piel.models.physical.electrical.transmission_lines.microstrip

piel.models.physical.electrical.transmission_lines.microstrip#

Functions#

epsilon_e(epsilon_r, width_m, dielectric_thickness_m)

Calculate the effective dielectric constant (ε_e) for a microstrip.

Z_0(width_m, dielectric_thickness_m, epsilon_e)

Calculate the characteristic impedance (Z₀) of a microstrip.

alpha_c(surface_resistance_ohms, ...)

Calculate the attenuation constant (α_c) in decibels per meter (dB/m).

R_s(frequency_Hz, conductivity_S_per_m[, ...])

Calculate the surface resistivity (R_s) of a conductor at a given frequency.

Module Contents#

epsilon_e(epsilon_r, width_m, dielectric_thickness_m)[source]#

Calculate the effective dielectric constant (ε_e) for a microstrip.

The effective dielectric constant accounts for the field distribution between the microstrip and the substrate, influencing signal propagation.

Parameters:

  • epsilon_r (float) – Relative permittivity (dielectric constant) of the substrate.

  • width_m (float) – Width of the microstrip line (meters).

  • dielectric_thickness_m (float) – Thickness of the substrate (meters).

Returns:

epsilon_e – Effective dielectric constant.

Return type:

float

References

Equation (2):

ε_e = (ε_r + 1)/2 + (ε_r - 1)/2 * 1/sqrt(1 + 12*dielectric_thickness_m/width_m)

Z_0(width_m, dielectric_thickness_m, epsilon_e)[source]#

Calculate the characteristic impedance (Z₀) of a microstrip.

The characteristic impedance represents the inherent resistance that the transmission line presents to the signal propagating through it.

Parameters:

  • width_m (float) – Width of the microstrip line (meters).

  • dielectric_thickness_m (float) – Thickness of the substrate (meters).

  • epsilon_e (float) – Effective dielectric constant of the microstrip.

Returns:

characteristic_impedance_ohms – Characteristic impedance in Ohms.

Return type:

float

References

Equation (1):

Z₀ = 120π / [√ε_e * (width_m/dielectric_thickness_m + 1.393 + 0.667 ln(width_m/dielectric_thickness_m + 1.444))]

alpha_c(surface_resistance_ohms, characteristic_impedance_ohms, width_m)[source]#

Calculate the attenuation constant (α_c) in decibels per meter (dB/m).

The attenuation constant measures how much signal is lost per meter due to resistive (ohmic) losses in the conductor of the microstrip line.

Parameters:

  • surface_resistance_ohms (float) – Surface resistance of the conductor (Ohms).

  • characteristic_impedance_ohms (float) – Characteristic impedance of the microstrip (Ohms).

  • width_m (float) – Width of the microstrip line (meters).

Returns:

alpha_c – Attenuation constant in dB/m.

Return type:

float

References

Equation (3):

α_c (dB/m) = 8.68588 * (R_s / (Z₀ * width_m))

R_s(frequency_Hz, conductivity_S_per_m, permeability_free_space=mu_0.value)[source]#

Calculate the surface resistivity (R_s) of a conductor at a given frequency.

The surface resistivity is a measure of how much a conductor resists current flow along its surface, and it increases with frequency due to the skin effect.

Parameters:

  • frequency_Hz (float) – Frequency at which the resistivity is calculated (Hz).

  • conductivity_S_per_m (float) – Electrical conductivity of the conductor (S/m).

  • permeability_free_space (float, optional) – Permeability of free space (H/m). Default is the value from mu_0.

Returns:

  • surface_resistance_ohms (float) – Surface resistivity in Ohms.

  • Formula

  • ——-

  • R_s = sqrt(ω * μ₀ / (2 * σ))

  • Where

  • ω = 2π * frequency_Hz (angular frequency in rad/s)

  • μ₀ = Permeability of free space (H/m)

  • σ = Conductivity (S/m)

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