The field-effect transistor (FET) is a three-terminal device used for a variety of applications that match, to a large extent, those of the bipolar-junction transistor (BJT).
The BJT transistor is a current-controlled device (current-controlled current source), whereas the FET transistor is a voltage-controlled device (voltage-controlled current source).
Just are there are npn and pnp bipolar transistors, there are n-channel and p-channel field-effect transistors. The BJT transistor is a bipolar device, the prefix bi indicates that the conduction level is a function of two charge carriers (electrons and holes). The FET is a unipolar device depending solely on either electron (n-channel) or hole (p-channel) conduction.
One of the most important characteristics of the FET is its high input impedance.
Typical ac voltage gains for BJT amplifiers are a great deal more than for FETs.
FETs are more temperature stable than BJTs, and FETs are usually smaller than BJTs, making them particularly useful in integrated-circuit (IC) chips.
Types of FET:
- Junction field-effect transistor (JFET)
- Metal-oxide-semiconductor field-effect transistor (MOSFET)
- Metal-semiconductor field-effect transistor (MESFET)
Biasing
DC Analysis
The general relationships that can be applied to the DC analysis of all FET amplifiers are:
$$\boxed{I_G \simeq 0\ A}$$
$$\boxed{I_D = I_S}$$
For JFETs and depletion-type MOSFETs and MESFETs, Shockley’s equation is applied to relate the input and output quantities:
$$\boxed{I_D = I_{DSS} \left( 1 - \frac{V_{GS}}{V_P} \right) ^ 2}$$
For enhancement-type MOSFETs and MESFETs, the following equation is applicable:
$$\boxed{I_D = k \left( V_{GS} - V_T \right) ^ 2}$$
AC Analysis
JFET Small-Signal Model
The ac analysis of a JFET configuration requires that a small-signal ac model for the JFET be developed.
The gate-to-source voltage controls the drain-to-source (channel) current of a JFET.
The change in drain current that will result from a change in gate-to-source voltage can be determined using the transconductance factor \(g_m\).
\(\boxed{\Delta I_D = g_m\,\Delta V_{GS}}\)
\(\boxed{g_m = \frac{\Delta I_D}{\Delta V_{GS}}}\)
If we take the derivative of \(I_D\) with respect to \(V_{GS}\) using Shockley’s equation, we can derive an equation for \(g_m\).
\(\displaystyle I_D = I_{DSS}\,\left(1 - \frac{V_{GS}}{V_P}\right)^2\)
\(\displaystyle \sqrt{\frac{I_D}{I_{DSS}}} = 1 - \frac{V_{GS}}{V_P}\)
\(\displaystyle g_m = \frac{dI_D}{dV_{GS}} = \frac{d}{dV_{GS}} \left[I_{DSS}\left(1 - \frac{V_{GS}}{V_P}\right)^2\right]\)
\(\displaystyle g_m = I_{DSS}\,\frac{d}{dV_{GS}} \left(1 - \frac{V_{GS}}{V_P}\right)^2\)
\(\displaystyle g_m = 2I_{DSS}\left(1 - \frac{V_{GS}}{V_P}\right)\frac{d}{dV_{GS}} \left(1 - \frac{V_{GS}}{V_P}\right)\)
\(\displaystyle g_m = -\frac{2I_{DSS}}{V_P}\left(1 - \frac{V_{GS}}{V_P}\right)\)
\(\boxed{g_m = \frac{2I_{DSS}}{\left|V_P\right|}\left(1 - \frac{V_{GS}}{V_P}\right) = \frac{2I_{DSS}}{\left|V_P\right|} \sqrt{\frac{I_D}{I_{DSS}}}}\)
where \(\left|V_P\right|\) denotes magnitude only, to ensure a positive value for \(g_m\).
On specification sheets, \(g_m\) is often provided as \(g_{fs}\) or \(y_{fs}\), where \(y\) indicates it is part of an admittance equivalent circuit. The \(f\) signifies forward transfer conductance, and the \(s\) indicates that it is connected to the source terminal.
\(\boxed{g_m = g_{fs} = y_{fs}}\)
The input impedance \(Z_i\) of all commercially available JFETs is sufficiently large to assume that the input terminals approximate an open circuit.
\(\boxed{Z_i = \infty\,\Omega}\)
On JFET specification sheets, the output impedance \(Z_o\) will typically appear as \(g_{os}\) or \(y_{os}\) with the unit \(\mu S\). The parameter \(y_{os}\) is a component of an admittance equivalent circuit, with the subscript \(o\) signifying an output network parameter and \(s\) the source terminal to which it is attached in the model.
\(\boxed{Z_o = r_d = \frac{1}{g_{os}} = \frac{1}{y_{os}}}\)
\(\boxed{r_d = \left.\frac{\Delta V_{DS}}{\Delta I_D}\right|_{V_{GS}\,=\,\mathrm{constant}}}\)
JFET AC Equivalent Circuit
The control of \(I_d\) by \(V_{gs}\) is included as a current source \(g_{m}V_{gs}\) connected from drain to source.
The input impedance is represented by the open circuit at the input terminals and the output impedance by the resistor \(r_d\) from drain to source. The gate-to-source voltage is represented by \(V_{gs}\) to distinguish it from dc levels.