This chapter turns the fundamental laws and transistor models into practical circuits. The emphasis is on understanding what each circuit does, how to estimate its behavior, and which nonideal effects must be considered before building real hardware.
Safety note: The examples use low-voltage concepts. Mains-powered circuits, high-energy batteries, large capacitors, and high-current supplies require appropriate isolation, protection, and qualified supervision.
Ideally, static current is very small in either stable logic state. Current flows mainly during transitions and because of leakage. Dynamic power is commonly approximated by:
Learning Objectives
After completing this chapter, you should be able to:- design and evaluate voltage and current dividers;
- predict basic RC and RL transient behavior;
- explain rectifier, clamp, and protection diode circuits;
- dimension simple BJT and MOSFET switches;
- describe common-emitter, common-source, and follower amplifiers;
- explain current sources, differential pairs, and the CMOS inverter;
- apply a systematic circuit-design and troubleshooting workflow.
1. Voltage Dividers
Two resistors in series form a voltage divider. With R1 connected to Vin and R2 connected to ground:\[V_{\mathrm{out}}=V_{\mathrm{in}}\,\frac{R_2}{R_1+R_2}\]
This equation assumes that the output is unloaded. A load resistance RL appears in parallel with R2, so the effective lower resistance becomes:
\[R_{\mathrm{lower}}=R_2\parallel R_L\]
Loading therefore usually reduces the output voltage. A divider is appropriate for references, biasing, and sensing when the load current is small relative to the divider current. It is generally not an efficient way to power a significant load.
Example
With Vin = 12 V, R1 = 30 kΩ, and R2 = 10 kΩ, the unloaded output is 3 V. If a 10 kΩ load is connected, the lower resistance becomes 5 kΩ and the output falls to approximately 1.71 V.2. Current Dividers
Current divides among parallel branches according to their conductance. For two resistors carrying total current I:\[I_1=I\,\frac{R_2}{R_1+R_2}\]
\[I_2=I\,\frac{R_1}{R_1+R_2}\]
The lower-resistance branch carries the larger current. Current-divider calculations are useful in parallel networks, current sensing, and estimating how unequal resistances share load current.
3. RC Circuits
A resistor-capacitor circuit produces a first-order time response. For a capacitor charging through R toward a DC voltage VS from zero:\[v_C(t)=V_S\left(1-e^{-t/(RC)}\right)\]
For discharge from an initial voltage V0:
\[v_C(t)=V_0e^{-t/(RC)}\]
The time constant is τ = RC. After one time constant, a charging capacitor reaches about 63.2% of its final value; after five time constants, the transition is more than 99% complete.
Applications
- low-pass and high-pass filters;
- timing and delay circuits;
- switch debouncing;
- AC coupling and DC blocking;
- power-supply decoupling.
4. RL Circuits
An inductor resists a change in current. For a series RL circuit driven by a DC step:\[i_L(t)=\frac{V_S}{R}\left(1-e^{-tR/L}\right)\]
The time constant is τ = L/R. When current through an inductor is interrupted, the collapsing magnetic field can generate a large voltage. Switching circuits must provide a safe path for this energy.
5. Diode Circuits
Half-Wave Rectifier
A series diode passes one polarity of an AC waveform and blocks the other. The output is pulsating DC. A capacitor can reduce ripple, but the charging current becomes concentrated near waveform peaks.Full-Wave Rectifier
A bridge rectifier uses four diodes so that both AC half-cycles produce the same load-current direction. Two diode drops occur in the conducting path. Rectifier voltage ratings, surge current, power loss, and capacitor ripple current must be checked.Clamping and Protection
Diodes can limit voltages, steer signals, protect against reverse polarity, and suppress inductive transients. A Zener or avalanche diode can provide a reference or overvoltage clamp when operated within its specified current and power range.6. Driving an LED
An LED requires current limiting. For a simple resistor-driven LED:\[R=\frac{V_S-V_F}{I_{\mathrm{LED}}}\]
For example, a 5 V supply, a 2 V LED drop, and a desired current of 10 mA give R = 300 Ω. A nearby standard value such as 330 Ω provides slightly lower current. The resistor power is approximately I2R.
LED forward voltage is not a precise constant and varies with current, temperature, color, and device. High-power LEDs normally require a regulated current driver and thermal management.
7. BJT Low-Side Switch
An npn transistor can switch a load connected between the positive supply and collector. The emitter is connected to ground, and a base resistor limits input current. A practical design method is:- Determine the required collector current from the load.
- Select a forced current gain lower than the transistor’s typical β, often around 10 for a conservative saturated switch.
- Estimate base current: \(I_B=I_C/\beta_{\mathrm{forced}}\).
- Choose the base resistor: \(R_B=(V_{\mathrm{drive}}-V_{BE})/I_B\).
- Verify that the control source can safely supply the base current.
- Check transistor voltage, current, power, and switching-speed limits.
8. MOSFET Low-Side Switch
An n-channel enhancement MOSFET can switch a load with very little steady-state gate current. The source is connected to ground, the drain to the load, and the gate is driven relative to the source. Important design checks include:- RDS(on) at the actual gate-drive voltage;
- drain-source voltage and pulsed-current ratings;
- gate charge and the required switching speed;
- conduction, switching, and reverse-recovery losses;
- junction temperature and safe operating area;
- inductive-load protection.
9. Common-Emitter Amplifier
A common-emitter BJT stage converts a small base-emitter voltage change into a collector-current change. A collector resistor converts this current change into an inverted output voltage. A simplified midband gain, with an unbypassed emitter resistance RE, is approximately:\[A_v\approx-\frac{R_{C,\mathrm{eff}}}{r_e+R_E}\]
Here, RC,eff includes the collector resistor in parallel with the load, and re is the intrinsic small-signal emitter resistance. Emitter degeneration lowers gain but improves bias stability, linearity, and input range.
Coupling capacitors can block DC between stages, while an emitter bypass capacitor can increase AC gain over a chosen frequency range.
10. Common-Source Amplifier
A common-source FET stage is analogous to the common-emitter stage. A small gate-source voltage variation produces a drain-current variation, and a drain load converts it into an inverted output voltage. A simplified gain is:\[A_v\approx-g_mR_{D,\mathrm{eff}}\]
A source resistor introduces negative feedback and makes the gain less sensitive to transistor parameters. The very small DC gate current allows high input resistance, although gate capacitance can limit high-frequency performance.
11. Emitter and Source Followers
An emitter follower or source follower has voltage gain below but often close to unity. Its main purpose is buffering: it presents a relatively high input resistance and a lower output resistance, allowing a weak signal source to drive a heavier load. Followers shift the DC voltage between input and output. Available output swing, bias current, device dissipation, and load current must be considered.12. Current Sources and Current Mirrors
A current source attempts to maintain a nearly constant current despite changes in load voltage. A simple transistor current source uses a reference voltage and an emitter or source resistor. A BJT current mirror uses matched base-emitter voltages to reproduce a reference current in another transistor. In the ideal matched case:\[I_{\mathrm{out}}\approx I_{\mathrm{ref}}\]
Real mirror accuracy is limited by finite β, transistor mismatch, temperature gradients, Early effect, and insufficient output voltage. MOSFET current mirrors are widely used in integrated circuits and are affected by threshold mismatch and channel-length modulation.
13. Differential Pair
A differential pair amplifies the difference between two input voltages while rejecting a voltage common to both inputs. It is a fundamental input stage in operational amplifiers, comparators, communication circuits, and analog integrated circuits. A shared tail current is steered between two matched transistors according to the input difference. Matching and a high-quality tail current source improve common-mode rejection and balance.14. Operational Amplifier Building Blocks
An operational amplifier combines a differential input stage, high-gain stages, level shifting, and an output stage. With negative feedback, the external circuit determines a predictable closed-loop function.Inverting Amplifier
For an ideal op-amp with resistors Rin and Rf:\[A_v=-\frac{R_f}{R_{\mathrm{in}}}\]
Non-Inverting Amplifier
\[A_v=1+\frac{R_f}{R_g}\]
Real designs must account for input common-mode range, output swing, gain-bandwidth product, slew rate, noise, input bias current, stability, and supply decoupling.
15. The CMOS Inverter
A CMOS inverter uses a pMOS transistor connected to the positive supply and an nMOS transistor connected to ground. Their gates form the input and their drains form the output.| Input | nMOS | pMOS | Output |
|---|---|---|---|
| Low | Off | On | High |
| High | On | Off | Low |
\[P_{\mathrm{dynamic}}\approx\alpha C_LV_{DD}^{2}f\]
Here, α is the activity factor, CL is the switched load capacitance, and f is the switching frequency. The quadratic voltage dependence is a major reason supply voltage strongly affects digital power consumption.
16. Power-Supply Decoupling
Circuits draw changing current from their supply. Wiring and traces have resistance and inductance, so rapid current changes can create voltage disturbances. A local decoupling capacitor supplies transient current close to the device and reduces the current loop area. Good practice includes:- placing a suitable ceramic capacitor close to each integrated circuit supply pin;
- using short, low-inductance connections to power and ground;
- adding bulk capacitance where slower load changes occur;
- checking capacitor voltage rating, effective capacitance, ESR, and ripple current.
17. Measurement and Troubleshooting
- Inspect the circuit for incorrect pinouts, polarity, solder bridges, and missing grounds.
- Verify supply voltage and current limit before applying a signal.
- Measure DC operating points and compare them with calculated values.
- Use an oscilloscope with an appropriate probe and a short ground connection.
- Check signal amplitude, offset, frequency, and source impedance.
- Work from the input toward the output to locate where behavior first differs from expectation.
- Check component tolerances, temperature, and loading by test equipment.
18. Practical Design Workflow
- Write measurable requirements: supply, input range, output load, gain, bandwidth, efficiency, and temperature.
- Select a circuit topology appropriate to those requirements.
- Calculate nominal values using simplified models.
- Check worst-case component tolerances and device parameter variation.
- Simulate when useful, while remembering that a simulation is only as accurate as its model and assumptions.
- Build and measure a prototype using current-limited supplies.
- Compare measurements with calculations and refine the design.
- Document final values, test conditions, and safety limits.