Wave impedance of even mode 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 coupling coefficient between the coupler segments, the wave impedance of the odd mode, as well as the number of coupler segments, it is possible to calculate the wave impedance for an even mode.

even_mode_wave_impedance

wave_impedance of the even mode.

Symbol:

eta_e

Latex:

\(\eta_\text{e}\)

Dimension:

impedance

odd_mode_wave_impedance

wave_impedance of the odd mode.

Symbol:

eta_o

Latex:

\(\eta_\text{o}\)

Dimension:

impedance

coupling_factor

Coupling factor between coupler segments.

Symbol:

C

Latex:

\(C\)

Dimension:

dimensionless

segment_count

Number of segments in Lange coupler. See positive_number.

Symbol:

N

Latex:

\(N\)

Dimension:

dimensionless

law

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

Latex:

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