---
title: "JFET VGS for given IDS and gm"
subject: "Electronics Devices and Circuit"
chapter: 3
key: "semester_3/electronics_devices_and_circuit:jfet-vgs-gm-numeric"
source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/jfet-vgs-gm-numeric
site: BCT Engineering
---

# JFET VGS for given IDS and gm

Electronics Devices and Circuit · Chapter 3: Field-Effect Transistor

- Asked in: 2071 Shrawan, 5 marks
- Video: [JFET small Signal Model| Transconductance|Transconductance versus VGS graph| Effect of ID on gm](https://www.youtube.com/watch?v=EN31hxWBoc4) — Technically Explained
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/jfet-vgs-gm-numeric
- Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-3

## Question

An n-channel JFET has a pinch-off voltage of -4.5V and IDSS = 9 mA. At what value of VGS will IDS be equal to 3 mA? What is its gm at this IDS?

## Short answer

VGS=VP(1−√(ID/IDSS))=−4.5(1−√(3/9))=−1.90V. gm=gm0√(ID/IDSS) with gm0=2IDSS/|VP|=4mS, giving gm=2.31mS.

## Answer

**Given:** VP = −4.5 V, IDSS = 9 mA, ID = 3 mA.

#### (a) VGS for ID = 3 mA
ID = IDSS (1 − VGS/VP)²

1 − VGS/VP = √(ID/IDSS) = √(3/9) = 0.5774

VGS = VP (1 − 0.5774) = −4.5 × 0.4226 = **−1.90 V**

(The other root, 1 − VGS/VP = −0.5774, gives VGS = 1.5774 VP = −7.10 V. This is beyond the pinch-off voltage, where the JFET is cut off and the equation does not apply, so it is not valid.)

#### (b) Transconductance at this ID
gm0 = 2 IDSS/|VP| = 2 × 9 / 4.5 = 4 mS

gm = gm0 (1 − VGS/VP) = 4 × 0.5774 = **2.31 mS**

Check: gm = gm0 √(ID/IDSS) = 4 × √(1/3) = 2.31 mS.

**Answer: VGS = −1.90 V, gm = 2.31 mS (2.31 mA/V).**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. For ID = 3 mA, IDSS = 9 mA, VP = -4.5 V, VGS is:
   A. -1.90 V
   B. -2.25 V
   C. -3.0 V
   D. -0.5 V
   Answer: A. VGS = VP(1 - sqrt(1/3)) = -4.5*0.4226 = -1.90 V. (Key point: Solving for VGS)

2. gm0 = 2 IDSS/|VP| equals:
   A. 4 mS
   B. 2 mS
   C. 9 mS
   D. 0.5 mS
   Answer: A. 2*9/4.5 = 4 mS. (Key point: gm0)

3. gm at ID = 3 mA is:
   A. 2.31 mS
   B. 4 mS
   C. 1.33 mS
   D. 3 mS
   Answer: A. gm = gm0 sqrt(ID/IDSS) = 4*0.577 = 2.31 mS. (Key point: gm at ID)

## Related in Electronics Devices and Circuit

- [JFET ID and VDS (VP -3.5 V, IDSS 10 mA), pinch-off check](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ajfet-self-bias-vp-3p5) — Electronics Devices and Circuit, chapter 3, asked 3×
- [JFET ID and VDS (VP -5.5 V, IDSS 10 mA), pinch-off check](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ajfet-self-bias-vp-5p5) — Electronics Devices and Circuit, chapter 3, asked 3×
- [JFET ID and VDS (VP -5.5 V, IDSS 12 mA)](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ajfet-self-bias-vp-5p5-idss12) — Electronics Devices and Circuit, chapter 3, asked 3×
- [JFET ID and VDS (IDSS 18 mA, VP -5 V)](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ajfet-divider-bias-idss18) — Electronics Devices and Circuit, chapter 3, asked 5×
- [JFET ID and VDS (IDSS 15 mA, VP -4.5 V)](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ajfet-divider-bias-idss15) — Electronics Devices and Circuit, chapter 3, asked 5×
- [JFET Q-point (IDSS 8 mA, VP -6 V)](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ajfet-self-bias-idss8-vp6) — Electronics Devices and Circuit, chapter 3, asked 2×