JFET: DC, small signal and switching
Two 2N5457s from the same bag, in the same circuit, can conduct 0.4 and 2.9 mA. The JFET is the lowest-noise transistor with high-impedance sources, and also the one with the greatest spread.
01A channel that pinches off
The junction field-effect transistor (JFET) is the most direct idea for controlling a current with a voltage. An N-type silicon channel joins two terminals, the drain and the source, and on its sides there are P⁺ regions connected together that form the gate. The gate-channel junction is reverse biased, and its depletion region, which does not conduct, extends into the channel and narrows it. More reverse voltage, narrower channel, less current.
Unlike the bipolar transistor, the gate does not inject anything: only the reverse current of a junction flows through it, on the order of picoamperes. The JFET is a voltage-controlled majority-carrier device with a very high input impedance. The physics of the depletion region is the same as in the PN junction: its width grows with the square root of the reverse voltage.
02Pinch-off and the Shockley equation
When the gate-source voltage reaches the pinch-off voltage \( V_P \) (datasheets call it \( V_{GS(\text{off})} \)), the two depletion regions touch and the channel closes. With \( V_{GS} = 0 \) the maximum current flows, \( I_{DSS} \). Between those extremes, and with enough drain voltage, the current follows a parabola:
With small \( V_{DS} \) the channel behaves as a resistor controlled by the gate (the ohmic or triode region):
The practical problem of the JFET is parameter spread. \( I_{DSS} \) and \( V_P \) depend on the doping and the thickness of the channel, which are poorly controlled: the 2N5457 datasheet allows \( I_{DSS} \) from 1 to 5 mA and \( V_{GS(\text{off})} \) from −0.5 to −6 V. Two transistors from the same bag can be very different.
03Biasing
Since the gate is reverse biased, the simplest circuit is self-bias: the gate goes to ground through a large resistor and a resistor \( R_S \) is placed in the source. The drain current lifts the source, and the gate ends up negative with respect to it:
The source resistor provides feedback: if the current rises, \( V_{GS} \) becomes more negative and holds it back. But with the spread of the 2N5457 it is not enough, as the lab shows. The design solution is a divider at the gate and a large \( R_S \), so that the current is set by \( (V_G - V_{GS})/R_S \) with \( V_G \) much larger than the variation of \( V_{GS} \); or simply selecting the transistors, which is what is done in audio preamplifiers.
The transistor's transfer curve \( I_D(V_{GS}) \) and the bias line \( V_{GS} = -I_D R_S \): the operating point is where they cross. You choose \( I_{DSS} \), \( V_P \), the resistors and the supply. With the spread option, the two extreme samples allowed by the 2N5457 datasheet are overlaid in the same circuit.
04Small-signal model
In saturation, the JFET is a current source controlled by \( v_{gs} \), with a transconductance that comes from differentiating the parabola:
The comparison with the bipolar transistor is instructive: at 1.5 mA a bipolar has \( g_m = 58 \) mS, more than twenty times more. The JFET amplifies less per milliampere, but in exchange its input draws no current and it has very little noise when the signal source has a high impedance.
05The JFET as an analog switch
In the ohmic region and with \( V_{GS} = 0 \), the channel is a small resistance that lets the signal through in both directions; with \( V_{GS} \) beyond \( V_P \), the channel opens up and the resistance is in the gigaohms. That makes it an analog switch: the J111 is specified with \( r_{DS(\text{on})} \leq 30 \) Ω. It was widely used in analog multiplexers, samplers and automatic gain control, where the channel works as a voltage-controlled variable resistor. Today those functions are mostly performed by integrated CMOS switches.
06Where it appears in electronics
| Case | Why a JFET |
|---|---|
| Electret microphone | The capsule has a JFET inside that matches the very high impedance of the charged diaphragm |
| Op amps with JFET inputs (TL072) | Bias currents of tens of picoamperes, versus nanoamperes for a bipolar |
| Preamplifiers for piezoelectric sensors and photodiodes | Low noise with high-impedance sources |
| Two-terminal current sources | A JFET with its gate tied to the source conducts \( I_{DSS} \) at almost any voltage: the “constant-current diode” |
| Silicon carbide power devices | SiC JFETs for switching hundreds of volts with low losses |
07In the lab
With a 2N5457, measure the drain current with the gate tied to the source and 10 V on the drain: that is \( I_{DSS} \). Then lower \( V_{GS} \) until the current drops to 10 µA: this is a good estimate of \( V_{GS(\text{off})} \). Compare three or four transistors from the same bag.
Measure \( I_D \) for five values of \( V_{GS} \) and fit the Shockley parabola. Calculate \( g_m \) at two points and verify that it grows with the square root of the current.
With \( V_{DS} \) of a few hundred millivolts, measure the channel resistance for several values of \( V_{GS} \) and use it in a divider to build a voltage-controlled attenuator.
08Common mistakes
- Forward biasing the gate. The junction conducts and the high input impedance is lost.
- Designing with the typical values of \( I_{DSS} \) and \( V_P \). The spread is enormous; the circuit has to be checked with the extremes.
- Confusing the saturation of the JFET with that of the bipolar. In the JFET, saturation is the amplifying region.
- Forgetting the condition \( V_{DS} \geq V_{GS} - V_P \). If it is not met, the transistor is in the ohmic region and the Shockley equation does not apply.
- Using the wrong sign of \( V_P \). In an N channel it is negative; in a P channel, positive.
09Self-assessment
Why is the gate current of a JFET so small?
Because the gate-channel junction is reverse biased and only its leakage current flows, on the order of picoamperes.
With \( I_{DSS} = 8 \) mA and \( V_P = -4 \) V, what is \( I_D \) with \( V_{GS} = -2 \) V?
\( 8 \times (1 - 0.5)^2 = 2 \) mA.
And the transconductance at that point?
\( g_m = \dfrac{2 \times 8}{4} \times 0.5 = 2 \) mS.
What source resistor self-biases that point?
\( R_S = 2 \text{ V} / 2 \text{ mA} = 1 \) kΩ.
Why is a JFET used inside an electret microphone?
Because the capsule has a very high impedance and the JFET, whose gate draws no current, matches it to a low-impedance output.
10Further reading
- Paul Horowitz and Winfield Hill. The Art of Electronics. 3rd ed., Cambridge University Press, 2015. The chapter on field-effect transistors, with the measured spread of JFETs and the circuits that tolerate it.
- Adel S. Sedra and Kenneth C. Smith. Microelectronic Circuits. 7th ed., Oxford University Press, 2014. The JFET in the same framework as the MOSFET, with biasing and the small-signal model.
- Ben G. Streetman and Sanjay Kumar Banerjee. Solid State Electronic Devices. 7th ed., Pearson, 2015. The derivation of the JFET curves from the width of the depletion region.