eldo_user

Working with S, Y, Z Parameters
Applications
reasons: the model-evaluation time in CPF is less by a factor of 5-7 than that for the
equivalent circuit built from the same poles.
Due to the very nature of fitting, the CPF method always results in a causal solution. It
also has a delay-extraction capability useful when simulating transmission lines or
connectors.
• Digital Signal Processing (DSP) technique is an alternative approach that transforms the
frequency-domain data into time domain parameters via inverse FFT, Hilbert transform
and convolution. Important modifications were made to these basic algorithms to enable
both periodic and non-periodic dependencies, to ensure the causality of the system, to
account for singularities in matrix representation and to ensure high-speed convolution.
If the circuit frequency response is naturally periodic (as for delay-containing operators)
and is given only in a fraction of a single period, the DSP method is recommended to
ensure accurate simulation. In this case, the last point given in the input data file should
correspond to the half-period of the dependence.
• System identification (SI) technique is a third method that represents S parameters in the
form of a rational function in ‘s’ (Laplace variable). These functions are then converted
into systems of linear differential equations so that Eldo can solve them during the
transient analysis.
With the above three methods, Eldo can efficiently solve a wide variety of problems. Frequency
dependencies can be either quite smooth or with a large number of sharp resonant peaks (up to
many hundred). The user may specify input data either with equidistant frequency points,
starting from zero or not; or give them in any other way, (for example, logarithmically spaced)
relevant to the method of data acquisition.
Of course, one can expect accurate simulations only if the original data is complete and
accurate. The frequency dependence given should completely encompass the range of interest,
from the lowest to the highest operation frequency. For example, high accuracy at DC is
unlikely if the data starts from non-zero frequency. Similarly, accurate simulation of short
transitions, lasting for hundred ps, is impossible if the highest point is far below tens of GHz.
Also, the data points should be given with good resolution, sufficient to reproduce the shape of
the dependencies. For example, many more points are needed to describe a dependence with
many sharp peaks than for a smooth one, even if they are both defined in the same frequency
range. Finally, the input data should be causal, so that the real and imaginary parts of the
frequency dependence satisfy the dispersion Kronig-Kramers relation. In reality, data becomes
slightly non-causal due to unavoidable measurement/simulation errors, especially (typically) at
higher frequencies. However, serious measurement errors (like taking the negated phase) cause
catastrophic non-causality that will lead to improper simulation results.
Applications
S parameters can originate from the following:
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Eldo® User's Manual, 15.3