FET Amplifiers in Electronic Circuits

Introduction

• FET amplifiers are preferred for:

  • High input resistance

  • Low noise

  • Low power consumption

• Widely used in:

  • Communication receivers

  • Switching circuits

  • Digital and analog systems

FET vs BJT Amplifiers

FET Amplifier Configurations

• Common-Source (CS): High voltage gain, inverted output

• Common-Drain (CD): Unity gain, no inversion (buffer)

• Common-Gate (CG): Gain with no inversion, low input impedance

Amplifier Classes with FETs

• Class A: Linear operation, low distortion

• Class B and AB: Improved efficiency

• Class C: High efficiency, used in RF

• Class D: Switching amplifier, very efficient

Note: FETs dominate in Class D due to superior switching performance

Switching and Digital Applications

• FETs are ideal for:

  • Analog/digital switches

  • CMOS logic circuits

  • Multiplexers, switched-capacitor circuits

• Enhancement-mode MOSFETs are widely used in CMOS

FET Characteristics and Modeling

• Voltage-controlled: Gate voltage controls drain current

• Transconductance \(g_m = \frac{\Delta I_D}{\Delta V_{GS}}\)

• AC Modeling: Simpler than BJT models

• Impedance:

  • Input: Very high

  • Output: Comparable to BJT

Application Areas

• Low-noise amplifiers

• RF and high-frequency designs

• Buffering and signal interfacing

• Power switching and control

THE COMMON-SOURCE AMPLIFIER

FET AC Model

• \(r_{gs}^{\prime}\) and \(r_{ds}^{\prime}\) are very high so neglected in the simplified circuit.

• The voltage gain :
\[\begin{aligned} A_v & = \dfrac{V_{out}}{V_{in}} = \dfrac{V_{ds}}{V_{gs}} = \dfrac{I_dR_d}{I_d/g_m} \quad (g_m \rightarrow~\text{ transconductance})\\ A_v &= g_mR_d \end{aligned}\]

Introduction to Common-Source JFET Amplifier

• A common-source JFET amplifier is characterized by:

  • AC input at the gate.

  • AC output from the drain.

  • The source terminal is common to both.

• Source is at AC ground:

  • No source resistor, or a bypassed one.

  • Ensures the amplifier gain is maximized.

Self-Biased JFET Configuration

• Circuit Overview :

  • Input signal coupled via capacitor to the gate.

  • \(R_G\) ensures:

    • Gate is held near 0 V (since \(I_{GSS} \approx 0\)).

    • Very high input resistance \(\rightarrow\) avoids loading the signal source.

• Bias voltage appears across \(R_S\), and bypass capacitor \(C_2\) ensures:

  • Source is at AC ground.

Signal Operation

• Gate-source voltage swings about its Q-point \(V_{GSQ}\).

• As \(V_{GS}\) becomes less negative, \(I_D\) increases.

• As \(I_D\) increases, \(V_D\) drops (since \(V_D = V_{DD} - I_D R_D\)).

• Result:

  • \(V_{DS}\) is 180° out of phase with \(V_{GS}\).

  • This is characteristic of a common-source amplifier.

Graphical Illustration

• Transfer Characteristic Curve :

  • Sinusoidal \(V_{GS}\) causes sinusoidal \(I_D\).

• Drain Curve : Signal causes Q-point to shift along the load line.

• Nonlinear nature of transfer curve causes distortion.

• Minimize distortion: Keep signal swing within a limited range on the load line.

DC Analysis – Graphical and Mathematical Approaches

• Objective: Find Q-point \((I_D, V_{GS})\)

• Graphical Method:

  • Use transconductance curve.

  • Plot load line: Intersection gives Q-point.

• Mathematical Method:

  • Based on the relation:

  • This results in a quadratic equation in \(I_D\).

\[\begin{aligned} I_D & = I_{DSS} \left( 1 - \frac{V_{GS}}{V_{GS(\text{off})}} \right)^2 \\ \text{Substitute:} ~V_{GS} &= I_D R_S \\ I_D & = I_{DSS} \left( 1 - \frac{I_D R_S}{V_{GS(\text{off})}} \right)^2 \end{aligned}\]

AC Analysis – Equivalent Circuit

• Replace capacitors with shorts (AC coupling).

• Replace \(V_{DD}\) with AC ground.

• Resulting AC equivalent circuit:

  • Drain and source both tied to AC ground.

Gate Signal and Input Resistance

• : appears at the Almost all of

  

\[V_{GS} = V_{\text{in}}\]

• Very high input resistance:

  • Due to reverse-biased gate–source junction.

• Total input resistance:
\[\begin{aligned} R_{\text{in}} & = R_G \parallel \left( \frac{V_{GS}}{I_{GSS}} \right) \\ \text{Typically:~} \frac{V_{GS}}{I_{GSS}} & \gg R_G \\ R_{\text{in}} & \approx R_G \end{aligned}\]

Voltage Gain of Common-Source Amplifier

• Voltage Gain:
\[A_v = g_m R_d\]
• Output Voltage:
\[V_{\text{out}} = V_{DS} = A_v V_{GS} = g_m R_d V_{\text{in}}\]
• Where:
\[R_d = R_D \parallel R_L = \frac{R_D R_L}{R_D + R_L}\]

• Important Note:

  • \(V_{\text{out}}\) is 180° out of phase with \(V_{\text{in}}\)

  • Hence, \(A_v\) is negative.

Summary of Common-Source JFET Amplifier

• Advantages:

  • High input resistance.

  • Voltage amplification with phase inversion.

• Key Equations
\[I_D = I_{DSS} \left( 1 - \frac{I_D R_S}{V_{GS(\text{off})}} \right)^2\]

• Design Consideration:

  • Ensure Q-point lies in the linear region for undistorted amplification.

D-MOSFET Amplifier Operation

• Configuration: Zero-biased common-source n-channel D-MOSFET

  

• DC Conditions:

  • Gate at \(0 \, \text{V dc}\)

  • Source grounded \(\rightarrow\) \(V_{GS} = 0 \, \text{V} \Rightarrow I_D = I_{DSS}\)

E-MOSFET Amplifier Operation

• Configuration: Common-source n-channel E-MOSFET with voltage-divider bias
  

  

• to ensure: Gate is
\[V_{GS} > V_{GS(\text{th})}\]

DC Analysis for E-MOSFET

• Gate Voltage
\[V_{GS} = \left( \frac{R_2}{R_1 + R_2} \right) V_{DD}\]
• Drain Current
\[I_D = K \left( V_{GS} - V_{GS(\text{th})} \right)^2\]
• Drain-to-Source Voltage
\[V_{DS} = V_{DD} - I_D R_D\]

AC Analysis and Input Resistance

• Voltage Gain
\[A_v = g_m R_d\]
• AC Input Resistance
\[R_{\text{in}} = R_1 \parallel R_2 \parallel R_{\text{IN (gate)}}\]
• Where:
\[R_{\text{IN (gate)}} = \frac{V_{GS}}{I_{GSS}}\]

Comparison of JFET, D-MOSFET, and E-MOSFET

The Common-Drain (CD) Amplifier

• Also known as a Source-Follower (analogous to the Emitter-Follower in BJT)

• Circuit Example:

  

  • Self-biased JFET

  • \(\mathbf{C_1}/\mathbf{C_2}\): Input/Output coupling capacitor

• Key Characteristics:

  • Input: Gate and Output: Source

  • Drain is common to both input and output \(\rightarrow\) No drain resistor needed

  • Output voltage follows input: \(V_{\text{source}} \approx V_{\text{gate}}\) (in phase)

Input Resistance of CD Amplifier

• As in common-source configuration:

  • Gate is reverse-biased \(\rightarrow\) Very high input resistance

• Total input resistance:
\[R_{\text{in}} = R_G \parallel R_{\text{IN(gate)}}\]
• Where:
\[R_{\text{IN(gate)}} = \frac{V_{GS}}{I_{GSS}}\]

• Conclusion:

  • \(R_{\text{in}}\) is typically very large, dominated by \(R_G\)

  • Excellent for buffering applications due to high input, low output impedance

The Common-Gate (CG) Amplifier

• Analogous to: Common-Base (CB) BJT amplifier

• Key Features:

  • Input: Source terminal

  • Output: Drain terminal

  • Gate is common \(\rightarrow\) connected to ground

  • Low input resistance (unlike CS and CD configurations)

• Circuit Reference:

  

  • Self-biased configuration

  • \(\mathbf{C_1}/\mathbf{C_2}\): Input/Output coupling capacitor

Voltage Gain of CG Amplifier

• Starting from definition:
\[A_v = \frac{V_{\text{out}}}{V_{\text{in}}} = \frac{V_d}{V_{gs}} = \frac{I_d R_d}{V_{gs}} = \frac{g_m V_{gs} R_d}{V_{gs}}\]
• Final expression:
\[\boxed{A_v = g_m R_d}\]

• Where: \(R_d = R_D \parallel R_L\)

• Observation:

  • Same gain expression as common-source amplifier

  • No phase inversion (output in phase with input)

Input Resistance of CG Amplifier

• Unlike CS and CD (which use gate as input), CG uses source as input:

• Input current
\[I_{\text{in}} = I_s = I_d = g_m V_{gs}\]
• Input voltage
\[V_{\text{in}} = V_{gs}\]
• Therefore:
\[R_{\text{in(source)}} = \frac{V_{\text{in}}}{I_{\text{in}}} = \frac{V_{gs}}{g_m V_{gs}} = \boxed{\frac{1}{g_m}}\]

• Conclusion:

  • Low input resistance

  • Suitable for low-impedance signal sources

Introduction to Class D Amplifier

• Uses: Primarily MOSFETs, not BJTs or linear-mode FETs

• Fundamental difference:

  • Operates with switching transistors (ON/OFF)

  • Not linear amplification like Class A, B, or AB

• Key advantage:

  • Theoretical Efficiency:\(100\%\)

  • Practical Efficiency: \(> 90\%\)

  • Compared to:

    • Class A: \(\sim 25\%\)

    • Class B/AB: \(\sim 79\%\)

• Block Diagram:

  

  • Pulse-width modulator → MOSFET switch stage → Low-pass filter → Speaker

Pulse-Width Modulation (PWM)

• PWM: Converts analog input to pulses of varying width

• Wider pulse = Higher input amplitude

• Narrower pulse = Lower input amplitude

• Zero input = Square wave output

• Generated using: Comparator

• Comparator Behavior:

  • Outputs high or low depending on input polarity

  • Operates with a sine wave (input) and triangular wave (carrier)

  • Output swings rail-to-rail (e.g., \(\pm 12\) V to \(\pm 24\) V)

Frequency Spectrum of PWM

• PWM spectrum includes:

  • Input signal frequency (\(f_{in}\))

  • Modulator frequency (\(f_m\))

  • Harmonics above and below \(f_m\)

  

• Requirement:

  • \(f_m\) must be much higher than max \(f_{in}\)

• Why?

  • To easily filter out harmonics

  • Pass only the original input signal through the low-pass filter

Power Stage & Switching

• MOSFET Configuration:

  • Complementary push-pull

  • Operate in ON/OFF mode, not linear

• Switching logic:

  • When \(Q_1\) is ON \(\rightarrow\) \(Q_2\) is OFF and vice versa

  • ON: High current, low voltage drop \(\rightarrow\) Low power dissipation

  • OFF: No current \(\rightarrow\) No power dissipation

• Power dissipation occurs only during switching transitions

Efficiency of Class D

• Ideal Power Dissipation:

  • \(P_{DQ1} = 0 \, \text{W}\), \(P_{DQ2} = 0 \, \text{W}\)

• Output Power
\[P_{out} = 2V_Q I_L\]
• Maximum Efficiency
\[\eta_{max} = \frac{P_{out}}{P_{out} + P_{DQ}} = \boxed{100\%}\]

• Practical Limitations:

  • Small \(V_{DS(on)}\)

  • Switching losses

  • Losses in comparators & wave generator

Signal Flow in Class D Amplifier

• Stages:

  1. Small analog audio input

  2. PWM modulator (Comparator + triangle wave)

  3. MOSFET switching stage (with gain)

  4. Low-pass filter \(\rightarrow\) Removes PWM carrier & harmonics

  5. Amplified analog output to speaker