# 1.2 JFET Internals

A simplified internal model of a JFET is shown in Figure 1.2.1. The main portion of the device is called the channel. The diagram illustrates an N-channel device. The channel is built upon a substrate (i.e., base layer) of oppositely doped material. Attached to the opposing ends of the channel are two terminals; the source and the drain. Embedded within the channel is a region using the opposite material type. A lead is attached to this as well and is called the gate. Although there is not perfect correspondence between them, the drain, source and gate are roughly analogous to the BJT’s collector, emitter and base, respectively.

This diagram is drawn symmetrically. Some devices are designed in this fashion and their drain and source terminals can be swapped with no change in operation. This is not true for all devices, though. For small values of drain-source voltage, the channel exhibits a certain amount of resistance that is dependent on the doping level and physical layout of the device. Further, under normal operation, πΌ_{π·} will equal πΌ_{π}.

To understand how the device behaves, refer to Figure 1.2.2. Here we shall consider electron flow (shown as a dashed line). First, a positive voltage, π* _{π·π·}*, is attached to the drain terminal along with a current limiting resistor, π

*. A negative supply, π*

_{π·}*, is applied to the gate terminal via resistor π*

_{πΊπΊ}_{πΊ}. Let’s start with the gate supply set to zero. If we start π

_{π·π·}at zero, here is what happens as we increase its value. Initially, an increase in drain-source voltage will elicit a proportional increase in the current flowing through the channel. In other words, the channel acts like a resistor. As the voltage across the drain-source increases further, at some point the current will saturate, and no further increases in current will occur in spite of further increases in π

_{π·π·}and π

*. At this point the device is behaving as a constant current source. The drain-source voltage where this transition occurs is called the pinch-off voltage, π*

_{π·π}*π.*If the drain-source voltage increases too much, breakdown will occur and current will begin to increase rapidly.

What’s particularly interesting is what happens when the gate supply is increased in the negative direction. This reverse-biases the gate-source PN junction and results in a larger depletion region being formed. The depletion region widens into the channel, thus restricting current flow sooner and at a lower level. The more negative we make π_{πΊπΊ}, the lower πΌπ· becomes. Eventually, when π_{πΊπΊ} goes negative enough, the drain current will turn off. This voltage is called π_{πΊπ}(πππ) and it has the same magnitude as π_{π} (i.e., π_{π}=|π_{πΊπ}(πππ)|). The action can be thought of as operating like a water valve: turning the gate source voltage more negative is like turning off the spigot and decreasing the flow.

The operation of the JFET can visualized nicely by plotting a set of drain curves, as shown in Figure 1.2.3.

The drain curve family plots drain current, πΌ_{π·}, versus drain-source voltage, π_{π·π}. We begin with the top-most curve. This is generated by setting the gate-source voltage, π_{πΊπ,} to zero. We then cycle π_{π·π} from zero to some higher value. Initially, we see a proportional rise in πΌ_{π·} as π_{π·π} increases. This is called the ohmic or triode region. Eventually, the channel saturates and the current levels out. This is the constant current or saturation region and it occurs for π_{π·π}>π_{π}. The breakdown voltage is called π΅π_{π·πΊπ}, or alternately, π_{(π΅π
)π·π}. Above this voltage the current increases rapidly. As usual, we do not wish to operate the device in this breakdown region.

If we now repeat the process but this time use a small negative value for π_{πΊπ}, we will trace out a curve of very similar shape. The transition to constant current mode will happen at a slightly lower voltage and the current value will be somewhat lower as well. This process continues in like fashion as we make ππΊπ more and more negative. Eventually, when π_{πΊπ}=π_{πΊπ}(πππ), the drain current drops to virtually zero (in fact, a small leakage current flows called πΌ_{π·(πππ))}. In contrast, if π_{πΊπ} was allowed to go positive, operation would be lost because the PN junction would become forward-biased and we would lose control of the current via the depletion region. This means that the JFET’s current control is entirely in the second quadrant and the largest drain current flows when π_{πΊπ}=0 V. This current is called πΌ_{π·ππ}, which stands for the drain current with a shorted gate-source (i.e, if it’s shorted, then π_{πΊπ}=0 V). The JFET cannot produce a continuous current larger than πΌ_{π·ππ} safely.

The characteristic equation relating drain current and gate-source voltage is shown below. This is valid for the constant current region (i.e., π_{π·π}>π_{π}).

(1.2.1)

Where

π_{πΊπ} is the gate-source voltage (ππΊπ(πππ)β€ππΊπβ€0),

πΌ_{π·} is the drain current,

πΌ_{π·ππ} is the maximum current,

π_{πΊπ(πππ)} is the turn-off voltage.

From this we see that the JFET is a square-law device rather than like the BJT which has a logarithmic characteristic.^{[1]} In essence, this curve is a portion of a parabola. This means that the JFET’s characteristic curve is much more gradual in slope than that of a BJT. This will have important implications when it comes to voltage gain potential and distortion, as we shall see in the following chapter.

It is useful to remember that π_{πΊπ(πππ)} and πΌ_{π·ππ} are unique to a given device, rather like π½ is for a BJT. There can also be a fairly large variation in these parameters. For example, a particular model of JFET might show an πΌ_{π·ππ} variation between 2 mA and 20 mA, and a π_{πΊπ(πππ)} variation between β2 V and β8 V. Generally, the most negative ππΊπ(πππ) values will be associated with the largest πΌ_{π·ππ }values.

Equation 1.2.1 is plotted in Figure 1.2.4. Compare this curve to the curve generated by the Shockley equation for BJTs, Figure 7.2.1. The graph is shown in normalized form. Instead of plotting for specific values of π_{πΊπ(πππ)} and πΌ_{π·ππ}, the axes are presented as fractional portions of the maximums (i.e., the horizontal axis is βπ_{πΊπ}/π_{πΊπ(πππ}) and the vertical axis is πΌ_{π·}/πΌ_{π·ππ}).

Example 1.2.1

Using both Equation 1.2.1 and the graph of Figure 1.2.4, determine the drain current if the gate-source voltage is β1 V and the JFET specs are πΌ_{π·ππ} = 8 mA and π_{πΊπ(πππ) }= β2 V.

First, using Equation 1.2.1

Using the graph, π_{πΊπ}/π_{πΊπ(πππ)}is 1 V/β2 V, or β0.5. Find this value on the horizontal axis, follow up to the curve and then across to the right vertical axis. The normalized drain current is 0.25, thus πΌπ· is 0.25 πΌ_{π·ππ}, or 2 mA.

As the characteristic curve plots output current versus input voltage, the slope of this represents the transconductance, an important characteristic for biasing and signal analysis. Device transconductance is denoted as ππ, or alternately as πππ , and given units of siemens. We can derive an equation for transconductance by taking the derivative of Equation 1.2.1.

The coefficient β2πΌ_{π·ππ}/π_{πΊπ(πππ)} is defined as ππ0, the transconductance when π_{πΊπ}=0V. This is the maximum transconductance of the device. Substituting, we arrive at

(1.2.2)

(1.2.3)

A normalized plot of transconductance versus π_{πΊπ} is shown in Figure 1.2.5. The horizontal axis is βπ_{πΊπ}/π_{πΊπ(πππ)} and the vertical axis is ππ/ππ0.

From this graph we see that the transconductance is a linear function.

Another item of interest regarding these device equations: If we combine Equations 1.2.1 and 1.2.3, we generate two equations that will prove useful in upcoming work.

(1.2.4)

(1.2.5)

Before moving on, the schematic symbols for JFETs are shown in Figure 1.2.6. The middle vertical line represents the channel, and as is usually the case, the arrow points to N material. Sometimes the gate arrow is draw in the middle rather than toward the source. Also, as is the case the BJT, sometimes these symbols are drawn within a circle.

- As evidenced in the Shockley equation, Equation 2.1.1. ↵