## 2 Materials and Methods
### Typical Characteristics of Signals on Interconnections  
The input data at the interconnection near end is a sequence of bits introduced as file associated to the ARBS element (arbitrary, user-specified bit sequence) as arbitrary 0 s and 1 s for binary signaling condition. The sequence highlights the difference in propagation of high-speed data rate signals versus time variation. In Figure 2a, typical representation of pulse is presented to explain the main parameters that are setup in the design. As different harmonics of a given signal travel down a transmission line with different velocities and arrive at the end point with different propagation times, another aspect that can be deduced is the dispersion of the signal. A delay can be associated to a phase shift as harmonics are out of phase with one another. Figure 1: Transversal sections illustrating the E and H field intensities lines: (**a**) microstrip, (**b**) stripline, and (**c**) equivalent circuit for a very small line length \(\Delta x\ll\lambda\). Figure 2: Pulse characteristics. Lossy line will make the pulse with altering amplitude and phase distortion have decreased amplitude, rounded edges, and its base will widen. The wider the base the smearer into adjacent bits, the bigger the energy spread of current bit. In Figure 3 on the left-hand side, a series of 1 s followed by a series of 0 s (in green) at the input of the line, with no rise and fall times and 1 V for the amplitude, will show increase overshoot and undershoot at the output of the line, as it results from the representation on the right-hand side (in red) (representation in a and b). Only changing the pattern in the data stream and alternate 1 and 0, the output waveform will evidentiate overshoot and undershoot similar as in previous case, but worth mentioning that a string of back-to-back 1 s reaches the receiver with higher amplitude than does the single 1 pulse. The lowpass characteristic of a lossy line, that includes losses in both dielectric and conductor materials, distorts the pulse shape. The pulse will be rounded as successive harmonics are eliminated given the distortion phenomena and the pulse will be attenuated with the increase of the line length or the increase of the losses. As the data stream contains pulses of various widths we will have gradually attenuated and phase shifts on the harmonics. Phase distortion in the pulse will give no longer flat-topped and bottomed and shows peaks as the improper phasing causes the harmonics to combine inadequately. Figure 3: Voltage as variation in time: (**a**) at the input of the interconnection for back-to-back same polarity and (**b–d**) output of a microstrip line; (**e**) input voltage for high-speed data rate and (**f**) output voltage at the far end of microstrip line. If only amplitude distortion is present, the lossy line attenuates each harmonic differently. The effect of the improper combination of the amplitudes results in an output waveform with severe rounding of the corners, eliminated sharp edges, smoothed pulse with lower overall amplitude as it can be seen in Figure 3d with a zoom in on the smoothed edge. Another very important aspect that should also be mentioned is the spread of the pulse outside of the region occupied by the undistorted pulse. Degradation of the signal is severe if the line cannot properly maintain the amplitude and phase distortions. The effect of a bandwidth-limited channel as a transmission line has on signal propagation is explained in next sections and in extenso in other texts [7,8]. Following, we present the steps for matching at \(\mathrm{f}=10\,\mathrm{GHz}\) the ports for a given substrate. RO3003 is used for the analyses.