Common-Source JFET Gain

Av = −gm · Rd

Quick answer

This calculator solves Av = −gm × Rd for Voltage Gain. With Transconductance 10 mS, Drain Resistor 10 kΩ, the result is -100. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Voltage Gain
—

Formula

Av = −gm × Rd

Description

The voltage gain of a common-source FET amplifier is the device transconductance times the drain load resistance, inverting. Because a FET’s gm is lower than a comparable BJT’s, common-source gains are modest, but the very high input impedance of the gate makes FET stages ideal as low-loading front ends and high-impedance buffers.

Variables

  • Av — Voltage gain (negative = inverting)
  • gm — Transconductance (S)
  • Rd — Drain load resistance (Ω)

Practical Notes

With a source degeneration resistor Rs, Av = −gm·Rd/(1 + gm·Rs), which linearises the stage. FET gm depends on bias current, so gain varies with operating point.

Symbols and units

Symbol Meaning Default unit Accepted units
Av Voltage Gain — —
gm Transconductance mS µS, mS, S
Rd Drain Resistor kΩ mΩ, Ω, kΩ, MΩ

Step by step

  1. 1. What you know: Transconductance 10 mS, Drain Resistor 10 kΩ
  2. 2. The relation: Av = −gm × Rd
  3. 3. Substitute: gm = 10 mS, Rd = 10 kΩ
  4. 4. Result: Voltage Gain = -100

Worked examples

Minimum range

Given: Transconductance 100 µS, Drain Resistor 100 Ω

Result: Voltage Gain = -0.01

Low range

Given: Transconductance 1 mS, Drain Resistor 1 kΩ

Result: Voltage Gain = -1

Typical

Given: Transconductance 10 mS, Drain Resistor 10 kΩ

Result: Voltage Gain = -100

High range

Given: Transconductance 100 mS, Drain Resistor 100 kΩ

Result: Voltage Gain = -10000

Maximum range

Given: Transconductance 1 S, Drain Resistor 1 MΩ

Result: Voltage Gain = -1 × 10⁶

Solving for each variable

Solve for Voltage Gain

Transconductance 100 µS, Drain Resistor 100 Ω → -0.01

Solve for Transconductance

Voltage Gain 0.025, Drain Resistor 100 Ω → -0.25 mS

Solve for Drain Resistor

Voltage Gain 0.025, Transconductance 100 µS → -0.25 kΩ

How Voltage Gain changes with Transconductance

Transconductance (input) Voltage Gain (result)
1 mS -10
2.5 mS -25
5 mS -50
7.5 mS -75
10 mS -100
15 mS -150
20 mS -200
40 mS -400
70 mS -700
100 mS -1000

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Frequently asked questions

How do you calculate Common-Source JFET Gain?

Use Av = −gm × Rd. With Transconductance 10 mS, Drain Resistor 10 kΩ, Voltage Gain works out to -100.

How do you calculate jfet common source amplifier gain calculation?

Rearrange for Voltage Gain: with Transconductance 1 mS, Drain Resistor 1 kΩ, Voltage Gain is -1.

What is the formula for Common-Source JFET Gain?

The formula is Av = −gm × Rd. The voltage gain of a common-source FET amplifier is the device transconductance times the drain load resistance, inverting.

How do you find Transconductance when you know the other values?

Rearrange for Transconductance: with Voltage Gain 0.025, Drain Resistor 100 Ω, Transconductance is -0.25 mS.

How do you find Drain Resistor when you know the other values?

Rearrange for Drain Resistor: with Voltage Gain 0.025, Transconductance 100 µS, Drain Resistor is -0.25 kΩ.

Related Concepts

All Discrete Amplifiers formulas →
Thermal Voltage Small-Signal Emitter Resistance Transistor Transconductance Diode Dynamic Resistance Common-Emitter Voltage Gain BJT Alpha–Beta Relationship Darlington Pair Current Gain Emitter-Follower Input Impedance

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