6.1.11                    Power dissipated, energy stored and Q-factors

QuickWave enables the calculation of power dissipated, energy stored, and Q-factors. The values of those parameters are the results of dissipated power and stored energy integration over the whole circuit (for more information concerning calculation of dissipated power in each FDTD cell refer to Dissipated power and dissipated power density). The Q-factors are extracted from the ratio of the above quantities.

Note that spatial integration of power and energy is carried out at each time step, over the whole computational volume, and therefore significantly slows down the FDTD analysis.

The dissipated power (Pdiss), stored energy (Energy), and Q-factors values are available in the Power, Energy & Q-factor window. Upon invoking Power,Energy&Q-factor window the QW-Simulator starts searching for time-maximum and time-minimum values of power dissipated and energy stored in the circuit. At each time-step it integrates (over the whole circuit) power and energy. At the iteration when the window is opened, it sets the maximum and minimum values of all quantities to their current values. Then at the iteration it re-calculates their maxima and minima, and presents the results in the Power,Energy&Q-factor window.

The Q-factors are calculated as the ratio of energy stored and power dissipated, according to the formulas given in the following subsection.

 

The values of power dissipated are given in [W] and energy stored in [nJ].

 

Note that power dissipated, energy stored, and Q-factor are physically meaningful only with a sinusoidal excitation.

 

The options available for dissipated power, stored energy, and Q-factors calculation are discussed in the following subsections.

 

6.1.11.1   In electric and magnetic field

 

QuickWave offers the calculation of power dissipated in electric and magnetic fields, and a total value of power dissipated in the circuit. The values of power dissipated are given as: time-minimum (MIN), time-maximum (MAX), and time-average (AVR).

At each FDTD iteration the software performs the following operations:

Then it compares current value of each quantity to its time-minimum (MIN) and time-maximum (MAX), appropriately modifies MIN or MAX, and re-calculates time-average (AVR) defined as AVR = 0.5 (MIN + MAX).

Note that spatial integration of dissipated power is time consuming. Thus, the check boxes are available to suppress the integration of electric or magnetic dissipated power, if unneeded.

 

QuickWave offers the calculation of energy stored in electric and magnetic fields, and a total value of energy stored in the circuit. The values of energy stored are given as: time-minimum (MIN), time-maximum (MAX), and time-average (AVR).

At each FDTD iteration the software performs the following operations:

Then it compares current value of each quantity to its time-minimum (MIN) and time-maximum (MAX), appropriately modifies MIN or MAX, and re-calculates time-average (AVR) defined as AVR = 0.5 (MIN + MAX).

The check boxes are available to suppress the integration of electric or magnetic stored energy, if unneeded.

 

As a result of the above calculations the three quality factors, Qe, Qm, and Qt, can be extracted following the below formulas:

The Reference Energy can be selected in Power, Energy & Q-factor window:

- electric  Ee:              AVR Reference Energy = 2 * AVR Electric Energy

- magnetic  Em:          AVR Reference Energy = 2 * AVR Magnetic Energy

- total  Et:                   AVR Reference Energy = AVR Total Energy

 

It is worth noting at this point that the default Reference Energy depends on the exciting field component set in the Input Interface. If the structure is excited with electric field component, the Reference Energy is set to be magnetic energy Em. For excitation with magnetic field component, electric energy Ee is set. During the sinusoidal excitation phase of mode template generation, bigger field disturbance appears for the exciting field component that is why for higher calculation accuracy, the energy of the dual field has been chosen as the Reference Energy.

 

6.1.11.2   In the lossy volume

In typical cases the power dissipated, energy stored, and Q-factors are calculated through the integration over the whole circuit. However, in some applications we would like to know how much power is dissipated and energy is stored only in a particular object or group of objects. QuickWave enables such functionality with Dense regions only and Selected Dense Media options.

The Dense regions only option allows space-selective integration of dissipated power and stored energy. When this option is enabled the software takes into account only the regions composed of the media that were previously declared as having non-zero density. The density value has no significant meaning here and it is treated only as a marker for dissipated power and stored energy calculation. Thus, if one wants to calculate the dissipated power or energy stored in a part of a resonator, and take only this part into consideration when calculating the Q-factors, one should fill this part with a medium of non-zero density and use Dense regions only option.

The Dense region only option is available separately for Pdiss and Energy.

 

Let us further consider a simulation scenario with several lossy objects, where it is required to calculate the power dissipated and stored energy, separately in each of the objects or in some groups of the objects. For that purpose Dense regions only option needs to be activated (non-zero density must be set for appropriate media), what additionally enables Selected Dense Media option. Selected Dense Media option allows selecting which dense media will be used in Pdiss (if Dense regions only option for Pdiss is ON) and/or Energy (if Dense regions only option for Energy is ON) calculations. The user may choose any combination of the media for Pdiss/Energy calculation but at least one medium must be chosen. The choice in Selected Dense Media applies for both Pdiss and Energy if Dense regions only option is active.

 

Note that medium density is specified in the Project Media window of the Input Interface. Since QuickWave allows FDTD cells filled by more than one medium, ambiguity of "density" to be assigned to such cells has to be resolved. Since the criterion is, that the dielectric medium of the highest "conductivity" decides whether a cell is "dense", the density of this medium is treated as "density" of the cell. Density assigned to metallic and PEC media is ignored in this consideration. "Conductivity" is understood as the sum of X, Y, and Z components of Sigma and SigmaM. The medium of highest "conductivity" in the above sense also becomes a dominant cell medium for QW-BHM operation.

 

6.1.11.3   For periodic structures

 

QuickWave enables the calculation of power dissipated and energy stored in the circuit also for periodic structures. When invoking power dissipated, energy stored, and Q-factor calculation in the analysis of periodic structures, the values of power and energy may concern the real (ReG) or the imaginary (ImG) grid. The choice of the grid is made by the user in the Power,Energy&Q-factor window.