**4. Multistage LC-ladder divider**

#### **4.1 Circuit construction and design results**

By increasing the number of stages of the LC-ladder circuit, the operating band can be expanded, corresponding to the number of stages. In this section, the number of stages of the LC-ladder circuit on the input side is set to 8, and the ultra-wideband (relative bandwidth 100% over), an equal power division circuit with characteristics, will be described.

As a design method that uses lumped elements and realizes wideband characteristics while avoiding an increase in circuit size, there is a method that uses an LC-ladder impedance transformer. Here, we show the design method of the multiband LC-ladder divider proposed by Okada et al. and focus on the viewpoint of wideband and multiband. **Figure 11a** shows a multiband power divider consisting of multiple LCladder circuits and an RL series circuit on the output side. The figure shows an *N*-stage LC-ladder circuit (*L*<sup>1</sup> *<sup>N</sup>*, *C*<sup>1</sup> *<sup>N</sup>*) connected between Port1 and Port 2/3 and a ladder circuit with *L* and *C* interchanged between Port2/3 (*C*(*<sup>N</sup>* + 1) (2*<sup>N</sup>* 1), *L*(*<sup>N</sup>* + 1) (2*<sup>N</sup>* 1)), *RL*2*<sup>N</sup>* series circuit. Since the number of matching frequencies in this circuit corresponds to the number of stages *N* of the LC-ladder circuit, it can operate as a power divider with arbitrary *N* frequency matching according to the number of stages. In applying the even-/odd-mode excitation method to the circuit in **Figure 11a**, consider an equivalent circuit having a mirror image symmetry structure in the vertical direction as described above. **Figure 11b** shows the equivalent circuit of a multiband circuit with the plane AA' as the plane of symmetry. Considering this figure, each input/output port has terminal resistors *R*1, *R*2, and *R*3, the input side element is doubled in parallel, and the output side

**Figure 12.**

*Frequency characteristics of scattering parameters for N-section LC-ladder dividers: (a) four-section, (b) sixsection, and (c) eight-section LC-ladder dividers.*

element is divided, and the value is halved. The circuit design is possible using even-/ odd-mode excitation methods as in Sections 2 and 3. As a result of designing the circuit, it can be seen that the relative bandwidth is expanded by increasing the number of stages of the LC-ladder divider. In **Figure 12a**-**c** are the cases where the number of stages is 4, 6, and 8, and the specific bandwidths are 98%, 108%, and 115%, respectively. By increasing the number of stages, the band becomes a wide band, but it becomes saturated to some extent when the number of stages is about 8.
