## Static Parameters of JFET: Theory and Practice

Engineers and radio amateurs are interested in the static parameters of JFETs (Junction gate Field Effect Transistor), such as the zero-gate voltage drain current (IDSS) and the gate-to-source cutoff voltage (VGS(off)), as a rule, either when choosing JFET with the best parameters, or when selecting a pair of JFETs with the equal parameters for the differential stage. In this article, we will focus on the use of static parameters in the calculation of circuits based on JFETs.

### Definitions

In Fig.1 the schematic symbol of a field-effect transistor with an n-channel and a control p-n-junction on the gate is shown:

The designation of JFET’s leads, respectively, is as follows:

G – Gate;
S – Source;
D – Drain.

The main static parameters of JFETs are a zero-gate voltage drain current (IDSS) and a gate-to-source cutoff voltage (VGS(off)). The zero-gate voltage drain current (IDSS) of JFET is defined at the given constant drain-to-source voltage (VDS = const).

The gate-to-source cutoff voltage (VGS(off)) is such a threshold value of the gate-source voltage, upon reaching which the current through the channel of JFET no longer changes and is practically equal to zero. It is also measured at a fixed drain-to-source voltage (VDS = const).

As an amplifying element, JFET operates at a sufficiently high drain-to-source voltage (VDS) – on the graph of the JFET’s output characteristics family this voltage value is located in the saturation region. This means that the drain current (ID) of JFET depends mainly on the magnitude of the gate-to-source voltage (VGS). This dependence of the drain current (ID) on the input gate-source voltage (VGS) is described by the so-called transfer characteristic of JFET (drain current versus gate-to-source voltage characteristic). It is usually approximated by the following expression:

(1)

Thus, the drain current (ID) of JFET versus gate-to-source voltage (VGS) changes according to a quadratic law. Graphically, this dependence is illustrated by the diagram in Fig.2: Fig.2. An example of approximating the dependence of the drain current ID on the gate-to-source voltage VGS by a quadratic function with a zero-gate voltage drain current IDSS = 9,5 mA and a gate-to-source cutoff voltage VGS(off) = -2,8 V.

In such a change in the drain current ID with a change in the gate-source voltage VGS, the amplifying properties of JFET appear. Quantitatively, these properties are characterized by such a parameter as the transconductance, defined as:

(2)

It is clear that the value of the transconductance, expressed in terms of the JFET’s static parameters IDSS and VGS(off), can be obtained by differentiating the expression (1) for the transfer characteristic with respect to dVGS:

That is, for JFET with known values of the zero-gate voltage drain current IDSS and the gate-to-source cutoff voltage VGS(off) at a given gate-to-source voltage VGS, the slope of the transfer characteristic can be calculated by the formula:

(3)

or, given the equality:

we get another expression for the slope at a given drain current ID:

(4)

### Setting the DC operating point of JFET

Fig.3 shows the generally known circuits with junction gate field effect transistors:

a) amplifier stage with a common source;
b) source follower;
c) two-terminal network – current stabilizer.

Fig.3 The generally known circuits with junction gate field effect transistors.

In all these circuits, the resistor RS included in the source circuit is used to set the required value of the drain current ID. The gate electrical potential of the JFET is equal to the electrical potential of the lower terminate of the RS resistor, therefore, the drain current ID, the gate-to-source voltage VGS and the resistance of the RS resistor are elementarily related to each other by Ohm’s law:

(5)

The resistance of the resistor RS calculation to set the required drain current ID for JFET with known values of the zero-gate voltage drain current IDSS and the gate-to-source cutoff voltage VGS(off) can also be made based on the expression for the transfer characteristic (1):

whence we get the equality:

(6)

We divide both parts of equality (6) by RS and, taking into account expression (5), we get:

Accordingly, the expression for the resistance of the resistor RS calculation will take the following form:

(7)

### Theory and practice

Based on the above mathematical expressions, it is logical to assume that the measured values of the zero-gate voltage drain current IDSS and the gate-to-source cutoff voltage VGS(off) determine the slope of JFET’s transfer characteristic at the given operating point or allow you to calculate the operating point of JFET so as to obtain the required slope value of JFET’s transfer characteristic. But the practical results are often far from the calculated ones.

Since we are talking about the most accurate determination of the transfer characteristic of JFET, the gate-to-source cutoff voltage VGS(off) of a real junction gate field effect transistor is important only as a parameter in expression (1), at which this expression most closely matches the real transfer characteristic of this transistor. The same can be said about the value of the zero-gate voltage drain current (IDSS). Thus, it may turn out that direct measurement of the static parameters of JFET does not make much practical sense, since these parameters do not describe the transfer characteristic of a transistor with sufficient accuracy.

In practice, when designing based on JFET amplifying stage circuits, their operating point is never chosen so that the gate-to-source voltage VGS is close to the gate-to-source cutoff voltage VGS(off) or zero. Therefore, there is no need to describe the transfer characteristic (1) throughout its length from ID=0 to ID=IDSS, it is enough to do this for a certain working section from ID1=ID(VGS1) to ID2=ID(VGS2). To do this, we will solve the following mathematical task.

Assume that for two given gate-source voltages VGS1 and VGS2, two corresponding drain currents ID1 and ID2 were measured. It is necessary to calculate the parameters of formula (1) the zero-gate voltage drain current and the gate-to-source cutoff voltage that are more appropriate for the real transfer characteristic of the junction gate field effect transistor.

To do this, we solve the system of equations (8-9) with respect to the values of the zero-gate voltage drain current and the gate-to-source cutoff voltage :

(8-9)

First, let’s find out a new value of the gate-to-source cutoff voltage . To reduce the equation by the multiplier and get one equation with one unknown we divide the second equation by the first. Next, we solve the resulting equation:

Thus, the desired value of the gate-to-source cutoff voltage in formula (1) is determined by the expression:

(10)

And for the corresponding new value of the zero-gate voltage drain current , the expression is as follows:

(11)

### Experimental data

The replacements for the gate-to-source cutoff voltage ( ) and the zero-gate voltage drain current ( ) calculated by formulas (10) and (11) after substitution into formula (1) should give a more accurate correspondence of this formula to the real transfer characteristic of JFET. To test this, the parameters of twelve JFETs were measured. The measurements were carried out for four types of JFETs, three transistors of each type.

The measurement order for each JFET was as follows. First, the zero-gate voltage drain current IDSS and the gate-to-source cutoff voltage VGS(off) of JFETs were measured. Then, the two values of the gate-source voltages VGS1 and VGS2 were measured for the two corresponding values of the drain current ID1 and ID2, which are different from the zero value at VGS=VGS(off) and the zero-gate voltage drain current IDSS. Substituting VGS1, VGS2, ID1, and ID2 into formulas (10) and (11) have the sought-for values and . After that, the drain current ID0 of JFET was set to approximately half the measured zero-gate voltage drain current IDSS and the corresponding gate-to-source voltage VGS0 was measured. The values of ID0 and VGS0 obtained in this way are the coordinates of an arbitrarily chosen operating point of JFET on its real transfer characteristic. Now it remains to substitute the value of VGS0 into formula (1), first with a pair of parameters IDSS and VGS(off), and then with and , and compare both calculated values of the drain current with the measured ID0. Then we will know which pair of parameters, IDSS and VGS(off) or and , after substitution in the expression (1) gives a more accurate match to the real transfer characteristic of the junction gate field effect transistor.

The results of measuring the parameters of twelve JFETs are shown in the table below.

 No JFET Measured parameters Calculated with expressions (10) and (11) parameters VGS0, V ID0, mA Drain current ID, calculated by formula (1) with IDSS and VGS(off) Drain current I’D, calculated by formula (1) with I’DSS and V’GS(off) IDSS,mA VGS(off),V I’DSS,mA V’GS(off),V ID,mA Error,% I’D,mA Error,% 1 KP303V 2,95 -1,23 2,98 -1,35 -0,40 1,52 1,33 -12,5 1,47 -3,6 2 KP303V 2,89 -1,20 2,95 -1,32 -0,40 1,48 1,28 -13,1 1,43 -3,2 3 KP303V 2,66 -1,16 2,70 -1,24 -0,36 1,41 1,26 -10,2 1,35 -3,8 4 2P303E 12,06 -4,26 12,73 -4,90 -1,49 6,49 5,09 -21,5 6,16 -5,2 5 2P303E 11,24 -3,94 11,69 -4,50 -1,37 6,06 4,79 -20,9 5,67 -6,5 6 2P303E 10,92 -3,77 11,26 -4,31 -1,29 5,91 4,73 -20,0 5,53 -6,3 7 2N3819 10,64 -3,47 10,76 -3,91 -1,08 5,90 5,05 -14,4 5,64 -4,4 8 2N3819 10,22 -3,51 10,29 -3,90 -1,06 5,73 4,98 -13,1 5,46 -4,8 9 2N3819 10,30 -3,38 10,46 -3,80 -1,07 5,67 4,81 -15,2 5,40 -4,8 10 2N4416A 8,79 -2,98 9,05 -3,27 -1,04 4,46 3,71 -16,9 4,20 -5,9 11 2N4416A 10,10 -3,22 10,31 -3,55 -1,18 4,98 4,04 -19,0 4,58 -8,0 12 2N4416A 10,92 -3,93 12,66 -4,32 -1,63 5,36 4,09 -23,6 4,92 -8,2

The error values highlighted in color speak for themselves. If we compare the transfer characteristic graphs similar to those shown in Fig.2, then the line plotted using the values ( ; ) will pass much closer to the point (VGS0; ID0) than the line plotted using the measured gate-to-source cutoff voltage and zero-gate voltage drain current (VGS (off); IDSS). It should be especially noted that this method for determining the static parameters of JFETs is indispensable for transistors with a large zero-gate voltage drain current (IDSS), for example, for such as J310.