Calculating the Q of a Resonant Cavity
Description
This recipe permits you to calculate the Q in a homogeneous dielectric-filled cavity with uniform wall losses, using the equation:
where s is skin depth, tg is dielectric loss tangent, n is the surface normal for the cavity wall faces, and and represent wall surface area and cavity volume, respectively.
Usage Examples
To calculate the Q of an air- or solid-dielectric filled cavity, fed with a below-cutoff port aperture, or obtained via an eigen solution.
Prerequisites
The Object (or Object List) representing the cavity total volume must already exist, as must the Face List corresponding to the total wall surface area of the cavity. You can create both via the Modeler menu. The solution should be tuned to the desired resonant frequency for evaluation.
Calculator Operation |
Resulting Stack Display (top entry only unless noted) |
Quantity>H |
CVc : <Hx, Hy, Hz> |
Push |
(above entry duplicated) |
Complex>Conj |
CVc : Conj(<Hx, Hy, Hz>) |
Dot |
CSc : Dot(<Hx, Hy, Hz>, Conj(... |
Complex>Real |
Scl : Real(Dot(<Hx, Hy, ... |
Geometry>Volume>{select cavity volume} |
Vol : Volume(cav_total) |
|
Scl : Integrate(Volume(cav... |
Push |
(above entry duplicated) |
Number>Scalar>{enter loss tan for volume} |
Scl : {numerical value} (loss tangent for dielectric fill in cavity) |
The above equation is only valid for cavities filled with one dielectric material across the entire volume. For cavities with different dielectric fills (e.g., a dielectric resonator within a larger metal cavity), dielectric loss must be evaluated using integration by parts for each dielectric material volume. The equation also assumes the same conductivity for all walls, and no nonreciprocal (e.g., ferrite) property to either walls or fill.
* |
Scl : *(Integrate(Volume(...
|
Quantity>H |
CVc : <Hx, Hy, Hz> |
Geometry>Surface>{select cavity surfaces} |
Srf : Surface(cav_tot_faces) |
Unit Vec>Normal |
Vec : NormalSurfaceNormal |
Cross : |
Cross(<Hx, Hy, Hz>, SurfaceNormal) |
Push |
(above entry duplicated) |
Complex>Conj |
CVc : Conj(Cross(<Hx, Hy, Hz>, ... |
Dot |
CSc : Dot(Cross(<Hx, Hy, Hz>, ... |
Complex>Real |
Scl : Real(Dot(Cross(<Hx, ... |
Geometry>Surface>{select cavity surfaces} |
Srf : Surface(cav_tot_faces) |
|
Scl : Integrate(SurFace(... |
Number>Scalar>2 |
Scl : 2 |
Constant>Pi |
Scl : 3.14159265358979 |
Function>Scalar>Freq |
Scl : {current freq, in Hz} |
* |
Scl : {numerical result, pi*f} |
Number>Scalar>{enter r for walls} |
Scl : {entered value, unitless} |
* |
Scl : {numerical result, pi*f*mur} |
Constant>Mu0 |
Scl : 1.25663706143592E-006 |
* |
Scl : {numerical, pi*f*mur*mu0} |
Number>Scalar>{enter wall conductivity} |
Scl : {entered value, s/meter} |
* |
Scl : {numerical, pi*f*mur*mu0*} |
|
Scl : {numerical, sqrt of above} |
* |
Scl : {numerical result, 2*above} |
1/x |
Scl : {numerical result} |
* |
Scl : *(Integrate(... |
+ |
Scl : +(*(Integrate(... |
/ |
Scl : /(+(*(Integrate(... |
Eval |
Scl : {numerical result} |