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Correction Factor for Characteristic Impedance

To calculate the characteristic impedance in the symmetric model,
correction factor for the characteristic impedance must be properly set.
How to determine the proper correction factor is explained as follows.

Full Model

Port
Voltage [V]	V
Characteristic Impedance [Ω]	Z0
Input Power [W]	P
Correction Factor for Characteristic Impedance	1 (No correction)

For the full model, the equation below is true where
P[W] is input power to the port, Z₀[Ω] is characteristic impedance of the port,
and V[V] is voltage given by the integrated electric field along the integral path.

P = V²/(2Z₀) ------ (1)

Impedance correction is not required for the full model.
Correction factor for the characteristic impedance is 1.

In Femtet, input power is always P = 1 regardless of full model or symmetric model.
Input power set in the analysis condition is not taken into account when the characteristic impedance is calculated.

Symmetric Model

		Half Model A	Half Model B	Quarter Model
Symmetric Model	Port
	Voltage [V]	V'	V''	V'''
	Characteristic Impedance [Ω]	Z'0	Z''0	Z'''0
	Input Power [W]	P	P	P
Full Model	Port
	Voltage [V]	2V'	V''	2V'''
	Characteristic Impedance [Ω]	Z0	Z0	Z0
	Input Power [W]	2P	2P	4P
Correction Factor for Characteristic Impedance		2	0.5	1 (No correction)

For the "half model A" in the list above, the equation below is true where
Z'₀[Ω] is characteristic impedance of the port,
V'[V] is voltage given by the integrated electric field along the integral path,
and P[W] is input power to the port.

P = V'²/(2Z'₀) ------ (2)

If this half model is converted to the full model, the equation below is true where the characteristic impedance is Z₀[Ω],
the input power is 2P[W],
and the voltage given by the integrated electric field along the integral path is 2V'[V].

2P = (2V')²/(2Z₀) ------ (3)

From equations (2) and (3), equation (4) is obtained as below.

Z'₀ = Z₀/2 ------ (4)

From this, it can be said that if the port is cut as in the "half model A",
calculated impedance Z'₀ will be half of the original impedance Z_0,
and the correction factor must be 2 to obtain the original characteristic impedance.

 

If the port is cut as in the "half model B", the equation below is true where
Z"₀[Ω] is characteristic impedance of the port,
V"[V] is voltage given by the integrated electric field along the integral path,
and P[W] is input power to the port.

P = V''²/(2Z''₀) ------ (5)

If this half model is converted to the full model, the equation below is true where the characteristic impedance is Z₀[Ω],
the input power is 2P[W],
and the voltage given by the integrated electric field along the integral path is V"[V].

2P = V''²/(2Z₀) ------ (6)

From equations (5) and (6), equation (7) is obtained as below.

Z''₀ = 2Z₀ ------ (7)

From this, it can be said that If the port is cut as in the "half model B",
calculated impedance Z"₀ will be twice the original impedance Z_0,
and the correction factor must be 0.5 to obtain the original characteristic impedance.

 

If the port is cut as in the "quarter model" in the list above, the equation below is true where
Z'''₀[Ω] is characteristic impedance of the port,
V'''[V] is voltage given by the integrated electric field along the integral path,
and P[W] is input power to the port.

P = V'''²/(2Z'''₀) ------ (8)

If this quarter model is converted to the full model, the equation below is true where the characteristic impedance is Z₀[Ω],
the input power is 4P[W],
and the voltage given by the integrated electric field along the integral path is 2V'''[V].

4P = (2V''')²/(2Z₀) ------ (9)

From equations (8) and (9), equation (10) is obtained as below.

Z'''₀ = Z₀ ------ (10)

From this, it can be said that if the port is cut as in the "quarter model",
calculated impedance Z'''₀ will be equal to the original impedance Z_0,
and the correction factor is 1. Correction is not required.