Sources and References

Primary texts: Electrical Engineering: Principles and Applications by Hambley (Pearson); Fundamentals of Electric Circuits by Alexander and Sadiku (McGraw-Hill); Engineering Circuit Analysis by Hayt, Kemmerly, and Durbin.

Supplementary texts: The Art of Electronics by Horowitz and Hill; Electrical Engineering for Non-Electrical Engineers by Toro; Microelectronic Circuits by Sedra and Smith.

Online resources: MIT OpenCourseWare 6.002 Circuits and Electronics; Stanford EE101A; IEEE Spectrum educational series; NI Multisim tutorials; SPICE reference documentation.

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Chapter 1: Electric and Magnetic Fields

1.1 Electric Charge and Force

Charge is quantised in units of the elementary charge \( e = 1.602 \times 10^{-19} \) C. Coulomb’s law gives the force between two point charges \( q_1 \) and \( q_2 \) separated by distance \( r \):

\[ \mathbf{F} = \frac{1}{4\pi \varepsilon_0}\,\frac{q_1 q_2}{r^2}\,\hat{\mathbf{r}}. \]

The electric field at a point is \( \mathbf{E} = \mathbf{F}/q \) where \( q \) is a positive test charge. Gauss’s law states that the flux of \( \mathbf{E} \) through a closed surface equals enclosed charge divided by permittivity.

1.2 Potential and Capacitance

Electric potential is the work per unit charge to bring a test charge from a reference to a point: \( V = -\int \mathbf{E}\!\cdot\!d\boldsymbol{\ell} \). A capacitor relates stored charge to voltage through \( Q = C V \). For a parallel-plate capacitor with area \( A \) and plate separation \( d \), \( C = \varepsilon_0 \varepsilon_r A/d \).

1.3 Magnetic Fields

Moving charges produce magnetic fields. Ampere’s law and the Biot–Savart law describe the fields of currents. A long straight wire carrying current \( I \) produces \( B = \mu_0 I / (2\pi r) \). An inductor stores energy \( \tfrac{1}{2} L I^2 \), with self-inductance depending on geometry and magnetic permeability.

Chapter 2: DC Circuit Analysis

2.1 Kirchhoff’s Laws

Kirchhoff’s current law expresses charge conservation: \( \sum I_{in} = \sum I_{out} \) at any node. Kirchhoff’s voltage law expresses energy conservation around any loop: \( \sum V = 0 \). Ohm’s law \( V = IR \) governs resistive elements.

2.2 Systematic Methods

Nodal analysis writes KCL at every non-reference node in terms of node voltages. Mesh analysis writes KVL around every independent loop in terms of mesh currents. Both methods produce a linear system \( \mathbf{A}\mathbf{x} = \mathbf{b} \) solvable by matrix inversion or Gaussian elimination.

2.3 Thevenin and Norton Equivalents

Any linear two-terminal network is equivalent to a voltage source \( V_{th} \) in series with resistance \( R_{th} \) (Thevenin) or a current source \( I_N \) in parallel with \( R_N \) (Norton), with \( V_{th} = I_N R_N \). These equivalents simplify analysis of load variations and maximum power transfer:

\[ P_{L,max} = \frac{V_{th}^2}{4 R_{th}}\quad\text{when}\quad R_L = R_{th}. \]

Chapter 3: Transient Analysis and Reactive Elements

3.1 RC and RL Natural Response

A charged capacitor discharging through a resistor follows \( v(t) = V_0 e^{-t/\tau} \) with \( \tau = RC \). An inductor with initial current discharging through a resistor follows \( i(t) = I_0 e^{-t R/L} \).

3.2 Step Response

For a first-order circuit driven by a step source, the solution is

\[ x(t) = x(\infty) + \left[x(0^+) - x(\infty)\right] e^{-t/\tau}. \]

Engineering design uses \( \tau \) to choose components achieving target rise or settling times.

3.3 Second-Order Circuits

Series RLC circuits obey

\[ L\frac{d^2 i}{dt^2} + R\frac{di}{dt} + \frac{1}{C} i = \frac{dv_s}{dt}. \]

The damping ratio \( \zeta = R/(2)\sqrt{C/L} \) and natural frequency \( \omega_n = 1/\sqrt{LC} \) determine overdamped, critically damped, or underdamped response.

Chapter 4: AC Circuits and Phasors

4.1 Sinusoidal Steady State

A sinusoid \( v(t) = V_m \cos(\omega t + \phi) \) is represented by a phasor \( \mathbf{V} = V_m e^{j\phi} \). Derivatives become multiplications by \( j\omega \). Resistors, inductors, and capacitors present impedances \( R \), \( j\omega L \), and \( 1/(j\omega C) \).

4.2 Power

Instantaneous power \( p(t) = v(t) i(t) \) has an average component \( P = V_{rms} I_{rms} \cos\theta \), the real power, and an oscillating component with amplitude \( Q = V_{rms} I_{rms} \sin\theta \), the reactive power. Apparent power \( S = V_{rms} I_{rms} \) satisfies \( S^2 = P^2 + Q^2 \). Power factor \( \cos\theta = P/S \) governs the efficiency of transmission.

4.3 Frequency Response and Filters

Transfer functions \( H(j\omega) = V_{out}/V_{in} \) characterise filter behaviour. A first-order RC low-pass filter has \( |H| = 1/\sqrt{1 + (\omega/\omega_c)^2} \) with cutoff \( \omega_c = 1/(RC) \). Bode plots display magnitude and phase against logarithmic frequency.

Chapter 5: Three-Phase Systems

5.1 Balanced Three-Phase Sources

A balanced three-phase source provides three voltages of equal magnitude with 120° phase separation. Line-to-line voltage \( V_{LL} \) relates to line-to-neutral \( V_{LN} \) by \( V_{LL} = \sqrt{3}\, V_{LN} \). Three-phase sources deliver constant instantaneous power, crucial for motors.

5.2 Wye and Delta Connections

Sources and loads connect in wye (Y) or delta (Δ). In a balanced wye, neutral current is zero and per-phase analysis reduces the problem to single-phase. Delta loads relate line currents to phase currents by \( I_L = \sqrt{3} I_\phi \).

5.3 Power Delivery

Total three-phase power is

\[ P_{3\phi} = \sqrt{3}\, V_{LL} I_L \cos\theta. \]

Power-factor correction capacitors reduce reactive demand, lowering line losses and utility penalties.

Chapter 6: Operational Amplifiers

6.1 Ideal Op-Amp

An ideal operational amplifier has infinite open-loop gain, infinite input impedance, zero output impedance, and zero offset. With negative feedback, the golden rules are that \( v_+ = v_- \) and input currents are zero.

6.2 Standard Configurations

The inverting amplifier has gain \( -R_f/R_{in} \). The non-inverting amplifier has gain \( 1 + R_f/R_g \). The summing amplifier adds weighted inputs. The difference amplifier rejects common-mode signals, scored by the common-mode rejection ratio.

6.3 Real Op-Amps

Real devices have finite gain-bandwidth product, input bias currents, offset voltage, slew rate, and saturation. Good design recognises these non-idealities in the context of measurement chains, instrumentation amplifiers, and filter realisations.

Chapter 7: Electronic Devices and Applications

7.1 Diodes

A pn-junction diode obeys the Shockley equation \( i = I_s(e^{v/V_T} - 1) \). Applications include half- and full-wave rectifiers, clipping and clamping circuits, and voltage-regulation with Zener diodes.

7.2 Bipolar and Field-Effect Transistors

The BJT has regions of cutoff, active, and saturation governed by base current and collector-emitter voltage. The MOSFET operates in cutoff, triode, or saturation. Both devices amplify and switch; they form the basis of digital logic, analogue amplification, and power electronics.

7.3 Interfacing to Mechanical Systems

Mechanical engineers interface with electrical systems through sensors (strain gauges, thermocouples, accelerometers), actuators (DC motors, solenoids, piezoelectrics), and power electronics (H-bridges, variable-frequency drives). Impedance matching, grounding strategy, shielding, and protection circuits transform a textbook circuit into a robust product.