BJT and MOSFET Circuits

Introduction

Bipolar junction transistors (BJTs) and metal–oxide–semiconductor field-effect transistors (MOSFETs) are the principal semiconductor devices used for amplification, switching, signal conditioning, power conversion, and embedded control. In mechatronic systems, they interface low-power controllers with motors, relays, solenoids, sensors, and analog loads. A transistor is not simply an electronically controlled resistor: its behavior depends strongly on terminal voltages, currents, device construction, temperature, and operating region.

This chapter develops practical models for the two device families. It emphasizes operating regions, biasing, switching behavior, thermal reliability, design calculations, and selection criteria. The equations use simplified models suitable for introductory design; real components require verification against manufacturer data sheets.

Learning Objectives

By the end of this chapter, the reader should be able to:

1. Explain the physical operation and terminal relationships of BJTs and MOSFETs.
2. Identify cutoff, forward-active, saturation, triode, and saturation regions.
3. Design basic fixed-bias and voltage-divider BJT circuits.
4. Design low-side BJT and MOSFET switches.
5. Analyze common-emitter and common-source amplification stages.
6. Estimate power dissipation, switching loss, and thermal limits.
7. Select an appropriate transistor using electrical, thermal, switching, and reliability requirements.

1. Transistor Fundamentals

A BJT is a current-controlled device with three terminals: emitter, base, and collector. In an NPN transistor, a small base current controls a substantially larger collector current. A PNP transistor has reversed polarities and current directions. The base–emitter junction and base–collector junction behave approximately as semiconductor diodes.

A MOSFET is a voltage-controlled device with gate, drain, and source terminals. The gate is insulated from the channel by an oxide, so its steady-state DC gate current is ideally zero. Practical MOSFETs have gate leakage, capacitance, a body diode, and limits on gate voltage and drain current.

The most important distinction is that BJT conduction is commonly modeled through base current, whereas MOSFET conduction is controlled primarily by gate-to-source voltage. Neither description means that a BJT is unsuitable for voltage drive or that a MOSFET draws no current during switching; they describe the dominant design mechanism.

Important terminal quantities

For a BJT, Kirchhoff’s current law gives:

The common-emitter current gain is:

where β is dimensionless. This relationship is useful in forward-active operation, but β varies widely with current, temperature, and device sample. A robust switch design therefore uses a forced gain lower than the data-sheet typical value.

2. BJT Operation and Models

2.1 Operating regions

For an NPN BJT, the principal regions are:

• Cutoff: both junctions are effectively reverse biased; collector current is approximately zero.
• Forward-active: the base–emitter junction is forward biased and the base–collector junction is reverse biased. The transistor provides amplification, approximately I_C = β I_B.
• Saturation: both junctions are forward biased. The transistor is strongly on, and V_CE(sat) is usually about 0.1–0.3 V for a small transistor at its specified current.
• Reverse-active: the transistor operates with collector and emitter roles effectively exchanged. This region is rarely used in ordinary circuits.

The silicon base–emitter voltage is often approximated as 0.7 V at moderate current. This is not a universal constant; it changes with current and temperature. A more physical relationship is the exponential diode model:

where I_S is a scale current, V_T = kT/q is the thermal voltage, k is Boltzmann’s constant, T is absolute temperature in kelvin, and q is electron charge. At room temperature, V_T is approximately 25.9 mV. This model applies in forward-active operation and neglects several nonideal effects.

2.2 BJT biasing

Biasing establishes the quiescent operating point, or Q-point. A useful design must keep the Q-point in the intended region despite supply variation, transistor gain variation, and temperature changes.

For a simple base-resistor circuit driven from V_{CC]:

where V_BB is the base supply, R_B is the base resistor, and the equation assumes the transistor is forward active and the source resistance is negligible. Then I_C ≈ βI_B, provided the calculated collector current does not exceed the load-limited value.

A voltage-divider bias circuit is more stable. If R₁ connects V_CC to the base and R₂ connects the base to ground, its Thevenin equivalent is:

With emitter resistor R_E, the approximate base current is:

This equation assumes forward-active operation, a constant V_BE, and a Thevenin source. The emitter and collector voltages then follow from:

The result must be checked: if V_CE is too small, the active-region assumption is invalid and the transistor may be saturated.

Worked Example 1: Voltage-divider bias

An NPN transistor has V_CC=12 V, R₁=47 kΩ, R₂=10 kΩ, R_C=2.2 kΩ, R_E=1.0 kΩ, and assumed β=100. Let V_BE=0.70 V.

First,

V_TH=12(10)/(47+10)=2.105 V

and

R_TH=47×10/(47+10)=8.246 kΩ.

Therefore,

I_B=(2.105-0.70)/[8.246 kΩ+101(1.0 kΩ)] = 12.85 μA.

Thus I_C≈1.285 mA and I_E≈1.298 mA. The emitter voltage is approximately 1.298 V, while the collector voltage is 12-(1.285 mA)(2.2 kΩ)=9.17 V. Hence V_CE≈7.87 V, confirming forward-active operation. The Q-point is therefore approximately I_C=1.29 mA, V_CE=7.87 V.

2.3 BJT amplification

The common-emitter amplifier provides voltage gain with phase inversion. For a bypassed emitter resistor, a first-order midband gain is:

where R_L is the load resistance and g_m = I_C/V_T is transconductance in siemens. If the emitter resistor is not bypassed, emitter degeneration improves bias stability and linearity but reduces gain. A useful approximate expression when the intrinsic emitter resistance is included is:

where r_e ≈ V_T/I_E. These small-signal formulas apply around a Q-point, for sufficiently small signal excursions, and within the amplifier’s frequency range.

3. MOSFET Operation and Models

3.1 Enhancement MOSFET regions

For an n-channel enhancement MOSFET:

• Cutoff: V_GS<V_TH, ideally I_D≈0.
• Triode or ohmic region: V_GS>V_TH and V_DS<V_GS-V_TH. The device behaves approximately as a voltage-controlled resistor.
• Saturation region: V_DS≥V_GS-V_TH. The drain current is primarily controlled by V_GS, and the device is useful for amplification.

The word “saturation” has different practical meanings. In a MOSFET it generally denotes the constant-current amplification region; in a BJT, saturation denotes the strongly-on switching condition.

Ignoring channel-length modulation, the long-channel square-law model is:

in the triode region, and

in saturation. Here K=μ_n C_ox(W/L) is a device constant in the chosen model, μ_n is carrier mobility, C_ox is oxide capacitance per area, and W/L is channel width-to-length ratio. These equations are idealized; short-channel devices are more accurately designed using data-sheet curves or SPICE models.

For switching, the most useful parameter is R_DS(on), specified at a particular gate voltage. The conduction loss is:

The value must be taken at the actual gate drive, temperature, and current. A threshold voltage is not an adequate substitute for a specified on-resistance: V_TH indicates the onset of conduction at a small test current, not a fully enhanced state.

3.2 MOSFET amplification

A common-source amplifier is analogous to a common-emitter stage and also inverts voltage. Its small-signal gain is approximately:

where R_D is the drain resistor and g_m is MOSFET transconductance. For the ideal square-law model in saturation:

A source resistor improves bias stability and linearity but reduces gain unless bypassed. Gate bias networks must provide a defined DC gate voltage because the gate’s near-zero DC current does not establish its own operating point.

4. Transistors as Switches

4.1 Low-side BJT switch

A low-side BJT switch places the load between the positive supply and the collector; the emitter connects to ground. A controller drives the base through a resistor. To guarantee saturation, designers choose a forced gain:

with β_forced deliberately smaller than the transistor’s nominal gain, commonly between 5 and 20 depending on the application. The required base current is:

and the base resistor is approximately:

where V_DRV is the logic-driver voltage. The resistor must also limit the microcontroller pin current to its rated value.

4.2 Low-side MOSFET switch

An n-channel logic-level MOSFET is often preferred when a controller must switch moderate or high current. The source connects to ground, the load connects to the positive supply, and the drain connects to the load’s low side. A gate resistor limits transient current and ringing; a gate-to-source pull-down ensures turn-off during reset or high impedance. The MOSFET must be specified for low R_DS(on) at the available V_GS, not merely at 10 V if the controller supplies 3.3 V.

For inductive loads such as relays, motors, and solenoids, stored magnetic energy produces a high-voltage transient when current is interrupted. A flyback diode, appropriately rated for load current and decay requirements, provides a current path. Alternative clamps include TVS diodes, Zener networks, and active freewheel circuits.

4.3 Switching time and loss

A MOSFET gate requires charge rather than steady-state power. Approximate average gate-drive power is:

where Q_G is total gate charge, V_GS is the gate-drive voltage, and f_s is switching frequency. This approximation represents energy supplied per cycle and neglects driver losses.

During transitions, voltage and current overlap. A first-order switching-loss estimate is:

where t_r and t_f are rise and fall times. Conduction and switching losses combine approximately as:

A BJT may also suffer storage delay when driven deeply into saturation. Therefore, a MOSFET is usually favored for high-frequency switching, while a BJT can remain economical and effective for low-current, low-frequency switching.

Worked Example 2: MOSFET load switch

A 12 V solenoid draws 2 A. A MOSFET has R_DS(on)=40 mΩ at the available gate voltage. Its conduction loss is:

P_on=(2 A)²(0.040 Ω)=0.16 W.

If the total switching transition time is 2 μs and the switching frequency is 1 kHz, the approximate switching loss is:

P_sw=0.5(12 V)(2 A)(2 μs)(1000 Hz)=0.024 W.

The estimated semiconductor loss, excluding gate-driver and other losses, is 0.184 W. A flyback diode is still required because the solenoid is inductive. The MOSFET voltage rating must exceed the supply and transient voltage with an appropriate engineering margin.

5. Thermal Effects and Reliability

Transistor parameters vary with temperature. BJT V_BE generally decreases as temperature rises, while collector current can increase under fixed-bias conditions. This positive feedback can cause thermal runaway: increased current raises power dissipation, which raises temperature and further increases current. Emitter resistance, feedback, current limiting, and suitable heat removal reduce this risk.

MOSFET on-resistance normally increases with junction temperature. This creates a useful tendency toward current sharing among parallel MOSFETs, although layout and dynamic effects still matter. Threshold voltage generally decreases with temperature, so threshold data must not be used as the sole switching criterion.

The junction temperature estimate is:

where T_J is junction temperature, T_A is ambient temperature, P_D is device power dissipation, and θ_JA is junction-to-ambient thermal resistance, all with temperature in °C and power in W. With a heat sink, use the thermal-resistance chain:

The terms are junction-to-case, case-to-sink, and sink-to-ambient thermal resistances in °C/W. The design condition is:

with margin for ambient temperature, enclosure heating, manufacturing variation, and transient conditions. Safe operating area (SOA) graphs are essential for BJTs and for MOSFET linear-mode operation, where simultaneous high voltage and current can cause failure even if average power appears acceptable.

6. Device Selection and Design Practice

Selection should begin with the load and environment rather than with a preferred transistor type.

A professional design checklist includes:

1. Confirm maximum load voltage, current, inrush current, duty cycle, and frequency.
2. Identify whether the device is switching or operating linearly.
3. Check voltage rating, current rating, SOA, avalanche capability, and pulse rating.
4. Verify R_DS(on) at the actual gate voltage and temperature, or verify BJT saturation voltage at the intended current.
5. Calculate conduction, switching, and gate-drive losses.
6. Design the driver, grounding, decoupling, protection, and PCB current paths.
7. Check heat spreading, junction temperature, and fault conditions.
8. Test worst-case supply, load, ambient temperature, and startup behavior.

7. Illustrative Mechatronics Case: 24 V Solenoid Controller

Background

A pneumatic actuator requires a 24 V solenoid rated at 1.5 A. A 3.3 V microcontroller must command the solenoid, which is inductive and may be switched several times per second.

Problem

A direct microcontroller connection is impossible because the controller cannot supply the solenoid current and cannot tolerate the inductive voltage generated when the coil is switched off. The design must provide reliable turn-on, rapid enough turn-off, and protection against transients.

Analysis

A BJT would require a base current selected using forced gain. If β_forced=10, the minimum base current is 1.5 A/10=150 mA, too high for most microcontroller pins. A logic-level n-channel MOSFET is therefore more suitable. Its data sheet must specify low R_DS(on) at 2.5 or 3.3 V gate drive. A 40 V device may have inadequate transient margin on a 24 V rail; a 60 V or higher rating is often more appropriate, subject to the actual transient environment.

Approach and solution

The circuit uses a low-side MOSFET, a gate resistor, a gate-to-source pull-down, a local supply bypass capacitor, and a flyback diode across the solenoid. The diode is oriented reverse-biased during normal operation and forward-biased when the MOSFET turns off. The PCB places the diode, solenoid return path, and MOSFET close together to minimize loop inductance.

Suppose the selected MOSFET has R_DS(on)=60 mΩ at the actual gate voltage. The steady conduction loss is:

P_on=(1.5 A)²(0.060 Ω)=0.135 W.

At T_A=45 °C and θ_JA=50 °C/W, a simplified estimate gives:

T_J≈45+0.135(50)=51.8 °C,

before adding switching and board-heating effects. This is comfortably below a typical maximum junction temperature, but the final design must include the manufacturer’s thermal data and worst-case conditions.

Outcome

The MOSFET meets the controller-drive constraint, dissipates little power, and avoids excessive microcontroller current. The flyback diode protects the transistor, while the pull-down ensures the solenoid remains off during processor reset. Prototype testing should measure drain voltage, gate waveform, coil current, and temperature rather than relying only on nominal calculations.

Learning points

The case illustrates that transistor selection is a system decision. Current gain alone does not make a BJT suitable, and a MOSFET’s threshold voltage alone does not prove that it is logic-level. Protection, layout, thermal behavior, and fault operation are part of the transistor circuit.

8. Limitations, Safety, and Contemporary Practice

The simplified constant-voltage BJT model and square-law MOSFET model are useful for hand analysis but do not predict all real behavior. Package inductance, parasitic capacitance, Miller effect, body-diode recovery, gate-driver impedance, electromagnetic interference, and semiconductor parameter spread can dominate fast circuits.

Power electronics also requires attention to isolation, creepage and clearance, fusing, touch safety, and applicable electrical standards. A transistor circuit connected to hazardous voltage must not be treated as a low-voltage laboratory circuit. Protective components should be selected for energy, pulse duration, and failure mode, not merely nominal voltage.

Modern devices include trench MOSFETs, superjunction MOSFETs, insulated-gate bipolar transistors, silicon-carbide MOSFETs, and gallium-nitride transistors. These technologies extend voltage, frequency, and efficiency performance, but they impose stricter requirements on gate drive, layout, insulation, and measurement. Computer-aided simulation and data-sheet models are valuable for design verification; they supplement rather than replace measurements and engineering judgment.

Chapter Summary

BJTs are primarily modeled as current-controlled devices, while MOSFETs are primarily controlled by gate-to-source voltage. BJT cutoff, forward-active, and saturation regions support switching and amplification analysis. MOSFET cutoff, triode, and saturation regions have different meanings from the corresponding BJT terms. Voltage-divider bias and emitter resistance improve BJT operating-point stability. Common-emitter and common-source stages provide voltage gain with phase inversion.

For switches, a BJT requires deliberate base-current design using forced gain, whereas a MOSFET requires verification of logic-level R_DS(on), gate charge, voltage rating, and transient protection. Inductive loads require a flyback or other clamp. Conduction and switching losses determine thermal performance, and junction temperature must remain below its rated limit. Effective transistor selection integrates electrical, thermal, dynamic, mechanical, safety, and system-level requirements.

Key Terms

BJT: Bipolar junction transistor controlled principally by base current.

MOSFET: Insulated-gate field-effect transistor controlled principally by gate voltage.

Cutoff: Operating region in which transistor current is ideally negligible.

Forward-active: BJT region used for amplification.

Saturation (BJT): Strongly-on BJT switching region.

Triode region: MOSFET low-resistance region used for conduction.

Saturation (MOSFET): MOSFET constant-current region used for amplification.

Q-point: Quiescent DC operating point of an amplifier.

Biasing: Establishment of a transistor’s DC operating condition.

Transconductance: Change in output current per change in controlling voltage.

Forced beta: Deliberately conservative current-gain value used in BJT switching design.

Logic-level MOSFET: MOSFET specified for low on-resistance at a logic gate voltage.

Gate charge: Charge required to change a MOSFET gate voltage and state.

Flyback diode: Diode that conducts inductive current when a switch turns off.

Safe operating area: Voltage-current-time limits within which a device can operate safely.

Thermal resistance: Temperature rise per unit dissipated power.

Junction temperature: Temperature of the semiconductor junction.

Emitter degeneration: Use of emitter resistance to improve BJT stability and linearity.

Common-emitter amplifier: BJT amplifier configuration with emitter common to input and output reference.

Common-source amplifier: MOSFET amplifier configuration with source common to input and output reference.

Review Questions

Short Answer Questions

1. What distinguishes a BJT’s forward-active region from its saturation region?
2. Why is MOSFET threshold voltage not sufficient for selecting a logic-level switch?
3. State the purpose of an emitter resistor in a BJT bias circuit.
4. Why is a flyback diode used with a solenoid?
5. Define junction-to-ambient thermal resistance.

Long Answer Questions

1. Explain the operating regions of an NPN BJT and an n-channel enhancement MOSFET, noting the different meaning of saturation.
2. Derive the Thevenin-equivalent voltage-divider bias equations for a BJT with an emitter resistor.
3. Compare common-emitter and common-source amplifiers in terms of gain, input behavior, biasing, and limitations.
4. Explain the sources of MOSFET switching loss and describe methods for reducing them.
5. Develop a transistor-selection procedure for a mechatronic actuator driver.

Analytical / Application Questions

1. Design a low-side BJT switch for a 200 mA load using a 5 V controller and forced gain of 10. Select a base resistor using V_BE(sat)=0.8 V, and check whether the controller can supply the required base current.
2. A MOSFET carries 4 A with R_DS(on)=25 mΩ. Calculate conduction loss and estimate junction temperature if T_A=40 °C and θ_JA=35 °C/W, ignoring switching loss. Discuss why the estimate may be optimistic.
3. Compare a BJT and a logic-level MOSFET for a 24 V, 2 A inductive load switched at 20 kHz. Justify the choice using drive current, conduction loss, switching behavior, protection, and thermal considerations.

Multiple Choice Questions with Answers

Question 1

Which BJT operating region is normally used for linear voltage amplification?

A. Cutoff

B. Forward-active

C. Saturation

D. Reverse breakdown

Correct Answer: B. Forward-active

Question 2

For a BJT switch designed with a forced gain of 10 and a collector current of 0.5 A, what minimum base current is required?

A. 5 mA

B. 20 mA

C. 50 mA

D. 500 mA

Correct Answer: C. 50 mA

Question 3

A MOSFET is approximately fully controlled as a low-resistance switch using which data-sheet parameter at the actual gate voltage?

A. Gate threshold voltage only

B. Drain–source breakdown voltage only

C. On-state drain–source resistance

D. Reverse transfer capacitance only

Correct Answer: C. On-state drain–source resistance

Question 4

In an n-channel enhancement MOSFET, cutoff occurs approximately when:

A. VGS is less than VTH

B. VDS is greater than VGS − VTH

C. VGS equals the supply voltage always

D. The body diode is forward biased

Correct Answer: A. VGS is less than VTH

Question 5

A 2 A current flows through a MOSFET with RDS(on) = 50 mΩ. What is its conduction loss?

A. 0.02 W

B. 0.10 W

C. 0.20 W

D. 2.50 W

Correct Answer: C. 0.20 W

Question 6

What is the principal purpose of a flyback diode across a DC solenoid?

A. To increase the coil current during steady state

B. To provide a path for inductive current when the switch turns off

C. To bias the transistor in forward-active operation

D. To reduce the controller’s clock frequency

Correct Answer: B. To provide a path for inductive current when the switch turns off

Question 7

Which amplifier configuration normally produces phase inversion?

A. Common-emitter only

B. Common-source only

C. Both common-emitter and common-source

D. Neither configuration

Correct Answer: C. Both common-emitter and common-source

Question 8

If a device dissipates 0.2 W and has junction-to-ambient thermal resistance of 50 °C/W, the estimated junction rise above ambient is:

A. 0.004 °C

B. 2.5 °C

C. 10 °C

D. 250 °C

Correct Answer: C. 10 °C

Question 9

Why can deep BJT saturation be undesirable in high-frequency switching?

A. It eliminates all collector current

B. It can introduce charge-storage delay

C. It makes the base completely open circuit

D. It prevents any thermal dissipation

Correct Answer: B. It can introduce charge-storage delay

Question 10

Which specification is most directly associated with MOSFET gate-drive energy per switching cycle?

A. Total gate charge

B. Emitter current

C. BJT beta

D. Collector saturation voltage

Correct Answer: A. Total gate charge