**1. Introduction**

In recent years, wireless communication equipment has been rapidly researched and developed such as Internet of Things (IoT), wireless local area network (LAN), and 5G, and it is expected that the demand for wireless communication equipment will become more widespread in the future. Along with this, various microwave circuit elements mounted on wireless communication devices are also required to have higher performance, such as miniaturization, low loss, high integration, and wideband/multiband. The authors are paying attention to the power divider/combiner that divides/combines microwave signals among various microwave circuit elements. The reason is that the power divider/combiner is considered to be an important circuit element that is directly linked to its performance in microwave circuits.

As a power divider/combiner for a three-port network, the Wilkinson power divider (hereinafter referred to as a conventional circuit) composed of two quarter wavelength transmission lines at a design frequency and an absorption resistor connected between two output ports is widely used at several microwave/millimeterwave circuit system such as a balanced amplifier, a mixer, a phase shifter, an antenna feeding network, and so on [1]. However, since the circuit size depends on the wavelength due to the distributed circuit configuration, there arises a problem that the area occupied by the circuit system becomes especially large in a low-frequency band. As a method for reducing the size of a microwave circuit, a method of replacing a transmission line with a Π-type/T-type circuit equivalent to that at the design frequency is often used, but the equivalence between the two circuits is guaranteed only at the design frequency [2]. Therefore, such a circuit generally has a narrow band

characteristic. In addition to that, as a method of shortening the transmission line, methods of loading parallel capacitances or parallel open-circuited stubs at both ends or the center of the transmission line have been reported [3–6]. In addition, some miniaturization design methods using composite right-/left-handed transmission lines and lumped elements have also been proposed [7–10]. However, their operation bands are still narrower than that of the conventional circuit. Therefore, it is considered difficult to achieve both miniaturization and wide bandwidth of the circuit at the same time. On the other hand, our research group proposes a configuration using an LCladder circuit as a lumped-element circuit type Wilkinson power divider. It has been analytically and experimentally clarified that a configuration using a two-stage LCladder circuit on the input side can realize frequency characteristics equal to or higher than those of the conventional circuit. Furthermore, ultra-wideband power dividers, unequal power dividers, and *N*-way power dividers, etc., in a circuit configuration, using LC-ladder circuits have been also reported [11–15].

This chapter shows how to design a power divider that can be matched at arbitrary two frequencies with a simple circuit configuration with 9 lumped elements. The circuit is designed for application in IoT (920 MHz) and 5G (sub6 band: 3.7 GHz). The influence of the self-resonant frequency of the chip element used in the circuit configuration is considered in the SHF-band, so the inductance is realized using a meander line or a bent line. Electromagnetic field simulations and prototype experiments confirm the effectiveness of the two-frequency matching circuit with a quasi-lumpedelement circuit configuration. It should be noted that this circuit also has a feature that high-pass or low-pass characteristics can be selected by replacing the inductance L and the capacitance C of the components.

In the circuit configuration described above, the frequency characteristic of either the high-frequency or the low-frequency band becomes a narrow band. Therefore, the number of stages of the LC-ladder circuit was increased, and a circuit with 15 elements in which an LC-ladder circuit and an LR/CR circuit were connected in parallel between the output ports enabled three-frequency matching. It was shown that by moving the matching frequency in the middle of the three matching frequencies closer to the low-frequency side or the high-frequency side, a divider having an absolute constant bandwidth in the low-frequency and high-frequency bands becomes possible.

Furthermore, ultra-wideband characteristics are possible by increasing the number of stages in the LC-ladder circuit. As a method for widening the bandwidth of impedance transformers, quarter wavelength multistage transformers are also described in Pozer's book and are often used. By using the concept of this multistage impedance transformer [16] and L-type matching circuit [17], a circuit with a relative bandwidth exceeding 100% in the UHF band was realized. Specifically, we have experimentally confirmed an ultra-wideband divider with a relative bandwidth of 100% or more, which covers the 80 MHz–370 MHz band used for public radio in Japan, with a lumped-element circuit configuration.
