# A Novel UWB Pulse Expander Using an Integrated Microstrip Splitter, Delay Lines, and a Combiner
## 2 Design and Modeling
### Pulse Splitter Selection and Design  
Preliminary calculations were performed to choose the appropriate pulse splitter. The calculations involve a set of parameters--the limits on waveform aberrations in the expanded pulse and expanded pulse duration, as well as the durations of the first and second transitions, shown in Table 1. Options for attaining the desired waveform were examined for cases when 2, 3, or 4 pulses with different time shifts between them were added, keeping in mind that these pulses can differ in waveform shape from a Gaussian pulse with a 200 ps duration, and the given pulse amplitude, by no more than 5-10%. Other pulse durations were also examined. It was determined that the sum of two primary pulses is insufficient for the given requirements. The sum of three primary pulses produced satisfactory results, as shown in Figure 4, where multiple relative offsets between the primary pulses with the same amplitude are shown. Even though the sum of 4 or more primary pulses improves expanded pulse shape, this was not chosen for implementation. It was decided to implement a 3-way pulse splitter, which splits the input pulse in equal proportions (1:1:1), considering the low expected manufacturing cost, the design's simplicity, and the implementation's practical aspects. The primary purpose of the splitter is to split the input pulse into three identical pulses of the same shape and duration without reflecting the pulse to the input. This device is henceforth called a pulse splitter. Building such a device is challenging due to the large bandwidth of the UWB input signal. However, it is sufficient if the pulse waveform and amplitude differ slightly. It was decided to design the pulse splitter based on a power divider or power coupler [41]. The ability to use the pulse splitter as a pulse combiner was also foreseen. \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Value** \\ \hline Input pulse duration & 200 ps \\ \hline Expanded pulse duration & 420–500 ps \\ \hline Expanded pulse first (rising) transition duration related to the input & \(<\)1.25 \\ pulse first transition duration & \\ \hline Expanded pulse second (falling) transition duration related to the input & \(<\)1.25 \\ pulse second transition duration & \\ \hline Waveform amplitude aberrations & \(<\)0.1 \\ \hline Waveform amplitude ripples after the pulse & \(<\)0.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Pulse expander requirements. Figure 3: (a) Waveform of a 200 ps Gaussian pulse and its (b) spectral density. Such devices can be broadly divided into two categories--couplers (power dividers or power splitters), which can be used in reverse as power combiners, and directional couplers, which couple power flowing in one direction. These devices can also be categorized based on the need for additional externally mounted resistors and having at least one terminated isolated port, or the device has internal resistors and no isolated ports. As possible pulse splitter options, some prototypes were examined, which are based on the following power dividers or combiners: n-way branch-line hybrid [42], Wilkinson n-way hybrid [43], and split-tee power dividers [44]. A power divider needs at least \(n-1\) isolation resistors, but the divider described in Ref. [45] or similar dividers require considerably more than \(n-1\) isolation resistors in order to obtain the desired matching and isolation [46]. Over the years, many different coupler hybrid systems have been developed. The most widely known are based on the Wilkinson divider [47], but various implementations of Lange couplers [48, 49] are also used. Another essential addition to the coupler and divider field is the introduction of directional couplers [50, 51, 52], which include different forms, such as the quadrature coupler [53] and the hybrid branch-line coupler [54, 55]. The evolution of these technologies is described in [56]. Various branch lines and directional couplers of different microstrip constructions have been widely researched and used [57].