EEE: Basic Circuit Concepts & Ohm's Law

Electrical and Electronics Engineering (EEE) involves the design, development, and testing of electrical and electronic systems and components

• Circuit analysis is a fundamental aspect of EEE, focusing on understanding the behavior of electrical circuits

Basic Circuit Concepts

• An electrical circuit is a closed loop that provides a path for electrical current to flow
• Key components include voltage sources, current sources, resistors, capacitors, and inductors
• Voltage (V) is the electrical potential difference or pressure that drives current through a circuit, measured in volts
• Current (I) is the flow of electric charge, measured in amperes (amps)
• Resistance (R) is the opposition to current flow, measured in ohms
• Conductance (G) is the reciprocal of resistance (G = 1/R), measured in siemens

Ohm's Law

• Ohm's Law describes the relationship between voltage, current, and resistance in a circuit
• The formula is: V = I * R, where V is voltage, I is current, and R is resistance
• Current is directly proportional to voltage and inversely proportional to resistance
• Ohm's Law is fundamental for analyzing simple resistive circuits

Series and Parallel Resistors

• Resistors in series are connected end-to-end, so the same current flows through each resistor
• The equivalent resistance (Req) of resistors in series is the sum of individual resistances: Req = R1 + R2 + R3 + ...
• Resistors in parallel are connected side-by-side, so the voltage across each resistor is the same
• The equivalent resistance (Req) of resistors in parallel is calculated as: 1/Req = 1/R1 + 1/R2 + 1/R3 + ...

Kirchhoff's Laws

• Kirchhoff's Current Law (KCL) states that the algebraic sum of currents entering a node (junction) is zero
• KCL is based on the conservation of electric charge
• Kirchhoff's Voltage Law (KVL) states that the algebraic sum of voltages around any closed loop in a circuit is zero
• KVL is based on the conservation of energy

Voltage and Current Division

• Voltage division occurs when voltage is distributed across series resistors
• In a series circuit with resistors R1, R2, ..., the voltage across resistor Ri is Vi = Vtotal * (Ri / Req), where Req is the total equivalent resistance
• Current division occurs when current is divided among parallel resistors
• In a parallel circuit with resistors R1, R2, ..., the current through resistor Ri is Ii = Itotal * (Req / Ri), where Req is the total equivalent resistance

Circuit Analysis Techniques

• Nodal analysis is a method for determining node voltages in a circuit using KCL
• Choose a reference node (ground), then apply KCL at each non-reference node
• Express currents in terms of node voltages and solve the resulting system of equations
• Mesh analysis is a method for determining loop currents in a circuit using KVL
• Define loop currents for each independent loop in the circuit, then apply KVL around each loop
• Express voltages in terms of loop currents and solve the resulting system of equations
• Superposition theorem states that the voltage or current in any element of a linear circuit is the algebraic sum of the voltages or currents produced by each independent source acting alone
• Consider each independent source separately while turning off all other independent sources (voltage sources shorted, current sources open)
• Then, algebraically add the individual contributions to find the total voltage or current

Thevenin's and Norton's Theorems

• Thevenin's theorem states that any linear circuit can be replaced by an equivalent circuit consisting of a voltage source (Vth) in series with a resistor (Rth)
• Vth is the open-circuit voltage at the terminals of interest
• Rth is the equivalent resistance at the terminals of interest, with all independent sources turned off
• Norton's theorem states that any linear circuit can be replaced by an equivalent circuit consisting of a current source (In) in parallel with a resistor (Rn)
• In is the short-circuit current at the terminals of interest
• Rn is the equivalent resistance at the terminals of interest, with all independent sources turned off
• Rth and Rn are equal

Capacitors

• A capacitor stores electrical energy in an electric field
• Capacitance (C) is the measure of a capacitor's ability to store charge, measured in farads (F)
• The relationship between charge (Q), capacitance (C), and voltage (V) is: Q = C * V
• The current through a capacitor is: I = C * (dV/dt), where dV/dt is the rate of change of voltage with respect to time
• Capacitors in series: 1/Ceq = 1/C1 + 1/C2 + 1/C3 + ...
• Capacitors in parallel: Ceq = C1 + C2 + C3 + ...

Inductors

• An inductor stores electrical energy in a magnetic field
• Inductance (L) is the measure of an inductor's ability to store energy, measured in henries (H)
• The voltage across an inductor is: V = L * (dI/dt), where dI/dt is the rate of change of current with respect to time
• Inductors in series: Leq = L1 + L2 + L3 + ...
• Inductors in parallel: 1/Leq = 1/L1 + 1/L2 + 1/L3 + ...

AC Circuit Analysis

• Alternating current (AC) is a type of electrical current that periodically reverses direction
• AC signals are typically sinusoidal, described by amplitude, frequency, and phase
• Frequency (f) is the number of cycles per second, measured in hertz (Hz)
• Period (T) is the time required for one complete cycle: T = 1/f
• Phasors are complex numbers that represent sinusoidal voltages and currents in the frequency domain
• Impedance (Z) is the AC equivalent of resistance, which includes the effects of resistance, capacitance, and inductance
• Impedance is a complex number with a magnitude and a phase angle
• For a resistor, Z = R
• For an inductor, Z = jωL (where j is the imaginary unit and ω is the angular frequency, ω = 2πf)
• For a capacitor, Z = 1/(jωC)
• AC circuit analysis uses similar techniques to DC analysis, but with impedances instead of resistances
• Ohm's law for AC circuits: V = I * Z

Power in AC Circuits

• Instantaneous power (p(t)) is the power at any given instant in time: p(t) = v(t) * i(t)
• Average power (P) is the average value of instantaneous power over one period, also known as real power, measured in watts (W)
• Reactive power (Q) is the power exchanged between the source and reactive components (capacitors and inductors), measured in volt-amperes reactive (VAR)
• Apparent power (S) is the vector sum of real power and reactive power, measured in volt-amperes (VA)
• Power factor (PF) is the ratio of real power to apparent power: PF = P/S = cos(θ), where θ is the phase angle between voltage and current
• Power factor correction involves adding capacitance to a circuit to improve the power factor, reducing energy losses and improving efficiency

Diodes

• A diode is a two-terminal semiconductor device that conducts current primarily in one direction
• Diodes have a p-n junction, formed by joining p-type and n-type semiconductor materials
• Forward bias occurs when the p-side is at a higher potential than the n-side, allowing current to flow
• Reverse bias occurs when the n-side is at a higher potential than the p-side, blocking current flow (except for a small leakage current)
• The ideal diode model is a simple approximation where the diode acts as a short circuit in forward bias and an open circuit in reverse bias
• The practical diode model includes a forward voltage drop (typically 0.7V for silicon diodes) when conducting
• Diode applications include rectifiers (converting AC to DC), clippers, clampers, and voltage regulators

Transistors

• A transistor is a semiconductor device used to amplify or switch electronic signals and electrical power
• Bipolar Junction Transistors (BJTs) are current-controlled devices with three terminals: base, collector, and emitter
• BJTs come in two types: NPN and PNP
• Field-Effect Transistors (FETs) are voltage-controlled devices with three terminals: gate, source, and drain
• FETs come in two main types: Junction FETs (JFETs) and Metal-Oxide-Semiconductor FETs (MOSFETs)
• MOSFETs are widely used in digital circuits and come in two types: enhancement-mode and depletion-mode
• Transistors can be used as amplifiers or switches in electronic circuits

Operational Amplifiers (Op-Amps)

• An operational amplifier (op-amp) is a high-gain electronic voltage amplifier with differential inputs and a single-ended output
• Op-amps are typically used with external feedback components to control their behavior
• Ideal op-amp characteristics include infinite input impedance, zero output impedance, infinite open-loop gain, and infinite bandwidth
• Common op-amp configurations include inverting amplifier, non-inverting amplifier, voltage follower, summing amplifier, and differential amplifier
• Op-amps are used in a wide range of applications, including signal amplification, filtering, and signal conditioning