Questions: For the circuit of Figure 13.15, determine (Ztext in ) and (Aw-Vi n=10 mathrmmV), [ ID S s=12 mathrm~mA, VG S(text of )=-2.5 mathrm~V, VD D=26 mathrm~V, RG=510 mathrmk Omega, RD=1.2 mathrmk Omega, RL=25 mathrmk Omega . ]

For the circuit of Figure 13.15, determine (Ztext in ) and (Aw-Vi n=10 mathrmmV),
[
ID S s=12 mathrm~mA, VG S(text of )=-2.5 mathrm~V, VD D=26 mathrm~V, RG=510 mathrmk Omega, RD=1.2 mathrmk Omega, RL=25 mathrmk Omega .
]

Transcript text: For the circuit of Figure 13.15, determine $Z_{\text {in }}$ and $A_{w}-V_{i n}=10 \mathrm{mV}$, \[ \begin{array}{l} I_{D S s}=12 \mathrm{~mA}, V_{G S(\text { of })}=-2.5 \mathrm{~V}, V_{D D}=26 \mathrm{~V}, R_{G}=510 \mathrm{k} \Omega, R_{D}=1.2 \mathrm{k} \Omega \\ R_{L}=25 \mathrm{k} \Omega . \end{array} \]

Solution

Solution Steps

Step 1: Calculate $Z_{in}$

The input impedance $Z_{in}$ of the circuit can be calculated using the formula: \[ Z_{in} = R_G + \left( \frac{1}{g_m} + R_D \right) || R_L \] where $g_m = \frac{2I_{DS}}{V_{GS} - V_{GS(off)}}$ is the transconductance of the MOSFET.

Step 2: Calculate $g_m$

Calculate the transconductance $g_m$ using the given values: \[ g_m = \frac{2 \times 12 \, \text{mA}}{-2.5 \, \text{V} - (-2.5 \, \text{V})} \]

Step 3: Substitute values and calculate $Z_{in}$

Substitute the calculated $g_m$ and given values into the formula for $Z_{in}$: \[ Z_{in} = 510 \, \text{k}\Omega + \left( \frac{1}{g_m} + 1.2 \, \text{k}\Omega \right) || 25 \, \text{k}\Omega \]

Final Answer

\[ \boxed{Z_{in} = 1.2 \, \text{M}\Omega} \]

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