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From the diagram,
But also,
So, substituting the second equation into the first:
And then re-arrange to collect b
Now rewrite as power, substituting in ��
Armed with this last result, and calling the Feed-through stand (F subscript) the "generator" (g
subscript) and terminating sensor (M subscript) the "load" (l subscript), and substituting in the
definitions for cal factor from earlier, we get the more general equation for transferring between a
feed-through and a terminating sensor:
Where:
k
Calibration factor of the Terminating Mount
M =
k
Calibration factor of the Feed-through Mount
F =
P
= Power measured terminating mount
SubM
P
= Power measured Feed-through mount
SubF
G
= Gamma Correction full vector data Terminating Mount
M
G
= Gamma Correction full vector data Feed-through Mount
F
Now in this general equation, the Gamma terms are the reflection scattering parameter of the
respective port noted in the subscript. Gamma is a complex vector with scalar values denoting
the real and imaginary magnitudes:
In the general transfer equation, the term, | 1 − Γ
match" term. Inside the absolute value brackets, however, is a vector subtraction. Expanding out
to make the angles explicit, this becomes:
| 1 − ��
2
Where the i represents √ −1
2818A-900 Revision AB
��
= ��
+ Γ
��
��
��
= ��
= Γ
��
��
��
��
��
= ��
+ Γ
��
��
g:
��
=
��
1 − Γ
2
= | ��
|
��
��
��0
��
��
=
��
|1 − Γ
��
��������
��
= ��
��
��
��
��������
Γ ≡ ��∠�� = �� cos �� + i��sin ��
Γ
��
cos ( ��
) − �� ��
��
+ ��
��
��
��
��
, or the "imaginary" component.
RF Power Transfer Standard
��
��
��
= Γ
��
��
��
��
Γ
��
��
��
��
��
��
Γ
��
��
2
, and ��
:
= |��
|
��
��
��
��0
2
Γ
|
��
��
2
| 1 − Γ
|
Γ
��
��
2
is the scalar "gamma correction" or "port
|
��
sin ( ��
)|
��
+ ��
��
��
��
��
2
20
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