Problem Breakdown

Given:

1. PMOS differential amplifier circuit as per Fig. P9.2.
2. $V_{tp} = -0.4 \, \text{V}$
3. $k_p = \frac{W}{L} \cdot \mu_p C_{ox} = 5 \, \text{mA/V}^2$
4. Neglect channel-length modulation.

Tasks:

1. Calculate:
   • $|V_{OV}|$ (overdrive voltage),
   • $V_{SG}$ (source-gate voltage),
   • $V_S$ (source voltage),
   • $V_{D1}, V_{D2}, V_O$ (drain voltages).
2. Determine the input common-mode range given the current source requires a minimum voltage of 0.2 V.

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Step-by-Step Solution:

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(a) Find $|V_{OV}|$ and $V_{SG}$:

The overdrive voltage for PMOS is given as: $|V_{OV}| = \sqrt{\frac{I_D}{k_p}}$

Where $I_D$ is the drain current through each transistor ($Q_1$ and $Q_2$). For a symmetric PMOS differential amplifier, the tail current $I$ splits equally between $Q_1$ and $Q_2$, i.e., $I_D = \frac{I}{2}$.

Let $I$ (tail current) be defined. Then: $|V_{OV}| = \sqrt{\frac{\frac{I}{2}}{5}}$

The source-gate voltage $V_{SG}$ for each PMOS transistor is: $V_{SG} = |V_{OV}| + |V_{tp}|$

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(b) Find $V_S, V_{D1}, V_{D2}, V_O$:

1. Source Voltage ($V_S$): This is set by the current source. Assume $V_S = V_S$.

2. Drain Voltages ($V_{D1}, V_{D2}$): The drain voltages depend on the current through the load resistors $R_D$. If the output resistance of the current source is very high, we assume the drains are at the same potential.

   Let: $V_{D1} = V_{D2} = V_O = V_{DD} - I_D R_D$

Where $V_{DD}$ is the supply voltage.

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(c) Determine the Input Common-Mode Range (ICMR):

For the PMOS differential amplifier, the input common-mode voltage ($V_{CM}$) is limited by:

1. The need to keep $Q_1$ and $Q_2$ in saturation, requiring: $V_{SG} > |V_{tp}|$

2. The current source requiring a minimum voltage of $0.2 \, \text{V}$, imposing a lower limit on $V_S$: $V_S > V_{CM,min} = 0.2 \, \text{V}$

Thus, the ICMR is bounded by: $V_{CM,min} = 0.2 \, \text{V}, \quad V_{CM,max} = V_{DD} - |V_{OV}|$

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Final Results:

1. $|V_{OV}|$: Depends on $I$, calculated as: $|V_{OV}| = \sqrt{\frac{\frac{I}{2}}{5}}$

2. $V_{SG}$: $V_{SG} = |V_{OV}| + 0.4 \, \text{V}$

3. $V_S$: From the current source: $V_S > 0.2 \, \text{V}$

4. $V_{D1}, V_{D2}, V_O$: $V_{D1} = V_{D2} = V_O = V_{DD} - I_D R_D$

5. ICMR: $0.2 \, \text{V} < V_{CM} < V_{DD} - |V_{OV}|$

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Questions:

1. What is the significance of the overdrive voltage $|V_{OV}|$ in PMOS operation?
2. How does the current source requirement affect the input common-mode range?
3. Why is channel-length modulation neglected in this analysis?
4. How would the presence of mismatch between $Q_1$ and $Q_2$ affect the results?
5. What design considerations arise from the ICMR of the differential amplifier?

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Tip:

When calculating overdrive voltage and saturation conditions, always check if the assumed current splits symmetr