Realizing the Small-Signal Model Using JFET Parameters for Circuit Behavioral Studies

Key Takeaways

• BJTs are current controlled devices, whereas JFETs are voltage-controlled devices. The voltagesV_DS and V_GS control the drain current I_D.

• JFETs operating regions can be classified into the following: Ohmic region, Pinch-off or Amplifier region, and Breakdown region.

• The dynamic resistance❲ r_d ❳ , amplification factor ❲❳ and transconductance❲ g_m❳are the parameters that determine the performance of JFETs. The parameters satisfy the relationship:

=r_dg_m

When choosing between two bowls of ice cream, which would you prefer— a bowl of plain vanilla ice cream or a bowl of ice cream covered with all your favorite toppings? It's a human tendency to choose an advanced version over a plainer, basic version of something, so I would guess you would choose the bowl of ice cream with the toppings. 

If the Bipolar Junction Transistor ❲BJT❳ is a basic bowl of plain vanilla ice cream, then the Field-Effect Transistor ❲FET❳ is the delicious bowl full of toppings. FETs maintain an edge over BJTs when it comes to characteristics, operation, and applications. FETs possess all the merits of BJTs, along with extras such as reduced noise level and high input impedance. There are two classifications in the FET family; namely, Junction FET ❲JFET❳ and Insulated-Gate FET, most commonly known as Metal-Oxide-Semiconductor FET ❲MOSFET❳. We are going to explore more on the construction, operation, parameters, and small-signal model of the JFET.  

JFET Construction Details

Just like NPN and PNP transistors, JFETs offer N-channel JFET and P-channel JFET with three terminals: gate ❲G❳, source ❲S❳, and drain ❲D❳ analogous to base, emitter, and collector of ordinary transistors. We will stick to N-channel JFET in our further discussion. If the arrow direction of the N-channel JFET symbol is reversed, then it gets transformed to P-channel JFET. 

In N-channel JFET construction, an N-type silicon material forms the substrate layer called the channel and two P-type layers are diffused onto it, forming two PN junctions. The P-type materials are internally connected and form the gate terminal of N-channel JFET. The two leads coming out of the longitudinal ends of the N-channel correspond to the drain and source terminals. In the datasheets of  JFETs, you can see that drain and source are interchangeable. 

JFET Operating Regions

In the operation of the N-channel JFET, the voltage V_DD represents the voltage source applied to the drain terminal and I_D gives the drain current flowing in the FET. The polarities of voltages V_DS and V_GS are mentioned with respect to the source.

• Case 1: V_GS=0 and V_DS=0

In this case, identical depletion regions are formed around the two PN junctions. The thickness of

the depletion regions is uniform along the length. The drain current is equal to zero. 

• Case 2: V_GS = 0 and V_DS + ve

The electrons in the N-channel drift from source to drain, allowing I_D flow from drain to source. Till the knee point, ‘K’, the N-channel JFET can be described as operating in the ohmic region as I_D and V_DS share a linear relationship.

When V_DS is applied, the uniform voltage drops formed in the channel reverse biases the gate-channel PN junctions. The strength of the reverse-bias is more towards the drain than the source side, thus establishing a wider depletion region near to the drain side. 

The voltage V_DS at which the width of the N-channel reaches its minimum and the current I_D becomes constant is called pinch-voltage, V_P. The pinch-off point is marked by ‘P’, and in the area under the curve ‘KP’, I_D follows a reverse square law with V_DS. The drain-source saturation current I_DSS is the drain current corresponding to  V_DS=V_P and V_GS=0. In the region beyond point P—called a pinch-off region, active region, or amplifier region—JFET is analogous to a constant-current source. 

The drain current remains constant at I_DSS with any further increase in V_DS in the pinch-off region. However, the avalanche breakdown occurs in the gate-channel junction at a particular  V_DS > V_P, denoted by V_DS, max. At V_DS, max, I_D increases rapidly and the JFET behaves like a constant-voltage source.

• Case 3: V_GS -ve  and V_DS +ve

To the internal condition persisting in case 2 of N-channel JFET, what happens when a gate reverse 

bias, V_GS is applied?  The external voltage V_GS applied brings the following changes:

• The ohmic operating region of the JFET decreases considerably

• The pinch-off voltage V_P is reached for less value of I_D

• As V_GS increases,  I_DSS andV_DS, max decreases

The voltage V_GS required to reduce drain current I_D=0 is called the gate-source cut-off voltage,   V_GS,❲off❳.

We can summarize from the above cases that by applying reverse bias to the gate, the electric field

associated with the depletion region is varied, thereby the drain current is also varied. Hence the JFET takes the name Field-Effect Transistor. 

JFET Drain Resistance and Transconductance

The drain resistance, transconductance, and amplification factor are the parameters that determine the performance of the JFET. Table. 1 displays the details of the JFET parameters: 

Table.1 JFET parameters

The parameters follow the relationship given by the following equation:

Small-Signal Model of JFETs 

JFETs are an ideal replacement for BJTs, especially at low frequencies. At low frequency, the input impedance is so high that it provides a better amplification process. The noise level is also comparatively less for low-frequency operation. As we know, I_D can be controlled by varying V_GS and V_DS, the Taylor series expansion of I_D can be written as equation (2):

Replacing the ratios by JFET parameters from Table.1 and quantities by small-signal notations i_d, v_gs and v_ds in equation (2), equation (3) is obtained as

The small-signal model of JFETs satisfies equation (3).

The behavior of the JFET analyzed using the small-signal model leads to the design of FET circuits with better performance. Performing small-signal analysis of JFET before fabricating the amplifier circuits. The selection of V_DS and V_GS after understanding the I_D function and its correlation with JFET parameters can help you to achieve a stable amplifier operation.