1. Which combination is correct? 10 V K = 2 mA/V² G₁ M1 V₁=1V S 5 V VO G D K = 64 mA/V² S VT = 1 V M2 2 V a. Solve for vo assuming that both M1 and M2 operate in saturation. Then check the assumption based on the operating point you determine, is the solution valid? b. Repeat (a) assuming that both M1 and M2 operate in triode. c. Repeat (a) assuming that M1 operates in triode and M2 operates in saturation. d. Repeat (a) assuming that M1 operates in saturation and M2 operates in triode. iD

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### Question 1: Which combination is correct?

#### Circuit Diagram Explanation
The given circuit comprises two MOSFETs (M1 and M2) connected in series. It includes:
- A voltage source of 10V connected to the drain (D) of M1.
- M1 has the following parameters: \( K = 2 \, \text{mA/V}^2 \) and \( V_T = 1 \, \text{V} \).
- M1's source (S) is connected to a junction point of 5V, which is also connected to the drain (D) of M2.
- M2 has the following parameters: \( K = 64 \, \text{mA/V}^2 \) and \( V_T = 1 \, \text{V} \).
- M2's source (S) is connected to another voltage source of 2V.
- The output voltage \( v_O \) is measured at the junction between M1's source and M2's drain.
- The current \( i_D \) flows through both MOSFETs.

#### Questions
a. **Solve for \( v_O \) assuming that both M1 and M2 operate in saturation. Then check the assumption based on the operating point you determine. Is the solution valid?**

b. **Repeat (a) assuming that both M1 and M2 operate in triode.**

c. **Repeat (a) assuming that M1 operates in triode and M2 operates in saturation.**

d. **Repeat (a) assuming that M1 operates in saturation and M2 operates in triode.**

#### Detailed Solution Guide
1. **For part (a):**
    - Assume both M1 and M2 operate in saturation.
    - Use the saturation current equations \( i_D = K (\frac{v_{GS} - V_T}{2})^2 \) for each MOSFET.
    - Determine \( v_{GS} \) for each MOSFET from the given voltage points.
    - Calculate \( i_D \) and \( v_O \) accordingly.
    - Verify if the initial assumption holds by checking the operating points.

2. **For part (b):**
    - Assume both M1 and M2 operate in triode.
    - Use the triode current equations \( i_D = K [(v_{GS} - V
Transcribed Image Text:### Question 1: Which combination is correct? #### Circuit Diagram Explanation The given circuit comprises two MOSFETs (M1 and M2) connected in series. It includes: - A voltage source of 10V connected to the drain (D) of M1. - M1 has the following parameters: \( K = 2 \, \text{mA/V}^2 \) and \( V_T = 1 \, \text{V} \). - M1's source (S) is connected to a junction point of 5V, which is also connected to the drain (D) of M2. - M2 has the following parameters: \( K = 64 \, \text{mA/V}^2 \) and \( V_T = 1 \, \text{V} \). - M2's source (S) is connected to another voltage source of 2V. - The output voltage \( v_O \) is measured at the junction between M1's source and M2's drain. - The current \( i_D \) flows through both MOSFETs. #### Questions a. **Solve for \( v_O \) assuming that both M1 and M2 operate in saturation. Then check the assumption based on the operating point you determine. Is the solution valid?** b. **Repeat (a) assuming that both M1 and M2 operate in triode.** c. **Repeat (a) assuming that M1 operates in triode and M2 operates in saturation.** d. **Repeat (a) assuming that M1 operates in saturation and M2 operates in triode.** #### Detailed Solution Guide 1. **For part (a):** - Assume both M1 and M2 operate in saturation. - Use the saturation current equations \( i_D = K (\frac{v_{GS} - V_T}{2})^2 \) for each MOSFET. - Determine \( v_{GS} \) for each MOSFET from the given voltage points. - Calculate \( i_D \) and \( v_O \) accordingly. - Verify if the initial assumption holds by checking the operating points. 2. **For part (b):** - Assume both M1 and M2 operate in triode. - Use the triode current equations \( i_D = K [(v_{GS} - V
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