RRB JE CBT 2 - Electronics cheat sheet

Intrinsic carrier concentration: n_i = A·T^(3/2)·e^(−E_g/2kT); roughly 1.5×10^10 cm^-3 for Si at 300 K.

Mass-action law: n·p = n_i^2 in thermal equilibrium; doping one carrier type suppresses the other.

Diode equation: I = I_s(e^(V/ηV_T) − 1), with V_T = kT/q ≈ 26 mV at 300 K; η = 1 for Ge, 1–2 for Si.

Barrier potential: Si ≈ 0.7 V, Ge ≈ 0.3 V, GaAs ≈ 1.2 V; cut-in voltage equals barrier potential for practical models.

Depletion width W ∝ √((V_bi − V)(1/N_A + 1/N_D)); reverse bias widens it, forward bias narrows it.

Zener diode operates in reverse breakdown: V_Z nearly constant; temperature coefficient positive for V_Z > 6 V, negative below.

BJT relations: α = β/(1+β), β = α/(1−α); I_E = I_B + I_C; transconductance g_m = I_C/V_T.

MOSFET saturation: I_D = ½μ_nC_ox(W/L)(V_GS − V_th)^2; triode region when V_DS < V_GS − V_th.

CE amplifier: voltage gain A_v = −g_m(R_C ∥ R_L); input resistance ≈ r_π; output resistance ≈ R_C.

Emitter follower (CC): gain ≈ 1, no phase inversion, high input resistance, low output resistance - used as buffer.

Class A efficiency ≤ 25% (resistive load) or ≤ 50% (transformer coupled); Class B push-pull ≤ 78.5%; Class AB reduces crossover distortion.

Negative feedback: A_f = A/(1+Aβ); bandwidth increases by (1+Aβ), distortion and output resistance fall by the same factor.

Barkhausen criterion for oscillation: loop gain |Aβ| = 1 and phase shift of 360° (0°) at the oscillation frequency.

Op-amp ideal: infinite open-loop gain, infinite input impedance, zero output impedance, infinite CMRR and slew rate.

Inverting amplifier gain = −R_f/R_in; non-inverting gain = 1 + R_f/R_in; integrator uses capacitor in feedback.

RC phase-shift oscillator frequency f = 1/(2πRC√6); Wien bridge f = 1/(2πRC) with gain of 3 required.

Boolean identities: A + A'B = A + B; A + AB = A; De Morgan: (A·B)' = A' + B', (A + B)' = A'·B'.

Universal gates: NAND and NOR alone can realize any logic function; XOR is not universal.

K-map grouping uses powers of two (1, 2, 4, 8) and wrap-around adjacency; don't-care terms may be grouped freely.

Half adder: Sum = A ⊕ B, Carry = AB. Full adder: Sum = A ⊕ B ⊕ C_in, C_out = AB + C_in(A ⊕ B).

n-bit ripple carry adder needs n full adders; propagation delay grows linearly with n.

Flip-flop excitation: JK toggles when J = K = 1; D flip-flop output follows D at clock edge; T toggles when T = 1.

n flip-flops give modulus up to 2^n; a MOD-N counter needs at least ⌈log2 N⌉ flip-flops.

Setup time is data-stable time before clock edge; hold time is data-stable time after edge; violation causes metastability.

AM: modulation index m = V_m/V_c; total power P_t = P_c(1 + m^2/2); sideband power is m^2/2 of carrier power.

AM bandwidth = 2f_m; DSB-SC and SSB save carrier and one sideband respectively; SSB bandwidth = f_m.

FM: Carson's rule B ≈ 2(Δf + f_m); modulation index β = Δf/f_m; FM has constant envelope and better noise immunity than AM.

FM bandwidth for large β approximates 2Δf; deviation ratio = maximum deviation / maximum modulating frequency.

Shannon capacity: C = B·log2(1 + S/N); channel capacity rises linearly with bandwidth, logarithmically with SNR.

Quantization noise in PCM: SNR_dB ≈ 6.02n + 1.76 for n-bit uniform quantization of a full-scale sinusoid.

Nyquist rate: sample at least twice the highest signal frequency to avoid aliasing; anti-alias filter precedes sampling.

Superheterodyne receiver: image frequency f_img = f_LO + f_IF = f_s + 2f_IF; IF rejection by RF filter.

8085: 8-bit data bus, 16-bit address bus, 64 KB address space, 40-pin DIP, clock 3 MHz typical, 5 flags (S, Z, AC, P, CY).

8085 has 6 general-purpose registers (B, C, D, E, H, L) paired as BC, DE, HL; A is the accumulator; SP and PC are 16-bit.

8086: 16-bit data bus, 20-bit address bus (1 MB), segmented memory (CS, DS, SS, ES), pipelined BIU/EU, 6-byte instruction queue.

8051: 8-bit MCU, 4 KB ROM, 128 bytes RAM, 4 ports, two 16-bit timers, 5 interrupt sources, 12 MHz crystal gives 1 μs machine cycle.

Addressing modes: immediate, direct, indirect, register, register-indirect, implied, relative, indexed.

Interrupt priorities in 8085: TRAP > RST 7.5 > RST 6.5 > RST 5.5 > INTR; TRAP is non-maskable and vectored to 0024H.

Memory-mapped I/O uses same address space as memory; isolated (port-mapped) I/O uses IN/OUT with separate space.

DMA transfers data between memory and I/O without CPU involvement; CPU is halted via HOLD/HLDA in 8085.

Ohm's law V = IR; power P = VI = I^2R = V^2/R; energy W = Pt in joules (1 kWh = 3.6 MJ).

Series: R_eq = ΣR, current same; parallel: 1/R_eq = Σ1/R, voltage same.

Kirchhoff's laws: KCL sums currents at a node to zero; KVL sums voltages around a loop to zero.

Thevenin: V_th = open-circuit voltage, R_th = V_oc/I_sc with sources killed; Norton is the dual with I_N = V_th/R_th.

Superposition applies only to linear circuits; maximum power transfer when R_L = R_th, efficiency then 50%.

RC time constant τ = RC; inductor τ = L/R; capacitor impedance 1/(jωC), inductor impedance jωL.

Resonance: f_0 = 1/(2π√(LC)); series resonance gives minimum impedance and unity power factor.

Three-phase: line voltage = √3 × phase voltage in star; line current = √3 × phase current in delta; P = √3 V_L I_L cos φ.

PMMC meter deflects proportional to average current; it measures DC only unless a rectifier is added.

Ammeter uses a low shunt resistance; voltmeter uses a high series multiplier: R_s = (V/V_m − 1)R_m.

Loading effect: voltmeter with finite resistance reads low across high-resistance circuits; sensitivity in Ω/V = 1/I_fsd.

Wheatstone bridge balance: R1/R2 = R3/R4; used for medium resistance; Kelvin bridge for low resistance.

Maxwell bridge measures inductance, Schering bridge capacitance and loss angle, Wien bridge frequency.

CRO: deflection sensitivity in V/div; time base in s/div; bandwidth limits accurate amplitude at high frequency.

Digital multimeter accuracy stated as ±(% reading + counts); resolution is the smallest display increment.

Energy meter: 1 unit = 1 kWh; meter constant in revolutions per kWh links disc rotation to energy consumed.

SCR latches on when gate current flows and anode is positive; turns off only when anode current falls below holding current.

Thyristor conduction angle control in AC phase control varies RMS output: V_rms = V_m√((π−α)/2π + sin2α/(4π)).

Diode rectifiers: half-wave ripple factor 1.21, full-wave 0.48; bridge gives higher transformer utilization.

Buck converter steps voltage down (V_o = D·V_in); boost steps up (V_o = V_in/(1−D)); buck-boost inverts.

IGBT combines MOS gate drive with low ON-state drop of a BJT; used in inverters and motor drives.

TRIAC is a bidirectional SCR used for AC dimming and fan regulators; DIAC triggers it symmetrically.

SMPS efficiency typically 70–95%, higher than linear regulators, but generates switching EMI.

Inverters convert DC to AC; VFDs vary motor speed by adjusting supply frequency and voltage (V/f control).

1 byte = 8 bits; 1 KB = 1024 bytes; 1 MB = 1024 KB; 1 GB = 1024 MB; 1 TB = 1024 GB.

Number systems: binary base 2, octal base 8, decimal base 10, hexadecimal base 16; each hex digit = 4 bits.

Two's complement: invert bits and add 1; n-bit range is −2^(n−1) to 2^(n−1) − 1.

In C, sizeof(int) is typically 4 bytes; array indexing starts at 0; '&' gives address, '*' dereferences a pointer.

Structured programming constructs: sequence, selection (if/switch), iteration (for/while/do-while).

Compiler translates the whole program before execution; interpreter translates line by line.

OS functions: process management, memory management, file system, device I/O; RAM is volatile, ROM is non-volatile.

Logic gates map to hardware: AND, OR, NOT, NAND, NOR, XOR; ALU performs arithmetic and logical operations.

Indian Railways zones: 18 zones; headquarters include New Delhi, Mumbai CSMT, Kolkata, Chennai, Secunderabad.

RRB was established in 1947; headquarters at Railway Board, New Delhi; conducts recruitment for railway posts.

Indian Railways is the fourth-largest rail network in the world; broad gauge is 1676 mm.

Vande Bharat Express is an indigenously built semi-high-speed train; first service 2019 on Delhi–Varanasi route.

Kavach is an indigenous automatic train protection system developed by RDSO.

Constitutional bodies: UPSC, Election Commission, CAG, Finance Commission; statutory bodies include NITI Aayog (non-constitutional).

ISRO missions include Chandrayaan, Mangalyaan, and Aditya-L1; DRDO develops defence technology.

Current affairs items are time-sensitive; verify dates and appointments against official sources before answering.

Series: identify arithmetic (+d), geometric (×r), or alternating patterns before applying the next step.

Coding-decoding: check letter position shifts (A=1…Z=26) and reversal patterns; apply the same rule to the target word.

Blood relations: draw a family tree, using vertical lines for generations and horizontal lines for siblings/spouses.

Direction sense: track net displacement with vector addition; final direction depends on the last move, not the total.

Syllogism: use Venn diagrams; only conclusions true in every possible diagram are valid.

Analogy: identify the relation type (part-whole, cause-effect, synonym, category) and match it, not the words.

Odd-one-out: look for the property shared by all but one item, e.g., prime status, divisibility, or letter count.

Non-verbal reasoning: count sides, rotations, and symmetry; a 90° rotation preserves shape but changes orientation.

Newton's laws: F = ma; momentum p = mv; work W = F·d·cos θ; kinetic energy ½mv^2.

Ohm's law and power formulas recur in physics sections: V = IR, P = VI, P = I^2R.

Speed of light c ≈ 3×10^8 m/s; sound in air ≈ 343 m/s at 20 °C; light travels faster than sound.

Chemical: pH < 7 acidic, 7 neutral, > 7 basic; acids turn blue litmus red.

Biology: photosynthesis converts CO2 and water to glucose using light; chlorophyll is the pigment.

Percentage change = (new − old)/old × 100; profit% = profit/CP × 100; simple interest SI = P·R·T/100.

Quadratic roots: x = (−b ± √(b^2 − 4ac))/2a; discriminant b^2 − 4ac decides real, equal, or complex roots.

Trigonometry: sin^2 θ + cos^2 θ = 1; sin 30° = ½, cos 60° = ½, tan 45° = 1.