# Range of Drain-to-Source Resistance for Overdrive Voltage ## Step 1: Understanding Overdrive Voltage - **Overdrive voltage (V_ov)** is defined as: \[ V_{ov} = V_{GS} - V_{th} \] where \( V_{GS} \) is the gate-to-source voltage and \( V_{th} \) is the threshold voltage. ## Step 2: Drain-to-Source Resistance in Saturation For a MOSFET operating in (active) region, the **small-signal drain-to-source resistance**( r_{ds} \)) is very high and often ignored. But if the MOSFET is in **linear (triode) region**, use the following formula for resistance: \[ R_{DS(on)} \approx \frac{1}{\mu_n C_{ox} \frac{W}{L} V_{ov}} \] - \( \mu_n \): Electron mobility (process parameter) - \( C_{ox} \): Gate oxide capacitance per unit area (process parameter) - \( W \): Channel width - \( L \): Channel length Let’s denote \( K = \mu_n C_{ox} \frac{W}{L} \), a constant for a given device, so: \[ R_{DS(on)} = \frac{1}{K V_{ov}} \] ## Step 3: Calculate Range for Given \( V_{ov} \) Given: \( V_{ov} \) ranges from \( .5\,\text{V} \) to \( 2\,\text{V} \). - For minimum \( V_{ov} = .5\,\text{V} \): \[ R_{DS(on), \text{max}} = \frac{1}{K \times .5} \] - For maximum \( V_{ov} = 2\,\text{V} \): \[ R_{DS(on), \text{min}} = \frac{1}{K \times 2} \] ## Step 4: Express as a Range \[ R_{DS(on)} \text{ ranges from } \frac{1}{2K} \text{ (at } V_{ov}=2\text{V) to } \frac{1}{.5K} = \frac{2}{K} \text{ (at } V_{ov}=.5\text{V)} \] or, more simply: \[ \boxed{ R_{DS(on)} \text{ ranges from } \frac{1}{2K} \;\text{to}\; \frac{2}{K} } \] where \( K = \mu_n C_{ox} \frac{W}{L} \). ## Step 5: Final Answer **The drain-to-source resistance \( R_{DS(on)} \) corresponding to an overdrive voltage range of .5 V to 2 V is:** \[ \boxed{ R_{DS(on)} = \frac{1}{K V_{ov}} \qquad \text{so it ranges from } \frac{1}{2K} \text{ to } \frac{2}{K} } \] **where \( K = \mu_n C_{ox} \frac{W}{L} \) is a device/process constant.**