IESL Part II Electrical flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Per-unit base change

Convert per-unit impedance between bases with Z_pu,new = Z_pu,old × (S_new/S_old) × (V_old/V_new)². This lets transformer and generator data be placed on one common system base before fault or load-flow calculation.

Zero-sequence current path

Zero-sequence current requires a return path through ground or a neutral. Delta windings and ungrounded neutrals block it, so a delta-star transformer passes zero sequence on only one side, which shapes ground-fault protection design.

Fault current from Thevenin impedance

Three-phase fault current in per unit equals one divided by the Thevenin positive-sequence impedance at the fault point. Multiply by base current S_base/(√3·V_base) to obtain amperes.

Long line hyperbolic constants

For lines above roughly 250 km, ABCD constants use hyperbolic functions: A = D = cosh γl, B = Z_c sinh γl, C = sinh γl/Z_c, where γ = √(zy) is the propagation constant and Z_c = √(z/y) the surge impedance.

Surge impedance loading

SIL equals V_L²/Z_c, about V_L²/400 MW for overhead lines where Z_c is near 400 ohms and V_L is in kV. Loading below SIL leaves the line net capacitive, causing voltage rise; above SIL it turns net inductive.

Induction motor slip

Slip s = (Ns − Nr)/Ns, with synchronous speed Ns = 120f/p. Slip rises with load, and rotor frequency equals s·f. Breakdown torque scales with voltage squared, so a 10 percent voltage dip cuts maximum torque about 19 percent.

Transformer parallel conditions

Parallel transformers need identical polarity, voltage ratio, vector group and phase sequence, with per-unit impedances close in value. Mismatched ratios or vector groups cause circulating current; load shares inversely with per-unit impedance.

IDMT relay operating time

Standard inverse time t = TMS × 0.14/((I/Is)^0.02 − 1). The time multiplier setting shifts the whole curve vertically while pickup current Is sets its start, allowing grading between upstream and downstream relays.

CT secondary open circuit hazard

A current transformer must never be open-circuited on the secondary while primary current flows. The collapsing flux induces very high voltage, risking insulation failure and personnel injury, so secondary terminals are shorted before removal.

Three-phase voltage drop

Approximate voltage drop equals √3 × I × (R cos φ + X sin φ) for a three-phase feeder, with R and X per phase. This governs cable sizing alongside ampacity, derating factors and short-circuit withstand.

BJT operating regions

Cutoff has both junctions off; active has base-emitter forward and base-collector reverse, giving amplification with I_C = βI_B; saturation has both forward and is used for switching. Silicon base-emitter conduction begins near 0.7 V.

MOSFET saturation current

In saturation, I_D = ½μ_nC_ox(W/L)(V_GS − V_th)², valid when V_DS exceeds the overdrive V_GS − V_th. Below that the device is in triode and acts as a voltage-controlled resistor.

CMOS dynamic power

Dynamic power equals αCV_DD²f, where α is switching activity. Static CMOS draws essentially only leakage current, which is why supply scaling and clock gating dominate low-power digital design.

Op-amp virtual short

With negative feedback and ideal infinite gain, the differential input voltage is driven to zero and input current is zero. These two rules yield inverting gain −R_f/R_in and non-inverting gain 1 + R_f/R_g.

Op-amp slew rate limit

Slew rate caps the maximum frequency a full-scale sine can pass without distortion: f_max = SR/(2πV_peak). Exceeding it turns a sine into a triangle and adds harmonic distortion independent of small-signal bandwidth.

Nyquist sampling criterion

Sampling frequency must exceed twice the highest signal frequency. Otherwise spectral components fold to |f − k·f_s|, creating aliases that cannot be removed afterward, so an analog anti-alias filter precedes the converter.

ADC quantization SNR

For a full-scale sine, ideal signal-to-quantization-noise ratio is approximately 6.02N + 1.76 dB for an N-bit converter. Each added bit improves SNR about 6 dB, equivalent to doubling resolution.

LTI convolution and stability

A linear time-invariant system's output is the convolution of input with impulse response. In the Laplace domain, stability requires every pole of H(s) to lie strictly in the left half-plane.

RC low-pass cutoff

A first-order RC low-pass has cutoff frequency 1/(2πRC), rolls off at 20 dB per decade, and shows 45 degrees phase shift at cutoff. It is the standard model for probe and filter bandwidth questions.

Universal logic gates

NAND and NOR each alone can implement any Boolean function, so they are functionally complete. De Morgan's laws convert between AND-OR and NAND-NAND forms, which is why NAND dominates CMOS standard-cell libraries.

JK and D flip-flops

A JK flip-flop toggles when J and K are both high, and holds when both are low. A D flip-flop simply samples its input on the active clock edge, making it the basic register and pipeline element.

AM power and bandwidth

Amplitude modulation occupies twice the modulating frequency and delivers total power P_c(1 + m²/2). At full modulation the sidebands carry one third of total power, so the carrier wastes two thirds.

FM Carson bandwidth rule

Carson's rule gives FM bandwidth approximately 2(Δf + f_m), where Δf is peak deviation. FM has a constant envelope, so amplitude noise and fading are largely rejected by a limiter.

Thermal noise floor

Available thermal noise power is kTB with Boltzmann constant 1.38×10⁻²³ J/K. At 290 K this is about −174 dBm per hertz, the reference floor for receiver sensitivity and link-budget calculations.

Shannon channel capacity

Capacity C = B log₂(1 + S/N) bits per second sets the error-free limit for a band-limited channel with additive white Gaussian noise. Bandwidth and signal-to-noise ratio trade off logarithmically.

Free-space path loss

Free-space loss in dB equals 32.45 + 20log₁₀(d_km) + 20log₁₀(f_MHz). Loss rises 6 dB per doubling of distance or frequency, which is why higher bands need more antenna gain or denser cells.

Reflection coefficient and VSWR

Reflection coefficient Γ = (Z_L − Z_0)/(Z_L + Z_0); VSWR = (1+|Γ|)/(1−|Γ|). A matched load gives zero reflection and VSWR of one; total reflection gives infinite VSWR.

Quarter-wave transformer matching

A quarter-wavelength line of impedance √(Z_0·Z_L) matches a real load to the feed line at the design frequency. A shorted quarter-wave stub instead presents an open circuit at its input.

Ferranti effect

On a lightly loaded or open long transmission line, the receiving-end voltage exceeds the sending-end voltage because charging current through series inductance adds voltage. Shunt reactors at the receiving end compensate it.

Skin effect in conductors

Alternating current crowds toward the conductor surface as frequency rises, increasing effective resistance through the skin depth δ = √(ρ/(πfμ)). It drives AC resistance, busbar design and deep-bar rotor behavior.

Differential protection bias

A differential relay compares currents entering and leaving a protected zone. Percentage bias restrains tripping as through-current rises, preventing maloperation from CT saturation and ratio mismatch during external faults.

Cable derating factors

A cable's tabulated current rating is multiplied by correction factors for ambient temperature, soil thermal resistivity, grouping and installation depth. The product gives the installed ampacity used for sizing.