# Highly Adaptive Reconfigurable Receiver Front-End for 5G and Satellite Applications
## 3 Switchable Receiver Front-End Architecture: HARRF LNA and SPDT Integration
### Impedance Matching Between the Switch and the LNA  
The incorporation of the Single-Pole Double-Throw (SPDT) switch with the Low Noise Amplifier (LNA) in the Highly Adaptive Reconfigurable Receiver Front-End (HARRF) design entails significant impedance matching challenges. Efficient impedance matching between these two components is crucial to reduce reflection losses, improve power transmission, and guarantee excellent noise performance throughout the operational frequency ranges. This section offers a comprehensive analysis of the impedance matching techniques utilised between the SPDT switch and the LNA, encompassing theoretical aspects, practical design approaches, and performance compromises.  
The impedance disparity between the SPDT switch and the LNA may result in power losses and signal deterioration. The essential criterion for optimal power transmission is defined by the conjugate matching condition:  
\[Z_{LNA}^{*}=Z_{Switch}, \tag{13}\]  
where \(Z_{LNA}^{*}\) is the complex conjugate of the LNA input impedance, and \(Z_{Switch}\) is the output impedance of the SPDT switch.  
At microwave and millimeter-wave frequencies, the impedance observed at the input of the LNA is affected by both the nominal switch impedance and parasitic factors, including switch capacitance, substrate losses, and transmission line discontinuities. The comprehensive impedance transformation can be expressed as:  
\[Z_{in}=Z_{0}\frac{1+\Gamma_{in}}{1-\Gamma_{in}}, \tag{14}\]where \(Z_{0}\) is the characteristic impedance (typically 50 \(\Omega\)) and \(\Gamma_{in}\) is the input reflection coefficient.  
In cascaded networks, such as the switch-LNA combination, the impedance matching condition is determined by the transmission and reflection coefficients at the interface. The reflection coefficient at the input of the LNA resulting from the SPDT switch can be expressed as:  
\[\Gamma_{LNA}=\frac{Z_{LNA}-Z_{Switch}}{Z_{LNA}+Z_{Switch}}. \tag{15}\]  
For ideal matching, \(\Gamma_{LNA}\) should be minimised to ensure negligible reflection.  
To comprehensively analyse the impedance mismatch, we consider the total voltage transfer function across the cascaded network, expressed as:  
\[H(f)=\frac{V_{out}}{V_{in}}=\frac{Z_{LNA}}{Z_{LNA}+Z_{Switch}+j\omega L+\frac{ 1}{j\omega\mathcal{C}}}, \tag{16}\]  
where \(L\) and \(C\) represent the parasitic inductance and capacitance of the transmission line interconnecting the switch and the LNA. The reflection coefficient, incorporating transmission line effects, is given by:  
\[\Gamma(f)=\frac{Z_{LNA}-Z_{Switch}-jX_{TL}}{Z_{LNA}+Z_{Switch}+jX_{TL}}, \tag{17}\]  
where \(X_{TL}\) is the reactance of the transmission line connecting the two elements, given by:  
\[X_{TL}=Z_{0}\tan(\beta l), \tag{18}\]  
and \(\beta\) is the propagation constant.  
To mitigate impedance mismatch effects, a multi-stage matching network is employed to ensure efficient signal transfer. The impedance transformation ratio is determined as:  
\[T_{match}=\frac{Z_{LNA}}{Z_{Switch}}, \tag{19}\]  
and the required reactance values for an L-section matching network can be derived from:  
\[X_{L}=\sqrt{R_{LNA}(R_{Switch}-R_{LNA})}, \tag{20}\]  
\[X_{C}=\frac{R_{LNA}R_{Switch}}{X_{L}}. \tag{21}\]  
For a broadband Pi-matching network, the impedance transformation function is given by:  
\[Z_{in}=\frac{Z_{LNA}Z_{Switch}+j\omega L-\frac{1}{j\omega\mathcal{C}}}{Z_{Switch }+j\omega L}. \tag{22}\]  
Using a quarter-wave transformer, the impedance transformation equation simplifies to:  
\[Z_{in}=\frac{Z_{0}^{2}}{Z_{out}}, \tag{23}\]  
where \(Z_{out}\) is the transformed impedance at the LNA input.