# A Novel UWB Pulse Expander Using an Integrated Microstrip Splitter, Delay Lines, and a Combiner
## 2 Design and Modeling
### Pulse Splitter Selection and Design
New combiner implementations have been developed, based on the Lim-Eom 3-way power splitter [58]. A lot of research is also dedicated to the development of UWB combiners [59], but this field still has many unsolved problems. For this research, we examined various implementations of combiners/splitters and their respective advantages and drawbacks. One of the main aspects is the simplicity and low cost of the design of the pulse splitter, which produces three identical output pulses. Therefore, it was determined that the most suitable construction for manufacturing is one that has no internal resistors in it. Such construction eliminates the need for additional components and solder joints, which is advantageous for devices with a working frequency in the GHz range. Also, rapid changes of parameters at one frequency, such as the rapid trending to zero of the reflection coefficient, which is ideal if the device is designed for use at one frequency, can be detrimental to the UWB signal. A microstrip-based branch-line coupler is excellent for this research. Single-box branch-line couplers [60] and two-section branch-line couplers [55] have only two outputs, thus, they are unsuitable for this application. A 3-way coupler, shown in Figure 5, is achieved when two identical, symmetrically placed branch-line couplers [61, 62] are connected in a way so that the axis of symmetry is a horizontal line dividing the coupler in half. In this paper, such a coupler is used as a pulse splitter and a pulse combiner. Figure 4: Initial calculations of the impact of delays between different paths on the summary waveform. Such a construction consists of seven microstrip transmission lines of specified width and length. In the classical implementation of a branch-line splitter, a fixed central operating frequency \(f_{\text{op}}\) is chosen. The length of each transmission line is \(\lambda_{\text{op}}/4\), where \(\lambda_{\text{op}}\) is the wavelength in microstrip transmission lines. All six ports of this splitter are designed with the same impedance \(Z_{0}\). It is expected that the connections to input port 1 and output ports 2, 3, and 4 are matched, while isolation resistors are connected to isolation ports 5 and 6. Different output power ratios in ports 2, 3, and 4 can be achieved by adjusting the characteristic resistance of the transmission lines (series and branch lines) and the resistance values of the isolation resistors. However, specific conditions that are set for the splitter's characteristics must also be met. In the general case, the splitter shown in Figure 5 can be described with S-parameters of a 6-port circuit. In many applications, the output power ratio of such a splitter is symmetrical so that we have the following:  
\[\left|S_{21}\right|=\left|S_{41}\right|. \tag{8}\]  
If the desired output power ratio is 1:1:1, the power divider should ensure the following:  
\[\left|S_{21}\right|=\left|S_{41}\right|=\left|S_{31}\right|. \tag{9}\]  
The efficiency of power transmission from input port 1 to output ports 2, 3, and 4 is described by directivity. Directivity is defined as the difference in power levels, in dB, between the output port and input port, as follows:  
\[D_{i}=10\text{lg}(P_{i}/P_{1}),\text{where }i=2,3,4 \tag{10}\]  
and for an ideal lossless splitter, the following rule must be fulfilled:  
\[\sum_{i=2}^{4}(P_{i}/P_{1})=\sum_{i=2}^{4}10^{(D_{i}/10)}=1\,. \tag{11}\]  
In the ideal case, the splitter design must ensure that there is no reflection from ports 1, 2, 3, 4, 5, and 6 so that respective S-parameters are as follows:  
\[\left|S_{ii}\right|=0,\text{where }i=1\ldots 6\,. \tag{12}\]  
Isolation of a symmetrical splitter (see Figure 5) is defined as the difference in power levels, in dB, between the isolated ports and input port when the output ports are terminated by matched loads, as follows:  
Figure 5: A 3-way splitter–combiner, which is made as a parallel connection of two directional couplers.