FET Amplifiers: An Overview

Introduction to FET Amplifiers

• Field-effect transistor amplifiers provide excellent voltage gain and high input impedance.
• They also offer low-power-consumption configurations with good frequency range, minimal size, and weight.
• JFETs, depletion MOSFETs, and MESFETs can be used to design amplifiers with similar voltage gains.
• Depletion MOSFET (MESFET) circuits have a much higher input impedance than similar JFET configurations.
• BJT devices control a large output (collector) current with a relatively small input (base) current.
• FET devices control an output (drain) current with a small input (gate-voltage) voltage.
• BJTs are current-controlled devices, while FETs are voltage-controlled devices.
• FETs have a high input characteristic, making their AC equivalent model simpler than that of BJTs.
• BJTs have an amplification factor, β (beta), while FETs have a transconductance factor, gm.

JFET Small-Signal Model

• The gate-to-source voltage controls the drain-to-source (channel) current of a JFET.
• The change in drain current from a change in gate-to-source voltage can be determined using the transconductance factor gm.
• The prefix "trans" in transconductance establishes a relationship between an output and an input quantity.
• Conductance is used because gm is determined by a current-to-voltage ratio, similar to the ratio that defines the conductance of a resistor.

Mathematical Definition of Transconductance (gm)

• The derivative of a function at a point equals the slope of the tangent line at that point.
• The magnitude ensures a positive value for gm.
• The slope of the transfer curve is at its maximum when VGS = 0 V.
• The subscript 0 indicates that it is the value of gm when VGS = 0 V.

Example 1: Determining the Magnitude of gm

• Determine the magnitude of gm for a JFET with IDSS = 8 mA and VP = -4 V at various DC bias points: VGS = -0.5 V, VGS = -1.5 V, VGS = -2.5 V.
• gm is calculated at each VGS value using the change in drain current divided by the change in gate-source voltage.
• gm values: At −0.5 V = 3.5 mS, At −1.5 V = 2.57 mS, At −2.5 V = 1.5 mS.
• gm decreases as VGS approaches VP.

Example 2: Finding Maximum gm and Comparing with Graphical Results

• Determine the maximum value of gm and the value of gm at each operating point from Example 1 using the formula and compare with graphical results.
• Calculated maximum possible value of gm: 4 mS
• Compared to original calculations at same voltages, the new values are; At VGS = -0.5 V = 3.5 mS. At VGS = -1.5 V = 2.5 mS. At VGS = -2.5 V = 1.5 mS.

Transconductance (gm) on Specification Sheets

• On specification sheets, gm is often provided as gfs or yfs, where y indicates it's part of an admittance equivalent circuit.
• The 'f' signifies forward transfer conductance, and 's' indicates connection to the source terminal.

General Properties of gm

• The maximum value of gm occurs where VGS = 0 V, and the minimum value occurs at VGS = VP.
• When VGS is one-half the pinch-off value, gm is one-half the maximum value.

Effect of ID on gm

• The mathematical relationship between gm and the DC bias current ID is derived from Shockley's equation.
• The highest values of gm are obtained when VGS approaches 0 V and ID approaches its maximum value of IDSS.
• If ID = IDSS, gm = gm0
• If ID = IDSS/2, gm = 0.707gm0
• If ID = IDSS/4, gm = 0.5gm0

JFET Input Impedance (Zi)

• The input impedance of commercially available JFETs is large enough to assume the input terminals approximate an open circuit.
• ZI (JFET) = ∞ Ω
• A practical value for a JFET is 10^9 Ω (1000 MΩ), while for MOSFETs and MESFETs, it's typically 10^12 Ω to 10^15 Ω.

JFET Output Impedance (Zo)

• Zo (JFET) = rd = 1/gos = 1/yos
• The output impedance of JFETs is similar in magnitude to that of conventional BJTs.
• Output impedance typically appears as gos or yos, with units of µS.
• The parameter yos is a component of an admittance equivalent circuit, with the subscript 'o' signifying an output network parameter and 's' indicating the terminal (source).
• Output impedance is defined as the slope of the horizontal characteristic curve at the point of operation.
• The more horizontal the curve, the greater the output impedance.
• A perfectly horizontal curve indicates infinite output impedance (an open circuit).

JFET AC Equivalent Circuit

• The JFET AC equivalent circuit includes a voltage-controlled current source (gmVgs) and an output resistance (rd).

Example 3: Sketching the FET AC Equivalent Model

• Given gfs = 3.8 mS and gos = 20 µS.
• Calculate the value of the certain parameters to sketch the FET ac equivalent model.
• Solution; gm = gfs = 3.8 mS, rd = 1/gos = 1/(20 μS) = 50 kΩ

Fixed-Bias Configuration

• Zi = RG due to infinite input impedance.
• Setting Vi = 0 V establishes Vgs as 0 V, resulting in the current source being replaced by an open circuit, resulting in Zo = RD||rd
• If rd is significantly larger than RD (at least 10:1), Zo ≈ RD.
• Voltage gain: Av = Vo/Vi = -gm(rd||RD), or if rd ≥ 10RD, Av = -gmRD.
• Phase Relationship: A negative sign indicates a 180° phase shift between input and output voltages.

Example 8.7:

• The fixed-bias configuration operating point is defined by VGSQ = -2 V and IDQ = 5.625 mA, with IDSS = 10 mA and VP = -8 V; yos is 40 μS.
• gm0 = 2.5 mS
• gm = 1.88 mS
• rd = 25 kΩ
• Zi = 1 MΩ
• Zo = 1.85 kΩ
• Av = -3.48 (accounting for rd)
• Av = -3.76 (ignoring rd)
• The 8% difference in solution results because a ratio of 25 kΩ:2 kΩ = 12.5:1 exists between rd and RD.