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Qwestrum Engineering360 · Electrical & Electronics · Analog Electronics

BJT and FET Amplifiers

Transistor amplifiers first set a stable DC operating point (Q-point), then use the small-signal parameters (g_m = I_C/V_T for a BJT) to find gain; the common-emitter/common-source stage gives high voltage gain.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.

Key formulas & points

Skim these first — then read the full notes below.

  • CE/CS: voltage gain high; CB/GC: high bandwidth
  • Biasing: fixed, emitter feedback, voltage divider for Q-point stability
  • Early effect (V_A) causes finite output resistance r_o

Topic details

Introduction

Design proceeds in two steps: DC bias analysis fixes I_C (or I_D) and the operating point; then small-signal analysis linearises around it. For a BJT, transconductance g_m = I_C/V_T and input resistance r_π = β/g_m.

Scope in B.Tech and GATE syllabus

Voltage-divider bias is favoured because it stabilises the Q-point against β variation and temperature. The common-emitter voltage gain is approximately −g_m R_C (or −g_m(R_C∥r_o) including the Early effect).

Key relations & formulas

Formulas (Indian textbook notation)

  • BJT:IC=βIB;IE=IC+IBBJT: I_{C} = \beta I_{B}; I_{E} = I_{C} + I_{B}

Formulas (Indian textbook notation)

  • Small−signalrπ=VTIC;gm=ICVTSmall-signal r_\pi = \frac{V_{T}}{I_{C}}; g_{m} = \frac{I_{C}}{V_{T}}
MOSFET:ID=(K2)(VGS−Vt)2MOSFET: I_{D} = (\frac{K}{2})(V_{GS} - V_{t})^{2}
(saturation, long channel)

Notation and sign conventions

Relation 1 —
BJT:IC=βIB;IE=IC+IBBJT: I_{C} = \beta I_{B}; I_{E} = I_{C} + I_{B}

Formulas (Indian textbook notation)

  • BJT:IC=βIB;IE=IC+IBBJT: I_{C} = \beta I_{B}; I_{E} = I_{C} + I_{B}
Write this relation with symbols exactly as in Microelectronic Circuits — Sedra & Smith before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
Small−signalrπ=VTIC;gm=ICVTSmall-signal r_\pi = \frac{V_{T}}{I_{C}}; g_{m} = \frac{I_{C}}{V_{T}}

Formulas (Indian textbook notation)

  • Small−signalrπ=VTIC;gm=ICVTSmall-signal r_\pi = \frac{V_{T}}{I_{C}}; g_{m} = \frac{I_{C}}{V_{T}}
Write this relation with symbols exactly as in Microelectronic Circuits — Sedra & Smith before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
MOSFET:ID=MOSFET: I_{D} =
MOSFET:ID=(K2)(VGS−Vt)2MOSFET: I_{D} = (\frac{K}{2})(V_{GS} - V_{t})^{2}
(saturation, long channel)
Write this relation with symbols exactly as in Microelectronic Circuits — Sedra & Smith before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Fundamentals and definitions

For a MOSFET in saturation, I_D = (K/2)(V_GS − V_t)² and g_m = √(2K·I_D); the gain of a common-source stage is −g_m R_D.

Governing relations in practice

The common-emitter (BJT) and common-source (MOSFET) give high inverting voltage gain; the common-collector/common-drain (follower) gives near-unity gain but high current gain and low output impedance for buffering; the common-base/common-gate gives high bandwidth.

Design and analysis considerations

The Early effect introduces a finite output resistance r_o = V_A/I_C, which limits the maximum achievable gain and matters for current-source loads.

Assumptions and validity limits

State assumptions explicitly before using any relation for bjt and fet amplifiers — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Analog Electronics viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Analog Electronics papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to bjt and fet amplifiers.
4. Use equation 1:
BJT:IC=βIB;IE=IC+IBBJT: I_{C} = \beta I_{B}; I_{E} = I_{C} + I_{B}
.
5. Use equation 2:
Small−signalrπ=VTIC;gm=ICVTSmall-signal r_\pi = \frac{V_{T}}{I_{C}}; g_{m} = \frac{I_{C}}{V_{T}}
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

BJT and FET Amplifiers appears in signal conditioning and audio. In Indian electrical curricula this topic is tested because it connects theory to amplifiers and op-amp circuits.
GATE and semester exams often combine bjt and fet amplifiers with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use bjt and fet amplifiers?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

• Using I_E instead of I_C in g_m = I_C/V_T
• Forgetting the negative sign (phase inversion) of the CE/CS gain
• Ignoring the emitter degeneration resistor when computing gain
• Applying the saturation MOSFET equation in the triode region

Quick revision checklist

Before attempting bjt and fet amplifiers problems, confirm you can:
1. CE/CS: voltage gain high; CB/GC: high bandwidth
2. Biasing: fixed, emitter feedback, voltage divider for Q-point stability
3. Early effect (V_A) causes finite output resistance r_o
Revise the solved examples in Microelectronic Circuits — Sedra & Smith and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Common-emitter voltage gain

Problem

A BJT common-emitter amplifier operates at I_C = 1 mA with a collector resistor R_C = 5 kΩ. Take V_T = 26 mV. Find g_m and the small-signal voltage gain (ignore r_o).

Solution

g_m = I_C/V_T = 1×10⁻³ / 26×10⁻³ = 0.03846 S = 38.46 mS.
Voltage gain A_v = −g_m R_C = −0.03846 × 5000.
A_v = −192.3.
The negative sign shows the output is inverted.

Conceptual check — BJT and FET Amplifiers

Problem

In a Analog Electronics semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of bjt and fet amplifiers." What should a complete answer include?

Exams & GATE

Sedra & Smith — small-signal model and Av calculation.

📖 Standard books (India)

  • Microelectronic Circuits — Sedra & Smith

    Read: Syllabus unit

    Analog electronics reference

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