6.2.4 Power Balance
Power balancepost-processing is active for S-Parameters post-processing and allows one to calculate the balance between power entering and leaving the N-port circuit through the ports. In other words, the power balance post-processing gives the user the information about what part of the power injected into the circuit is dissipated in all defined ports. In QuickWave the power balance can be observed in the Results window and have two different definitions depending on whether the Extended Results option is off or on. With Extended Results off, we do not extract the information about the phase of the reference impedance at each port. In such a case the power balance is calculated as:
Pow.Sk1= sqrt[(S11)2+(S21)2+..+(SN1)2].
In the case of imaginary or complex reference impedances (like for example in waveguides below the cutoff frequency) this formula does not describe the actual balance of input and output power. With Extended Results on, the software directly integrates power flow through the ports. The power balance curve is then called Pow.Bal and denotes a square root of the ratio of total output power (sum of power dissipated in all output ports of the S-Parameters post-processing) to the reference input power (power actually delivered into the circuit from the input port of the S-Parameters post-processing). For circuits with N=1 (a single port assigned to S-Parameters), when port is unmatched or works below cut-off, the injected power may drop to zero. In such cases, Pow.Bal=0 irrespectively of radiation from (or losses in) the circuit. For multiport (N>1) radiating (or lossy) structures, 1-(Pow.Bal)2 is interpreted as the ratio of radiated (or dissipated) power to power delivered through the input port. This information is complementary to that of Near To Far post-processing, where radiation efficiency is calculated with respect to the net power delivered through all the S-Parameters ports. Note that the reference input power for Pow.Bal calculations tends to zero in the case of full reflection or if the input port is assigned to a mode significantly below cutoff. To avoid ill-conditioned calculations of Pow.Bal, its value is set to zero if the reference input power drops below 0.001 W threshold. This threshold has been chosen as it corresponds to a very small portion (order of 0.1%) of power available from the source (1W), with the source set as a transmission line port or a point port with finite output resistance, with QuickWave default setting of input signal amplitude equal to unity. The threshold value of 0.001 W does not depend on the actually set amplitude, so by increasing the amplitude (which is otherwise arbitrary from the viewpoint of S-parameters extraction), the user extends the frequency range where QW-Simulator attempts to calculate the actual value of Pow.Bal. For lossless and non-radiating circuits, both Pow.Sk1 and Pow.Bal tend to unity if the following two conditions are met: reference impedances at all ports are real (as for propagating modes in lossless transmission lines or point ports with finite output resistance) and power above the 0.001 W threshold is injected through the input port.
Note that the information about Pow.Bal. is not saved to a file upon Save command. Therefore importing power balance results via Saved Results orLoad commands always produces Pow.Sk1. For more interpretations of the power balance, refer to in User Guide 3D: Advanced S-parameter problems for waveguide-to-coax example or User Guide V2D: Circular waveguide discontinuity example.
There may be several reasons for the power balance not to be equal unity:
In the case of lossy circuits power balance indicates efficiency of energy transmission.
In the case of transient states during the simulation power balance can be a good indicator of convergence, showing how much energy is still inside the circuit and thus whether we need to prolong the FDTD analysis.
If the power balance does not converge to unity in a case of a lossless structure, this may indicate that some of the energy is dissipated in the source or/and load in modes not considered in the S-parameter extraction. Discussion about such case can be found in User Guide 3D: Advanced S-parameter problems for waveguide-to-coax example.
Power balance below cutoff equals zero. This indicates that the real power injected into the circuit at these frequencies is so small that the software cannot calculate the power balance with acceptable accuracy and sets the result to zero to avoid displaying a curve of irrelevant shape. Discussion about such case can be found in User Guide 3D: Advanced S-parameter problems for waveguide-to-coax example.
Note that there may be a difference between the power balance calculated with standard and extended S-parameters also above the waveguide cutoff frequency, if |S11| is very close to unity. With the standard S-parameters the power balance calculated as sqrt(|S11|2+|S21|2) firmly indicates unity. Physically, we can say that the reference power is the available power of the source and thus the power balance is calculated accurately even with high input reflections. In the case of power balance calculated with extended S-parameters the software takes as reference the net power actually entering the circuit, which is small due to a high reflection coefficient. Thus it tries to numerically compare very small power dissipated in the output to the very small power entering the input. The result may be somewhat different than obtained in the previous case. Let us note however that each of the results has clear physical interpretation and availability of each of them may be useful for the circuit designer.
Note: The above-described option of calculating power balance with extended S-parameters is available only when the results are displayed during the simulation. The display of saved results stored on disk uses always the power balance formula for the standard S-parameters (sqrt(|S11|2 +|S21|2).
In case of the power balance calculation the user can also see the effect of having declared the circuit as reciprocal lossless 2-port. While reciprocity permits to correct the reflection coefficient for numerical reflections from imperfect absorbing boundaries at loads, the lossless flag additionally permits to correct the transmission coefficient in a two-port circuit. Consequently, we can expect better convergence of the power balance (see User Guide 3D: A simple waveguide example).