## 6 Conclusions  
Two innovative lateral-space-independent dielectric resonator-based microstrip filters (DRMFs) have been successfully developed and experimentally validated as follows: one incorporating transmission zeros (TZs) and another utilizing equalization zeros (EZs). The designs differ exclusively in the rotation direction of their curved cross-coupling transmission lines. Both were originally designed for 60 MHz bandwidth in X-band, though the 4-2-0 configuration could only be adjusted to 45 MHz, while the equalization-based 4-0-2 version achieved the full 60 MHz bandwidth without compromise. These solutions demonstrate precise control of zero positioning, input-output coupling, inter-resonator coupling, and frequency tuning. While prior literature has extensively studied dielectric resonator cavity filters (DRCFs) [14; 15], and the \(TE_{01\delta}\) mode, no microstrip-based multi-resonator dielectric filters had been implemented previously--with research limited to standalone DR characterization, alternative resonance modes, or stop-band applications [37], primarily due to their high quality factor requirements. This work advances the state-of-the-art by establishing an intermediate technology between DRCFs and conventional microstrip filters (MFs) through the following three key innovations: novel transmission/equalization zero implementations, an innovative input coupling topology, and the first comprehensive characterization of the \(TE_{01\delta}\) mode in this configuration. The characterization methodology optimizes dielectric resonator geometry and aspect ratio to maximize the intrinsic quality factor \(Q_{i}\) via efficient energy confinement when coupled to the microstrip curved transmission line (C-TL). A novel input-output coupling technique employing open-ended high-impedance stubs enhances maximum coupling while compensating for the \(TE_{01\delta}\) mode's characteristic behavior, where coupling strength oscillates between constructive maxima (phase-aligned \begin{table}
\begin{tabular}{l l l l} \hline
**Parameter** & **DRCF** & **MF** & **DRMF** \\ \hline Frequency stability & Excellent & Moderate & Excellent \\ Q-factor & High & Low & Medium \\ Insertion Loss & Low & High & Medium \\ Size/Envelope & Large & Small & Medium \\ Mass & Heavy & Light & Medium \\ Manufacturing complexity & High & Low & Medium \\ Temperature stability & Excellent & Moderate & Excellent \\ Tuning flexibility & Mechanical & None & Mechanical \\ \hline \end{tabular}
\end{table} 
Table 6: DRCF vs. MF vs. DRMF Comparison for Space Applications \begin{table}
\begin{tabular}{l c} \hline
**Parameter** & **Value/Type** \\ \hline Bandwidth (BW) & 60.0 MHz \\ Insertion Loss (IL) & 1.9 dB \\ Quality Factor (\(Q_{L}\)) & \textgreater{}4000 \\ Return Loss (RL) & 16.5 dB \\ Group Delay Variation & 9 ns \\ \hline
**Tuning Type** & **Implementation** \\ \hline I/O Coupling & Phase-aligned stubs \\ Inter-resonator Coupling & Iris tuning \\ Frequency Tuning & Screw over resonators \\ EZ Generation & TL (length in multiples of N\(\lambda\)/4, with \(N\in\{1,3,5,\dots\}\)) \\ \multicolumn{2}{l}{C-TL arc} \\ Frequency Tuning & Capacitive loading screws \\ \hline \end{tabular}
\end{table} 
Table 5: 4-0-2 Topology with Equalization Zeros (EZs)transmission-line/resonator fields) and destructive minima (phase-opposed fields) as a function of electrical length. This length-dependent coupling mechanism has been thoroughly analyzed, physically interpreted, and mathematically modeled to enable efficient filter design. The measured results demonstrate strong correlation with simulations when using adjustment screws, achieving RL exceeding 18 dB (TZ filter) and 16.5 dB (EZ filter), with maximum insertion losses of 2.4 dB and 1.9 dB, respectively. This represents a significant improvement over conventional microstrip filters. The loaded quality factors \(Q_{L}\) reach approximately 3000 for the TZ configuration and exceed 4000 for the EZ implementation, with the EZ filter showing superior group delay ripple reduction as theoretically predicted.