Layout of Resonator4, developed by extending the vertical stub of Resonator3 to shift the resonance frequency and improve filtering performance. (b) Simulated S-parameters indicating two transmission zeros around 3.2 GHz and 9.8 GHz with enhanced stopband rejection and improved insertion loss characteristics, making it suitable for targeted frequency applications.

The equivalent circuit and frequency response of Resonator4 is shown in Fig. 6. This T-shaped resonator can be modeled using simple L and C components, as shown in Fig. 6a,b. In Resonator4, the input and output coupling are modeled as series capacitors (C₁ and C₂) because the ports couple directly to the resonator arms through electric fields. The vertical stub acts as an inductor (L₁), while the short horizontal section to ground is modeled as a capacitor (C₃). Together, L₁ and C₃ form a resonant tank, while C₁ and C₂ control the external coupling. Since the resonant frequency is defined as f₀ = 1/2π, the values of L₁ and C₃ can be obtained from Eqs. (1) and (2), based on the target resonant frequency (f₀).

Fig. 6.

(a) LC equivalent circuit of Resonator4, where capacitors C₁​ and C₂​ model the input and output coupling, while inductor L₁​ and capacitor C₃ form the resonant tank. (b) Transfer function model of the LC circuit used for theoretical analysis, with normalized characteristic impedance Z₀ = 1. (c) Simulated frequency response of the LC equivalent model, showing good agreement with EM simulation results. (d) Theoretically derived frequency response illustrating the resonance behavior and validating the analytical model of the resonator. The values of inductors and capacitors in the equivalent circuit model of Resonator4 are: L₁ = 8.5 nH, C₁ = C₂ = 0.16 pF, and C₃ = 0.3 pF respectively.

1

2

To analyze the filter more generally, the transfer function H(s) of the LC equivalent circuit is derived. This function represents the signal transmission behavior of the resonator. In a normalized two-port network, H(s) directly corresponds to the theoretical S₂₁​ parameter, allowing us to compare the analytical and simulated results. The transfer function of the resonator is extracted as written in Eqs. (3) and (4), which shows how the circuit passes or blocks signals at different frequencies. In this case, the LC components (L₁ and C₃) create a notch, at a certain frequency. Also, the characteristic impedance Z₀ is normalized to 1 (i.e., Z₀ = 1). The results show that the extracted transfer function from theory and the simulated frequency response has good agreement which verifies the validity of the design. It should be noted that the small differences between Fig. 6c,d come from simplifications in the theory. The theoretical model does not include parasitic effects and losses, while the simulator does. This makes the simulated result closer to real circuit behavior.

3

4

The extracted lumped components represent a high-frequency resonator circuit operating in the 3.1 GHz range. The inductor L₁ = 8.5 models the vertical stub, while the capacitors C₁ = 0.17 pF and C2 = 0.16 pF represent the input and output coupling. The capacitor C₃ = 0.3 pF corresponds to the bottom horizontal segment of the structure. Together, these components form a resonator centered around the resonant frequency defined by L₁and C₃.

By considering Z₀ = 1, from Eqs. (3) and (4), the transfer function can be extracted as written in Eq. (5). Also, according to the obtained transfer function, group delay can be written as shown in Eq. (6). Figure 7a identifies the working passband and Fig. 7b shows that the calculated in-band group delay is low and smooth, varying approximately from 0.2 ns to 0.7 ns across the 500 MHz operating bandwidth, which indicates low in-band dispersion and supports the filter suitability for 5G C-band operation.

Fig. 7.

Theoretical frequency response and group-delay of the proposed MTSIR network extracted from analyses. (a) Simulated transmission magnitude ∣S21​∣ from 2.5 to 6 GHz. The operational − 3 dB bandwidth around the passband center is indicated by the dashed lines. (b) Closed-form group delay evaluated over a 500 MHz service band.

5

6

To improve Resonator4, a curved structure can be utilized to form the filter. The obtained filter structure not only reduces the circuit size but also improves its performance. This structure can be introduced as Filter1, operating at a frequency of 4.2 GHz with insertion and return losses of 0.5 dB and 27 dB, respectively. Additionally, it produces two suitable zeros at frequencies of 3.1 GHz and 8.75 GHz, which enhance the sharpness and provide an appropriate stopband. The structure of Filter1 and its response are illustrated in Fig. 8a,b.

Fig. 8.

(a) Layout of Filter1 (first modified T-shaped step-impedance resonator (MTSIR)), developed from Resonator4 with an enhanced and folded structure to reduce physical size and introduce additional transmission zeros. (b) Simulated S-parameters of Filter1, showing a main passband centered at 4.2 GHz with insertion and return losses of 0.5 dB and 27 dB, respectively, and strong stopband rejection near 3.1 GHz and 8.75 GHz, indicating high selectivity and improved filtering characteristics.

Second filter design

As seen in the previous subsection, an air gap was used to design a band-pass filter. In this section, the focus is on modifying the dimensions of the lines to adjust the key frequencies. To change the frequency, based on the previous section, the length of the lines added to the coupler must be altered. The length of main vertical branch has been increased to decrease the operating frequency. However, increasing the length of the line has resulted in a larger filter size. To address this issue, the method of bending the line is employed, which reduces the circuit size and resulted in Filter2 structure. This circuit is shown in Fig. 9a and based on its response in Fig. 9b, the filter operates at a frequency of 3.5 GHz with an insertion loss of 0.4 dB and a return loss of 41 dB. Additionally, this filter features two transmission zeros at 2.6 GHz and 7.3 GHz.

Fig. 9.

(a) Layout of Filter2 (second modified T-shaped step-impedance resonator (MTSIR)), employing a meandered vertical stub structure to reduce circuit size while tuning the resonance frequency downward. (b) Simulated S-parameters of Filter2, showing a passband centered at 3.5 GHz with low insertion loss (0.4 dB) and high return loss (41 dB), along with transmission zeros at 2.6 GHz and 7.3 GHz, indicating excellent stopband suppression and compact filter performance.

Proposed diplexer design

This Fig. 10 shows the LC equivalent circuit model of the proposed diplexer, which consists of inductors and capacitors arranged to achieve the desired frequency response. Figure 10a illustrates the simulated frequency response of the diplexer in terms of S-parameters, while Fig. 10b depicts the lumped-element circuit that represents the diplexer functionality. Figure 10c,d demonstrate how varying the inductor L₁ and L₁′​ affects the diplexer performance, particularly the resonance frequencies and isolation levels, providing insight into the design flexibility and tuning of the diplexer.

Fig. 10.

LC equivalent circuit of the proposed diplexer. (a) Simulated S-parameters of the LC circuit, showing the frequency response across the 1–7 GHz range. (b) The equivalent LC circuit model for the diplexer, including capacitors and inductors​. (c) Variation of the S-parameters with changes in the value of L₁′​ (9.5 nH, 8.5 nH, 8 nH, 7.5 nH, and 6.5 nH) and its impact on the diplexer response. (d) Further examination of the S-parameters responses with respect to different values of L₁ (12 nH, 13 nH, 13.5 nH, 14 nH, and 15 nH) ​, highlighting the effect of varying inductance on the diplexer performance.

To realize the proposed diplexer, the two filters developed in the previous sections are connected at their input ports, as illustrated in Fig. 11. The diplexer is designed and simulated on an RT-Duroid 5880 substrate with a thickness of 31 mils. The simulated frequency responses are presented in Fig. 11a,b, while the diplexer layout is shown in Fig. 11c. The diplexer exhibits two passbands centered at 3.5 GHz and 4.2 GHz, with insertion losses below 0.7 dB in both channels. The return loss and isolation exceed 20 dB, indicating excellent filtering performance. Moreover, the design is highly compact, with overall dimensions of approximately 18.3 mm × 10.9 mm, corresponding to a normalized size of 0.16 λg × 0.28 λg, making it well-suited for C-band 5G applications. When the two filters are combined, some interaction between their resonators can create small glitches in the isolation curves. To reduce this, the coupling gaps and stub lengths were re-optimized after combination. As a result, the glitches remain minor (below − 20 dB) and do not affect proper diplexer operation.

Fig. 11.

(a) Simulated S-parameters S_11​ and S₃₂ of the proposed diplexer, showing strong isolation and return loss around the operating frequencies of 3.5 GHz and 4.2 GHz. (b) Simulated transmission responses S_21​ and S₃₁​, indicating low insertion losses at the two operating bands, confirming efficient signal separation. (c) Layout of the proposed compact diplexer combining Filter1 and Filter2, with detailed dimensional annotations demonstrating a total size of 18.2 mm × 10.9 mm, corresponding to a normalized footprint of 0.16 λg × 0.28 λg, suitable for 5G C-band applications.

Figure 12. Simulated surface current distributions of the proposed diplexer at different frequencies: (top-left) 3.5 GHz, (top-right) 4.2 GHz, (bottom-left) 2.9 GHz, and (bottom-right) 5.2 GHz. At the operating frequencies (3.5 GHz and 4.2 GHz), strong current concentration is observed along the corresponding filter paths, indicating efficient channel selection and isolation. In contrast, at out-of-band frequencies (2.9 GHz and 5.2 GHz), minimal current flows through the output ports, confirming high suppression and effective filtering behavior of the diplexer.

Fig. 12.

shows the simulated current distribution of the proposed diplexer at different frequencies. At 3.5 GHz, the current flows mainly toward Port 3, while at 4.2 GHz, it flows toward Port 2, confirming correct signal separation for each channel. At 2.9 GHz and 5.2 GHz, the current is weak at both outputs, indicating good suppression of unwanted signals. These results verify the diplexer’s proper operation and high isolation between channels.

Figure 13 shows the fabricated diplexer and its measured performance. The measured and simulated S-parameters, as shown in Fig. 10b and 13a, are in good agreement, confirming the diplexer operates well at 3.5 GHz and 4.2 GHz with low insertion loss and good isolation. Small differences are due to fabrication and measurement variations. The prototype and test setup using a vector network analyzer are shown in Fig. 13c, demonstrating the design’s successful practical implementation. The measured insertion losses of the diplexer are better than 0.8 dB in both operating channels. The measured results show that the diplexer achieves an isolation of 20 dB at 3.5 GHz and 18 dB at 4.2 GHz for the S₃₂ parameter. The return losses (S₁₁) are 17 dB at 3.5 GHz and 23 dB at 4.2 GHz, indicating good matching and low reflection at both operating frequencies. These values confirm the diplexer effective channel separation and impedance matching in the desired bands. Although the harmonic suppression beyond the second channel is not very strong, the proposed diplexer provides key advantages such as very low insertion loss, high isolation, and compact size in the 5G extended C-band, while maintaining a very low frequency ratio through the use of the proposed MTSIR structure. These benefits show the potential of the design for next generation wireless systems.

Fig. 13.

(a) and (b) show the measured and EM-simulated S-parameters of the proposed diplexer, demonstrating good agreement in terms of passband location and insertion/return losses around 3.5 GHz and 4.2 GHz. Minor differences are due to fabrication and measurement tolerances. (c) Displays the fabricated prototype and its test setup using a vector network analyzer, validating the diplexer’s practical performance and confirming its effectiveness for 5G applications.

Table 1 compares the proposed diplexer with several others based on performance metrics such as center frequencies, insertion losses (IL1 and IL2), and size (in terms of guided wavelength, λg). The table highlights the superior performance of the proposed diplexer, which operates at 3.5 GHz and 4.2 GHz with low insertion losses of 0.5 dB and 0.8 dB, respectively. Additionally, its compact size sets it apart, indicating a significant improvement in miniaturization while maintaining excellent performance. The measured − 3 dB fractional bandwidth is 3.38 to 3.7 (10% FBW) for the lower channel and 4.1 to 4.28 (4.3%) for the upper channel. Return loss and isolation are measured 17 dB and 20 dB in the lower band, while they are 29 dB and 18 dB in the upper band. The provided comparison in Table 1 demonstrates the proposed diplexer’s efficiency and suitability for 5G applications, especially in achieving a balance between minimal size and optimal electrical characteristics.

Table 1.

Performance comparison of the proposed diplexer with previously reported designs. The proposed diplexer achieves a superior balance of miniaturization, low loss, and simplicity using the modified T-shaped step-impedance resonator (MTSIR), demonstrating its suitability for compact 5G applications.

Ref.	Center frequency (GHz)	Freq. ratio	IL1 (dB)	IL2 (dB)	Size (λg2)	FBW (%)	Isolation (dB)	S11 (dB)	Technique
5	3.2/4.7	1.46	0.3	0.7	0.48 × 0.36	2.8/0.98	> 27	30/19	Step impedance resonator (SIR); Uniform impedance resonator (UIR)
15	0.9/1.8	2	1.4	2.3	0.19 × 0.47	4/6.1	> 45	20/15	Folded open loop ring resonator (OLRR)
22	3/5.8	1.93	3	3	0.27 × 0.28	80/3.4	> 37.5	10.3	Coupling quarter-wavelength resonators (QWR)
23	3/2.4	1.25	1.6	1.4	0.19 × 0.64	8/10.7	> 40	18/16	New matching network
24	10.7/14.1	1.31	0.8	1.3	2.1 × 1.3	4.4/2.1	> 42	18	Substrate integrated waveguide (SIW)
25	1.5/2.15	1.43	2	4.8	0.39 × 0.6	14/4.5	> 35	10/10	Varactors; Vias
26	2.3/29.8	12.9	0.9	1.3	0.34 × 0.46	19/6.2	> 22	13	Aperture coupling mechanism; Air-filled substrate-integrated waveguide circular cavities
27	12/14	1.16	1.3	1.4	2 × 1.4	4.9/5.6	> 27	20	Substrate integrated waveguide (SIW); Dual-mode cavity
28	2/2.7	1.35	1.5	2	0.45 × 0.48	5.1/3	> 36	18/28	Substrate integrated waveguide (SIW); Single-ended and balanced ports
29	10/11	1.1	1.8	2.5	4.1 × 1.6	1/1.7	> 35	12	Substrate integrated waveguide (SIW); Dual-mode cavity filter
30	2.02/ 3.61	1.78	0.35	0.28	0.5 × 0.4	40/20	34/26	20/33	Complementary spiral resonators
31	1.8/2.45	1.36	2.2	1.8	0.32 × 0.28	4.9/5.1	> 31	16/21	Modified meander line resonators
32	0.9/1.8	2	0.17	0.14	0.095 × 0.042	21/24.3	> 20	15/17	Coupled lines
33	2.8/4	1.42	0.7	0.9	0.41 × 0.31	1.4/2.2	> 35	21/17	Step impedance resonator (SIR); Uniform impedance resonator (UIR)
This work	3.5/4.2	1.2	0.5	0.8	0.16 × 0.28	10/4.3	20/18	17/29	Modified T-shaped step-impedance resonator (MTSIR)

Conclusions

This paper presents a novel and compact diplexer design for 5G networks, using modified new resonators and innovative structural adjustments. The proposed diplexer operates efficiently at 3.5 GHz and 4.2 GHz with low insertion losses and a compact size of 18.2 mm × 10.9 mm (0.16λg × 0.28λg). The proposed design achieves excellent stopband performance, minimal return losses, and high isolation. These improvements demonstrate the significant advantages of the proposed resonator for compact filters used in C-band diplexers, showing its potential for next-generation wireless applications. Compared to existing diplexers, the proposed design offers a superior balance of size, performance, and efficiency, addressing key challenges in wireless communication systems. This work underscores a significant advancement in diplexer technology, paving the way for more compact and efficient RF designs.

Author contributions

F.H., S.I.Y., F.B., M.A.C., M.A., F.A.H., Sa.R., and So.R. contributed equally to this work. All authors participated in the conceptual design, simulation, data analysis, and interpretation of results. F.H., F.B., and S.Ro. prepared the manuscript text. M.A.C., M.A., and F.A.H. contributed to figures and tables. S.I.Y. and S.R. performed literature review and comparisons. All authors reviewed and approved the final manuscript.

Funding

The authors declare that no funding was received for this research or the publication of the article.

Data availability

The corresponding author can be contacted on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.