By Professor Dr. Takanori Okoshi (auth.)
Until lately, 3 relevant periods were identified within the electric cir cuitry. They have been as follows: 1) The lumped-constant circuit, which could be known as a zero-dimensional circuit, within the feel that the circuit parts are a lot smaller in measurement in comparison with the wavelength in all 3 spatial instructions. 2) The distributed-constant circuit, which will be known as a one-dimensional circuit, within the experience that the circuit parts are a lot smaller than the wavelength in instructions yet akin to the wavelength in a single di rection. three) The waveguide circuit, which could be known as a third-dimensional circuit, within the feel that the circuit components are such as the wavelength in all 3 instructions. The relevant topic of this booklet is the research and layout (synthesis) theories for an additional circuit category which seemed within the past due Sixties and have become universal within the Seventies. This new circuit classification is four) the planar circuit, which could be referred to as a two-dimensional circuit, within the experience that the circuit components are a lot smaller in dimension in comparison with the wavelength in a single path, yet resembling the wavelength within the different directions.
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Extra info for Planar Circuits for Microwaves and Lightwaves
Example text
Instead, annular sectors as well as circular sectors are frequently found in actual MIC circuit components. 7]. 10 shows some of the practical cases in which such planar circuit elements constitute microstrip bends and tapers. 7] Green's functions for a circular sector and an annular sector are derived. However, the details are omitted here because of space limitations. 6 Open-Ended Stripline (Comparison with Distributed-Constant Line Theory) Finally, an open-ended stripline (Fig. 11) is analyzed to compare the result with that of distributed-constant line theory.
27), i(xo, Yo) denotes an assumed (fictitious) rf current density injected normally into the circuit (Fig. 4). In ordinary triplate-type planar circuits, however, current is injected not normally, but from the periphery where coupling ports are present. Moreover, as to the rf voltage V, we are usually concerned only with the voltage along the periphery. 29) where s and So are used to denote distance along C, and in is the line current density outward normal to C at coupling ports. 29) shows that the rf voltage along the periphery is determined if the current density along the periphery is given, provided that the Green's function is known.
Is Euler's constant, and I j = - 2in Wj represents the total current flowing into thejth port on both the upper and lower surfaces of the circuit plate. 4) has been derived by integrating the asymptotic expression of Hb2 )(kr) for kr ~ 1, assuming that the ith section is straight. The other formulas may be obtained in a straightforward manner. 3) gives Uii = 1 when Wi is small. 5) Here Vand I denote column vectors consisting of Vi and hand U and Hare NxN matrices consisting of uij and hij, respectively.