Impedances of π-type circuit of transmission line

The π-type circuit consists of the first impedance connected in parallel, the third impedance connected in series, and the second impedance connected in parallel. For a transmission line, these impedances can be calculated for an equivalent replacement circuit by knowing the transmission line parameters.

first_impedance

First electrical_impedance.

Symbol:

Z_1

Latex:

Z1

Dimension:

impedance

second_impedance

Second electrical_impedance.

Symbol:

Z_2

Latex:

Z2

Dimension:

impedance

third_impedance

Third electrical_impedance.

Symbol:

Z_3

Latex:

Z3

Dimension:

impedance

surge_impedance

surge_impedance of the transmission line.

Symbol:

Z_S

Latex:

ZS

Dimension:

impedance

length

length of the transmission line.

Symbol:

l

Latex:

l

Dimension:

length

propagation_constant

propagation_constant.

Symbol:

gamma

Latex:

γ

Dimension:

1/length

law

[Z_1, Z_2, Z_3] = [Z_S * coth(l * gamma / 2), Z_S * coth(l * gamma / 2), Z_S * sinh(l * gamma)]

Latex:
(Z1Z2Z3)=(ZScoth(lγ2)ZScoth(lγ2)ZSsinh(lγ))