## 1 Introduction  
The challenge to transmit speeds of tens of gigabit per second in current state-of-the-art systems comes with several aspects concerning transmission media. Both frequency and time domains allow characterization of how distortion of a waveform travelling along a trace, even when high-performance techniques and materials are used. Clearly, the investigation is beyond the trace geometry or type of dielectric material used. The reason is that we are unable to solve the issue of trace loss effect on signals for high lengths and high data rates. Compensation techniques are applied in this specific case in a manner to gain a flat response in frequency, low and high equally. The basics of passive equalization was elaborated in [1]. Signals must have a finite propagation time or delay in reaching the destination due to a finite velocity for a given length of the interconnection between transmitter and receiver. Bits will arrive at a different time, with an offset, than when were sent. One must determine the sample time at the receiver for correct reconstruction of the original signal. We will consider for transmitter a digital non-return to zero signal type (NRZ). Another signaling option for high speed is multi-level pulse amplitude modulation (PAM) scheme for optimized interconnects as in the chip-to-chip applications, or backplanes [2, 3]. For these variants the length will vary from few centimeters to one meter that will need to support high enough data rates. In the past, increase of data rates came with increased performance of I/O circuits (input/output), complex coding and modulation schemes, and use of more complex equalization. A lossy line with both phase and amplitude distortion will have height pulse reduction and dispersion so the pulse smears outside of its assigned bit boundaries. Low frequency energy present in a transmission line will interfere with highly attenuated energy from the high frequency domain causing intersymbol interference (ISI). In practice, it has been demonstrated that for better synthesis of a device, networks with equalizer (EQ) are positioned in the test fixture as presented in [4]. Jitter histogram, time, and frequency characteristics are more accurate in this case. As the data rate increases, the intersymbol interference effects on the jitter increase as well. A line that does not preserve the proper amplitude and phase relations between harmonics will yield to distorted pulses. Because line losses are in direct proportion with the length of the line, the distortion will grow with the line's length. Additionally, the characteristics of the lossy line of a lowpass filter, bandwidth limitation, and length dependency of the insertion loss (IL) result in amplitude attenuation and altering the phase relationship between harmonics. Since most digital signals have high edge rates, they will combine odd harmonics of the fundamental frequency. The transmission line's loss is given by dielectric, conductor, and radiation characteristics, but for the present work the significant ones are the dielectric loss and skin depth due to conductor loss [5]. Several references provide analytical solutions to compute losses in a transmission line designed in a certain technology [5] but also software tools [6] are highly suitable to evaluate properly, accurately, the loss profile to be frequency dependent if algorithms are developed for materials parameter. The width of the line is a factor that influences the losses, as skin effect is inverse proportional to the width's trace. In the time domain, the effect of ISI is summarized as spread of the pulses travelling along the line with bandwidth limitation and in worst-case scenario it will smear into the neighboring time slots, leading to distortion of a bit within a symbol due to interference caused by pre- or post- bit from the transmitted stream.