PE Electrical Electronics flashcards

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

Per-unit impedance formula

Z_pu equals actual impedance divided by base impedance, where Z_base = V_base squared over S_base. Using line-to-line voltage and three-phase power keeps per-unit values consistent across transformer banks.

Per-unit transformer advantage

Per-unit impedance is the same whether referred to the primary or secondary of an ideal transformer, so a two-winding transformer is modeled as a single series impedance plus shunt magnetizing branch.

Symmetrical component operator a

The operator a equals 1 at 120 degrees, so a squared is 1 at 240 degrees and a cubed is 1. It shifts phase quantities into positive, negative, and zero sequence sets.

Zero-sequence current definition

I0 equals one third of the phasor sum Ia plus Ib plus Ic. It is nonzero only when the three phase currents have a common in-phase component, as in a ground fault.

Line-to-ground fault current

For a bolted single line-to-ground fault, fault current equals three times I0, which equals three times phase voltage divided by the sum of positive, negative, and zero sequence impedances.

Delta winding zero-sequence block

A delta-connected winding provides no external zero-sequence path, so zero-sequence current cannot flow through the line terminals. Circulating current can flow inside the closed delta.

Balanced three-phase power

Apparent power equals square root of three times line-to-line voltage times line current. Real power multiplies by power factor and reactive power multiplies by sine of the impedance angle.

Wye versus delta relations

In a balanced wye, line voltage is square root of three times phase voltage and line current equals phase current. In a balanced delta, line current is square root of three times phase current.

Open-circuit transformer test

Applying rated voltage with the other winding open measures core loss and magnetizing current, yielding the shunt magnetizing branch and the turns ratio. It is performed at rated frequency.

Short-circuit transformer test

Applying reduced voltage to circulate rated current with the other winding shorted measures copper loss and series leakage impedance. Core loss is negligible because applied voltage is low.

Synchronous speed formula

Synchronous speed in rpm equals 120 times frequency in hertz divided by number of poles. A 60 Hz, four-pole machine runs at 1800 rpm; a six-pole machine at 1200 rpm.

Induction motor slip

Slip equals synchronous speed minus rotor speed, divided by synchronous speed. Rotor electrical frequency equals slip times stator frequency, and slip is small at light load.

Induction motor torque relation

Developed torque equals air-gap power divided by synchronous angular speed. Breakdown torque occurs near the slip where rotor resistance equals rotor reactance, independent of supply voltage magnitude except for torque scaling.

DC machine EMF equation

Generated armature voltage equals the machine constant times flux per pole times angular speed. For a shunt motor, speed drops with load because armature resistance drop reduces net back EMF.

DC motor starting resistance

At standstill back EMF is zero, so armature current is limited only by armature resistance. External starting resistance is inserted to limit inrush current to a safe multiple of rated current.

Characteristic impedance of line

For a lossless transmission line, characteristic impedance equals square root of inductance over capacitance. It is purely resistive and sets the ratio of voltage to current for a forward wave.

Reflection coefficient formula

Reflection coefficient equals load impedance minus characteristic impedance, divided by their sum. A matched load gives zero reflection; an open circuit gives plus one; a short gives minus one.

VSWR from reflection coefficient

Voltage standing wave ratio equals one plus magnitude of reflection coefficient divided by one minus that magnitude. A perfect match gives VSWR of one; total reflection gives infinity.

Quarter-wave line transformation

A quarter-wavelength line inverts the load: a short circuit appears as an open circuit and vice versa. Input impedance equals characteristic impedance squared divided by load impedance.

Power factor correction

Adding parallel capacitance supplies reactive power locally, reducing line current and losses while keeping real power constant. Required kvar equals P times tangent of initial angle minus tangent of target angle.

Thevenin equivalent method

Open-circuit the load to find Thevenin voltage, then deactivate independent sources and find equivalent resistance looking into the terminals. Maximum power transfer occurs when load equals Thevenin resistance.

Norton equivalent conversion

Norton current equals Thevenin voltage divided by Thevenin resistance, and the Norton resistance equals the Thevenin resistance in parallel with the load terminals. Sources are deactivated the same way.

Superposition principle limits

Superposition applies only to linear circuits: compute each source response separately with other independent sources deactivated, then sum. It cannot be used directly for power because power is nonlinear.

RMS value of sinusoid

For a pure sine wave, RMS equals peak divided by square root of two. Average value over a full cycle is zero; half-cycle average equals two times peak divided by pi.

Three-phase rectifier ripple

A six-pulse bridge produces output ripple at six times line frequency. Average DC output is approximately 1.35 times line-to-line RMS voltage for an ideal uncontrolled bridge.

BJT operating regions

In active mode the base-emitter junction is forward biased and base-collector reverse biased; collector current equals beta times base current. Saturation and cutoff are the switching extremes.

Op-amp ideal assumptions

An ideal op amp has infinite open-loop gain and input impedance, zero output impedance, and zero input offset. With negative feedback, input terminals are treated as at equal voltage.

Inverting amplifier gain

Closed-loop gain equals negative feedback resistance divided by input resistance, with the noninverting input grounded. Input impedance equals the input resistor, which limits source loading.

Boolean DeMorgan laws

The complement of a product equals the sum of the complements, and the complement of a sum equals the product of the complements. These laws convert between AND and OR logic forms.

Karnaugh map minimization

Adjacent cells differing in one variable are grouped in powers of two to eliminate that variable. Groups may wrap around edges and must be as large as possible for minimal logic.

Inverse-time overcurrent coordination

Relay time-current curves are coordinated so the downstream device clears faults first, with a time margin between curves. Pickup settings must exceed maximum load current.

Current transformer saturation

Severe DC offset or high primary current can saturate a CT, distorting secondary current and delaying relay operation. Accuracy limit factor and burden determine saturation margin.