JFET Characteristics

JFET characteristics describe how drain current responds to both gate voltage and drain voltage, and understanding these two regions is essential for every amplifier and switch design. The 2N5459 datasheet plots these curves, and reading them correctly separates a working circuit from one that distorts.

Core Concept

The JFET output characteristic has two distinct operating regions. In the ohmic region (also called the triode or linear region), V_DS is small and the channel acts like a voltage-controlled resistor. Drain current increases almost linearly with V_DS. This region is used when the JFET operates as an analog switch or variable resistor.

As V_DS increases, the drain end of the channel becomes more reverse-biased relative to the gate. At the point where V_DS = V_GS - V_P, the channel just pinches off at the drain end. Beyond this, the device enters the saturation region where I_D remains nearly constant regardless of further V_DS increases. Amplifiers operate in this region because I_D depends only on V_GS.

The transfer characteristic is the plot of I_D versus V_GS with V_DS held constant in saturation. It follows a square law: I_D = I_DSS × (1 - V_GS/V_P)^2. This is the curve used to set the Q-point of a JFET amplifier stage. For the 2N5459, I_DSS is typically 9 mA and V_P is -8V.

Key Equations

In the ohmic region: I_D = I_DSS × [2(1 - V_GS/V_P)(V_DS/V_P) - (V_DS/V_P)^2] valid when V_DS < V_GS - V_P.

In the saturation region: I_D = I_DSS × (1 - V_GS/V_P)^2 valid when V_DS ≥ V_GS - V_P. This is the standard amplifier equation.

Channel resistance in ohmic region (small V_DS): r_ds = V_P / (2 × I_DSS × (1 - V_GS/V_P)) in ohms. This is the basis for the JFET as a voltage-controlled resistor (VCR).

Given:
  N-channel JFET 2N5459
  I_DSS = 9 mA
  V_P = -8 V
  V_DD = 15 V
  R_D = 1.5 kΩ
  V_GS = -2 V (set by bias network)

Why this formula:
  Check saturation: V_DS(sat) = V_GS - V_P = -2 - (-8) = 6 V
  We need to verify V_DS > 6V for saturation.

Formula:
  I_D = I_DSS × (1 - V_GS/V_P)^2
  V_DS = V_DD - I_D × R_D

Substitution:
  I_D = 9 × (1 - (-2)/(-8))^2
      = 9 × (1 - 0.25)^2
      = 9 × (0.75)^2

Calculation:
  I_D = 9 × 0.5625 = 5.06 mA
  V_DS = 15 - 5.06×10^-3 × 1500
       = 15 - 7.59
       = 7.41 V

  Check: V_DS = 7.41V > V_DS(sat) = 6V. Device is in saturation.

Final Answer:
  I_D = 5.06 mA
  V_DS = 7.41 V
  Operating in saturation region (confirmed).

Exam Tip: GATE tests the saturation condition V_DS ≥ V_GS - V_P carefully. For N-channel with V_GS = -2V and V_P = -4V: V_DS(sat) = -2 - (-4) = 2V. Students often forget to subtract a negative V_P and write V_DS(sat) = V_GS + V_P, giving a wrong answer. Also, the transfer curve is parabolic (square law), not linear. Treating it as linear to find Q-point intersections leads to errors.

Key Properties

• Ohmic region: V_DS < (V_GS - V_P). Channel acts as a resistor. JFET used as analog switch or VCR here.
• Saturation region: V_DS ≥ (V_GS - V_P). I_D nearly constant. JFET used as amplifier here.
• Transfer characteristic is a downward-opening parabola from (0, I_DSS) to (V_P, 0).
• Maximum transconductance g_m0 = 2 I_DSS / |V_P| occurs at V_GS = 0.
• Output resistance r_o in saturation is typically 10 kΩ to 100 kΩ, representing the slight slope of I_D vs V_DS curves.
• Breakdown occurs at V_DS = BV_DSS, typically 25V to 40V for signal JFETs. Operating above this destroys the device.

Quick Revision

• Two regions: ohmic (V_DS < V_GS - V_P) and saturation (V_DS ≥ V_GS - V_P).
• Amplifiers use saturation region where I_D ≈ I_DSS (1 - V_GS/V_P)^2.
• Switches use ohmic region where JFET behaves as r_ds controlled by V_GS.
• Transfer curve is parabolic from (V_P, 0) to (0, I_DSS).
• g_m is maximum at V_GS = 0 and zero at V_GS = V_P.
• V_DS(sat) = V_GS - V_P: must verify device is in saturation before applying square-law formula.
• Output curves are nearly flat in saturation: I_D varies little with V_DS.
• Exam trap: Applying the saturation formula without checking the saturation condition. If V_DS < V_GS - V_P, the device is in the ohmic region and you must use the full two-term equation instead.