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22 The PCB Design Magazine • October 2014 problems. Comparison with TDR/TDT response that is measured directly with TDR scope re- quires modeling with the step function with the shape and spectrum matching to one used in the experiment. Similar situation is with the eye diagrams. Use of the ideal ramp step functions or PRBS with ideal trapezoidal shaped pulses may obfuscate and distort the results. Alter- natively, measured and modeled S-parameters should be used to do all time domain computa- tions with exactly the same stimuli matching the bandwidth of the model. This can be done in two ways: either with convolution with the impulse response comput- ed directly from discrete S-parameters with IFFT, or with the rational approximation and fast re- cursive convolution as it is done here. The ratio- nal approximation is frequency-continuous and naturally extends S-parameters to DC and to in- finite frequencies. It is also causal by definition if passivity is ensured. The accuracy of the time domain analysis in this case is defined only by the accuracy of the rational approximation. In other words, the accuracy is always under con- trol, unlike in case of analysis with IFFT where interpolation and extrapolation introduce un- controlled errors. In addition, the recursive con- volution is exact for piecewise linear signals and feature SINk OR SWIM AT 28 GBPS continues Figure 6: Model-to-measurement validation results for 8-inch stripline link (Figure 1, structure 2): Mag- nitudes of the transmission and reflection parameters (top left); group and phase delays of the trans- mission (top right), TDrs computed with 20 ps rise time Gaussian step (bottom left); eye diagrams for 28 Gbps PrBS signal (bottom right, on top of each other, literally).