XF displays discrete frequency results for a circuit component in a table containing all of the available results for the selected port. The columns report results for each steady-state frequency that was specified when creating the simulation.

There are two types of circuit components in XF, each with a different impact on results. Lumped component results are computed based on the single cell edge where the excitation is placed, and distributed component results are determined based on the area associated with the excitation.

## Single Active Component

An active component has a feed circuit component definition and excites the simulation space. When S-parameters are requested, there is only one active component at a time and all other feeds are treated as passive components. The active circuit component's results are defined as follows.

Characteristic impedance, $Z_c$, is the impedance of the circuit component. It is determined based on the circuit component definition rather than by running a simulation. For example, a voltage source with a resistance of 50 ohm has a characteristic impedance of 50 ohm regardless the impedance of the structure it is exciting.

Available power, $P_{av}$, is the maximum delivered power possible when the complex conjugate of the source impedance is matched to the load, $Z_c^*=Z$. It is determined based on both $Z_c$ and the amplitude of the input waveform. When the source and load are matched, the voltage across each one is $V_s/2$ and the current is $V_s/(2\text{Re}\{Z_s\})$. The time-averaged available power is then

$$P_{av}=\frac{1}{2}\text{Re}\{VI\}=\frac{1}{2}\frac{V_s}{2}\frac{Vs}{2\text{Re}\{Z_s\}}=\frac{V_s^2}{8\text{Re}\{Z_s\}}$$

For a voltage source with a 50 ohm internal resistor and 1V amplitude, $P_{av}$ = 2.5 mW.

Available power for a current source is derived in a similar manner. It is

$$P_{av}=\frac{1}{8}I_s^2\text{Re}\{Z_s\}$$

Voltage, $V$, is the simulated value across the component. It is commonly defined as

$$V=-\int_LE\cdot dl$$

The finite-difference time-domain (FDTD) method is the numerical method used during the calculation, so there is an electric field associated with every edge on the grid. For a lumped component, the line integral is the single cell edge where the excitation is located and does not include the PEC leads that complete the full length of the circuit component. For a distributed component, the line integral includes multiple cell edges from one endpoint to the other and XF expects the voltage to be evenly distributed under the transmission line.

Current, $I$, is the measured value though the component. It is commonly defined as

$$I = \oint_L H\cdot dl$$

In FDTD, there are four magnetic fields around each electric field. For a lumped component, current is computed from the loop of four magnetic fields surrounding the excitation. For a distributed component, the loop encompasses the entire width of the component and XF expects the current to be evenly distributed below the transmission line.

Impedance, $Z$, is the input impedance of the structure seen looking through the component into the simulation space. It is computed as

$$Z = \frac{V}{I}$$

S-parameters, $S_{ii}$ or $S_{ij}$, are a measure of how much of the transmitted signal arrives at the receiving port. An XF simulation will compute an $N$x$N$ S-parameter matrix, where $N$ is the number of active ports specified when creating the simulation. When viewing a circuit component sensor result table, the S-parameter result will correspond to a single component in that matrix.

When the transmitting and receiving ports are the same,

$$S_{ii} = \frac{V-Z_c^*I}{V+Z_c^*I}$$

Reflection coefficient, $\Gamma$, is a measure of how much of the transmitted signal is reflected at the terminals of the circuit component due to an impedance mismatch between $Z_c$ and $Z$. It is equal to $S_{ii}$.

Input power, $P_{in}$, is the amount of power delivered to the simulation space. It is computed as

$$P_{in} = \frac{1}{2}VI^*$$ An active component's available power, input power, and reflection coefficient are related by $P_{in}=P_{av}(1-|\Gamma|^2)$.

Voltage standing wave ratio, $\text{VSWR}$, is another measure of the impedance mismatch between the circuit component and either the transmission line or simulation space it is connected to. It is computed as

$$\text{VSWR} = \frac{1+|\Gamma|}{1-|\Gamma|}$$

Matching circuit loss, $P_{mcl}$, is computed only when the active feed has a matching circuit defined. It is the amount of power lost in the matching circuit portion of the feed.

Additional component loss, $P_{acl}$, is computed only for distributed components. XF expects and reports output for a constant voltage and even distribution of current density across the component width. Any signal that is reflected back into the component that is not accounted for in this expectation is reported as $P_{acl}$. $P_{acl}$ may become significant when other structures cause the field distribution to deviate from XF's assumption. This can be reduced by moving the component to a more uniform section of the transmission line.

## Passive Component

A passive component has a passive load definition, netlist component definition, or a feed definition that is treated as a passive load because S-parameters are enabled. The results for passive components are defined below.

Diode, nonlinear capacitor, photoconductive semiconductor switch, and switch component definitions are passive loads because they do not excite the simulation space, but the results below are not typically valid for these component types. Discrete frequency results rely on linear system theory and these components have nonlinear behavior. XF reports results for these component types, but users must account for this when analyzing them.

Characteristic impedance, $Z_c$, is the impedance of the circuit component. It is determined based on the circuit component definition rather then by running a simulation. Consider a passive load with a resistance of 50 ohm in series with a capacitance of 0.2 pF. Its characteristic impedance is 50 $-$ j331.6 ohm at 2.4 GHz.

Voltage, $V$, is the simulated value across the component. It is commonly defined as

$$V=-\int_LE\cdot dl$$

FDTD is the numerical method used during the calculation, so there is an electric field associated with every edge on the grid. For a lumped component, the line integral is the single cell edge where the excitation is located and does not include the PEC leads that complete the full length of the circuit component. For a distributed component, the line integral includes multiple cell edges from one endpoint to the other and XF expects the voltage to be evenly distributed across the transmission line.

Current, $I$, is the simulated value thought the component. It is commonly defined as

$$I = \oint_L H\cdot dl$$

In FDTD, there are four magnetic fields around each electric field. For a lumped component, current is computed from the loop of four magnetic fields surrounding the excitation. For a distributed component, the loop encompasses the entire width of the component and XF expects the current to be evenly distributed below the transmission line.

Impedance, $Z$, is the impedance of the component based on the measured voltage and current. It is computed as

$$Z = \frac{V}{I}$$

S-parameters, $S_{ii}$ or $S_{ij}$, are a measure of how much of the transmitted signal arrives at the receiving port. An XF simulation will compute an $N$x$N$ S-parameter matrix, where $N$ is the number of active ports specified when creating the simulation. When viewing a circuit component sensor result table, the S-parameter result will correspond to a single component in that matrix.

inf will be displayed when the associated component's characteristic impedance is purely imaginary. For example, S-parameters cannot be computed for a component that is either an ideal inductor or capacitor.

Component loss, $P_{cl}$, is the amount of power absorbed from the simulation space. It is computed as

$$P_{cl} = \frac{1}{2}VI^*$$

Matching circuit loss, $P_{mcl}$, is only computed when a passive feed has a matching circuit defined. It is the amount of power lost in the matching circuit portion of the feed.

Additional component loss, $P_{acl}$, is computed only for distributed components. XF expects and reports output for a constant voltage and even distribution of current density across the component width. Any signal that is measured at the component that is not accounted for in this expectation is reported as $P_{acl}$. $P_{acl}$ may become significant when other structures cause the field distribution to deviate from XF's assumption. This can be reduced by moving the component to a more uniform section of the transmission line.