Shielded symmetrical bandline transmission lines offer some noteworthy characteristics for high-frequency designs, including low signal loss. In order to better understand the nature of these transmission lines, they were examined using the finite-element method (FEM) ^1,2 method-of-moments (MoM) analysis, ³ and curve-fitting techniques. Through these analysis approaches, a set of closed-form equations was developed to determine the characteristic impedances and the primary inductance and capacitance matrices (the [L] and [C] matrices, respectively) for a shielded symmetrical bandline. These general expressions provide good accuracy for shielded symmetrical bandlines with a wide range of discontinuity angles, and can be used with band-lines having outer-to-inner conductor-radius ratios of 2 to 7. The design equations were applied to create an RF coupler with high coupling ratio, and can be readily implemented in modern computer-aided-engineering (CAE) software tools for the design of couplers, resonators, ⁴ filters, and probes among other microwave and wireless components.

and

L_O = the proper inductance of the isolated line,

C_O = the proper capacitance of the isolated line,

M = the mutual inductance of the coupled line, and

γ= the coupling capacitance of the coupled line.

A variety of numerical techniques are available to accurately determine the characteristic impedance and the primary parameters of the coupled line. But they are time-consuming and too tedious for use in circuit design, where closed-form analytical models are to be preferred. By applying FEM and MoM analyses along with curve-fitting strategies, it is possible to develop these closed-form expressions for determining the characteristic impedance and primary parameters of coupled shielded symmetrical bandline. Figure 1 offers a cross-sectional view of a shielded symmetrical bandline. The line is assumed to be lossless. It has inner conductor radius of r_o, with negligible thickness w, outer shield radius of r_b, and discontinuity angle of θ.

Numerical results for the characteristic impedances of a shielded symmetrical bandline as determined by the FEM and MoM approaches are shown in Fig. 2 and Fig. 3. The close match of the results demonstrates good coherence between the two methods. The FEM analysis approach was also used to determine the effects of the discontinuity angle on different parameters for the shielded symmetrical bandline, with the results shown in Fig. 4, Fig. 5, Fig. 6, and Fig. 7.