MicrostripLine

class pmrf.models.components.lines.MicrostripLine(length: Any = 1.0, w: Any = 0.003, h: Any = 0.0016, epr: Any = 4.3, tand: Any = 0.0, rho: Any = 0.0, *, name: str | None = None, z0: complex = 50 + 0j)

Bases: RLGCLine

Microstrip line defined by standard geometric and material properties.

Relies on standard Wheeler approximations. Note that configurations where height > width (h > w) are not yet supported.

Mathematical Formulation

With ratio \(u = \frac{W}{H}\), the effective relative permittivity (\(\varepsilon_e\)) and ideal impedance terms (\(Z_a, Z_e\)) are:

\[\varepsilon_e = \frac{\varepsilon_r + 1}{2} + \frac{\varepsilon_r - 1}{2} \frac{1}{\sqrt{1 + 12/u}}\]

\[Z_a = \frac{120\pi}{u + 1.393 + 0.667 \ln(u + 1.444)}\]

\[Z_e = \frac{Z_a}{\sqrt{\varepsilon_e}}\]

Which provide the per-unit-length components:

\[L = \frac{Z_e \sqrt{\varepsilon_e}}{c}\]

\[C = \frac{\sqrt{\varepsilon_e}}{Z_e c}\]

\[R = \frac{1}{W} \sqrt{2 \mu_0 \rho \omega}\]

\[G = \frac{1}{Z_a c} \frac{\varepsilon_r (\varepsilon_e - 1)}{\varepsilon_r - 1} \tan\delta \cdot \omega\]

Example

import pmrf as prf
from pmrf.core import MicrostripLine

phys_microstrip = MicrostripLine(
    w=4e-3,
    h=2.0e-3,
    epr=4.6,
    tand=0.025,
    rho=1.72e-8,
    length=0.5
)

freq = prf.Frequency(start=1, stop=20, npoints=101, unit='ghz')
s_phys = phys_microstrip.s(freq)

Variables:

• w (Parameter, default=3e-3) – Width of the microstrip trace in meters.

• h (Parameter, default=1.6e-3) – Height of the dielectric substrate in meters.

• epr (Parameter, default=4.3) – Relative permittivity of the dielectric substrate.

• tand (Parameter, default=0.0) – Dielectric loss tangent.

• rho (Parameter, default=0.0) – Resistivity of the conductor trace and ground plane in Ohm-meters.

rlgc(freq: Frequency) → tuple[Array, Array, Array, Array]

Calculates the frequency-dependent RLGC parameters.

Parameters:

freq (Frequency) – The frequency axis.

Returns:

The R, L, G, and C parameter vectors.

Return type:

tuple

epr: Parameter = 4.3

h: Parameter = 0.0016

rho: Parameter = 0.0

tand: Parameter = 0.0

w: Parameter = 0.003