--- title: "Depletion MOSFET Q-points (IDSS 10 mA, VP -4 V)" subject: "Electronics Devices and Circuit" chapter: 3 key: "semester_3/electronics_devices_and_circuit:depletion-mosfet-qpoints" source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/depletion-mosfet-qpoints site: BCT Engineering --- # Depletion MOSFET Q-points (IDSS 10 mA, VP -4 V) Electronics Devices and Circuit · Chapter 3: Field-Effect Transistor - Asked in: 2082 Baisakh, 8 marks - Video: [Electronics Basics #26 | Depletion MOSFET DC Analysis: Voltage-Divider Bias](https://www.youtube.com/watch?v=IJ1OX3K92MA) — AcEdumy EN | EngineeringENG - Page: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/depletion-mosfet-qpoints - Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-3 ## Question The depletion type N channel MOSFET has IDSS= 10 mA and Vp= -4V. [Figure: n-channel depletion MOSFET with drain resistor RD from +VDD to drain, gate resistor RG from gate to -VGG, source grounded, signal Vin through coupling capacitor C to the gate, output Vout at the drain] a) Find the quiescent values of ID and VDS when VGS = -1V b) Repeat when VGS = +2V c) Which, if either, of these Q-points is in pinch off region? d) At which, if either, of these Q-points is the device operating in enhancement mode ## Short answer Assuming VDD = 20 V, RD = 500 Ω. For VGS = –1 V: ID = 5.625 mA, VDS = 17.19 V. For VGS = +2 V: ID = 22.5 mA, VDS = 8.75 V. Both Q-points have VDS > VGS – VP, so both are in pinch-off. Only VGS = +2 V (ID > IDSS) is enhancement mode. ## Answer The n-channel depletion MOSFET is biased by a negative gate supply -VGG (through RG, with no gate current, so VGS is set directly by the supply). The drain current follows the same equation as a JFET, but VGS may also be positive. ```text ID = IDSS (1 - VGS/VP)² , VDS = VDD - ID RD ``` IDSS = 10 mA, VP = -4 V. VDD and RD are not given in the question, so VDS is shown as a formula and then evaluated for an assumed VDD = 20 V and RD = 500 Ω (assumption). #### a) VGS = -1 V ```text ID = 10 (1 - (-1)/(-4))² = 10 (1 - 0.25)² = 10 × 0.5625 = 5.625 mA VDS = VDD - ID RD = 20 - 5.625 mA × 0.5 kΩ = 17.19 V ``` #### b) VGS = +2 V ```text ID = 10 (1 - 2/(-4))² = 10 (1 + 0.5)² = 10 × 2.25 = 22.5 mA VDS = 20 - 22.5 mA × 0.5 kΩ = 8.75 V ``` #### c) Pinch-off (saturation) region The condition for pinch-off operation is VDS ≥ VGS - VP (= VGS + 4 V). - (a) VGS - VP = -1 + 4 = 3 V; VDS = 17.19 V > 3 V, so **Q-point (a) is in the pinch-off region**. - (b) VGS - VP = 2 + 4 = 6 V; VDS = 8.75 V > 6 V, so **Q-point (b) is also in the pinch-off region** (for the assumed VDD and RD). In general the check is VDD - ID RD > VGS - VP. #### d) Enhancement mode A depletion MOSFET works in the depletion mode for VGS < 0 (channel width reduced, ID < IDSS) and in the **enhancement mode for VGS > 0** (channel gets more carriers, ID > IDSS). Hence Q-point (b), VGS = +2 V with ID = 22.5 mA > IDSS, is in the enhancement mode; Q-point (a) (VGS = -1 V, ID = 5.6 mA < IDSS) is in the depletion mode. **Answer:** (a) ID = 5.625 mA, VDS = VDD - 5.625 RD; (b) ID = 22.5 mA, VDS = VDD - 22.5 RD; (c) both are in pinch-off if VDS exceeds 3 V and 6 V respectively; (d) only (b). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is ID at VGS = -1 V for IDSS = 10 mA and VP = -4 V? A. 5.625 mA B. 7.5 mA C. 2.5 mA D. 10 mA Answer: A. ID = 10(1 - 0.25)^2 = 5.625 mA. (Key point: Drain current at VGS=-1) 2. What is ID at VGS = +2 V? A. 22.5 mA B. 15 mA C. 10 mA D. 12.5 mA Answer: A. ID = 10(1 + 0.5)^2 = 22.5 mA. (Key point: Drain current at VGS=+2) 3. What is the pinch-off (saturation) condition? A. VDS ≥ VGS - VP B. VDS ≤ VGS - VP C. VGS ≥ 0 D. VDS = VDD Answer: A. The device is in pinch-off when VDS is at least VGS - VP. (Key point: Pinch-off condition) 4. Which Q-point is in enhancement mode? A. VGS = +2 V, since ID exceeds IDSS B. VGS = -1 V C. Both D. Neither Answer: A. Positive VGS in a depletion MOSFET gives enhancement, with ID > IDSS. 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