Wave impedance of odd 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 surge impedance of the transmission line to which the coupler is connected, as well as the number of coupler segments, it is possible to calculate the wave impedance for an odd mode.

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

surge_impedance

surge_impedance of the transmission line.

Symbol:

Z_S

Latex:

\(Z_\text{S}\)

Dimension:

impedance

segment_count

Number of segments in Lange coupler. See positive_number.

Symbol:

N

Latex:

\(N\)

Dimension:

dimensionless

law

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

Latex:

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