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Physical Length Spec, Floating Shield (Closed Form): COAXI4

Symbol

Summary

COAXI4 simulates a lossy transmission line with a floating shield. This model implies that the total loss is proportional to the square root of the evaluation frequency and demands that you input a specified loss at a specified frequency. Characteristic impedance is represented by user specified input.

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 the 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.

Parameters

Name Description Unit Type Default
ID Element ID Text CX1
Z Characteristic impedance   50
L Length Length 0 um
K Dielectric constant   2.3
A Loss in dB/meter   0.0833
F Frequency loss is specified at Frequency 0.1 GHz

Parameter Details

A and F. These parameters 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 zero at all frequencies. Note that attenuation is extrapolated across frequency sweep so do not set F to an extremely low value.

Implementation Details

Dielectric constant K and computed (see the previous details of parameters A and F) attenuation are used to obtain a complex propagation constant. Entries of Y-matrix of a grounded transmission line system are determined via the characteristic impedance and computed complex propagation constant that you specify.

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

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

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

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

where R is a real resistance approaching zero.

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

You can use this model along with additional components to model transmission line baluns and transmission line transformers.

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.

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