Wave impedance of Lange coupler

The Lange coupler is based on microstrip transmission lines. When this coupler is in operation, both even and odd modes are distributed. Knowing the wave impedance for even and odd modes, it is possible to calculate the equivalent wave impedance of the coupler.

wave_impedance

wave_impedance of the Lange coupler.

Symbol:

eta

Latex:

\(\eta\)

Dimension:

impedance

odd_mode_wave_impedance

wave_impedance of the odd mode.

Symbol:

eta_o

Latex:

\(\eta_\text{o}\)

Dimension:

impedance

even_mode_wave_impedance

wave_impedance of the even mode.

Symbol:

eta_e

Latex:

\(\eta_\text{e}\)

Dimension:

impedance

segment_count

Number of the segments of the Lange coupler. See positive_number.

Symbol:

N

Latex:

\(N\)

Dimension:

dimensionless

law

eta = sqrt(eta_o * eta_e * (eta_o + eta_e)^2 / ((eta_o + eta_e * (N - 1)) * (eta_e + eta_o * (N - 1))))

Latex:

\[\eta = \sqrt{\frac{\eta_\text{o} \eta_\text{e} \left(\eta_\text{o} + \eta_\text{e}\right)^{2}}{\left(\eta_\text{o} + \eta_\text{e} \left(N - 1\right)\right) \left(\eta_\text{e} + \eta_\text{o} \left(N - 1\right)\right)}}\]