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In this paper, a compact filtering coupler is presented using a new microstrip configuration. To improve the frequency response, achieve good phase balance and reduce the losses of the proposed coupler, an optimization method is used along with a mathematical analysis method. Our coupler works at 1.9 GHz, which is suitable for 5G and GSM applications. The working frequency range of our designed coupler is from 1.84 GHz to 2.11 GHz, where it has a fractional bandwidth (FBW) of 13.7%. The phase and magnitude imbalances are only $0.029^{o}$ and 0.08 dB, respectively, making it suitable for applications in microwave components, communication and radar systems. The maximum group delays at the direct and coupling ports are 1.9 ns and 2.3 ns, respectively. This is an advantage because most of the previously reported microstrip couplers have not addressed the group delay improvement. The other advantages of our coupler are its filtering frequency response and a good isolation factor of -42 dB around the operating frequency. The proposed structure is mathematically analyzed and optimized. It is fabricated and measured to verify the simulation results and the proposed mathematical analysis. The results show that all mathematical analysis, simulation and measurement results are in good agreement. The experimental results confirm its performance in terms of low losses, low group delay and low phase and magnitude imbalances. Therefore, the presented design offers a significant improvement over the traditional couplers, which generally suffer from the large size, high group delay and poor phase and magnitude balances.

A new microstrip triplexer with a compact size of $0.007~\lambda _{\mathrm {g}}^{2}$ is proposed in this work, where designing a microstrip triplexer with a size less than $0.01~\lambda _{\mathrm {g}}^{2}$ is a big challenge. In addition to the compact size, it shows a high performance i.e. its channels are wide with low insertion losses. Moreover, the channels are flat with three low group delays (GDs) of 0.65, 0.95 and 1.17 ns, while most of the previously reported triplexers have not considered this important parameter. The proposed resonator is mathematically analyzed to find a method to get rid of harmonics and tune the resonance frequency. Meanwhile, the $1^{st}$ , $2^{nd}$ , $3^{rd}$ and $4^{th}$ harmonics are suppressed above the first channel. The designed triplexer is suitable for 5G mid-band applications. The proposed triplexer is exactly fabricated and then measured to confirm the designing method and simulation results. The obtained results show that all the simulation, mathematical analysis and experimental results are in good agreement. Therefore, the proposed triplexer can be easily used in designing high-performance RF communication systems.