JFET pinch-off behavior (n-channel): At what condition does an n-channel JFET reach pinch-off, meaning further increases in drain-to-source voltage no longer increase the drain current (ID)?

Introduction / Context:
An n-channel Junction Field-Effect Transistor (JFET) is a depletion-mode device whose channel conductivity is controlled by the reverse-bias on its gate-to-channel PN junction. A key operating point is the pinch-off condition, where the channel is sufficiently depleted so that increasing the drain-to-source voltage (VDS) does not significantly increase the drain current (ID). This question checks your grasp of the JFET output characteristics and the definition of pinch-off in the saturation (constant-current) region.

Given Data / Assumptions:

• An n-channel JFET operating with gate-to-source voltage VGS fixed (often at or below 0 V).
• Device modeled under typical small-signal conditions, ignoring channel-length modulation for the ideal definition.
• Temperature and process variations neglected for clarity.

Concept / Approach:

For a given VGS, as VDS rises, the reverse bias along the channel increases and the channel narrows. At the pinch-off voltage Vp (for that VGS), the channel is just pinched near the drain end and the device enters the so-called saturation or constant-current region: ID remains approximately constant even if VDS increases further.

Step-by-Step Solution:

Verification / Alternative check:

Inspect a JFET family of output curves (ID vs. VDS for several VGS). Each curve shows a knee where it flattens: that knee corresponds to the onset of pinch-off (saturation region). Measuring ID beyond the knee shows minimal change with VDS.

Why Other Options Are Wrong:

• VGS-based definitions (options b and d) describe cutoff or transconductance behavior, not the VDS pinch-off onset.
• VDG (option c) is not the standard defining parameter for the pinch-off condition in output characteristics.
• ID at threshold (option e) confuses MOSFET terminology with JFET behavior.

Common Pitfalls:

• Confusing pinch-off (constant-current region) with cutoff (ID ≈ 0).
• Ignoring channel-length modulation, which causes a slight upward slope in real devices but does not change the basic definition.

Final Answer:

the value of VDS at which further increases in VDS will cause no further increase in ID