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Physical Specification: Floating Shield, Improved Causality (Closed Form): COAXC



COAXC simulates a lossy, optionally coated coaxial transmission line with isolated shield terminals. The physical model fully accounts for the complex skin effect in the inner conductor and outer (shield) conductor as well as in the metal coating. COAXC is able to model causal frequency-dependence of material properties of the filling dielectric. COAXC is recommended for modeling in both time and frequency domains.

Topology (Cross-section)


Name Description Unit Type Default
ID Element ID Text CX1
Di Diameter of inner conductor (with coating) Length 2.9027 mm
Doi Inner diameter of outer conductor (with coating) Length 10.287 mm
Doo Outer diameter of outer conductor Length 10.387 mm
Tc Thickness of coating metal Length 0 mm
L Line length Length 10 mm
Er Relative dielectric constant of filling dielectric   1
Tand Dielectric loss tangent of filling dielectric   0
Rho Coaxial metal bulk resistivity normalized to gold   1
RhoC Coating metal bulk resistivity normalized to gold   1
Mur Relative permeability of filling dielectric   1
*IsEpsFreqDep Switch: Dielectric constant is frequency dependent/independent   Frequency independent dielectric constant
*Fmin Low roll-off frequency of Tand frequency dependence Frequency 1 KHz
*Fmax High roll-off frequency of Tand frequency dependence Frequency 1 THz
*Fspec Er and Tand are specified at this frequency Frequency 1 GHz

* indicates a secondary parameter

Parameter Details

Di, Doi, Doo. These parameters define inner and outer diameters of internal cross-section of coaxial line. Default values are set to dimensions of RG-213 50 ohm coax. Note that coating thickness Tc is included in values Di and Doi (see the "Topology" section).

IsEpsFreqDep. This parameter assumes two options: "Frequency independent dielectric constant" and "Frequency dependent dielectric constant". The first option implies that Er and Tand do not change with frequency. The second option applies frequency dependence on Er and Tand based on the causal model suggested in [4], which employs parameters Fdef, Fmin, and Fmax.

Fmin, Fspec, Fmax. These parameters are in effect only if IsEpsFreqDep = "Frequency dependent dielectric constant". Those are frequencies defining behavior of the causal model suggested in [4]. Fspec is the frequency at which COAXC parameters Er and Tand are specified; Fmin and Fmax are frequencies at which frequency dependences of Er and Tand roll off. Mandatory relation between these frequencies is: Fmin<<Fspec<<Fmax.

Implementation Details

Implementation is based on modeling the coax as TEM line and the determination of primary per-unit-length RLGC parameters ([1]). R and L parameters fully account for the skin effect ([2], [3]). Causal frequency-dependence of dielectric constant and loss tangent is implemented after [4]. These RLGC parameters are used to obtain complex characteristic parameters of dominant propagating TEM mode (characteristic impedance and propagation constant). This model does not account for the possible propagation of higher-order modes.

See the descriptions of the TLIN4 model for details of implementation of models with floating ground.

Circuit Model Synthesis

COAXC supports synthesis of physical parameters based on electrical specifications using the Transmission Line Calculator. To open the Transmission Line Calculator, right-click a transmission line element in a schematic and choose Synthesize.

To perform transmission line synthesis:

  1. In the Electrical property grid, select Target check boxes for desired electrical parameters and enter a corresponding value.

  2. In the Physical property grid, update frequency and substrate parameters if needed, then select Synthesize check boxes for transmission line physical parameters to synthesize based on the targets.

  3. Click the Synthesize left arrow to run the synthesis program. The values in both property grids update with the synthesized results. An analysis is also performed with the final physical values. If synthesis cannot achieve the target values, it shows how close it came.

  4. Click OK to update the selected transmission line element with the synthesized physical parameters. Expressions are overwritten with the new, evaluated values. You can click the Undo button on the program toolbar to revert all parameters in the schematic document to their pre-synthesized state. Parameters from substrate elements are never updated since typically substrate elements are used by more than one transmission line element. Click Cancel to close the dialog box without setting the parameters into the element.

Recommendations for Use

You should exercise extreme care with this element as it is meant to work in concert with additional elements which relate the voltages at both ends of the transmission line to the global ground.

NOTE: Because the model definition does not include interactions with the global ground, unusual and unexpected results can occur if other components are not used to relate the voltage on both sides of the transmission line to global ground.


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.


[1] M.Gunston, Microwave Transmission Line Impedance Data: Noble Publishing Corporation, Tucker,GA, 1997, (reprint), Section 2.3

[2] S.Ramo and J.R.Whinnery, Fields and Waves in Modern Radio, 1st ed., General Electric Advanced Engineering Program, New York, NY; London, England: J.Wiley and Sons, Inc.; Chapman and Hall, 1944"

[3] S. A. Schelkunoff, "The Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields", Bell System Technical Journal, Vol. 13, No. 4, pp. 532–579, October 1934

[4] A.R. Djordjevic et al., "Wideband Frequency-Domain Characterization of FR-4 and Time-Domain Causality", IEEE Trans. of Electromagn. Compat., Vol. 43, No. 4, Nov. 2001

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