JFET Transconductance Calculation Explained

Transconductance ($g_m$) is a fundamental parameter for JFETs (Junction Field-Effect Transistors). It measures how effectively the gate-source voltage ($V_{GS}$) controls the drain current ($I_D$). A higher transconductance signifies that a small change in $V_{GS}$ results in a larger change in $I_D$. Understanding JFET transconductance is key to analyzing JFET amplifier circuits.

The Transconductance Formula

The transconductance ($g_m$) is mathematically defined as the ratio of the change in drain current ($\Delta I_D$) to the change in gate-source voltage ($\Delta V_{GS}$) applied, assuming other operating conditions remain constant. The formula is:

$g_m = \frac{\Delta I_D}{\Delta V_{GS}}$

Given Parameters for JFET

From the question, we have the following specific values related to the JFET operation:

• The change in Drain Current, $\Delta I_D = 4.3 \text{ mA}$
• The change in Gate-Source Voltage, $\Delta V_{GS} = 1.25 \text{ V} $

Calculating the Transconductance ($g_m$)

To find the JFET transconductance, we substitute the given values into the formula:

1. Write down the formula for transconductance:

   $g_m = \frac{\Delta I_D}{\Delta V_{GS}}$

2. Insert the provided values for $\Delta I_D$ and $\Delta V_{GS}$:

   $g_m = \frac{4.3 \text{ mA}}{1.25 \text{ V}}$

3. Compute the result by dividing the current change by the voltage change:

   $g_m = 3.44 \text{ mA/V}$

The calculation yields a transconductance value of $3.44 \text{ mA/V}$.

Matching with Options

Let's compare our calculated value ($3.44 \text{ mA/V}$) with the provided options:

• Option 1: 3.4 mA/V
• Option 2: 2.3 mA/V
• Option 3: 4.8 mA/V
• Option 4: 2.8 mA/V

The calculated value $3.44 \text{ mA/V}$ is approximately equal to $3.4 \text{ mA/V}$. This value closely matches Option 1.

Therefore, the Transconductance ($g_m$) for the JFET is determined to be 3.4 mA/V.