MOSFET: Biasing for Saturation: Compute R2 from Target Node Voltage Assessment

Assignment

Questions

1. The transistor shown in Figure 1 has the following parameters:
|Vt|=1 V, Kp’ (W/L)= 2 mA/V^2.
Determine the resistor R2 based on Vx=10 V. Note that R2 should be determined so as to maintain the transistor in saturation mode.
Assume R1=10 KΩ, R3=8 KΩ, R4=1 MΩ, VSS=20 V.

2. The amplifier shown in Figure 2 has the following parameters:
Kn’(W/L)=1 mA/V^2, Vt=1 V.
Determine
a) Voltage gain (vo/vi)
b) Input resistance (Ri)
c) Output resistance (Ro)
d) Maximum output voltage swing as the amplifier stays in saturation mode.
Assume VDD=20 V, RD=2.5 KΩ, RS=1 KΩ, RD=0.5 KΩ, RG=5 MΩ, RS=1MΩ.

3. Determine the voltage gain of the amplifier (vo/vi) shown in Figure 3. Assume VDD= 20 V, Kn’ (W/L)= 2 mA/V^2, Vt=1 V, R1=2.5 KΩ, R2=2.5KΩ, R3=0.25 KΩ, R4=400 KΩ, R5=100 KΩ, R6=1 MΩ.

Summary of Assessment Requirements

The assignment focuses on analyzing and solving problems related to MOSFET biasing, amplifier parameters, and voltage gain determination. The key requirements are:

1. Transistor Biasing (Q1)

   • Calculate resistor R2 to maintain the MOSFET in saturation mode.
   • Apply the given conditions: |Vt|=1 V, Kp’(W/L)=2 mA/V⊃2;, Vx=10 V, and resistor values R1, R3, R4 with VSS=20 V.

2. Amplifier Analysis (Q2)

   • For the given amplifier circuit, determine:
     a) Voltage gain (vo/vi)
     b) Input resistance (Ri)
     c) Output resistance (Ro)
     d) Maximum output voltage swing while staying in saturation.
   • Consider circuit parameters: Kn’(W/L)=1 mA/V⊃2;, Vt=1 V, VDD=20 V, with given resistor values.

3. Voltage Gain of Another Amplifier (Q3)

   • Calculate the voltage gain (vo/vi) for a second amplifier circuit.
   • Use parameters: VDD=20 V, Kn’(W/L)=2 mA/V⊃2;, Vt=1 V, with resistors R1–R6 as provided.

The central aim is to apply MOSFET theory, amplifier design principles, and circuit analysis techniques to ensure correct operation in saturation and to compute gain/resistance parameters.

Step-by-Step Approach by the Academic Mentor

1. Understanding the Problem Statement

   The mentor first explained how MOSFET operation depends on ensuring VDS ≥ VGS - Vt to keep the transistor in saturation mode. This set the foundation for Q1 and Q2.

2. Question 1: Resistor R2 Calculation

   • The mentor guided the student in setting up equations based on the node voltage at Vx and applying the transistor current equations.
   • Step-by-step, the student calculated the biasing condition, ensuring that the chosen R2 value guarantees saturation.
   • The solution included checking whether the calculated VDS meets the saturation criterion.

3. Question 2: Amplifier Characteristics

   • The mentor introduced small-signal analysis to evaluate voltage gain, input resistance, and output resistance.
   • For (a) Voltage Gain, the student applied the small-signal transconductance (gm) and resistance relationships.
   • For (b) Input Resistance, the impact of RG and gate biasing was explained.
   • For (c) Output Resistance, the role of RD and transistor output parameters was derived.
   • For (d) Voltage Swing, the student checked the condition for saturation, ensuring the MOSFET does not enter triode mode.

4. Question 3: Voltage Gain of Another Amplifier

   • The mentor explained how to combine resistor divider biasing (R1–R6) with MOSFET equations.
   • The student then derived gain equations using the effective transconductance and resistive loads.
   • Verification was carried out to confirm that the transistor remained in the correct operating region.

Final Outcome and Learning Objectives Covered

• The student successfully calculated R2 for correct MOSFET biasing, ensuring saturation operation.
• The amplifier’s voltage gain, input resistance, output resistance, and maximum swing were derived with clarity.
• The voltage gain of the second amplifier was determined accurately using biasing networks and small-signal analysis.

Learning Objectives Achieved:

• Applied MOSFET biasing conditions to maintain operation in saturation.
• Conducted small-signal amplifier analysis with correct parameter evaluation.
• Enhanced problem-solving skills by working through multi-step circuit analysis.
• Strengthened ability to connect theoretical concepts with practical circuit design.

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