Engineer Electronics flashcards

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

Diode equation

I = I_S (e^{V/(nV_T)} − 1), where V_T ≈ 26 mV at room temperature, n is ideality factor (1–2), and I_S is reverse saturation current. Describes forward and reverse behavior of a pn junction.

BJT active region

Base-emitter forward biased, base-collector reverse biased. Collector current I_C = β I_B, and I_C = I_S e^{V_BE/V_T}. Used for amplification; base-emitter voltage about 0.7 V for silicon.

MOSFET saturation condition

V_DS ≥ V_GS − V_T (or V_DS ≥ V_GS − V_T for enhancement NMOS). Drain current I_D = ½ k_n' (W/L)(V_GS − V_T)² (1 + λV_DS). Channel is pinched off near drain.

Zener regulator design

Series resistor R_S = (V_in − V_Z)/(I_Z + I_L). Zener must remain in breakdown: I_Z between I_ZK and I_ZM. Choose R_S so I_Z stays in range over input and load variations.

Op-amp virtual short

With negative feedback and ideal op-amp, the differential input voltage is driven to zero: V+ = V−. Input currents are zero. This enables gain calculations for inverting and non-inverting configurations.

Op-amp slew rate

Maximum rate of change of output voltage, SR = dV_o/dt (V/μs). Full-power bandwidth f_max = SR/(2π V_peak). Exceeding SR causes sinusoidal output to become triangular.

Barkhausen oscillation criterion

For sustained oscillation, loop gain magnitude must equal 1 and total loop phase shift must be 0° or 360° at the oscillation frequency. Satisfied by positive feedback with a frequency-selective network.

Class B efficiency

Maximum theoretical efficiency of a Class B push-pull amplifier is π/4 ≈ 78.5%. Each transistor conducts for half the cycle; crossover distortion occurs near zero crossing without bias.

De Morgan's theorems

(AB)' = A' + B' and (A + B)' = A'B'. Allow conversion between AND and OR forms using complemented inputs and outputs. Fundamental for NAND/NOR gate implementations.

Setup and hold time

Setup time t_su: data must be stable before the active clock edge. Hold time t_h: data must remain stable after the edge. Violations cause metastability in flip-flops.

CMOS dynamic power

P_dyn = α C V_DD² f, where α is switching activity factor, C is load capacitance, V_DD supply voltage, f clock frequency. Static power is near zero except leakage.

Two's complement range

For n-bit signed integers, range is −2^{n−1} to 2^{n−1} − 1. Overflow occurs when carry into and out of the most significant bit differ. Negation is bitwise complement plus one.

Nyquist sampling theorem

A bandlimited signal with maximum frequency f_max must be sampled at f_s > 2 f_max to allow perfect reconstruction. Otherwise aliasing occurs. Anti-alias filter before sampling is required.

AM modulation index

μ = A_m/A_c, ratio of modulating signal amplitude to carrier amplitude. For μ ≤ 1, envelope does not cross zero. Overmodulation (μ > 1) causes envelope distortion and spectral splatter.

Carson's rule for FM

Approximate FM bandwidth B ≈ 2(Δf + f_m), where Δf is peak frequency deviation and f_m is highest modulating frequency. Modulation index β = Δf/f_m. Wideband FM trades bandwidth for noise immunity.

Shannon channel capacity

C = B log2(1 + S/N) bits per second, where B is bandwidth in Hz and S/N is linear signal-to-noise power ratio. Gives maximum error-free data rate over a noisy channel.

Transmission line reflection coefficient

Γ = (Z_L − Z_0)/(Z_L + Z_0). Magnitude between 0 and 1. VSWR = (1+|Γ|)/(1−|Γ|). Γ = 0 for matched load; Γ = −1 for short circuit; Γ = +1 for open circuit.

Intrinsic impedance of free space

η_0 = √(μ_0/ε_0) ≈ 377 Ω. For a uniform plane wave, E/H = η. Average power density = |E|²/(2η). In a dielectric, η = √(μ/ε).

Skin depth

δ = √(2/(ωμσ)) for good conductors. Current density decays to 1/e at depth δ. Attenuation increases with √f. Used to size conductors and calculate AC resistance.

Quarter-wave transformer

A λ/4 transmission line section matches real load Z_L to feedline Z_0 when its characteristic impedance is √(Z_0 Z_L). Provides narrowband matching; bandwidth increases with lower impedance ratio.

Buck converter voltage ratio

V_o = D V_in in continuous conduction mode, where D is duty cycle (0 to 1). Output voltage is always less than input. Inductor ripple current ΔI_L = V_o(1−D)/(L f_s).

Induction motor slip

s = (n_s − n_r)/n_s, where n_s = 120f/P is synchronous speed in rpm and n_r is rotor speed. Slip is small at no load and increases with load. Rotor frequency = s f.

Thyristor holding current

Minimum anode current required to keep an SCR conducting after gate pulse removal. Below holding current, device turns off. Latching current is the turn-on threshold, typically higher than holding current.

Transformer EMF equation

E = 4.44 f N Φ_max, where f is frequency, N turns, Φ_max peak core flux. Voltage per turn is set by core area and frequency. Core saturation limits maximum flux.

Second-order overshoot

Percent overshoot = 100 e^{−πζ/√(1−ζ²)} for a step input. Depends only on damping ratio ζ. Settling time (2% band) ≈ 4/(ζω_n).

Routh-Hurwitz stability criterion

Construct Routh array from characteristic polynomial coefficients. Number of sign changes in first column equals number of right-half-plane poles. Zero first-column element replaced by small ε.

Phase margin

PM = 180° + ∠G(jω_gc), where ω_gc is gain crossover frequency (|G| = 0 dB). Positive PM indicates stability. PM ≈ 45°–60° gives good damping and response.

Wheatstone bridge balance

Bridge balanced when R_1/R_2 = R_3/R_4, giving zero detector voltage. Used with strain gauges and sensors. Small resistance changes produce output voltage proportional to ΔR.

ARM Cortex-M NVIC

Nested Vectored Interrupt Controller handles interrupts with programmable priority. Supports tail-chaining and late arrival to reduce latency. Interrupt vector table resides at start of memory.

UART baud rate

Asynchronous serial rate; baud = f_clk/(16 × divisor) for 16× oversampling. Frame includes start bit, data bits, optional parity, stop bits. Both ends must agree on baud rate.

I2C bus

Two-wire synchronous serial bus using SDA and SCL with open-drain drivers and pull-up resistors. Supports 7-bit or 10-bit addressing and multiple masters. Standard modes up to 100 kHz, 400 kHz, and higher.

Newton-Raphson method

Iteration x_{n+1} = x_n − f(x_n)/f'(x_n) for root finding. Quadratic convergence near a simple root. Fails if derivative is zero or initial guess is poor.

Simpson's 1/3 rule

Numerical integration using parabolic approximations over pairs of intervals. Requires even number of intervals. Error ≈ −(b−a)⁵ f⁽⁴⁾(ξ)/180, more accurate than trapezoidal for smooth functions.

Bayes' theorem

P(A|B) = P(B|A)P(A)/P(B). Updates prior probability P(A) with likelihood P(B|A) to obtain posterior P(A|B). P(B) = Σ P(B|A_i)P(A_i) over mutually exclusive events.