## 2 Circuit Design and Performance
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Element Type** & **Element ID** & **Value** \\ \hline Resistor & R1, R2 & 2 \(\Omega\) \\ Inductor & L1, L6 & 9.19 nH \\ Inductor & L2, L7 & 8.07 pH \\ Inductor & L3, L8 & 15.3 nH \\ Inductor & L4, L9 & 7.33 pH \\ Inductor & L5 & 15.74 nH \\ Capacitor & C1, C6 & 3.24 fF \\ Capacitor & C2, C7 & 3.70 pF \\ Capacitor & C3, C8 & 1.95 fF \\ Capacitor & C4, C9 & 4.07 pF \\ Capacitor & C5 & 1.90 fF \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Values of the simulated filter elements. Figure 4: Power spectrum of the down-converted IF signal after the VLF-1500+ filter. Figure 5: Power budget of the down converter with OP1 dB line marks. Due to the accurate identification of the required components, the proposed system exhibits the flat conversion gain shown in Figure 6.  
Unfortunately, different models and data files of the components employed in the schematic are not furnished with noisy elements and parameters, respectively. As a consequence, it was not possible to simulate the noise behavior of the system, which was instead analytically estimated. In detail, the noise factor, \(F_{\text{cass}}\), of all the cascaded components in the path from the signal input up to the IF was computed by using the well-known Friis formula [24; 26; 27; 28; 29]. \[ \begin{array}{c}F_{\text{cass}}=F_{\text{LNA}}+\frac{(F_{\text{MIX}}-1)}{G_{ \text{LNA}}}+\frac{(F_{\text{AMPL}}-1)}{G_{\text{LNA}}G_{\text{MIX}}}+\frac{(F_ {\text{FLIT}}-1)}{G_{\text{LNA}}G_{\text{MIX}}G_{\text{AMPL}}}+\\ +\frac{(F_{\text{MIX}}-1)}{G_{\text{LNA}}G_{\text{MIX}}G_{\text{AMPL}}G_{ \text{FLIT}}}+\frac{(F_{\text{FLIT}}-1)}{G_{\text{LNA}}G_{\text{MIX}}G_{ \text{AMPL}}G_{\text{FLIT}}G_{\text{MIX}}}\end{array}  \tag{1}\]  
where \(F_{\text{LNA}}\), \(F_{\text{MIX}}\), \(F_{\text{AMPL}}\), \(F_{\text{FLIT1}}\) and \(F_{\text{FLIT2}}\) are the noise factors of the CMD240C4 LNA, MM1-1467H mixer, AMM-6702 amplifier, PB1182 WB filter and VLF-1500+ filter, respectively, whereas \(G_{\text{LNA}}\), \(G_{\text{MIX}}\), \(G_{\text{AMPL}}\) and \(G_{\text{FLIT1}}\) are the related gains. According to Equation (1), the \(NF\) of the down converter is equal to 3.18 dB. It is worth noting that the noise figure is defined for a matched input source, and for a noise source equivalent to a matched load at the temperature \(T_{0}=290\). This hypothesis is reasonably verified for the employed components whose input/output impedance is very close to 50 \(\Omega\). Mismatches at the component ports would imply higher noise temperatures and thus increased noise figures. Thereafter, the output noise power \(N_{0}\) was calculated in Equation (2) by assuming the receiving antenna is pointed toward the Earth, thus using the equivalent temperature of the receiving antenna \(T_{A}\) equal to \(T_{0}\)[24]. \[N_{0}=k(T_{A}+T_{\text{cass}})BG_{\text{cass}} \tag{2}\]  
where \(k\) is the Boltzmann constant of 1.38 \(\times\) 10\({}^{-23}\) J K\({}^{-1}\), \(B\) is the system bandwidth and \(T_{\text{cass}}\) and \(G_{\text{cass}}\) are the equivalent noise temperature and the gain of the overall system, as expressed in Equations (3) and (4), respectively. \[T_{\text{cass}}=(F_{\text{cass}}-1)T_{0} \tag{3}\]  
\[G_{\text{cass}}=G_{\text{LNA}}G_{\text{MIX}}G_{\text{AMPL}}G_{\text{FLIT1}}G_ {\text{MIX}}G_{\text{FLIT2}} \tag{4}\]  
The output noise power of -52.5 dBm was employed to calculate both the \(LDR\) and the \(SFDR\) by Equations (5) and (6), respectively. \[LDR=OP_{\text{L}dB\text{ }cas}-N_{0} \tag{5}\]  
\[SFDR=\frac{2}{3}(OP_{3\text{ }cas}-N_{0})-SNR \tag{6}\]  
Figure 6: Conversion gain of the down converter. where both the output 1 dB compression point, \(OP_{1 dB\,\,\text{as}}\), and the output third-order intercept point, \(OIP_{3\,\,\text{c}ss}\), hereafter indicated as \(OP_{\text{c}ss}\), were calculated as:  
\[\small OP_{\text{c}ss}=\left(