ESE ECE Prelims flashcards

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

Thevenin's theorem

Any linear two-terminal network can be replaced by one voltage source V_th (the open-circuit voltage) in series with one resistance R_th (resistance seen with sources deactivated).

Maximum power transfer theorem

A source delivers maximum power to a load when load resistance equals Thevenin resistance; the delivered power is V_th squared divided by four times R_th, at 50 percent efficiency.

Quality factor of series RLC

At resonance Q equals (1/R) times the square root of L over C. It also equals resonant frequency divided by bandwidth, so higher Q means a sharper, narrower resonance peak.

Shockley diode equation

The diode current is I_s times (e to the power V divided by nV_T, minus one), where V_T is about 26 millivolts at room temperature and n is the ideality factor.

MOSFET saturation condition

An enhancement MOSFET operates in saturation when drain-source voltage exceeds the overdrive, V_GS minus V_T. Drain current then depends mainly on gate overdrive and only weakly on V_DS.

BJT current gain beta

In forward-active mode the collector current equals beta times base current, and emitter current equals beta plus one times base current. Beta falls at high current and low temperature.

Virtual short in op-amps

With negative feedback and ideal infinite gain, the differential input voltage is forced to nearly zero, so the inverting node sits at the same potential as the non-inverting node.

De Morgan's theorems

The complement of a product equals the sum of the complements, and the complement of a sum equals the product of the complements. These rules convert AND-OR logic to NAND-NAND forms.

JK flip-flop toggle state

When both J and K inputs are high, the JK flip-flop complements its stored output on each active clock edge. This removes the forbidden state that limits the SR flip-flop.

Nyquist sampling theorem

A bandlimited signal whose highest frequency is f_m can be reconstructed exactly from samples taken at a rate strictly greater than twice f_m. Sampling slower causes aliasing.

Convolution in LTI systems

The output of a linear time-invariant system is the convolution of its input with its impulse response. In the transform domain this becomes simple multiplication of spectra.

Region of convergence

The set of complex frequencies where the Laplace or z-transform converges. For a causal system the ROC lies outside the outermost pole, and stability requires it to include the axis.

AM modulation index

The ratio of modulating amplitude to carrier amplitude. Total transmitted power equals carrier power times one plus half the square of the index; overmodulation causes envelope distortion.

Carson's rule for FM

The bandwidth of a frequency-modulated signal is approximately twice the sum of peak frequency deviation and highest modulating frequency. It captures the significant sideband pairs.

Shannon channel capacity

The maximum error-free data rate over a channel equals bandwidth times the base-two logarithm of one plus signal-to-noise ratio, in bits per second.

PCM quantization SNR

For a full-scale sinusoid with n-bit uniform quantization, the signal-to-quantization-noise ratio is approximately 6.02n plus 1.76 decibels. Each extra bit improves it by about 6 dB.

Poynting vector

The cross product of electric and magnetic field intensities gives power flow per unit area. Its time average for sinusoids is half the real part of E cross H conjugate.

Voltage standing wave ratio

VSWR equals one plus the reflection coefficient magnitude divided by one minus it. A perfect match gives VSWR of one; total reflection gives infinity.

Friis path loss

Free-space path loss between isotropic antennas is the square of four pi times distance divided by wavelength. Received power falls as the square of distance.

Peak overshoot formula

For a second-order underdamped system, peak overshoot equals e to the power minus pi zeta divided by the square root of one minus zeta squared, expressed as a fraction.

Routh-Hurwitz stability criterion

The number of closed-loop poles in the right half-plane equals the number of sign changes in the first column of the Routh array. Zero sign changes means stability.

Gain and phase margin

Gain margin is the negative decibel gain at phase crossover; phase margin is 180 degrees plus phase at gain crossover. Both indicate relative stability of a feedback loop.

Wheatstone bridge balance

The bridge is balanced when the galvanometer reads zero, which occurs when the ratio of two adjacent arms equals the ratio of the other two arms.

Current transformer safety

The secondary of a current transformer must never be open-circuited while primary current flows, because the collapsing flux induces a dangerously high secondary voltage.

Strain gauge gauge factor

Gauge factor is the fractional change in resistance divided by the applied strain. Metal foil gauges have factors near two; semiconductor gauges are far more sensitive.

Physical address in 8086

The 8086 forms a 20-bit physical address by shifting the 16-bit segment register left four bits and adding the 16-bit offset. Segments therefore overlap.

8085 TRAP interrupt

TRAP is the highest-priority, non-maskable interrupt on the 8085, vectored to address 0024 hexadecimal. It is used for power-failure and critical fault handling.

Memory-mapped I/O

Input and output devices are assigned addresses in the same address space as memory and accessed with ordinary load and store instructions, simplifying addressing at the cost of address space.

Two's complement range

For n-bit two's complement numbers the representable range is minus two to the power n minus one, up to two to the power n minus one, minus one.

Dimensional homogeneity

Every term of a physically valid equation must have identical dimensions. Dimensional analysis checks equations and derives dimensionless groups used in model scaling.

Critical path method

The critical path is the longest-duration sequence of dependent activities in a project network. Its total float is zero, so any delay there delays the whole project.

SI unit of capacitance

The farad equals one coulomb per volt. Typical discrete capacitors are rated in microfarads, nanofarads, or picofarads because one farad is a very large capacitance.

Slew rate limitation

Slew rate is the maximum rate of change of an op-amp output, in volts per microsecond. It limits full-power bandwidth to slew rate divided by two pi times peak voltage.