1/2*abs((0.5+0.3i)*(0.9678-0.25103i))^2=0.1699
What do you mean ?The definition of the scattering parameters in HFSS and Designer is common, not so special.
Did you took these definitions in Designer or HFSS's help ?For 1W input power, a1 = sqrt(2) + 0*j (and not 1)
This is because:
P_incident = |V+|² / (2*Zo) (V is peak value)
and
an = Vn+ / sqrt(Zo)
In the simple one-port case, S11 relates an incident mode to a reflected mode in the manner
b = S11 a
where "a" and "b" are complex numbers representing the inward and outward travelling modal fields.
The total voltage V at the port plane is related to a and b using the port impedance Zo:
V = sqrt(Zo) (a + b)
Combing the above two equations gives the expression for V in terms of a:
V = sqrt(Zo) (1 + S11) a
When Designer pushes V, the quantity a is computed by solving this expression for a in terms of V, Zo, and S11. The displayed Edit-Sources scaling factor is then
Scaling_Factor = 0.5 * |a|^2
The 0.5 factor is applied since the incoming voltage V is a peak-phasor quantity and HFSS operates using RMS phasors. The physical interpretation of the Scaling_Factor here is the incident modal power due to the source in Designer.
Are all of your ports (in HFSS and designer) normalized to the same impedance (e.g. 50 Ohm)?
Both formulas are from this lecture note:
**broken link removed**
At each port, the modal representations of the electric and magnetic fields assuming K modes are:
\[E = \sum_{m=1} (a_m+b_m) e_m\]
\[H = \sum_{m=1} (a_m-b_m) h_m\]
where am and bm are unitless complex amplitudes of the incident and reflected modal fields, respectively. Given a particular electromagnetic structure, it can be categorized in terms of the incident and reflected/transmitted modal amplitudes using the NxN generalized S-matrix, S:
\[b=Sa \]
where a and b are unitless complex modal coefficient vectors. The size of these vectors, N, is the total number of modes obtained by adding up the number of the modes on all ports.
• The excitation’s magnitude specifies time-averaged incident power in watts.
[...]
• Generally, use the default value of 1. This specifies that the solution’s E- and H-fields be scaled such that the excitation wave delivers 1 watt of power. To view the solution at some other power, enter a positive value.
Looking at your results, I've a few comments/questions :I have found a way to calculate ScaleFactor / OffsetPhase, using Qucs:
Qucs project: Quite Universal Circuit Simulator
It works for my project.
The frequency property of the power source can be ignored. It is overridden by the ac simulation block- The frequency used in my test case is 3.7 GHz (in your file, the power source was @1GHz, but the results is the same : what mean this parameter ?)
- The offset phase sign in HFSS is defined by the sign of the port field line. So a +/- 180° difference is understable.
Do you mean the paragraphOK, I've found in the Qucs documentation that the quantities are defined in RMS, not peak. This explain the factor 2 of the scaling factor.
Yes, this is what I understood from this doc. Am I wrong ?Do you mean the paragraph
"Sometimes waves are defined with peak voltages and peak currents. The only difference that appears then
is the relation to power "
in the "technical papers? (link: **broken link removed** )
The qucs "Workbook" (link: **broken link removed** )
says:
"Please note that all voltages and currents are peak values and all noise voltages are RMS values at 1Hz bandwidth."
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