# Analysis and Experimental Test of Electrical Characteristics on Bonding Wire
## 4 Bonding Wire Design and Measurement Experiment
### Port Extension  
Based on network analysis theory, the measured S parameters will inevitably have a fixture effect because the measured parameter is a joint cascading result with DUT and the fixture. The port extension is to move the position of the calibration reference and compensate the transmission line loss by measuring the electrical delay and loss for each single port. That is to say, the fixture is equivalent to a lossless transmission line (or lossy transmission line) under certain conditions. The measurement method is also used to measure the loss and phase shift of the transmission line. Finally, the reference surface is extended to the actual device to reduce the influence of the fixture on the final measuring results. The extension reference and actual reference in test are shown in Figure 23.  
Figure 22: Comparison between simulated and measured values: (**a**) S11; (**b**) S21. Based on the RF network theory:  
\[\left[ \begin{array}{c}b_{1}\\ b_{2}\end{array} \right]=\left[S\right]_{origin}\cdot\left[ \begin{array}{c}a_{1 }\\ a_{2}\end{array} \right]=\left[ \begin{array}{cc}S_{11}&S_{12}\\ S_{21}&S_{22}\end{array} \right]\cdot\left[ \begin{array}{c}a_{1}\\ a_{2}\end{array} \right] \tag{9}\]  
\[\left[ \begin{array}{c}b_{1}^{\prime}\\ b_{2}^{\prime}\end{array} \right]=\left[S\right]_{extension}\cdot\left[ \begin{array} []{c}a_{1}^{\prime}\\ a_{2}^{\prime}\end{array} \right]=\left[ \begin{array}{cc}S_{11}^{\prime}&S_{12 }^{\prime}\\ S_{21}^{\prime}&S_{22}^{\prime}\end{array} \right]\cdot\left[ \begin{array}{c} a_{1}^{\prime}\\ a_{2}^{\prime}\end{array} \right] \tag{10}\]  
From the signal flow graph in Figure 24, the relationship between normalized reflection wave and incident wave is as follows:  
\[\left[ \begin{array}{c}a_{1}\\ a_{2}\end{array} \right]=\left[ \begin{array}{c}a_{1}^{\prime}e^{-j\theta_{1}} \\ a_{2}^{\prime}e^{-j\theta_{2}}\end{array} \right]=\left[ \begin{array}{cc}e^{-j \theta_{1}}&0\\ 0&e^{-j\theta_{2}}\end{array} \right]\cdot\left[ \begin{array}{c}a_{1}^{\prime }\\ a_{2}^{\prime}\end{array} \right] \tag{11}\]  
\[\left[ \begin{array}{c}b_{1}^{\prime}\\ b_{2}^{\prime}\end{array} \right]=\left[ \begin{array}{c}b_{1}e^{-j\theta_{1}} \\ b_{2}e^{-j\theta_{2}}\end{array} \right]=\left[ \begin{array}{cc}e^{-j\theta_{1 }}&0\\ 0&e^{-j\theta_{2}}\end{array} \right]\cdot\left[ \begin{array}{c}b_{1}\\ b_{2}\end{array} \right] \tag{12}\]  
According to the relationship among the parameters, the scattering matrix of extended surface [S] extension can be obtained after the calculation:  
\[\left[ \begin{array}{c}b_{1}^{\prime}\\ b_{2}^{\prime}\end{array} \right]=\left[ \begin{array}{c}b_{1}e^{-j\theta_{1}} \\ b_{2}e^{-j\theta_{2}}\end{array} \right]\cdot\left[ \begin{array}{c}e^{-j \theta_{1}}&0\\ 0&e^{-j\theta_{2}}\end{array} \right]\cdot\left[ \begin{array}{c}b_{1}\\ b_{2}\end{array} \right]=\left[ \begin{array}{cc}e^{-j\theta_{1}}&0\\ 0&e^{-j\theta_{2}}\end{array} \right]\cdot\left[ \begin{array}{c}S_{11}&S_{12 }\\ S_{21}&S_{22}\end{array} \right]\cdot\left[ \begin{array}{c}a_{1}\\ a_{2}\end{array} \right] \tag{13}\]  
\[\left[S\right]_{extention}=\left[ \begin{array}{cc}e^{-j\theta_{1}}&0\\ 0&e^{-j\theta_{2}}\end{array} \right]\cdot\left[ \begin{array}{cc}S_{11}&S_{12 }\\ S_{21}&S_{22}\end{array} \right]\cdot\left[ \begin{array}{cc}e^{-j\theta_{1}}&0 \\ 0&e^{-j\theta_{2}}\end{array} \right]=\left[ \begin{array}{cc}S_{11}e^{-j \theta_{1}}&S_{12}e^{-j(\theta_{1}+\theta_{2})}\\ S_{21}e^{-j(\theta_{1}+\theta_{2})}&S_{22}e^{-j\theta_{2}}\end{array} \right] \tag{14}\]  
Figure 23: Extension reference and actual reference in test. Taking the bonding wire with 4480 \(\upmu\)m span as the example, the port extension and data analysis were performed at 2.5 GHz, 3.0 GHz, 3.5 GHz, 4.0 GHz and 4.5 GHz frequency points. After calibration of the VNA, the test circuit board was connected to Port 1, while Port 2 was kept empty. Then the reflection coefficient file was obtained. Furthermore, according to the cascade algorithm and signal flow chart, the port extension file was written in MATLAB.