# Intelligent Detection Methods of Electrical Connection Faults in RF Circuits
## 3 Intelligent Detection Method
### Filter Circuit with Electrical Connection Fault  
As shown in Figure 8, the signal is input from the SMA connector at one end of the circuit board and passes through the printed trace on the circuit board to the filter chip. Then, this filtered signal is output from the chip and passes through the printed trace to the SMA connector at the other end of the circuit board. In this filter circuit, the connectors are used to connect other functional circuit systems and the circuit board, the solder balls are used to connect the circuit board and the packaged chip, and the bonding wires are used to connect the chip external package and the internal bare chip. Figure 8: Schematic structure of a filter circuit, where position 1, 2 and 3 represent a connector connection, a bonding wire connection, and a solder ball connection, respectively. Figure 7: The normal and fault values of the connection resistance of solder balls in the experimental testing and model simulation. Consider three different fault modes for the circuit shown in Figure 8: the connector fault at position 1 is fault mode 1 (M1), the bonding wire fault at position 2 is fault mode 2 (M2), and the solder ball fault at position 3 is fault mode 3 (M3). The signal transmission path of the filter circuit is shown in Figure 9. The green boxes represent the interconnection structures of the filter circuit. Based on the signal transmission path, a model for the filter circuit was developed. When there is no fault in the circuit, the connectors and solder balls are each modeled as equivalent to a resistance of 5 m\(\Omega\), respectively, and the bonding wires are each modeled as equivalent to an inductance of 1 nH. As noted in Section 2, when a connection fault occurs in the circuit, the resistance (\(R_{connector1}\) or \(R_{solder2}\)) or inductance (\(L_{wire1}\)) in the model is replaced by the corresponding equivalent connection impedance network, as illustrated by the red components shown in Figure 10.  
For a faulty connector, with the increase of connector degradation, the connection resistance increases, and the connection capacitance decreases. As noted in Section 2, the change in the connection resistance is from about 5 m\(\Omega\) to 100 \(\Omega\). In accordance with the Ref. [13], in the current work, the corresponding change in the connection capacitance is from 7.65 pF to 0.15 pF. In addition, it is assumed that the connection resistance and connection capacitance are linearly related. Accordingly, the functional relationship between the equivalent connection capacitance (\(C_{1}\)) and connection resistance (\(R_{1}\)) can be modeled, as shown in Figure 11.  
Figure 10: Equivalent circuit model of the filter circuit. Figure 9: Signal transmission path. M1 represents that connector 1 is faulty. M2 represents that bonding wire 1 is faulty. M3 represents that solder ball 2 is faulty. In addition, for a faulty solder ball, with the increase of solder ball degradation, the connection resistance, capacitance and inductance increase. As noted in Section 2, the change in the connection resistance is from \(5\,\mathrm{m}\Omega\) to \(105\,\mathrm{m}\Omega\). In accordance with Ref. [15], in the current work, the corresponding change in the connection capacitance is from \(0.016\) pF to \(0.022\) pF. The corresponding change in the connection inductance is from \(0.006\) nH to \(0.036\) nH. In addition, it is assumed that the connection resistance and connection capacitance are linearly related, and the connection resistance and connection inductance are also linear. Then, the functional relationship between the equivalent connection capacitance (\(C_{3}\)), connection inductance (\(L_{3}\)) and connection resistance (\(R_{3}\)) can be modeled, as shown in Figure 12.  
Because the equivalent impedance networks are different when the connector, bonding wire and solder ball fail, the influence on signal transmission of these faults impacts different ranges of frequencies.