# A Space-Borne Ka-Band Tile-Type Phased Array Transmitter Module Based on HTCC Technology
## 3 Tile-Type Transmitter Module Based on HTCC Technology
### Reliability Analysis  
To ensure high reliability in soldering quality, it is important to predict and analyze the lifespan of the solder ball on the component mounting side. The dimension of the HTCC package is 12.2 mm \(\times\) 12.2 mm, with a pad diameter of 0.45 mm and a pitch of 0.75 mm. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Name** & **Heat Rate** & **Thermal** & **Shell Temperature** & **Junction** & **First-Level** \\
**(W)** & **Resistance (\({}^{\circ}\)C/W)** & **(\({}^{\circ}\)C)** & **Temperature (\({}^{\circ}\)C)** & **Derating** \\  & & & & & \\ \hline Power amplifier & 0.233 & 70 & 86.1 & 102.4 & 115 \\ Multifunctional chip & 0.313 & 80 & 84.9 & 109.9 & 115 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The junction temperature of the active components. Figure 10: The results of the thermal analysis. Figure 9: Tolerance analysis of BGA structure. High-lead solder balls with a diameter of 0.45 mm are used in the BGA structure. The spacing for the most distant signal BGA solder joint is 11.6 mm, while the maximum spacing for BGA solder joints is 15.05 mm. The HTCC module is mounted on a low-loss laminate PCB. The key parameters for lifespan analysis are listed in Table 5. The predicted number of cycles under accelerated thermal stress, \(N\), can be calculated via Equation (5) [30]. Based on the design conditions, the reliability criterion is set to a minimum of 500 temperature cycles, which means the solder joint should be in good condition within 500 temperature cycles. The assessment results indicate that under the conditions of the most distant solder joint, the number of temperature cycles is approximately 554, and the estimated lifespan for the signal solder joint is about 1065 cycles, which verifies the high reliability of the design. \[N=\left[\frac{0.5\cdot\left(2\cdot\varepsilon_{f}\cdot h\right)}{F\cdot L_{D} (\alpha_{s}\Delta T_{s}-\alpha_{c}\Delta T_{c})}\right]^{-\frac{1}{2}}\cdot \left[\frac{ln(1-0.01\cdot X)}{ln0.5}\right]^{\frac{1}{p}} \tag{5}\]  
To further assess the reliability of the module, a mechanical analysis is conducted to evaluate the mechanical stress at the BGA solder joint. Assuming the substrate does not undergo bending or warping, and the temperature at each solder joint is the same, the shear strain generated at the solder joint can be expressed as  
\[\gamma=\frac{L}{h}(\alpha_{b}-\alpha_{c})(T_{max}-T_{min}) \tag{6}\]  
where \(\alpha_{b}\), and \(\alpha_{c}\) are the thermal expansion coefficients of the PCB and ceramic substrate, respectively. \(L\) is the distance from the solder joint to the center. \(h\) represents the height of the solder ball; \(T_{max}\) and \(T_{min}\) indicate the maximum and minimum test temperature, respectively; and \(\gamma\) represents the shear strain at the solder joint [31]. It can be seen from the equation that when the temperature difference, thermal expansion coefficient difference, and solder ball height are constant, the farther the solder joint is from the center point, the greater the shear strain and stress, making the solder ball more prone to deformation. A mechanical response simulation under load vibration conditions is illustrated in Figure 11. The figure shows the 3D model of the component and the simulated stress at the solder ball. The simulation results indicate that the stress on the solder balls increases gradually from the center of the substrate to the edge of the substrate, and the solder balls at the edge of the module endure the highest levels of mechanical stress. The simulation results are in accordance with the analysis based on Equation (6).