From 4c2fb95adff6cf723055eb170629090695a75a0b Mon Sep 17 00:00:00 2001 From: Hugh Carson Date: Wed, 4 Sep 2024 16:09:00 -0400 Subject: [PATCH] Minor fixes to doc file --- docs/src/assets/examples/cavity-1.png | Bin 404883 -> 220849 bytes docs/src/examples/cylinder.md | 38 ++++++++++++++------------ 2 files changed, 21 insertions(+), 17 deletions(-) diff --git a/docs/src/assets/examples/cavity-1.png b/docs/src/assets/examples/cavity-1.png index 41dca76ba441ce8666b315c415e07bf087d1304b..0d7061bedaddf3e27d37271136e4db96dc6aa451 100644 GIT binary patch literal 220849 zcmeFY^;=Y5_b@y&3@x3~DIiiJ&A>>93eqLr-7(Z4D%~m4h=9bpFAxoU_+nz1P}n?+H_VC69+gg#!YC@Dvqf)IcD#Y!C>_j)eg{ zAq}bu2Z0_)+DJ>QDoRT;sJc2?+SprwKnh_=+L$`(edL+?YK+w&h?q%A!4QUbX%+eMl}T(P_@Ol#PB}<8C56XQRz3tx2V<@+ z#Y+gpWQP*{Uj2LKk5R-Uqu3ENP}m3IjI5D?;A;kuH>=7M4iJ)kZK!}W)Phngn=1$` z)vWq~pR8W(!%s4A)chlfWIPv6khvzec04w6*5W%qj?YI`=~4nyHXw4;Mc|#!jG4SUL`XB4A{2}G0+^16bgqsm=4L^U6xZfScr*P7qo1hol 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a/docs/src/examples/cylinder.md +++ b/docs/src/examples/cylinder.md @@ -115,7 +115,7 @@ the above formula for this problem are listed in the table below. | ``(2,1,2)`` | ``5.290341\text{ GHz}`` | ``7.269033\text{ GHz}`` | First, we examine the output of the `cavity_pec.json` simulation. The file -`postpro/pec/eig.csv` contains information about the computed eigenfrequencies and +`postpro/cavity_pec/eig.csv` contains information about the computed eigenfrequencies and associated quality factors: ``` @@ -142,7 +142,7 @@ obtained by *Palace*. Since the only source of loss in the simulation is the non dielectric loss tangent, we have ``Q = Q_d = 1/0.0004 = 2.50\times 10^3`` in all cases. Next, we run `cavity_impedance.json`, which adds the surface impedance boundary condition. -Examining `postpro/impedance/eig.csv` we see that the mode frequencies are roughly +Examining `postpro/cavity_impedance/eig.csv` we see that the mode frequencies are roughly unchanged but the quality factors have fallen due to the addition of imperfectly conducting walls to the model: @@ -166,7 +166,7 @@ walls to the model: ``` However, the bulk dielectric loss postprocessing results, computed from the energies written -to `postpro/impedance/domain-E.csv`, still give ``Q_d = 1/0.004 = 2.50\times 10^3`` for +to `postpro/cavity_impedance/domain-E.csv`, still give ``Q_d = 1/0.004 = 2.50\times 10^3`` for every mode as expected. Focusing on the ``\text{TE}_{011}`` mode with ``f_{\text{TE},010} = 5.00\text{ GHz}``, we @@ -221,23 +221,24 @@ may only become significant on sufficiently refined meshes. This example demonstrates the eigenmode simulation type in *Palace* to solve for the cutoff-frequencies of a circular waveguide. As with the cavity the interior material to be -Silicon (``\varepsilon_r = 2.08``, -``\tan\delta = 4\times 10^{-4}``), with cylindrical domain radius ``a = 2.74\text{ cm}``, -and length ``d=2*a = 5.48\text{ cm}``. -Periodic boundary conditions (BCs) are applied in the $z$-direction. -According to [[1]](#References), the cutoff frequencies for the transverse electric and -magnetic modes are given by the formulae: +Silicon (``\varepsilon_r = 2.08``, ``\tan\delta = 4\times 10^{-4}``), with cylindrical +domain radius ``a = 2.74\text{ cm}``, and length ``d=2a = 5.48\text{ cm}``, however now +periodic boundary conditions are applied in the $z$-direction. According to +[[1]](#References), the cutoff frequencies for the transverse electric and magnetic modes +are given by the formulae: ```math -f_{\text{TE},nm} = \frac{1}{2\pi\sqrt{\mu\varepsilon}} \frac{p'_{nm}}{a} \qquad -f_{\text{TM},nm} = \frac{1}{2\pi\sqrt{\mu\varepsilon}} \frac{p_{nm}}{a} +\begin{aligned} +f_{\text{TE},nm} &= \frac{1}{2\pi\sqrt{\mu\varepsilon}} \frac{p'_{nm}}{a}\\ +f_{\text{TM},nm} &= \frac{1}{2\pi\sqrt{\mu\varepsilon}} \frac{p_{nm}}{a} +\end{aligned} ``` which are identical to those for the cavity modes, in the special case of ``l=0``. In addition to these pure waveguide modes, there are aliasing cavity -modes corresponding to a full wavelength in the computational domain (``l==2``). In a -practical problem these are suppressed by choosing a smaller value of ``d`` which shifts +modes corresponding to a full wavelength in the computational domain (``l=2``). In a +practical problem these can be suppressed by choosing a smaller value of ``d`` which shifts such modes to higher frequencies. The relevant modes are tabulated as | ``(n,m,l)`` | ``f_{\text{TE}}`` | ``f_{\text{TM}}`` | @@ -263,6 +264,9 @@ in the `"Boundaries"` object: `waveguide.json` specifies a perfect electric cond attribute pairs are defined by `"DonorAttributes"` and `"ReceiverAttributes"`, and the distance between them is given by the `"Translation"` vector in mesh units. +The file `postpro/waveguide/eig.csv` contains information about the computed eigenfrequencies and +associated quality factors: + ``` m, Re{f} (GHz), Im{f} (GHz), Q, 1.000000000e+00, +2.223255722e+00, +4.446511256e-04, +2.500000155e+03, @@ -285,10 +289,10 @@ distance between them is given by the `"Translation"` vector in mesh units. ``` In common with the PEC cavity ``Q = Q_d = 1/0.0004 = 2.50\times 10^3`` in all cases, and all -the anticipated waveguide modes are recovered with ``TE_{1,1}`` having the lowest cutoff -frequency followed by ``TM_{0,1}`` and ``TE_{2,1}``, while the aliasing mode ``TE_{1,1,2}`` has -marginally lower frequency than the waveguide modes ``TE_{0,1}`` and ``TM_{1,1}`` -(``4.397\text{ GHz}`` compared to ``4.627\text{ GHz}``). +the anticipated waveguide modes are recovered with ``\text{TE}_{1,1}`` having the lowest +cutoff frequency followed by ``\text{TM}_{0,1}`` and ``\text{TE}_{2,1}``, while the aliasing +mode ``\text{TE}_{1,1,2}`` has marginally lower frequency than the waveguide modes +``\text{TE}_{0,1}`` and ``\text{TM}_{1,1}`` (``4.397\text{ GHz}`` compared to ``4.627\text{ GHz}``) and is thus found first. ## References

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