## Step-by-Step Solution Let's break down the problem and solve it step-by-step: --- ### **1. Requirements and Parameters** - **Reference current (\(I_{REF}\))**: 200 μA - **High input impedance**: Required (suggests MOSFET current mirror) - **Drive differential amplifier**: Output current mirror needed - **Common mode input voltage**: Should be supported by the circuit - **Given parameters**: - \(R = 2\,k\Omega\) - \(k'_{n2} = 10\) - \(k'_{n1} = 250\,\mu A/V^2\) - \(V_{DD} = 5\,V\) --- ### **2. Suitable Circuit Configuration** #### **MOSFET Current Mirror** A **Widlar current mirror** or **simple MOSFET current mirror** is suitable for high input impedance and current mirroring. We'll use **NMOS transistors**. **Circuit:** - **M1**: Reference transistor (gate and drain shorted, source to ground) - **M2**: Output transistor (gate tied to M1's gate, source to ground, drain gives mirrored current) - **R**: 2kΩ resistor to set reference current --- ### **3. Reference Leg Design** #### **Reference Current Setup** \[ I_{REF} = 200 \mu A \] \[ V_{DD} = 5V \] \[ R = 2\,k\Omega \] **Voltage across R:** \[ V_R = I_{REF} \times R = 200 \times 10^{-6} \times 2000 = 0.4\,V \] **Voltage at drain/gate of M1 (\(V_{GS}\)):** \[ V_{GS1} = V_{DD} - V_R = 5V - 0.4V = 4.6\,V \] --- ### **4. MOSFET Sizing** #### **NMOS Saturation Current Equation** \[ I_D = \frac{1}{2} k'_n \left(\frac{W}{L}\right) (V_{GS} - V_{th})^2 \] Assume \(V_{th} = 1V\) (not specified; typical for NMOS). #### **For M1:** \[ 200 \mu A = \frac{1}{2} \cdot 250 \mu A/V^2 \cdot \left(\frac{W}{L}\right)_1 (4.6V - 1V)^2 \] \[ 200 \mu A = 125 \mu A/V^2 \cdot \left(\frac{W}{L}\right)_1 \cdot (3.6V)^2 \] \[ 200 \mu A = 125 \mu A/V^2 \cdot \left(\frac{W}{L}\right)_1 \cdot 12.96 \] \[ 200 \mu A = 1620 \mu A \cdot \left(\frac{W}{L}\right)_1 \] \[ \left(\frac{W}{L}\right)_1 = \frac{200}{1620} \approx 0.123 \] --- ### **5. Output Transistor Sizing** #### **Matching the Output Current** To mirror the current exactly, set \((W/L)_2 = (W/L)_1\) if both use \(k'_{n1}\). If you use different \(k'_n\), scale accordingly. #### **If M2 uses \(k'_{n2} = 10\):** \[ I_{OUT} = \frac{1}{2} \cdot 10 \cdot \left(\frac{W}{L}\right)_2 (3.6)^2 \] Set \(I_{OUT} = 200 \mu A\): \[ 200 \mu A = 5 \cdot \left(\frac{W}{L}\right)_2 \cdot 12.96 \] \[ 200 \mu A = 64.8 \cdot \left(\frac{W}{L}\right)_2 \] \[ \left(\frac{W}{L}\right)_2 = \frac{200}{64.8} \approx 3.09 \] --- ### **6. Final Circuit & Explanation** **Circuit configuration:** - **Simple NMOS current mirror** - **M1:** Reference NMOS with \((W/L)_1 \approx 0.123\), \(k'_{n1} = 250 \mu A/V^2\) - **M2:** Output NMOS with \((W/L)_2 \approx 3.09\), \(k'_{n2} = 10\) - Reference current set by resistor \(R = 2\,k\Omega\) between \(V_{DD}\) and drain/gate of M1. - Both sources grounded. - Gates tied together. - Output current from drain of M2. --- ### **7. Final Answer (Summary Table)** | Parameter | Value / Description | |---------------|----------------------------------------------------------------------------------| | Circuit | NMOS Current Mirror (High input impedance) | | Reference Resistor | \(R = 2\,k\Omega\) | | Reference Current | \(I_{REF} = 200\,\mu A\) | | Sizing M1 | \((W/L)_1 \approx 0.123\), \(k'_{n1} = 250\,\mu A/V^2\) | | Sizing M2 | \((W/L)_2 \approx 3.09\), \(k'_{n2} = 10\) | | Supply Voltage | \(V_{DD} = 5V\) | | Output Current | \(I_{OUT} \approx 200\,\mu A\) | --- **Conclusion:** > **A simple NMOS current mirror with the above MOSFET sizing and resistor value will mirror the 200 μA reference current with high input impedance, suitable for driving a differential amplifier.** --- #### **[Optional: Circuit Diagram Sketch]** ``` VDD = 5V | [R = 2kΩ] | Drain/Gate--M1 (W/L = 0.123, k'n1 = 250μA/V²) | | | |---Gate--M2 (W/L = 3.09, k'n2 = 10) | | | Drain (Output) Source Source | | GND GND ``` --- ### **If you need the circuit drawn, let me know!**