# Analysis and Experimental Test of Electrical Characteristics on Bonding Wire
## 3 Frequency Domain Simulation
### SPICE Equivalent Circuit Model Of Bonding Wire  
As is shown in Figure 12, the SPICE (simulation program with integrated circuit emphasis) equivalent circuit model of bonding wire consists of resistance \(R\), inductance \(L\) and two different capacitors \(C_{1}\) and \(C_{2}\). The resistance \(R\) and the inductance \(L\) are related to the parameters of the bonding wire itself. The two ends of bonding wires are connected to different materials. Therefore, the equivalent capacitance \(C\) at the ends of the bonding wire is not the same. In Figure 12, There are four variables; \(V_{1}\), \(V_{2}\), \(I_{1}\) and \(I_{2}\). Based on Two Port Network Theory, the following equations can be obtained:  
\[\left\{ \begin{array}{l}V_{1}=I_{1}\cdot Z_{11}+I_{2}\cdot Z_{12}\\ V_{2}=I_{1}\cdot Z_{21}+I_{2}\cdot Z_{22}\end{array} \right. \tag{1}\]  
In this case the relationship between the port currents, port voltages and the Z-parameter is given by:  
\[ \begin{array}{l}Z_{11}=\left.\frac{V_{1}}{I_{1}}\right|_{I_{2}=0^{\prime}} Z_{12}=\left.\frac{V_{1}}{I_{2}}\right|_{I_{1}=0}\\ Z_{21}=\left.\frac{V_{2}}{I_{1}}\right|_{I_{2}=0^{\prime}}Z_{22}=\left.\frac{V_{ 2}}{I_{2}}\right|_{I_{1}=0}\end{array}  \tag{2}\] \begin{table}
\begin{tabular}{c l l} \hline \hline
**Factors** & \multicolumn{1}{c}{**Measurement**} & \multicolumn{1}{c}{**Restriction**} \\ \hline Flat Length & Flat length changes nonlinearly with return loss & Through the comparison of the data, it is \\ Flat Length & and insertion loss. & found that signal quality is the best when the \\ (S-loop wire) & The flat length only stands in a specific value, & flat ratio of length and span is 12\%, maybe \\  & and its signal transmission performance is good & the best L1/L is 11\% or 13\% in real operation. \\ \hline Diameter & The bigger diameter is, the better electrical & Excessive increase in wire diameter: \\ Diameter & properties are. & 1. Aggravate the cost of materials \\  & Insertion loss and equivalent inductance decline & 2. Decline in toughness \\  & with increasing diameter. & \\ \hline Span & The shorter loop span is, the better electrical & Too shorter span: \\  & properties are. & 1. Increase line tension, \\  & Shorter loop can reduce signal loss and improve & 2. Make welding spot unstable \\  & the quality of signal transmission. & 3. Cause wire sag and sweep problem \\ \hline Bonding Height & \multicolumn{1}{c}{} & Too lower height: \\  & The lower wire height is, the better electrical & 1. Stress concentration \\  & properties are. & 2. Phenomenon of expanding under hot \\  & condition and shrinking under cold condition \\  & in bonded component. & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The influence of WB parameters on electrical properties. Figure 12: The SPICE equivalent circuit model of bonding wire. Figure 13 shows the equivalent impedance model of \(Z_{11}\). Taking \(Z_{11}\) as an example, the following equations can be obtained through math deduction. \[Z_{11}(\omega)=\left.Z_{11}(s)\right|_{s=j\omega}=\frac{RC_{2}\omega+j\big{(}LC_{ 2}\omega^{2}-1\big{)}}{\omega(-LC_{1}C_{2}\omega^{2}+C_{1}+C_{2}+jRC_{1}C_{2} \omega)} \tag{3}\]  
Similarly, other parameters can be derived as follows:  
\[Z_{22}(\omega)=\left.Z_{22}(s)\right|_{s=j\omega}=\frac{RC_{1}\omega+j\big{(}LC _{1}\omega^{2}-1\big{)}}{\omega(-LC_{1}C_{2}\omega^{2}+C_{1}+C_{2}+jRC_{1}C_{2 }\omega)} \tag{4}\]  
\[Z_{12}(\omega)=Z_{21}(\omega)\!=\!Z_{12}(s)\big{|}_{s=j\omega}=\frac{1}{ \omega[-jLC_{1}C_{2}\omega^{2}-RC_{1}C_{2}\omega+j(C_{1}+C_{2})]} \tag{5}\]  
Based on the principle of RF circuit, the two-port S parameters can be obtained from the equivalent two-port \(Z\) parameters by means of the following expressions:  
\[