On a transmission line lowpass filter fabricated on a printed circuit board using open-circuited microstrip straight-line stubs, the frequency at the edge of a passband or stopband tends to be higher than the frequency determined by the filter synthesis theory. One of the reasons for this is thought to be the interconnection of a low-impedance straight-line stub and transmission lines. The length of a constituent transmission line cannot be determined precisely because of the finite width. Therefore, as a means of avoiding the frequency shift between a trial circuit and a theoretical one, we first introduce a radial-line stub, and then show the equivalency of a radial-line stub to a straight-line stub in a range of zero to the first resonant frequency from the view point of their input impedances. Dimensional data of radial-line stubs corresponding to low-impedance straight-line stubs are investigated with respect to examples of three-, five- and seven-element Butterworth and Chebyshev filters. It was found that frequency characteristics of trial lowpass filters using radial-line stubs agree well with theoretical characteristics known as the Butterworth or Chebyshev.

This study proposes a 3 dB branch-line coupler using radial stubs to achieve reduced coupler size and simplified stub arrangement. As the electrical lengths of stubs used here are less than 90at center frequency, a method of comparing input impedances to obtain radial stubs that are equivalent to straight stubs is discussed. The frequency characteristics of the proposed coupler are derived by combining classical transmission line theory with the computed data of radial stub input impedances. The methods presented here increase possibilities for realizing reduced branch-line couplers by means of stub design. Experimental results agree well with theoretical results except for slight differences in the high frequency region.

Network functions (NFs) such as network reflection and transmission coefficients are discussed about an interconnected network consisting of a lumped distributed N-port N non-commensurate line junction network (N-port) and a M-port. The derivation of the NFs can be done quite easily regardless of the complexity of the network by considering the flow of the traveling waves and conditions of the interconnected interface of the two multi-ports. The theory of this paper has been examined with respect to interconnected networks consisting of two 3-ports in both the time and frequency domains, and has shown good results consistent with other papers. The network functions described here can be used not only for the analysis of high-speed pulse propagation in digital systems with branches but also for the analysis of microwave distributed line networks such as hybird rings. In that sense, a new analysis method is presented in this paper.

Realization of a planar dual-band fork three-way power divider (PDBF3PD) with Cheng's equivalent structure is discussed. The Cheng's structure consists of two open-circuited stubs and a transmission line, and the characteristic impedances tend to be high. As a result, the realizable range of frequency ratios of upper frequency to lower frequency is limited in a narrow area. In this paper, an impedance scale factor is proposed to transform characteristic impedances into a realizable range and to facilitate the design of PDBF3PDs. Theoretical considerations are verified using a simulator of ADS2008U and by an experiment.

A rat-race hybrid-ring which includes a coupled-line called microwave C-section is proposed for size reduction. The perfect input match, isolation, equal power split and certain phase differences between two output ports can be satisfied at center frequency as in a normal hybrid-ring. The size of the proposed circuit becomes smaller than that of a normal rat-race built up with a folded non-coupled 3/4-wavelength transmission line, although the frequency characteristics are slightly damaged by the electromagnetic coupling between two folded strips. Theoretical results based on the even and odd mode decomposition method are in good agreement with those of the experimental circuit fabricated at 1 GHz.

Networks in this paper consist of non-commensurate transmission lines with branches and branching resistors at junctions. When signals on a transmission line are divided multiple ways at the junctions of branched lines, multiple reflection waves occur by the impedance mismatching. For the analysis of multiple reflections and network design, lattice diagrams have been used so far. However, the expansions of network transfer functions provide an easier way for the same purpose as in the case of lattice diagram. The output transient responses can be directly calculated from the expansions of network transfer functions or can be numerically calculated by software such as the fast Laplace transform. Therefore, once the network transfer functions are given, calculation of transient responses can be carried out quite easily. In this paper, the expansions of network transfer functions have been derived with respect to delay elements ξi=exp(-sτi) by formularizing the propagation of multiple reflection waves, and then the multi-variable rational network transfer functions have been obtained from the expansions. As an example, a 3-port transmission line network with normalized characteristic impedances 1, 1, 6 and normalized branching resistors 1/23, 1/23, 126/23 has been taken up. As the terminal resistances at output ports can be determined from the relation of the first arriving wave to the steady state, the design of 3-port transmission line networks which will furnish output waveforms similar to the waveform of the input within given tolerances has been considered. The output waveforms have been calculated for pure terminal resistances and for the pure terminal resistances plus parasitic parallel capacitances.

In the time domain, the single-element directional coupler will act as a digital frequency doubler, which converts a train of unipolar pulses into a train of faster bipolar pulses. This paper provides simulated output pulses for input Cosine half waves using measured phase and attenuation characteristics to show good agreement with both the theoretical response and previous experimental results.