The T1 matrix of the device under test is found as:
\begin{equation} T_{1}=\left[\begin{matrix}0 & 0\\- C s & - D s\end{matrix}\right] \end{equation}The matrix equation for the two-port (DUT) is found as:
\begin{equation} \left[\begin{matrix}V_{i}\\I_{i}\end{matrix}\right]=\left[\begin{matrix}0\\- C V_{o} s - D I_{o} s\end{matrix}\right] \end{equation}The source-to-load transfer is obtained as:
\begin{equation} A_{v}=- \frac{C_{A} R_{\ell}}{C R_{\ell} + D} \end{equation}The input impedance is found as:
\begin{equation} z_{i}=0 \end{equation}The output impedance is found as:
\begin{equation} z_{o}=\frac{D}{C} \end{equation}The numeric values are obtained after solving the equations for $z_o$ and $A_v$ for the target values given below.
Output impedance $z_o$:
\begin{equation} z_{o}=50 \end{equation}Source-to-load voltage transfer $A_v$:
\begin{equation} A_{v}=-1 \end{equation}Antenna capacitance $C_A$:
\begin{equation} C_{A}=6.3 \cdot 10^{-12} \end{equation}The value $R_s$ of R2:
\begin{equation} R_{s}=5 \end{equation}The value $C_2$ of C2:
\begin{equation} C_{2}=\frac{2.835 \cdot 10^{-11}}{n} \end{equation}The value $C_3$ of C3:
\begin{equation} C_{3}=3.15 \cdot 10^{-12} \end{equation}The T1 matrix of the amplifier:
\begin{equation} T_{1}=\left[\begin{matrix}0 & 0\\- 3.15 \cdot 10^{-12} s & - 1.575 \cdot 10^{-10} s\end{matrix}\right] \end{equation}The value of R2 can be much smaller than the load resistance. With a high turn ratio of the transformer, the influence of C2 on the noise can be kept small.
The amplifier has a current input. Hence, the signal voltage across the ESD device is zero which is beneficial to a low distortion.
The VCVS 'E1' can be omitted. It is used to drive C2 from an ideal voltage source which simplifies the design equations. If omitted the output impedance will drop at high frequencies. This effect can be kept outside the frequency range of interest.
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Last project update: 2022-04-01 08:22:20