Bipolar and Field-Effect Transistors

Introduction and Context

Transistors are three-terminal semiconductor devices used to control voltage, current, or power. In analog electronics they perform amplification, switching, buffering, signal conversion, regulation, and impedance transformation. The two principal transistor families are the bipolar junction transistor (BJT), whose operation depends on both electrons and holes, and the field-effect transistor (FET), whose conduction is controlled primarily by an electric field.

At postgraduate level, transistor analysis must go beyond memorized biasing formulas. A useful analysis connects semiconductor physics, large-signal terminal behavior, small-signal models, frequency response, noise, thermal effects, distortion, device variability, and circuit-level design constraints. The same transistor may be modeled differently depending on whether the purpose is device design, hand analysis, computer simulation, or high-frequency prediction.

Learning Objectives

After completing this chapter, the learner should be able to:

1. Explain the physical operation and terminal characteristics of BJTs and FETs.
2. Distinguish cutoff, active, saturation, triode, and pinch-off regions.
3. Derive and apply principal large-signal and small-signal equations.
4. Design and evaluate basic transistor bias networks and amplifiers.
5. Compare BJT and FET performance in gain, noise, impedance, linearity, and power.
6. Analyze thermal, frequency-dependent, and device-variation effects.
7. Select an appropriate transistor technology for an analog application.

1. Semiconductor Basis and Terminal Control

A pn junction is formed when p-type and n-type semiconductor regions are joined. Carrier diffusion creates a depletion region and a built-in electric field. Forward bias reduces the barrier and permits substantial diffusion current; reverse bias widens the depletion region and normally produces only a small leakage current until breakdown.

A BJT contains two pn junctions arranged as either npn or pnp. The emitter is heavily doped, the base is thin and lightly doped, and the collector is moderately doped and physically larger. In forward-active operation, the emitter-base junction is forward biased and the collector-base junction is reverse biased. Carriers injected from the emitter traverse the base and are swept into the collector.

A FET controls a channel by voltage. In a metal-oxide-semiconductor FET (MOSFET), an insulated gate produces an electric field that alters the carrier concentration near the semiconductor surface. Since the gate current is ideally zero, the input resistance is very high. In a junction FET (JFET), the gate-channel junction is reverse biased and its depletion region controls channel width.

The distinction is fundamental: a BJT is conventionally described as a current-controlled device in circuit models, whereas a FET is conventionally described as a voltage-controlled device. Neither statement is an absolute physical law; both devices involve coupled electric fields, charge transport, and terminal voltages.

2. Bipolar Junction Transistors

2.1 Large-Signal Operation

For an npn transistor in forward-active operation, the collector current is approximately governed by the base-emitter voltage:

Here, I_C is collector current, I_S is the scale or saturation current, V_BE is base-emitter voltage, and V_T = kT/q is thermal voltage. k is Boltzmann’s constant, T is absolute temperature in kelvin, and q is electronic charge. At 300 K, V_T is approximately 25.85 mV. The equation assumes forward-active operation and neglects high-level injection, Early effect, and leakage.

The common-emitter current gain is

where I_B is base current. Consequently,

The common-base current gain is

Although β_F may be large, it varies with current, temperature, manufacturing process, and collector-emitter voltage. Design should therefore avoid relying on an exact value of beta.

2.2 Operating Regions

In saturation, the simple exponential collector-current equation is not sufficient because both junctions are forward biased. For analog amplification, adequate collector-emitter voltage must be maintained so that the transistor remains in forward-active operation.

2.3 Early Effect and Output Resistance

Increasing V_CB widens the collector-base depletion region and reduces effective base width. This causes collector current to increase slightly with collector-emitter voltage, a phenomenon called the Early effect. A practical model is

where V_A is the Early voltage, usually specified in volts. The corresponding small-signal output resistance is approximately

This approximation applies in forward-active operation. Finite r_o reduces voltage gain and causes feedback between output voltage and collector current.

2.4 Small-Signal BJT Model

At a bias point, the transconductance is

where g_m is in siemens and I_C is the quiescent collector current. The intrinsic emitter resistance is

The base-emitter small-signal resistance in the hybrid-π model is

For a common-emitter stage with the emitter at ac ground and neglecting loading, the approximate voltage gain is

where R_C is collector resistance, R_L is load resistance, and the negative sign indicates phase inversion. The parallel operator satisfies R₁ ∥ R₂ = R₁R₂/(R₁ + R₂). If emitter degeneration is present, a useful approximation is

provided the emitter resistor is not bypassed for the signal and transistor parasitic effects are modest. Emitter degeneration improves linearity and bias stability but reduces gain.

2.5 BJT Biasing

A voltage-divider bias network establishes a base voltage approximately equal to

when divider current is sufficiently larger than base current. Then

and

For silicon transistors, V_BE is often estimated as 0.65–0.75 V near room temperature, but it is not a constant. The approximation is reliable only when divider loading is small. A more robust design uses a Thevenin equivalent: V_TH and R_TH = R₁ ∥ R₂. The base current is then estimated by

This equation assumes forward-active operation and neglects collector-base leakage.

3. Field-Effect Transistors

3.1 MOSFET Structure and Regions

An enhancement n-channel MOSFET has source and drain terminals in an n-type region separated by a body region. A positive gate voltage above threshold creates an inversion channel. The threshold voltage, V_TH, is the gate-source voltage at which strong inversion begins under a specified operating definition.

For a long-channel device, define overdrive voltage as

The ideal square-law model gives the following regions:

Cutoff: V_GS < V_TH, with drain current approximately zero apart from leakage.

Triode or linear region: V_GS > V_TH and V_DS < V_OV. The drain current is

Saturation or pinch-off region: V_GS > V_TH and V_DS ≥ V_OV. The ideal drain current is

Here, μ_n is electron mobility, C_ox is oxide capacitance per unit area, W is channel width, and L is channel length. These equations assume a long-channel device, gradual channel approximation, square-law behavior, negligible body effect, and negligible channel-length modulation.

With channel-length modulation included,

where k_n = μ_nC_ox(W/L) and λ is channel-length modulation coefficient in inverse volts. The small-signal output resistance is

for nonzero λ. In short-channel devices, velocity saturation, mobility degradation, drain-induced barrier lowering, and other effects make the square-law model inadequate.

3.2 JFET and Depletion MOSFET

A JFET normally conducts at zero gate bias. Reverse-biasing the gate-channel junction expands its depletion region and reduces drain current. The Shockley relation, applicable over a restricted operating range, is

where I_DSS is drain current at zero gate-source voltage and V_P is pinch-off voltage. Device polarity determines the signs. The relation should not be applied indiscriminately to modern short-channel FETs.

3.3 FET Small-Signal Parameters

For a long-channel MOSFET in saturation,

The transconductance is measured in siemens. A common-source amplifier has approximate gain

where R_D is drain resistance. A source resistor introduces local feedback:

if the resistor is not bypassed for ac. The MOSFET gate current is ideally zero, but practical input resistance is finite because of leakage, protection structures, bias resistors, and measurement equipment.

3.4 Body Effect

In an integrated MOSFET, source-to-body voltage changes threshold voltage. A commonly used model is

where V_TH0 is threshold voltage at zero body bias, γ is body-effect coefficient, φ_F is Fermi potential magnitude, and V_SB is source-to-body voltage. The equation assumes a bulk MOS structure and a simplified one-dimensional depletion model. Body effect is especially important in source followers, stacked devices, and analog integrated circuits.

4. Worked Design Example: Common-Emitter Amplifier

Consider an npn common-emitter amplifier biased at I_C = 1 mA, with β_F = 100, V_A = 100 V, R_C = 3.3 kΩ, and a load of R_L = 10 kΩ. At 300 K, take V_T = 25.85 mV.

First,

The output resistance is

The effective collector resistance is

Therefore,

The base input resistance is

Thus the stage offers high voltage gain but only moderate intrinsic input resistance. The result assumes the signal source resistance is negligible, the emitter is ac-grounded, the transistor remains active, and parasitic capacitances are insignificant at the operating frequency.

5. Frequency Response, Noise, and Linearity

Transistor gain falls at high frequency because of junction and overlap capacitances. For a BJT, important capacitances include base-emitter and base-collector capacitance. The latter is multiplied at the input by the Miller effect. For a FET, gate-source and gate-drain capacitances dominate, and gate-drain capacitance similarly produces Miller multiplication in common-source stages.

A simplified upper cutoff estimate for a single-pole input network is

where R_in is the resistance seen by the capacitance and C_in is the effective input capacitance. This is an estimate, not a universal transistor cutoff formula.

Noise consists of thermal noise, shot noise, flicker noise, and occasionally generation-recombination or burst noise. The BJT collector shot-noise current spectral density is approximately

where ∆f is bandwidth and the left side has units of amperes squared per hertz. A resistor at absolute temperature T has thermal-noise voltage spectral density

MOSFETs generally have very high input resistance but may exhibit substantial low-frequency flicker noise. BJTs can provide higher transconductance per unit current at moderate current density, often benefiting voltage-noise performance. Device choice must consider source impedance and signal bandwidth, not input resistance alone.

Linearity is improved by feedback, emitter or source degeneration, differential operation, and appropriate biasing. Large signals cause exponential BJT distortion and square-law or velocity-saturation-related FET distortion. Degeneration converts device nonlinearity into more predictable resistor-controlled behavior, at the cost of gain.

6. Comparative Engineering Analysis

A technically sound selection begins with source resistance, required gain, noise bandwidth, supply voltage, signal swing, power budget, linearity, temperature range, and fabrication availability. “FET input” is not automatically superior; a low-impedance sensor may benefit from a BJT input, while an electrochemical or capacitive sensor may require the leakage performance of a FET.

7. Thermal Stability and Reliability

Transistor parameters change with temperature. For a BJT, V_BE typically decreases as temperature rises at approximately 1.5–2.2 mV/°C near ordinary operating currents, although the precise value depends on current density and device structure. If collector current increases temperature, and temperature further increases collector current, positive feedback can produce thermal runaway.

Bias stabilization uses emitter resistance, collector-to-base feedback, thermal coupling, current mirrors, bandgap references, and active feedback. Power dissipation is

for a BJT, or approximately P_D ≈ V_DSI_D for a FET when terminal power dominates. Junction temperature can be estimated by

where T_J is junction temperature, T_A is ambient temperature, and θ_JA is junction-to-ambient thermal resistance in °C/W. Accurate design must include transient thermal impedance, package behavior, airflow, heat sinks, and maximum ratings.

Device reliability also depends on voltage overstress, oxide breakdown, electromigration, hot-carrier effects, latch-up in CMOS, electrostatic discharge, and repetitive avalanche. Designs must follow manufacturer limits and relevant safety and electromagnetic-compatibility standards.

8. Illustrative Application Case: Low-Noise Sensor Interface

Background. A laboratory instrument must amplify a signal from a resistive sensor whose source resistance is approximately 200 Ω. The useful band is 10 Hz–20 kHz, and the input-referred noise must be minimized without excessive power consumption.

Problem. A MOSFET input stage offers negligible gate-current noise and high input resistance, but its flicker noise at 10 Hz may be significant. A BJT input stage has base current and shot noise, yet can provide high transconductance at moderate bias current.

Analysis. Since the source resistance is low, input resistance is not the dominant requirement. Voltage noise is more important than gate leakage. A BJT differential pair operated at an appropriate current density may therefore achieve lower midband voltage noise. However, base current produces a current-noise contribution proportional to source resistance, and input protection leakage must be considered.

Approach. The design team evaluates both transistor types using measured or process-model noise parameters rather than relying only on textbook equations. Emitter degeneration is added to improve linearity, and a carefully designed current source establishes the tail current. Input filtering prevents out-of-band interference, while shielding and a proper printed-circuit-board ground strategy reduce electromagnetic pickup.

Outcome. The BJT solution provides lower integrated input-referred noise in the specified source-resistance and bandwidth range, while the FET solution provides greater tolerance to sensor disconnection and lower bias-current error. The final choice depends on whether minimum noise or input robustness is the primary specification.

Learning points. Device selection is an optimization problem. Noise must be integrated over bandwidth, source impedance must be included, and practical leakage, protection, layout, temperature, and availability can reverse a conclusion based solely on ideal device properties.

9. Contemporary Developments and Best Practices

Modern analog design increasingly uses CMOS, BiCMOS, SiGe HBT, GaN, and wide-bandgap power technologies. CMOS enables dense mixed-signal integration and low static power. BiCMOS combines CMOS logic and capacitors with high-transconductance bipolar devices. SiGe HBTs support high-speed and low-noise radio-frequency circuits. GaN and SiC FETs provide high breakdown voltage, temperature capability, and power efficiency, though their gate reliability and dynamic behavior require careful engineering.

Best practices include:

• Select a model whose accuracy matches the design question.
• Establish a valid dc operating point before applying small-signal analysis.
• Verify region conditions, signal swing, power dissipation, and maximum ratings.
• Include tolerances in β, threshold voltage, Early voltage, mobility, temperature, and passive components.
• Use simulation to explore behavior, not to replace physical reasoning.
• Validate simulations with datasheet limits, measurements, and corner analysis.
• Treat layout, grounding, thermal paths, parasitic capacitance, and electromagnetic coupling as part of the circuit.
• Use feedback and degeneration deliberately to trade gain for stability and linearity.

Chapter Summary

BJTs operate through carrier injection across two junctions, whereas FETs control a channel using an electric field. BJT forward-active behavior is described approximately by an exponential base-emitter relation, while the long-channel MOSFET model gives triode and saturation equations based on overdrive voltage. Small-signal transconductance, output resistance, and input resistance provide the bridge between device physics and amplifier design.

Biasing establishes a stable operating point; small-signal analysis predicts gain, impedance, and loading around that point. Early effect, channel-length modulation, body effect, parasitic capacitance, noise, temperature, and device variation limit ideal performance. BJT and FET selection must be based on source impedance, noise, gain, linearity, frequency, power, reliability, and manufacturing context. Contemporary analog systems often combine transistor technologies to exploit their complementary advantages.

Key Terms

Bipolar junction transistor: Three-terminal device in which both electrons and holes participate in conduction.

Field-effect transistor: Device whose channel current is controlled by an electric field.

Forward-active region: BJT region used for linear amplification.

Saturation region: BJT switching region with both junctions forward biased; also the high-V_DS MOSFET amplification region.

Cutoff: Operating condition in which conduction is ideally negligible.

Transconductance: Incremental output-current change per unit input-voltage change.

Early effect: BJT collector-current variation caused by base-width modulation.

Channel-length modulation: FET drain-current variation caused by effective channel shortening.

Threshold voltage: Gate-source voltage associated with formation of a conducting MOS inversion channel.

Overdrive voltage: Difference between gate-source voltage and threshold voltage.

Body effect: Threshold-voltage change caused by source-body bias.

Emitter degeneration: Local feedback produced by an emitter resistor.

Source degeneration: Local feedback produced by a source resistor.

Hybrid-π model: Small-signal model commonly used for BJTs.

Miller effect: Effective multiplication of a feedback capacitance by voltage gain.

Flicker noise: Low-frequency noise whose spectral density commonly varies inversely with frequency.

Thermal runaway: Positive electrothermal feedback causing increasing current and temperature.

Current mirror: Circuit that copies a reference current into another branch.

BiCMOS: Technology combining bipolar and CMOS devices.

Review Questions

Short Answer Questions

1. Why is the BJT base made thin and lightly doped?
2. State the conditions for forward-active operation of an npn BJT.
3. Define MOSFET overdrive voltage.
4. What physical effect produces finite BJT output resistance?
5. Why does source degeneration improve linearity?

Long Answer Questions

1. Explain the construction, operation, and characteristic regions of an npn BJT.
2. Derive the long-channel MOSFET drain-current expressions for triode and saturation operation, stating assumptions.
3. Develop the small-signal voltage gain of a common-emitter amplifier including load and output resistance.
4. Compare BJT and FET technologies for low-noise analog front ends.
5. Discuss thermal stability, parameter variation, and reliability in transistor amplifier design.

Analytical / Application Questions

1. A BJT operates at I_C = 2 mA and 300 K. Calculate g_m and r_e, and state the assumptions used.
2. A MOSFET has V_TH = 1 V, V_GS = 2 V, and V_DS = 3 V. Determine its ideal long-channel region of operation and justify the result.
3. For a common-source stage with g_m = 5 mS, R_D = 4.7 kΩ, R_L = 10 kΩ, and r_o = 50 kΩ, estimate voltage gain and explain how source degeneration would alter it.

Multiple Choice Questions with Answers

Question 1

For a BJT in forward-active operation, which junction bias condition is correct?

A. Both junctions are reverse biased

B. Emitter-base forward biased and collector-base reverse biased

C. Emitter-base reverse biased and collector-base forward biased

D. Both junctions are forward biased

Correct Answer: B. Emitter-base forward biased and collector-base reverse biased

Question 2

At 300 K, the approximate thermal voltage of a semiconductor junction is:

A. 2.585 mV

B. 25.85 mV

C. 258.5 mV

D. 1 V

Correct Answer: B. 25.85 mV

Question 3

If a BJT has I_C = 1 mA and V_T = 25 mV, its approximate transconductance is:

A. 4 μS

B. 25 μS

C. 40 mS

D. 250 mS

Correct Answer: C. 40 mS

Question 4

An enhancement n-channel MOSFET is in saturation when:

A. V_GS < V_TH

B. V_DS < 0 only

C. V_GS > V_TH and V_DS ≥ V_GS − V_TH

D. V_GS = 0 and V_DS = 0

Correct Answer: C. V_GS > V_TH and V_DS ≥ V_GS − V_TH

Question 5

The ideal gate current of a MOSFET is approximately zero because the gate is:

A. Shorted to the drain

B. Insulated from the channel

C. Forward biased

D. Heavily doped as a collector

Correct Answer: B. Insulated from the channel

Question 6

The Early effect primarily causes:

A. Infinite input resistance

B. Collector-current dependence on collector-emitter voltage

C. Threshold-voltage cancellation

D. Zero output conductance

Correct Answer: B. Collector-current dependence on collector-emitter voltage

Question 7

For a MOSFET in long-channel saturation, increasing overdrive voltage generally:

A. Decreases drain current

B. Increases drain current quadratically in the ideal model

C. Leaves drain current unchanged

D. Forces cutoff

Correct Answer: B. Increases drain current quadratically in the ideal model

Question 8

Which component commonly improves BJT bias stability through local negative feedback?

A. Emitter resistor

B. Collector short circuit

C. Base-ground capacitor only

D. Reverse-biased diode across the supply

Correct Answer: A. Emitter resistor

Question 9

The approximate thermal-noise voltage spectral density of a resistor is represented by:

A. 2qI

B. 4kTR

C. I_C/V_T

D. β/I_C

Correct Answer: B. 4kTR

Question 10

A common-emitter amplifier normally produces what phase relationship between voltage input and voltage output?

A. Zero phase shift

B. 90° lead

C. 180° inversion

D. 360° inversion only at cutoff

Correct Answer: C. 180° inversion