A Compact 6-Cavity LTCC Filter Featuring Four Transmission Zeros and Wide Stopband Based on a Single Cross-Coupling

Abstract

The high-density integration of low-temperature co-fired ceramic (LTCC) filters inevitably induces complex parasitic coupling. Traditional designs rely on forced isolation to mitigate this issue, often at the expense of increased physical footprints. To overcome this limitation, this paper proposes a strategy for the controlled utilization of parasitic effects. Methodologically, localized grounding structures are introduced to construct a controlled electromagnetic boundary. The system’s main path exhibits alternating inductive-capacitive (L-C) coupling, with a single explicit capacitive cross-coupling introduced between specific nodes (resonators 2 and 5). Based on the principle of multi-path signal cancellation, this explicit path synergizes with the implicit parasitic environment. By satisfying conditions of equal amplitude and a 180° phase difference at specific frequencies, a high-order hybrid network is equivalently reconstructed, generating four transmission zeros (TZs). A compact sixth-order LTCC filter was fabricated and tested. Measured results demonstrate a fractional bandwidth (FBW) of 38.6%, a shape factor of 1.16 (based on the 20-dB/3-dB bandwidth ratio), and a 20-dB upper stopband extending beyond $4.28f_0$. In conclusion, the rational utilization—rather than forced isolation—of inherent parasitic effects provides an effective solution for enhancing frequency selectivity and stopband performance in high-density integrated RF front-ends.

1. Introduction

Modern wireless communication and radar systems (particularly sub-6 GHz 5 G, Wi-Fi coexistence, and S-band aeronautical applications) are rapidly evolving toward high integration, imposing stringent requirements on the miniaturization and performance enhancement of radio frequency (RF) front-end passive components [1,2]. As core components for spectrum allocation, bandpass filters (BPFs) urgently require an optimal engineering balance among multidimensional metrics, including physical footprint, fractional bandwidth (FBW), frequency selectivity, and out-of-band suppression.

Although traditional metallic cavity filters exhibit high unloaded quality factors (Q-values) and excellent electromagnetic isolation, their bulky volumes are incompatible with modern highly integrated RF front-end architectures. Among existing miniaturization technologies, acoustic wave filters (SAW/BAW) are constrained by their acoustic resonance mechanisms, suffering from narrow stopbands and a vulnerability to transverse leakage and parasitic spurious modes at high frequencies [3]. Meanwhile, integrated passive devices (IPDs) operating in the S-band face limitations such as relatively low unloaded Q-values, high in-band insertion loss (IL), and large footprint requirements [4]. In contrast, low-temperature co-fired ceramic (LTCC) technology, leveraging its three-dimensional (3D) multilayer stacking capability [5], offers superior spatial utilization compared to IPDs in the same frequency band, along with Q-values bridging the gap between acoustic filters and IPDs. Consequently, it has emerged as a core technological pathway for designing high-density RF modules.

In addition to LTCC, substrate integrated waveguide (SIW) and multilayer folded half-mode substrate integrated waveguide (FHMSIW) technologies have been widely adopted for high-performance filter designs [6,7]. Compared to these technologies—which are typically based on standard planar processes and offer lower prototyping costs and clear electromagnetic field distributions—SIW/FHMSIW structures often occupy a larger planar footprint, limiting extreme spatial miniaturization. Furthermore, integrating SIW structures into compact modules frequently relies on wire-bonding interconnections, which introduce significant parasitic effects. In contrast, while LTCC technology involves higher initial manufacturing investments and complex 3D full-wave design challenges, its superior vertical integration capability supports wire-free interconnections (e.g., flip-chip), enabling true 3D system-in-package (SiP) integration. In large-scale production, LTCC becomes more cost-effective due to its extremely small unit area.

However, within compact 3D LTCC environments, intricate parasitic cross-couplings are inevitably induced between non-adjacent resonators. When traditional ideal microwave cavity synthesis theory is directly mapped onto LTCC designs, significant deviations frequently occur between the theoretical coupling matrix and the physical response. To mitigate this, conventional LTCC designs attempt to physically sever these parasitic paths by introducing dense shielding ground-via arrays [8] or constructing peripheral square via-walls [9]. Although such approaches maintain the purity of the main topology, they inevitably increase the overall volume of the filter and compromise the flexibility of 3D spatial routing.

Recently, several advanced studies have attempted to address parasitic effects by shifting from “forced isolation” to “parasitic handling.” For instance, “parasitic-aware” design strategies have been proposed to absorb via-induced parasitic inductances into equivalent circuits to generate additional zeros [10], or to transform spatial parasitic couplings into cascaded triplet (CT) structures for zero reconstruction [11]. However, these strategies essentially still treat the passively generated implicit parasitic effects as a negative burden that must be “hedged” or “compensated” for through precise modeling. Their design processes often require fine-grained extraction of local parasitic parameters and the complex synthesis of large-scale equivalent networks, which significantly increases design complexity and the sensitivity of physical implementation.

To bridge the gap between the physical constraints of forced isolation and the modeling complexity of existing parasitic-aware methods, this paper proposes a “controlled parasitic utilization” strategy. Unlike approaches aimed at individual parasitic compensation, this strategy treats the intricate 3D parasitic environment as a synergistic functional entity. By introducing localized grounding structures to establish controlled electromagnetic boundaries, we introduce only a single intentional cross-coupling path. This explicit path is designed to work in concert with the inherent implicit parasitic environment to achieve multi-path signal cancellation. Based on this method, a compact sixth-order LTCC BPF with four transmission zeros (TZs) was designed, fabricated, and tested. The main contributions of this work are summarized as follows:

• Proposal of a controlled parasitic utilization strategy: The feasibility of an engineering trade-off between the “partial isolation of higher-order modes” and the “partial utilization of residual parasitic fields” in compact LTCC structures is investigated. This approach effectively transforms “unavoidable parasitics” into ”designable degrees of freedom” by establishing controlled electromagnetic boundaries, providing a solid physical foundation for field-circuit co-design;
• Equivalent reconstruction of multiple TZs based on a minimalist physical architecture: Within the controlled boundaries, a single “dumbbell-shaped” explicit cross-coupling path is explored. Crucially, the four TZs are generated by the combined effect of different mechanisms: two TZs are physically contributed by the single explicitly designed cross-coupling path, while the other two TZs are inherently formed by the multipath parasitic couplings in the 3D LTCC environment. Their synergy achieves the equivalent reconstruction of a high-order hybrid network with four TZs without increasing layout complexity;
• Engineering realization of multidimensional metrics: The measured results demonstrate that, while achieving spatial compactness, the designed filter obtains an FBW of 38.6% and a shape factor of 1.16 (calculated based on the 20-dB/3-dB bandwidth ratio). Furthermore, it exhibits an upper stopband suppression extending up to $4.28f_0$, providing an effective and practical structural reference for high-density RF modules.

2. Theoretical Synthesis and Equivalent Topological Reconstruction Strategy

2.1. System-Level Synthesis and Ideal Coupling Topology

To meet the requirements of modern wireless systems for broadband transmission and high out-of-band rejection, a compact and highly selective LTCC bandpass filter was designed. Its core electrical specifications are detailed in

Table 1. Filter design specifications.

No.	Item	Characteristics
1	Center Frequency $f_0$	2850 MHz
2	Passband	2300–3400 MHz
3	Insertion Loss (IL)	≤3.0 dB
4	In-band VSWR	≤1.7
5	In-band Ripple	≤1.0 dB
6	Stopband Attenuation	≥35 dB (@ DC–1.9 GHz)
		≥25 dB (@ 1.9–2.1 GHz)
		≥20 dB (@ 3.7–4.0 GHz)
		≥35 dB (@ 4.0–8.0 GHz)
		≥15 dB (@ 8.0–13.4 GHz)
7	Input/Output Impedance	50 $\Omega$

.

The synthesis process is based on the Generalized Chebyshev method, incorporating the practical constraints of the LTCC process (where the unloaded quality factor of the resonators is set to approximately 90). In this synthesis, to ensure the impedance matching required by the in-band VSWR (≤1.7) in Table 1, an equi-ripple return loss level of approximately 20 dB was specified. Simultaneously, to satisfy the stringent stopband attenuation requirements, four transmission zeros (TZ1–TZ4) were strategically prescribed. These zeros are physically positioned at approximately 1.7 GHz and 2.1 GHz for the lower stopband, and 3.8 GHz and 4.8 GHz for the upper stopband, respectively.

Analysis indicates that to balance the impedance matching of a 38.6% FBW with out-of-band roll-off characteristics, the system must achieve a sixth-order (6-pole) filtering response featuring four transmission zeros (4-TZs). The ideal normalized coupling matrix M corresponding to this target response is synthesized as follows (Equation (1)):

$$M=\left(\begin{array}{cccccccc}0& -0.995& 0& 0& 0& 0& 0& 0\\ -0.995& -0.001& 0.830& 0& 0& 0.006& 0.123& 0\\ 0& 0.830& 0& -0.580& -0.050& -0.155& 0& 0\\ 0& 0& -0.580& 0.085& 0.698& 0& 0& 0\\ 0& 0& -0.050& 0.698& -0.025& -0.580& 0& 0\\ 0& 0.006& -0.155& 0& -0.580& -0.002& 0.830& 0\\ 0& 0.123& 0& 0& 0& 0.830& -0.002& -0.995\\ 0& 0& 0& 0& 0& 0& -0.995& 0\end{array}\right).$$

(1)

Figure 1b illustrates the theoretical coupling topology corresponding to Matrix M, which clearly defines the physical significance of each matrix element. The main transmission path consists of the source/load external couplings ($M_{S1},M_{6L}$) and the sequential inter-resonator couplings ($M_{12},M_{23},M_{34},M_{45},M_{56}$). To generate the four TZs, the theory requires a specific set of cross-couplings between non-adjacent nodes (namely $M_{15},M_{16},M_{24}$, and $M_{25}$).

It should be noted that in the compact 3D LTCC environment, distributed implicit parasitic couplings (indicated by the grey lines in Figure 1b) are often difficult to quantify and control independently. Therefore, the topology in Figure 1b serves as a macro-equivalent model. The design logic of this work is as follows: while ensuring the accurate construction of the main coupling path, only a single, unique explicit cross-coupling path is introduced (the red dashed line $M_{25}$ in Figure 1b). By tuning this single variable to interact synergistically with the complex implicit parasitic environment, multi-path signal interference is harnessed to equivalently achieve the multi-zero response required by the ideal matrix M. This strategy enables an optimal balance between high performance and compact physical dimensions within a constrained space.

2.2. Physical Implementation Constraints and Equivalent Topological Reconstruction Strategy

Figure 1b illustrates the theoretical coupling topology of the filter. If the topology in Equation (1) were to be strictly mapped in an ideal, parasitic-free environment, the system would require the construction of at least four independent explicit cross-coupling paths within the physical space. However, directly routing multiple independent paths in a 3D multilayer LTCC space would inevitably increase the physical volume and induce higher-order spurious modes. Traditional designs typically impose forced isolation on parasitic couplings, which becomes impractical under high-density integration conditions.

To address this limitation, a topological equivalent reconstruction strategy is adopted in this study: the physical implementation of the ideal matrix is decoupled into two phases: “main path construction” and a “parasitic-utilization cross-network”. First, a main path with relatively high isolation is established based on a modular physical structure (implementing only adjacent couplings $M_{i,i+1}$). Subsequently, a single explicit cross-coupling path is explored. By synergizing with the implicit parasitic environment within the 3D space, this explicit path equivalently reconstructs the hybrid coupling network required to generate multiple TZs in the circuit domain.

2.3. Mathematical Mapping of Target Parameters for the Main Path

To translate the aforementioned reconstruction strategy into a physical design, the normalized main-path coupling coefficients ($m_{i,i+1}$) and the external coupling coefficient ($m_{S1}$) must be mapped to the actual physical coupling coefficients ($M_{i,i+1}$) and external quality factor ($Q_e$). Their mathematical relationships are given by the following equations:

$$M_{i,i+1}=m_{i,i+1}\times \mathrm{FBW},$$

(2)

$$Q_e={\displaystyle \frac{1}{m_{S1}^2\times \mathrm{FBW}}},$$

(3)

where $\mathrm{FBW}$ represents the fractional bandwidth of the filter. Based on the system specifications in Table 1 and the synthesized normalized theoretical values, the initial target parameters extracted for the physical design are as follows:

• Target main-path coupling coefficients: $M_{12}=M_{56}\approx 0.32$, $M_{23}=M_{45}\approx -0.22$, $M_{34}\approx 0.27$;
• Target external quality factor: $Q_e\approx 2.6$.

These target values serve as the theoretical benchmark for the subsequent structural dimension optimization of the main path. The physical equivalent reconstruction process of the cross-coupling network will be elaborated in Section 3.

3. 3D Modular Architecture Design and Evolution Mechanism of Multi-Path Cancellation Zeros

3.1. Miniaturized Multilayer Resonator Unit

The resonator is the fundamental unit that determines the eigenfrequency and insertion loss (IL) of the filter. This design adopts a resonator topology based on 3D multilayer stacking, as illustrated in Figure 2.

In this architecture, the metal patch $C_1$ and the ground plane $G_1$ constitute the capacitive portion of the resonator, while the metalized vias $H{C}_1$ and $H{L}_1$, along with the multilayer strip $L_1$, form the inductive portion. Electromagnetic field distribution analysis, as shown in Figure 3a,b, reveals that, alternating between the 0° and 180° phases, the magnetic field is primarily concentrated in the central inductive structure; conversely, at the 90° and 270° phases, the electric field is predominantly distributed between the plates. This dynamic conversion process of electromagnetic energy verifies the parallel LC resonance characteristics of the structure.

3.2. Extraction of Main-Path Basic Parameters Based on the Modular Architecture

To mitigate cross-interference among non-adjacent components in a complex 3D environment, the initial physical dimensions of the main path are first extracted using a simplified eigenmode simulation model.

Inductive coupling control (taking ${\mathit{M}}_{\mathbf{12}}$ coupling as an example): To achieve the theoretically required inductive coupling (theoretical target value ${\mathit{M}}_{\mathbf{12}}\approx \mathbf{0.32}$), specific inductive coupling metal topologies are embedded between adjacent resonators (as indicated by the red sections in Figure 4). By parametrically sweeping the vertical position height (${\mathit{H}}_{\mathbf{2}}$) of the coupling strip, the fundamental dimension is determined to be ${\mathit{H}}_{\mathbf{2}}=\mathbf{207}\mathsf{\mu }\mathbf{m}$.

Capacitive coupling basic extraction (taking ${\mathit{M}}_{\mathbf{23}}$ as an example): For capacitive coupling nodes (theoretical target value ${\mathit{M}}_{\mathbf{23}}\approx -\mathbf{0.22}$), utilizing a simplified cross-coupling model (as shown in Figure 5), the overlapping area of the capacitive cross-stacking between the two resonators is adjusted. After sweeping and extraction, the fundamental dimension is determined to be ${\mathit{L}}_{\mathbf{1}}=\mathbf{61}\mathsf{\mu }\mathbf{m}$.

External feed control: The external quality factor (${\mathit{Q}}_{\mathit{e}}$) dictates the energy interaction between the system and the ports. By constructing a single-port loaded model (Figure 6), the group delay (${\mathit{\tau }}_{\mathit{S}\mathbf{11}}$) of the port reflection is extracted. The physical mapping relationship between ${\mathit{Q}}_{\mathit{e}}$ and the group delay ${\mathit{\tau }}_{\mathit{S}\mathbf{11}}$ can be calculated using Equation (4):

$${\mathit{Q}}_{\mathit{e}}={\displaystyle \frac{\mathit{\pi }{\mathit{f}}_{\mathbf{0}}{\mathit{\tau }}_{\mathit{S}\mathbf{11}}}{\mathbf{2}}},$$

(4)

where ${\mathit{f}}_{\mathbf{0}}$ is the center resonant frequency of the filter. Based on this theoretical mapping, a parametric sweep is conducted on the physical coupling length (${\mathit{L}}_{\mathit{tap}}$) of the tapped feed to ultimately determine the fundamental dimension ${\mathit{L}}_{\mathit{tap}}=\mathbf{1.1}\mathbf{mm}$, ensuring it satisfies the synthesized target values.

3.3. Reconstruction of Controlled EM Boundaries and Multi-Path Cancellation Mechanism

When integrating independent resonators into a high-density full model, implicit parasitic cross-couplings within the compact space inevitably deteriorate the out-of-band response. To address this, grounded isolation metal components are introduced at specific physical boundaries. The design adopts a synergistic strategy of “partial isolation of higher-order modes” and “controlled utilization of residual parasitic fields.” Specifically, the isolation boundaries sever the primary adjacent spurious couplings, restructuring the interior into an electromagnetic microenvironment with controlled parasitic effects. To rigorously verify its role, comparative 3D full-wave simulations were conducted. The results demonstrate that without these grounding structures, the uncontrollable spatial parasitics lead to a reduction in the number of transmission zeros (TZs) from four to three, and a significant degradation in passband return loss (${\mathit{S}}_{\mathbf{11}}$ degrades to approximately $-\mathbf{5}$ dB). This confirms that establishing the controlled boundary is an essential physical prerequisite for stabilizing the parasitic phases required to sustain the multi-zero response.

Based on this stabilized microenvironment, a single explicit capacitive cross-coupling path (${\mathit{M}}_{\mathbf{25}}$) is introduced between resonators 2 and 5. By tuning the physical overlapping length (${\mathit{M}}_{\mathbf{25}\_\mathit{dx}}$), its mechanism of action on the transmission response (${\mathit{S}}_{\mathbf{21}}$) is analyzed in Figure 7.

Evolution of Transmission Zeros: Full-wave simulation results (Figure 7) indicate that when the overlapping length is small, the system exhibits two TZs. As this physical parameter exceeds a specific “phase reconstruction threshold” ($\mathit{M}{\mathbf{25}}_{\mathit{dx}}\approx \mathbf{0.26}$ mm), the signal cancellation conditions at both ends of the stopband are sequentially triggered, evolving into four TZs. The physical significance of this threshold is that only when the explicit coupling path (${\mathit{M}}_{\mathbf{25}}$) reaches the same order of magnitude as the residual parasitic components in the 3D space can they form strong synergistic interference to jointly satisfy the cancellation conditions at additional frequency points.

Theoretical Mechanism and Circuit-Level Validation: To elucidate the specific generation mechanism, we decouple the signal transmission into three parallel interference paths, as illustrated in the Signal Flow Graph (SFG) in Figure 8a:

• Path A (${\mathit{P}}_{\mathit{main}}$): The sequential cascading path between adjacent nodes ($\mathbf{1}\to \mathbf{2}\to \mathbf{3}\to \mathbf{4}\to \mathbf{5}\to \mathbf{6}$);
• Path B (${\mathit{P}}_{\mathit{Explicit}}$): The explicit cross-coupling path introduced by the ${\mathit{M}}_{\mathbf{25}}$ structure ($\mathbf{2}\to \mathbf{5}$);
• Path C (${\mathit{P}}_{\mathit{Implicit}}$): The implicit parasitic path represented as an equivalent ${\mathit{M}}_{\mathbf{16}}$ coupling ($\mathbf{1}\to \mathbf{6}$).

To rigorously validate this theory, an equivalent circuit model was established in Advanced Design System (ADS) 2023 (Keysight Technologies, Santa Rosa, CA, USA). A circuit-level ablation study (Figure 8b) reveals the synergistic effect:

• With both couplings (Black line): The complete response with four TZs is achieved.
• Only ${\mathit{M}}_{\mathbf{25}}$ (Red line): When the implicit ${\mathit{M}}_{\mathbf{16}}$ path is removed, the far-end TZs disappear, and the response reverts to a standard 2-TZ dual-path cancellation.
• Only ${\mathit{M}}_{\mathbf{16}}$ (Grey line): When the explicit ${\mathit{M}}_{\mathbf{25}}$ branch is removed, all four TZs disappear, and the selectivity significantly degrades.

This evidence confirms that the controlled EM boundary stabilizes the implicit ${\mathit{M}}_{\mathbf{16}}$ path, which synergizes with the explicit ${\mathit{M}}_{\mathbf{25}}$ path to reconstruct a high-order hybrid network with four TZs.

4. Full-Model Simulation, Fabrication, and Experimental Validation

Based on the key physical dimensions determined previously, this section constructs a 3D full model of the filter for simulation validation. The simulated results are then compared with the measured data of the fabricated LTCC prototype to verify the effectiveness of the proposed equivalent reconstruction strategy.

4.1. Global Co-Optimization and Full-Model Electromagnetic Simulation

The independently extracted modular resonator units and the controlled coupling boundaries (including isolation components and explicit cross-coupling bridges) were integrated into a 3D full-wave electromagnetic simulation environment (HFSS 2023 R2 (ANSYS Inc., Canonsburg, PA, USA)) to establish the complete physical model (as shown in Figure 9). Due to the fringing effects induced by the multilayer stacked structure, the initial combined response exhibits a certain deviation from the ideal coupling matrix.

Consequently, a global joint optimization was performed on the entire full model. The optimized full-wave S-parameter response (Figure 10) satisfies the predefined system design specifications:

• Passband matching characteristics: Within the passband from 2.3 GHz to 3.4 GHz, the port return loss (${\mathit{S}}_{\mathbf{11}}$) is better than 15 dB. The insertion loss (${\mathit{S}}_{\mathbf{21}}$) at the center frequency is approximately 0.79 dB, indicating that the adopted multilayer stacked resonator architecture maintains a good unloaded quality factor within a compact volume;
• Stopband and multiple transmission zeros: The simulated response generates four transmission zeros on both sides of the passband. This result verifies the previous theoretical analysis: the single explicit structure synergizes with the implicit parasitic environment to equivalently reconstruct a multi-zero response based on the multi-path cancellation mechanism. Furthermore, the filter achieves a stopband suppression of greater than 20 dB in the upper stopband, extending up to $\mathbf{4.28}{\mathit{f}}_{\mathbf{0}}$.

4.2. Physical Lamination Process and Miniaturized Fabrication

To validate the aforementioned 3D electromagnetic model, dielectric lamination and layout fabrication were implemented based on standard low-temperature co-fired ceramic (LTCC) manufacturing processes.

Figure 11a illustrates the stacked cross-sectional structure of the filter and the thickness ratio of each dielectric layer. Figure 11b displays the layout of the key metal layers used for screen printing, while Figure 11c details the via layers used for vertical metallization. The detailed physical dimensions of the proposed LTCC filter are systematically summarized in

Table 2. Key Physical Dimensions of the Proposed LTCC Filter.

Parameter	Description	Value (Unit)
Overall & Dielectric Specifications
${\mathit{L}}_{\mathit{total}}\times {\mathit{W}}_{\mathit{total}}$	Total length and width of the LTCC chip	4.8 × 4.2 mm
${\mathit{H}}_{\mathbf{0}},{\mathit{H}}_{\mathbf{6}}$	Thickness of thick LTCC dielectric layers	484, 430 μm
${\mathit{H}}_{\mathbf{1}}-{\mathit{H}}_{\mathbf{5}}$	Thickness of standard LTCC layers	42 μm (each)
${\mathit{H}}_{\mathbf{7}}-{\mathit{H}}_{\mathbf{10}}$	Thickness of thin LTCC layers	30–40 μm
${\mathit{H}}_{\mathbf{11}}$	Thickness of bottom LTCC layer	126 μm
Resonator & Internal GND Parameters
${\mathit{L}}_{\mathit{res}}$	Length of the main vertical resonator traces	2.8 mm
${\mathit{W}}_{\mathit{res}}$	Width of the main vertical resonator traces	0.19 mm
${\mathit{L}}_{\mathit{slot}}$	Length of the slots on internal GND plane	1.3 mm
${\mathit{W}}_{\mathit{slot}}$	Width of the slots on internal GND plane	0.172 mm
Explicit Cross-Coupling Parameters
${\mathit{L}}_{\mathit{cross}}$	Total span of the explicit cross-coupling structure	1.67 mm
${\mathit{L}}_{\mathit{P}}$	Length of the narrow connective strip in cross-coupling	0.677 mm
${\mathit{W}}_{\mathit{C}}$	Width of the capacitive dumbbell p in cross-coupling	0.255 mm
Via Array Parameters
${\mathit{d}}_{\mathit{via}}$	Diameter of all vertical metallized vias	100 μm
${\mathit{S}}_{\mathit{via}}$	Gap between adjacent individual vias in resonators	0.30 mm
${\mathit{P}}_{\mathit{via}}$	Center-to-center pitch of the dense via array	0.375 mm

.

During the layout design and physical fabrication phases, the robustness of the proposed filter against practical manufacturing tolerances and LTCC process variations was systematically quantified and addressed:

• Tolerance to Lateral Alignment Errors (X/Y-axis): In standard LTCC stacking processes, lateral registration errors are typically strictly controlled within 10 μm. To completely immunize the design against such deviations, an asymmetric “oversized-pad” layout strategy was inherently applied to the critical capacitive coupling nodes (as observed in Figure 11b). By deliberately designing one capacitive plate larger than its overlapping counterpart, slight lateral misalignments do not alter the effective overlapping area. This ensures that the equivalent coupling coefficients remain exceptionally stable under transverse fabrication tolerances.
• Robustness to Vertical Shrinkage Variations (Z-axis): LTCC green tapes naturally experience vertical shrinkage variations (typically $\le \mathbf{5}\%$) during the high-temperature co-firing phase. Full-wave tolerance simulations in HFSS verify that a $\mathbf{5}\%$ fluctuation in the vertical dimension introduces acceptable variations in the overall S-parameters (such as slight fluctuations in passband matching and a minor frequency shift). Nevertheless, the critical four-TZ topology and stopband suppression levels are well preserved without severe deterioration. Furthermore, in practical fabrication, any systematic longitudinal shrinkage error can be effectively eliminated by fine-tuning the isostatic pressing pressure prior to the co-firing process.

Following the aforementioned physical layout, the fabricated LTCC bandpass filter prototype is shown in Figure 12, with physical dimensions of $\mathbf{4.8}\times \mathbf{4.2}\times \mathbf{1.5}{\mathbf{mm}}^{\mathbf{3}}$.

4.3. Measured Results and Comparative Analysis

A vector network analyzer (VNA) was used to conduct S-parameter measurements on the fabricated LTCC prototype. A comparison between the measured and full-wave simulated results is presented in Figure 13.

The measured data demonstrate that the tested curves agree well with the theoretical full-wave predictions, covering a fractional bandwidth of 38.6%. Four transmission zeros were successfully observed on the low-frequency side (approximately 1.7 GHz and 2.1 GHz) and the high-frequency side (approximately 3.8 GHz and 4.8 GHz).

The minor deviations between the measured and simulated curves in specific frequency bands are primarily attributed to the following two objective engineering factors:

• Slight frequency shift: Normal manufacturing tolerances in the actual 3D physical shrinkage rate of the LTCC green tapes during the high-temperature co-firing process cause slight variations in the physical dimensions and equivalent dielectric constant of the internal resonators, thereby inducing a slight shift in the overall spectrum;
• Parasitic perturbation and engineering mitigation in the high-frequency stopband: As shown in the updated Figure 13, the extended 14-GHz full-wave simulation confirms that the spurious passband around 12.5 GHz is an inherent higher-order mode of the structure, showing excellent agreement with the measurement and validating the accuracy of the 3D EM model. However, a slight degradation in the suppression level (floor lifting to approximately $-\mathbf{40}$ dB) is observed between 5 GHz and 11.5 GHz. This perturbation is primarily investigated as a substrate thickness discrepancy between the simulation (0.254 mm) and the practical test fixture (0.508 mm). For the 0.508 mm board used in the measurement, maintaining a 50-Ω impedance requires a wide microstrip line (approx. 1.015 mm), which introduces a significant geometric step-discontinuity against the narrow LTCC pads. This physical mismatch triggers high-frequency spatial radiation and substrate leakage. Although TRL (Thru-Reflect-Line) de-embedding was effectively applied, it cannot mathematically eliminate such unguided 3D radiations originating from physical structural mismatches. For practical integration, it is highly recommended to ensure the trace width physically matches the port size by selecting thinner substrates or materials with lower dielectric constants (e.g., Rogers), and to use staggered ground vias to suppress substrate modes. Nevertheless, the measured rejection consistently maintains over 35 dB up to 11.5 GHz, satisfying the practical requirements of the target application.

Overall, the successful reproduction of the four evolved transmission zeros and the wide stopband characteristics fully verify the theoretical correctness and physical realizability of the proposed topological equivalent reconstruction strategy.

5. Performance Comparison and Discussion

To evaluate the effectiveness of the proposed “controlled parasitic utilization” design methodology,

Table 3. Performance comparison with recently reported and commercial-grade filters.

Ref. & Year	Design Tech.	${\mathit{f}}_0$ (GHz)/FBW (%)	IL (dB)	No. of TZs	Shape Factor 1	20-dB Stopband	Normalized Size (${\mathit{\lambda }}_0^3$)
[12] 2018	PCB	0.35/101.8	0.6	>4	∼1.50	$\mathbf{10}{\mathit{f}}_{\mathbf{0}}$	$\mathbf{0.129}\times \mathbf{0.141}\times \mathbf{0.002}$
[13] 2021	PCB	8.25/91.0	<1.5	3	1.29	$\mathbf{1.6}{\mathit{f}}_{\mathbf{0}}$	$\mathbf{0.440}\times \mathbf{0.251}\times \mathbf{0.014}$
[14] 2023	BAW	1.90/2.1	1.5	Multi	<1.1	Limited 2	<0.001
[15] 2026	LTCC	3.60/160.0	<2.0	2	—	$\mathbf{4.4}{\mathit{f}}_{\mathbf{0}}$	$\mathbf{0.072}\times \mathbf{0.048}\times \mathbf{0.024}$
[16] 2022	LTCC	3.50/32.0	1.35	5	1.98	$\mathbf{2.2}{\mathit{f}}_{\mathbf{0}}$	$\mathbf{0.071}\times \mathbf{0.079}\times \mathbf{0.011}$
[17] 2025	LTCC	3.70/19.1	1.3	3	—	>10.8${\mathit{f}}_{\mathbf{0}}$	$\mathbf{0.068}\times \mathbf{0.041}\times \mathbf{0.023}$
This work	LTCC	2.85/38.6	<1.7	4	1.16	$\mathbf{4.28}{\mathit{f}}_{\mathbf{0}}$	$\mathbf{0.046}\times \mathbf{0.040}\times \mathbf{0.014}$

¹ Shape Factor: ${\mathrm{BW}}_{\mathbf{20}\mathrm{dB}}/{\mathrm{BW}}_{\mathbf{3}\mathrm{dB}}$. ² Acoustic filters often require external LPFs for extended stopband suppression in RF front-ends.

compares its performance with recently reported filters using planar PCB, acoustic-wave (BAW), and advanced LTCC technologies. Achieving an engineering trade-off among fractional bandwidth (FBW), frequency selectivity, out-of-band suppression, and normalized physical size is critical in passive RF design.

As summarized in Table 3, filters based on planar PCB technology [12,13] exhibit wideband characteristics but suffer from large normalized sizes and poor high-frequency stopbands. In contrast, acoustic-wave filters (BAW/SAW), such as [14], offer extreme die-level miniaturization and steep selectivity. However, their fractional bandwidth is inherently limited (only 2.1%), and their far-end stopband suppression is often restricted. In practical RF front-end applications, acoustic filters typically require additional external low-pass or band-stop filters to suppress harmonics. This multi-chip cascading not only increases insertion loss but also results in a total system-level footprint that significantly exceeds a single integrated LTCC solution.

Within the LTCC domain, different design philosophies lead to distinct trade-offs. The design in [15] achieves a massive 160% FBW using a composite cascaded topology; however, this architecture relies on a large number of discrete components, leading to an expanded normalized volume. The design in [16] provides high selectivity (5 TZs) via distributed stepped-impedance stubs (SIS) but at the cost of a significantly larger footprint. To further minimize size, recent work [17] introduces dense isolation via-walls to suppress parasitic couplings. While this facilitates compact folding, such “forced isolation” increases sensitivity to fabrication tolerances, which may lead to performance degradation during manufacturing as reflected in their measured results. Additionally, its FBW (19.1%) remains lower than that of the proposed design.

In contrast, this work adopts a “controlled parasitic utilization” strategy. It is worth noting that the adopted architecture theoretically supports much wider FBWs; the 38.6% FBW demonstrated here is not a topological limitation, but rather an optimized engineering choice tailored to specific 5G system requirements. Instead of resorting to volume-increasing forced isolation or complex cascading, we transform inevitable 3D parasitics into functional parts of the hybrid network. This allows for the realization of four TZs, a high-selectivity shape factor (1.16), and a wide stopband ($\mathbf{4.28}{\mathit{f}}_{\mathbf{0}}$) within a highly constrained physical space. Consequently, the proposed design offers an optimal engineering balance between wideband performance, out-of-band suppression, and single-chip compactness while maintaining high fabrication robustness, providing a highly competitive solution for high-density transceivers.

6. Conclusions

This paper proposes and experimentally verifies a design method for a compact LTCC wideband bandpass filter based on a controlled parasitic utilization strategy. Unlike traditional methods that rely on dense via arrays for the forced isolation of parasitic couplings, this study introduces localized grounding structures within the compact LTCC microenvironment to construct controlled electromagnetic boundaries. Specifically, the main path of the system exhibits alternating inductive-capacitive (L-C) coupling characteristics. Building upon this, a single explicit capacitive cross-coupling structure is introduced between specific nodes (resonators 2 and 5). Based on the principle of multi-path signal cancellation, this explicit path synergizes with the 3D implicit parasitic environment, satisfying the conditions of equal amplitude and a 180° phase difference at specific frequencies. This mechanism equivalently reconstructs a high-order hybrid coupling network, thereby generating four transmission zeros (TZs).

The fabricated sixth-order LTCC experimental prototype achieves a wide fractional bandwidth of 38.6%, a shape factor of 1.16, a broad 20-dB upper stopband extending beyond $\mathbf{4.28}{\mathit{f}}_{\mathbf{0}}$, and a highly compact spatial footprint. The high consistency between theoretical analysis and microwave measurements confirms the physical realizability of this method. This study demonstrates that the rational utilization and guidance of parasitic couplings in high-density 3D integration environments provide an effective engineering trade-off solution for enhancing the frequency selectivity and stopband performance of RF passive components.