• Supply Voltage, $V_{DD} = 40 , \text{V}$
• Resistors:
  • R1 = 22 MΩ
  • R2 = 18 MΩ
  • RD = 3 kΩ
  • Rs (denoted as "arsenal") = 0.82 kΩ (This might be a typo or misspelling for Rs)
• The MOSFET is a 2N4351.

1. Determine $I_D$ (Drain Current):
   Since it's a MOSFET and no current flows into the gate ($I_G = 0$), we can assume it's operating in saturation (if necessary conditions are met).
   The voltage divider formed by R1 and R2 gives the gate voltage $V_G$:
   $V_G = V_{DD} \cdot \frac{R2}{R1 + R2}$
   The source voltage $V_S$ can be calculated as $I_D \cdot R_S$.
   The gate-source voltage $V_{GS}$ is:
   $V_{GS} = V_G - V_S$
   We need to ensure $V_{GS}$ is above the threshold voltage $V_{GS(th)}$ for the MOSFET to be in saturation.
2. Use the MOSFET characteristic equation:
   If the MOSFET is in saturation:
   $I_D = \frac{1}{2} \cdot k_n \cdot (V_{GS} - V_{GS(th)})^2$
   where $k_n$ is the MOSFET transconductance parameter and $V_{GS(th)}$ is the threshold voltage. These values will depend on the specific MOSFET device characteristics. You'll likely need data from the datasheet for the 2N4351.
3. Determine $V_D$:
   $V_D = V_{DD} - I_D \cdot R_D$
4. Determine $V_{DS}$:
   $V_{DS} = V_D - V_S$

Python
# Given values
VDD = 40  # Supply voltage in volts
R1 = 22e6  # R1 in ohms
R2 = 18e6  # R2 in ohms
RD = 3e3   # RD in ohms
RS = 0.82e3  # Rs in ohms

# Threshold voltage and transconductance parameter assumed for 2N4351 (typical values)
VGS_th = 2  # Threshold voltage in volts, assumed
kn = 1e-6  # Transconductance parameter in A/V^2, assumed

# Calculate VG using voltage divider rule
VG = VDD * R2 / (R1 + R2)

# Calculate ID assuming operation in saturation region:
# ID = kn/2 * (VGS - VGS_th)^2
# However, first iteration requires VGS estimation

# Trial and error / iterative method would typically be used here
ID_estimated = kn * (VG - VGS_th)**2 / 2  # initial ID estimation

# Now use this estimated ID to adjust VS, and recalculate ID more accurately
# Usually an iterative method should be used, here's a simple estimation
VS = ID_estimated * RS
VGS = VG - VS

# Recalculate ID based on this improved VGS value
ID = kn * (VGS - VGS_th)**2 / 2

# Calculate VD
VD = VDD - ID * RD

# Calculate VDS
VDS = VD - VS

VG, VS, VGS, ID, VD, VDS

• Gate Voltage ($V_G$): $18 , \text{V}$
• Source Voltage ($V_S$): $0.105 , \text{V}$
• Gate-Source Voltage ($V_{GS}$): $17.895 , \text{V}$
• Drain Current ($I_D$): $126.33 , \mu\text{A}$
• Drain Voltage ($V_D$): $39.621 , \text{V}$
• Drain-Source Voltage ($V_{DS}$): $39.516 , \text{V}$

1. Gate Voltage ($V_G$):
   The gate voltage $V_G$ is determined by the voltage divider formed by R1 and R2.
   $V_G = V_{DD} \cdot \frac{R2}{R1 + R2}$
   $V_G = 40 \, \text{V} \cdot \frac{18 \times 10^6}{22 \times 10^6 + 18 \times 10^6}$
   $V_G = 40 \, \text{V} \cdot \frac{18}{40} = 18 \, \text{V}$
2. Assume initial conditions and calculate $I_D$:
   We'll assume the MOSFET is in the saturation region and start with some basic equations.
   For estimation, we will assume $V_{GS} > V_{GS(th)}$, but we will calculate $V_S$ and $V_{GS}$.
3. Source Voltage ($V_S$):
   $V_S = I_D \cdot R_S$
   We need $I_D$. Since we're estimating, let's layout the basics:
   $I_D$ in saturation can be represented initially as:
   $I_D = \frac{1}{2} \cdot k_n \cdot (V_{GS} - V_{GS(th)})^2$
4. Calculate $V_{GS}$ and iterate for $I_D$:
   $V_{GS} = V_G - V_S$
   Plugging back to stabilize $V_{GS}$:
   Let's use trial and error or iteration. Calculations provide estimates for initial values. Start at assumed $I_D$ and refine as needed.
5. Drain Voltage ($V_D$):
   $V_D = V_{DD} - I_D \cdot R_D$
6. Drain-Source Voltage ($V_{DS}$):
   $V_{DS} = V_D - V_S$

• $V_{DD} = 40 , \text{V}$
• $R_1 = 22, \text{M} \Omega$
• $R_2 = 18, \text{M} \Omega$
• $R_D = 3 , \text{k} \Omega$
• $R_S = 0.82 , \text{k} \Omega$
• MOSFET: 2N4351

• $I_D$ (Drain current)
• $V_D$ (Drain voltage)
• $V_{DS}$ (Drain-Source voltage)
• $V_{GS}$ (Gate-Source voltage)
• $V_S$ (Source voltage)

1. Voltage Divider Equation for $V_G$ (Gate Voltage):
   The gate voltage $V_G$ can be found using the voltage divider rule across $R_1$ and $R_2$:
   $$V_G = V_{DD} \times \frac{R_2}{R_1 + R_2}$$
2. Source Voltage $V_S$:
   Since $I_G = 0 , \text{A}$ (ideal MOSFET assumption), the current through $R_S$ is the same as the drain current $I_D$. The source voltage is:
   $$V_S = I_D \times R_S$$
3. Gate-Source Voltage $V_{GS}$:
   Using the obtained values:
   $$V_{GS} = V_G - V_S$$
4. Drain Current $I_D$:
   The drain current, assuming the MOSFET operates in the saturation region, is typically found using the MOSFET equation:
   $$I_D = \frac{1}{2} \cdot k_n \cdot (V_{GS} - V_{th})^2$$
   Here, $V_{th}$ is the threshold voltage for the MOSFET 2N4351, and $k_n$ is the transconductance parameter. Since these parameters are not given, you might want to find them in the datasheet or an assumption must be made (typically, $V_{th} \approx 3 , \text{V}$).
5. Drain Voltage $V_D$:
   $$V_D = V_{DD} - I_D \times R_D$$
6. Drain-Source Voltage $V_{DS}$:
   $$V_{DS} = V_D - V_S$$

• The MOSFET is in the saturation region.
• No specific values for $k_n$ and $V_{th}$ are given for the 2N4351, so assumptions are needed or datasheet consultation.