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WaveLength Spec, Floating Shield, Improved Accuracy (Closed Form): TLINP4NL



TLINP4NL simulates a transmission line with isolated (floating) ground terminals. The characteristics of the transmission line are specified as the characteristic impedance and the electrical length at a given frequency. By default, this model provides a partial account for circuit loss (insertion loss only). You can toggle the secondary parameter LossModel to access insertion loss, return loss, and dielectric loss (for example; for microstrips or stripline). Use 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. Unusual and unexpected behavior can result if these additional elements are omitted.

Equivalent Circuit

Note that any interaction with the ground on either side of the transmission line is ignored. All current on one conductor is equal and opposite to the current on the other at any given distance along the line. Importantly, this condition is enforced regardless of the length of the transmission line or the operating frequency. The exception to this behavior is at DC (Frequency = 0 Hz) where current on the two conductors can be unequal to allow both conductors to be used for biasing active devices. This change in behavior at DC causes a discontinuity of the model parameters at DC. This discontinuity is expected, and additional circuit components relating the voltage at each end of the transmission line to ground should be added, allowing flexibility in implementing the desired transition to the RF-to-DC performance.


Name Description Unit Type Default
ID Element ID Text TL1
Z Impedance   50
NL Number of wavelengths at F_NL   0.25
F_NL Frequency at NL wavelengths Frequency 1 GHz
K Dielectric constant   1
A Loss (dB/m)   0
F Frequency for scaling loss   0
*LossModel Partial/Full account for conductor and dielectric loss   Partial
*TanD Dielectric loss tangent   0
*Mur Relative dielectric permeability   1
*TanM Dielectric magnetic loss tangent   0
*Sigma Dielectric bulk conductivity (S/m)   0
*EpsFreqDep Dielectric constant is frequency dependent (No/Yes)   No
*Fmin Low roll-off frequency of Tand frequency dependence Frequency 1kHz
*Fmax High roll-off frequency of Tand frequency dependence Frequency 1THz
*Fspec Er and Tand are specified at this frequency Frequency 1GHz

* indicates a hidden secondary parameter

Parameter Details

Note that parameters marked by asterisk (*) are hidden/invisible while the control parameter LossModel=Partial (default value). Setting LossModel=Full displays these secondary parameters in the model's Element Options dialog box Parameters tab (except parameters Fmin, Fmax, and Fspec which are visible only when parameter EpsFreqDep=Yes).

NL and F_NL. Determine the frequency-dependence of the electrical length of the line, described as βL=2πNL(freq/F_NL) where freq is the evaluation frequency. The length of the line is given as L=(c·NL)/(F_NL√k) where c is the speed of light in a vacuum.

A and F. Determine the frequency-dependence of the attenuation constant. If F is not equal to zero (0.0), then

(dB/m) where freq is the evaluation frequency. If F is equal to zero, the attenuation is constant versus frequency and is equal to A (dB/m).

LossModel is a secondary control parameter that defines how the model accounts for loss and dielectric parameters. If LossModel=Partial (default value) then the model accounts for insertion loss (parameter Loss) only. If LossModel=Full then the model accounts for insertion loss, return loss, dielectric loss, and for frequency-dependent model of dielectric parameters (for example, for microstrips, stripline, or other).

NOTE: The secondary parameter LossModel displays when you click the Show or hide secondary parameters button on the toolbar of the the Element Options dialog box Parameters tab. If LossModel=Full, additional secondary parameters display.

EpsFreqDep is a (hidden, secondary) control parameter that defines if dielectric constant and dielectric loss tangent exhibit predefined frequency-dependence, suggested in [1]. This dependence is controlled by the three frequency parameters Fmin, Fmax, and Fspec, and imparts causal behavior to the model. Fmin, Fmax, and Fspec are hidden (invisible) if EpsFreqDep=No.

Implementation Details

The following is a Y-matrix for a grounded transmission line system:

where α+jβ represents the complex propagation constant, Z is the characteristic impedance of the line and L is the length of the line as derived from the input parameters.

Applying the equivalent circuit shown above, the Y-matrix of the floating transmission line system can be shown as follows:

At DC, the Y-matrix changes to a model of two wires above a ground plane:

where R is a real resistance approaching zero.


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

This model, along with additional components can be used to model transmission line baluns and transmission line transformers in which one of the conductors is shielded from ground, like a coaxial line.

NOTE: Because the model definition does not include interactions with the 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 ground.


[1] 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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