5.7 Determination of input power
In standard applications of QW-3D to S-parameters extraction of linear circuits, absolute value of input power is irrelevant since reflection and transmission are determined from ratios of incident and reflected waves at respective ports. However, the knowledge of power delivered to the circuit becomes necessary for calculating antenna efficiency and normalisation of specific absorption rate (SAR).
In QW-3D transmission lines are excited by template sources. The field templates are normalised in QW-Simulator in such a way that the maximum power available from the template source of unit amplitude equals:
PA = 1.0 [W]
Accordingly, time-averaged power available from template source of sinusoidal waveform is:
PA = 0.5 [W]
It is known from classical circuit theory that the net power actually delivered to the circuit by the source (PD) is:
PD = PA ( 1 - | GG| 2 ) ( 1 - | GL | 2 ) / |1 - GG GL | 2
where:
GG - reflection coefficient of the generator
GL - reflection coefficient of the load.
In QW-3D sources are matched to the appropriate transmission lines by means of impedance template so that we can safely assume GG ยป 0. Thus the maximum and average values of power delivered by the source of unit amplitude are:
PD = (1 - | GL | 2) [W]
PD = 0.5 (1 - | GL | 2) [W]
In general, the maximum and average values of power delivered by the source of amplitude set in Input Interface as A are:
PD = A 2(1 - | GL | 2) [W]
PD = 0.5 A 2 (1 - | GL | 2) [W]
Note that the amplitude is unambiguously enforced for delta and sinusoidal sources, for other waveforms the amplitude naturally varies with frequency. In case of pulses of limited spectrum (f<f2 or f1<f<f2), the value of A set in the Input Interface applies within the respective band (f<f2 or f1<f<f2), however, there will be in-band fluctuations due to finite duration of the pulse. Typically, duration about 30 set in the Input Interface results in a practically rectangular spectrum. For Gaussian pulses the value of A set in the Input Interface applies at the centre frequency. The Power Available post-processing shows variation of the power available from the source versus frequency.
The above remarks allow the user to estimate the power delivered to the circuit by the source, if there is only one source in the circuit, based on this source definition and input reflection coefficient (extracted in S-parameter post-processing, | GL | =| S11 |).
Internally, the QW-Simulator directly integrates the power flowing between all S-parameter ports in the circuit. It uses this rigorously calculated net value of the actually delivered power for radiation efficiency extraction. Note therefore that in the case of multi-port antennas, the value of delivered power, and hence calculated antenna efficiency, will change as one includes or excludes certain ports in S-Parameters post-processing.