Attenuation coefficient in metal of microstrip line when width is greater than thickness¶
Under the conditions described below, the attenuation coefficient of the microstrip metal can be calculated from the surge impedance of the line, the surface resistance of the metal, the effective permittivity of the substrate, and the physical dimensions of the system.
Conditions:
The thickness of the substrate of the microstrip line should be less than the effective width.
- attenuation_coefficient¶
attenuation_coefficientof the metal of the microstrip line.
- Symbol:
alpha- Latex:
\(\alpha\)
- Dimension:
1/length
- surface_resistance¶
electrical_resistanceof the surface of the metal strip.
- Symbol:
R_s- Latex:
\(R_\text{s}\)
- Dimension:
impedance
- surge_impedance¶
surge_impedanceof the microstrip line.
- Symbol:
Z_S- Latex:
\(Z_\text{S}\)
- Dimension:
impedance
- Symbol:
h- Latex:
\(h\)
- Dimension:
length
- effective_width¶
Effective width (see
length) of the microstrip line. See Effective width of microstrip line.
- Symbol:
w_eff- Latex:
\(w_\text{eff}\)
- Dimension:
length
- Symbol:
t- Latex:
\(t\)
- Dimension:
length
- effective_permittivity¶
Effective
relative_permittivityof the microstrip line. See Effective permittivity of microstrip line.
- Symbol:
epsilon_eff- Latex:
\(\varepsilon_\text{eff}\)
- Dimension:
dimensionless
- constant¶
Constant equal to \(6.1 \cdot 10^{-5} \, \Omega^{-2}\) (
6.1e-5 Ohm^(-2)).
- Symbol:
a- Latex:
\(a\)
- Dimension:
impedance**(-2)
- law¶
alpha = a * R_s * Z_S * epsilon_eff / h * (w_eff / h + 0.667 * w_eff / h / (w_eff / h + 1.444)) * (1 + (1 - 1.25 / pi * t / h + 1.25 / pi * log(2 * h / t)) / (w_eff / h))- Latex:
- \[\alpha = \frac{a R_\text{s} Z_\text{S} \varepsilon_\text{eff}}{h} \left(\frac{w_\text{eff}}{h} + \frac{0.667 \frac{w_\text{eff}}{h}}{\frac{w_\text{eff}}{h} + 1.444}\right) \left(1 + \frac{1 - \frac{1.25}{\pi} \frac{t}{h} + \frac{1.25}{\pi} \log \left( \frac{2 h}{t} \right)}{\frac{w_\text{eff}}{h}}\right)\]