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Step in Coaxial TEM Waveguide: CSTEPIO

Symbol

Summary

CSTEPIO is a closed form model of a double-step in inner and outer conductors. Both steps share the same cross-section and have a common reference plane. CSTEPIO allows a step in the dielectric constant at the same cross section. Step discontinuity is represented as shunt frequency-independent capacitance.

Topology

Parameters

Name Description Unit Type Default
Di1 Diameter of inner conductor @ Node 1 Length 2.9027 mm
Do1 Diameter of outer conductor @ Node 1 Length 10.287 mm
Di2 Diameter of inner conductor @ Node 2 Length 2.9027 mm
Do2 Diameter of outer conductor @ Node 2 Length 10.287 mm
Er1 Relative dielectric constant filling the coaxial waveguide @ Node 1   1
Er2 Relative dielectric constant filling the coaxial waveguide @ Node 2   1

Parameter Details

Er1, Er2. Dielectric constants of media filling the coaxial waveguide at both sides of the reference plane (see "Topology").

Implementation Details

CSTEPIO is implemented as a closed form approximation of total step capacitance based on [1]. Note that [1] uses the results of a full solution ([2]) to obtain this approximation. The absolute approximation error in capacitance (if εr1r2)can be estimated (according to [1]) as 0.18(Di+Do)pF where Di and Do stand for averaged inner and outer diameters (expressed in meters). If εr1≠εr2, then the error may increase because accounting for the inhomogeneous dielectric does not come from the approximation of the full solution, but is rather based on phenomenologically justified assumptions.

Layout

This element does not have an assigned layout cell. You can assign artwork cells to any element. See “Assigning Artwork Cells to Layout of Schematic Elements” for details.

Recommendations for Use

CSTEPIO allows any combination of Di1, Do1, Di2, Do2, Er1, Er2. However, the best results are achieved if the following inequalities hold:

0.01<α<0.7

1.5<τ<6

For outer step α is (Domin-Di)/(Domax-Di). Here Domin,Domax stands for the smaller and larger of the outer diameters and Di stands for each of the inner diameters. α should be tested for both Di. The τ variable should be evaluated and tested as Domax/Di for both Di.

For the inner step, α is (Do-Dimax)/(Domax-Dimin). Here Dimin, Dimax stands for the smaller and larger of the inner diameters and Do stands for each of the outer diameters. α should be tested for both Do. The τ variable should be evaluated and tested as Do/Dimin for both Do.

This model implies that step capacitance is frequency-independent. According to [1], step capacitance generally grows with frequency and deviates from static value at about 10% if the evaluation frequency exceeds 0.4 Fc, where Fc is the lower cutoff frequency of mode TM01 for coaxial waveguides at nodes 1 and 2.

This lower cutoff frequency may be evaluated as the lower value

(where c in the nominator is the speed of light, ε stands for dielectric constant, and Do,Di are outer and inner diameters) applied in turn to coaxial waveguides at node 1 and node 2.

NOTE: This model is developed to work in a frequency range where only dominant TEM mode propagates.

References

[1] Somlo, P.I, "The Computation of Coaxial Line Step Capacitances", IEEE Trans on MTT, vol. 15, No. 1, January 1967, pp. 48-53.

[2] Whinnery J.R, Jamieson H.W, Robins T.E, "Coaxial-lines discontinuities", Proc. of the IRE, vol. 32, November 1944, pp.695-709

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