AC Circuit and Electrons

Doping introduces controlled impurities to modify semiconductor characteristics. N-type doping adds pentavalent atoms (phosphorus, arsenic) that provide excess electrons as majority carriers. P-type doping uses trivalent atoms (boron, aluminum) creating electron deficiencies or "holes" as majority carriers. Even small doping concentrations (1 part per million) dramatically increase conductivity. The type and concentration of dopants determine the semiconductor's electrical properties and enable creating PN junctions essential for diodes and transistors.

Quality factor Q = ωL/R for series circuits represents the ratio of reactive power to real power, indicating resonance sharpness. Higher Q produces narrower bandwidth and more selective frequency response but lower damping. The relationship Q = f₀/BW shows that bandwidth decreases as Q increases. Practical Q values range from 10-100 for most applications. Very high Q circuits oscillate easily but have poor stability, while low Q circuits provide broad, stable response with less selectivity.

Choke coils are inductors with high reactance XL = ωL that oppose AC current flow without dissipating power like resistors. The opposition occurs through magnetic field energy storage rather than heat generation. Power consumption P = I²R occurs only due to the coil's small DC resistance, while reactive power circulates between source and inductor. This makes chokes efficient for current limiting in applications like fluorescent ballasts and motor starting circuits where power loss must be minimized.

Impedance matching maximizes power transfer between circuit stages according to the maximum power transfer theorem. When source impedance equals load impedance, the load receives maximum available power. Mismatched impedances cause signal reflections in transmission lines, leading to standing waves and power loss. In audio systems, impedance matching ensures optimal signal transfer between amplifiers and speakers. RF applications require precise impedance matching (typically 50Ω or 75Ω) to minimize reflections and maintain signal integrity.

Common-emitter voltage gain equals Av = -βRL/ri, where β is current gain, RL is load resistance, and ri is input resistance. The negative sign indicates 180-degree phase inversion. Current gain simply equals β = IC/IB, typically 50-200 for small-signal transistors. Power gain combines both: Ap = (β²RL)/ri, showing how transistors achieve significant power amplification. Transconductance gm = β/ri relates input voltage changes to output current changes, useful for small-signal analysis.

The active region occurs when the emitter-base junction is forward biased and collector-base junction is reverse biased, enabling linear amplification. The cutoff region has both junctions reverse biased, preventing current flow and representing the "off" state in digital applications. The saturation region has both junctions forward biased, allowing maximum current flow and representing the "on" state in switching applications. These regions enable transistors to function as both analog amplifiers and digital switches.

NPN transistors have P-type base material between N-type emitter and collector regions. Current flows from collector to emitter when the base receives positive voltage relative to the emitter. PNP transistors have N-type base between P-type emitter and collector, requiring negative base voltage for operation. Both types function identically but with opposite polarities. NPN transistors are more common due to higher electron mobility compared to hole mobility, providing better high-frequency performance.

Transistors use a small base current to control a much larger collector current through the current gain relationship β = IC/IB. In the active region, small base current variations produce proportional but amplified collector current changes. The thin base region (3-5 micrometers) allows most emitter-injected carriers to reach the collector rather than recombining in the base. This current amplification, combined with load resistance, produces voltage gain Av = -βRL/ri, enabling weak signals to drive larger loads.

Half-wave rectifiers use a single diode to convert AC to pulsating DC, conducting only during positive half-cycles. Full-wave rectifiers employ multiple diodes (center-tap or bridge configuration) to utilize both AC half-cycles, providing smoother DC output with less ripple. Voltage regulator circuits use Zener diodes operating in reverse breakdown mode to maintain constant output voltage despite input variations. Clipper circuits limit signal amplitude, while clamper circuits shift DC levels without changing AC components.

PN junctions form when P-type and N-type materials contact each other. Electrons from the N-side diffuse to the P-side, while holes move oppositely, creating a depletion region with an internal electric field. This field creates a potential barrier blocking further diffusion. Forward bias (positive voltage on P-side) reduces the barrier, enabling current flow. Reverse bias increases the barrier, blocking current except for minimal leakage. This unidirectional behavior makes PN junctions perfect for rectification and voltage regulation.

Alternating current (AC) periodically changes direction and magnitude, following a sinusoidal pattern described by i = I₀ sin ωt, where I₀ is the peak current and ω is the angular frequency. Direct current (DC) flows consistently in one direction with constant magnitude. AC enables efficient long-distance power transmission through transformers and naturally produces the sinusoidal waveforms essential for many electronic applications. Most household electrical systems use AC at 50-60 Hz, while electronic devices often convert AC to DC for internal operation.

Semiconductors have energy band gaps between valence and conduction bands that allow controlled conductivity. Pure silicon and germanium have filled valence bands at absolute zero, making them insulators. At room temperature, thermal energy promotes some electrons to the conduction band, creating electron-hole pairs for current flow. The controllable conductivity through doping and temperature makes semiconductors ideal for electronic devices, unlike conductors (always conductive) or insulators (always non-conductive).

Step-up transformers increase voltage (Ns > Np) while proportionally decreasing current, following the power conservation principle Pin = Pout. These enable efficient long-distance power transmission by reducing current and associated I²R losses. Step-down transformers reduce voltage (Ns < Np) for safe consumer applications. The turns ratio determines transformation: a 10:1 step-down transformer converts 2400V to 240V. Both types maintain power balance, with current changing inversely to voltage according to Ip/Is = Ns/Np.

Transformers operate on electromagnetic induction, requiring changing magnetic flux to induce voltage in the secondary winding. The voltage relationship Vp/Vs = Np/Ns depends on the turns ratio between primary and secondary coils. AC creates continuously changing flux, enabling voltage transformation. DC produces constant flux with no rate of change (dφ/dt = 0), preventing secondary voltage induction. This fundamental requirement for changing flux explains why transformers only function with AC and necessitates AC-DC conversion for DC power transmission.

Power factor correction typically involves adding capacitors to counteract inductive loads like motors and transformers. Since most industrial loads are inductive (current lagging voltage), strategically placed capacitors provide leading reactive power to balance the system. Automatic power factor correction systems monitor the phase angle and switch capacitor banks as needed. Alternatively, synchronous motors can operate at leading power factor to provide reactive power compensation.

Power factor equals cos φ, where φ is the phase angle between voltage and current. It represents the ratio of real power (watts) to apparent power (VA). Unity power factor (cos φ = 1) indicates maximum efficiency, while zero power factor means purely reactive power with no net energy transfer. Poor power factor increases current requirements for the same real power, causing higher transmission losses and requiring larger electrical infrastructure. Utilities often charge penalties for low power factor to encourage efficient power usage.

At resonance frequency f₀ = 1/(2π√LC), inductive and capacitive reactances cancel each other (XL = XC), leaving only resistance to oppose current flow. This results in minimum impedance, maximum current, and zero phase shift between voltage and current. The circuit behaves as purely resistive, making resonance valuable for frequency selection in radio tuners, oscillators, and filters. The quality factor Q = ωL/R determines resonance sharpness - higher Q produces more selective frequency response.

Capacitive reactance XC = 1/(ωC) inversely relates to frequency. At DC (ω = 0), reactance becomes infinite, completely blocking current flow. As frequency increases, reactance decreases, allowing more AC current to pass. This frequency-dependent behavior makes capacitors excellent for coupling AC signals between circuit stages while blocking DC bias voltages. Capacitors also introduce a 90-degree phase shift, with current leading voltage, which is crucial for timing and filtering applications.

Root Mean Square (RMS) values represent the effective value of AC quantities, calculated as Vrms = V₀/√2 for sinusoidal waveforms. RMS values indicate the equivalent DC value that would produce the same power dissipation. For example, household AC voltage of 120V RMS actually peaks at approximately 170V. All AC power calculations use RMS values: P = VrmsIrms cos φ. This standardization allows meaningful comparison between AC and DC systems and ensures accurate power measurements.

Impedance (Z) represents the total opposition to AC current flow, combining resistance and reactance. For a series RLC circuit, impedance is calculated using Z = √[R² + (XL - XC)²], where R is resistance, XL = ωL is inductive reactance, and XC = 1/(ωC) is capacitive reactance. The phase angle φ = tan⁻¹[(XL - XC)/R] indicates whether the circuit is predominantly inductive (positive angle) or capacitive (negative angle). At resonance, XL = XC, making impedance equal to resistance alone.