Maharashtra HSC Electronics (Bifocal) cheat sheet

Ohm's law: V = IR; power P = VI = I²R = V²/R. Applies to purely resistive DC circuits at constant temperature.

Series resistors add directly (R_T = R1 + R2 + …); parallel resistors add as reciprocals (1/R_T = 1/R1 + 1/R2 + …). Two in parallel: R_T = R1R2/(R1+R2).

Capacitors in parallel add (C_T = C1 + C2 + …); in series they add reciprocally - the reverse of resistors.

Capacitive reactance X_C = 1/(2πfC); inductive reactance X_L = 2πfL. Both are frequency-dependent; only resistance dissipates power.

Impedance of an RLC series circuit: Z = √(R² + (X_L − X_C)²); phase angle θ = tan⁻¹((X_L − X_C)/R).

Resonant frequency of an LC circuit: f_r = 1/(2π√(LC)). At resonance X_L = X_C, Z is minimum (series) or maximum (parallel).

Capacitor charge Q = CV; energy stored = ½CV². Inductor energy stored = ½LI².

Resistor colour code: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, grey 8, white 9; gold = ±5%, silver = ±10% tolerance.

A capacitor blocks DC and passes AC; an inductor passes DC and opposes AC. Time constant τ = RC for RC circuits, τ = L/R for RL circuits.

Intrinsic silicon has equal electron and hole concentrations; doping with pentavalent atoms (P, As) gives n-type (majority electrons), trivalent atoms (B, Ga) give p-type (majority holes).

PN junction: diffusion of majority carriers forms a depletion region with a barrier potential of about 0.7 V for silicon and 0.3 V for germanium.

Forward bias reduces the barrier and allows current; reverse bias widens the depletion layer and passes only a small leakage current until breakdown.

Diode current equation: I = I_s(e^(V/(nV_T)) − 1), where V_T ≈ 26 mV at room temperature and n ≈ 1–2.

Half-wave rectifier: output ripple frequency equals supply frequency; efficiency about 40.6%. Full-wave centre-tap and bridge rectifiers give ripple at twice the supply frequency.

Bridge rectifier uses four diodes, needs no centre-tapped transformer, and has peak inverse voltage per diode = V_m (versus 2V_m for centre-tap).

Zener diode operates in reverse breakdown as a voltage reference/regulator; the Zener voltage is nearly constant over a range of reverse currents.

LED emits light in forward bias (direct bandgap, GaAsP/GaN); photodiode is reverse biased and its reverse current increases with illumination.

Varactor diode acts as a voltage-variable capacitor in reverse bias; Schottky diode has a low forward drop and fast switching.

BJT regions: emitter (heavily doped), base (thin, lightly doped), collector (moderately doped, largest). Two types: npn and pnp.

Transistor relations: I_E = I_B + I_C; α = I_C/I_E; β = I_C/I_B; β = α/(1 − α) and α = β/(1 + β).

Active region: emitter-base forward biased, collector-base reverse biased - used for amplification. Saturation and cut-off are the switching states.

For silicon BJT, V_BE ≈ 0.7 V in active region; V_CE(sat) ≈ 0.2 V. Power dissipation P_D = V_CE × I_C.

JFET: gate-source junction reverse biased; drain current controlled by gate voltage. Transfer characteristic I_D = I_DSS(1 − V_GS/V_P)².

MOSFET has an insulated gate (no gate current); enhancement mode needs V_GS above threshold to conduct, depletion mode conducts at V_GS = 0.

FET advantages over BJT: very high input impedance, low noise, voltage-controlled, better thermal stability; disadvantage: lower transconductance and gain-bandwidth.

Transconductance g_m = ΔI_D/ΔV_GS (FET) or ΔI_C/ΔV_BE (BJT), expressed in siemens or mA/V.

Bias stability: voltage-divider bias with an emitter resistor gives the best Q-point stability against β variation and temperature.

CE amplifier: voltage gain A_v = −β(R_C ∥ R_L)/r_e where r_e ≈ 26 mV/I_E; output is 180° out of phase with input.

CC (emitter follower) has voltage gain slightly below 1, high input impedance, low output impedance - used as a buffer.

CB amplifier has low input impedance, high output impedance, no phase inversion, and good high-frequency response.

Class A conducts 360°, maximum efficiency 25% (resistive load) or 50% (transformer-coupled); Class B conducts 180° with efficiency up to 78.5%; Class AB reduces crossover distortion.

Gain in decibels: A_dB = 20 log₁₀(V_out/V_in) for voltage, 10 log₁₀(P_out/P_in) for power. Cascaded stages add gains in dB.

Negative feedback reduces gain by factor (1 + Aβ), widens bandwidth, reduces distortion and noise, and changes input/output impedance.

Barkhausen criterion for oscillation: loop gain Aβ ≥ 1 and total phase shift around the loop = 0° or 360°.

RC phase-shift oscillator uses three RC sections giving 180° plus a CE amplifier's 180°; f = 1/(2πRC√6).

Colpitts oscillator uses a tapped capacitive divider; Hartley uses a tapped inductive divider; crystal oscillators give the highest frequency stability.

Basic gates: AND (Y = A·B), OR (Y = A + B), NOT (Y = Ā). Universal gates NAND and NOR can implement any logic function.

De Morgan's theorems: (A·B)‾ = Ā + B̄ and (A + B)‾ = Ā · B̄.

XOR: Y = A⊕B = AB̄ + ĀB; output is 1 when inputs differ. XNOR is its complement (equality detector).

Binary to decimal: weight each bit by powers of 2 from the right. Hexadecimal uses 4 bits per digit; octal uses 3 bits per digit.

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

Flip-flops: SR (set-reset), JK (toggles when J = K = 1), D (data latch), T (toggle). Edge-triggered devices sample on a clock transition.

A register stores n bits using n flip-flops; a counter is a register with feedback. An n-bit counter divides frequency by 2ⁿ.

Karnaugh map groups of 1, 2, 4, 8 adjacent cells eliminate 0, 1, 2, 3 variables respectively - used to minimise Boolean expressions.

Logic families: TTL uses 5 V supply and bipolar transistors; CMOS uses MOSFETs, has very low static power and wider supply range.

Block sequence of a regulated supply: transformer → rectifier → filter → regulator → load.

Ripple factor: half-wave 1.21, full-wave centre-tap 0.48, bridge 0.48. Lower is better.

Filter capacitor for full-wave rectifier: C = I_load/(2f × V_ripple), where f is supply frequency and V_ripple is peak-to-peak ripple.

Three-terminal regulators: 78xx series gives fixed positive output (7805 = +5 V, 7812 = +12 V); 79xx gives fixed negative output.

LM317 is an adjustable positive regulator: V_out = 1.25(1 + R2/R1) + I_adj·R2, with a minimum load current requirement.

Zener shunt regulator: series resistor R_S = (V_in − V_Z)/(I_Z + I_L); choose I_Z above the knee current for regulation.

SMPS achieves high efficiency (70–90%) by switching at high frequency, reducing transformer size; linear regulators are simpler but dissipate (V_in − V_out) × I.

Voltage regulator parameters: line regulation (ΔV_out/ΔV_in), load regulation (ΔV_out/ΔI_L), and ripple rejection ratio.

Protection elements: fuse for overcurrent, MOV for surges, heat sink to keep regulator junction temperature within limits.

Analog multimeter: d'Arsonval moving-coil movement responds to average value; a rectifier is added for AC ranges, calibrated to RMS of a sine wave.

Digital multimeter uses a dual-slope ADC; input impedance typically 10 MΩ, giving less loading error than analog meters.

CRO block diagram: attenuator → vertical amplifier → deflection plates; time-base → horizontal amplifier; trigger circuit and CRT with electron gun.

CRO measurements: V_peak = vertical divisions × volts/div × probe factor; period T = horizontal divisions × time/div; f = 1/T.

Lissajous figures: ratio of horizontal to vertical frequency equals the ratio of tangencies; a circle indicates equal frequency and phase.

Wien bridge measures capacitance and dissipation factor; Maxwell bridge measures inductance; Wheatstone bridge measures medium resistance.

Ammeter is connected in series and should have low resistance; voltmeter in parallel with high resistance. Multirange meters use shunts and multipliers.

Continuity/diode test: forward-biased silicon junction reads about 0.5–0.7 V on the diode range; open circuit reads overload.

Oscilloscope probe compensation is adjusted with a square-wave calibrator to obtain a flat-topped square wave.

Modulation superimposes a message on a carrier. Need: antenna size reduction, multiplexing, and overcoming noise.

AM: carrier amplitude varies; bandwidth = 2f_m; modulation index m = V_m/V_c; sidebands at f_c ± f_m.

FM: carrier frequency varies; bandwidth by Carson's rule ≈ 2(Δf + f_m); FM has better noise immunity than AM but needs more bandwidth.

Superheterodyne receiver: RF amplifier → mixer → IF amplifier (455 kHz for AM, 10.7 MHz for FM) → detector → AF amplifier.

Image frequency rejection depends on the RF stage and IF selectivity; the local oscillator runs above or below the signal by the IF.

Sampling theorem: sampling rate must be at least twice the highest signal frequency (Nyquist) to allow reconstruction.

Pulse modulation types: PAM, PWM, PPM, and PCM (quantise then encode). PCM gives the best noise immunity at the cost of bandwidth.

Consumer systems: infrared remote uses ~38 kHz modulated IR; TV uses composite video with luminance and chrominance; FM radio band is 88–108 MHz.

Antenna basics: dipole length ≈ λ/2; λ = c/f. Higher carrier frequency allows smaller antennas.

8051 architecture: 8-bit CPU, 4 KB on-chip ROM, 128 bytes RAM, 4 register banks, 32 I/O lines in four ports, two 16-bit timers, one serial port.

8051 special function registers: ACC, B, PSW, SP, DPTR, P0–P3, TMOD, TCON, SCON, IE, IP. PSW carries the carry and overflow flags.

Memory organisation: program memory (code) and data memory (internal RAM plus external). Port 0 is multiplexed for address and data in external memory.

SFR addresses above 80H are bit-addressable only if the address ends in 0H or 8H (e.g., P1 at 90H, TCON at 88H).

Interrupt sources in 8051: two external (INT0, INT1), Timer 0, Timer 1, and serial port; enabled via the IE register, priority via IP.

Timer mode 1 is 16-bit; machine cycle = 12 oscillator periods for the classic 8051, so a 12 MHz crystal gives 1 µs per machine cycle.

Embedded system definition: dedicated computer inside a product with real-time constraints, usually with sensors, actuators, and firmware in ROM/flash.

Arduino-style boards use AVR/PIC/ARM MCUs; GPIO pins configured as input or output; ADC resolution of 10 bits gives 1024 steps.

Serial communication: UART frame = start bit + data bits + optional parity + stop bit; baud rate must match on both ends.

Soldering iron wattage: 25–30 W for PCB work; tip temperature 300–350 °C for tin-lead solder, higher for lead-free.

Good solder joint is shiny and concave; a dull, ball-shaped joint indicates a cold joint (insufficient heat or contaminated surface).

Use rosin-core solder for electronics; acid flux is for plumbing and corrodes copper tracks. Clean the tip with a damp sponge.

Resistor value check: read colour bands from the end nearest the tolerance band; measure with a meter to confirm before soldering.

Electrolytic capacitors are polarised - the striped side is negative. Reversed polarity causes bulging, leakage, or explosion.

ESD protection: wrist strap with 1 MΩ resistor to ground, grounded mats, and store ICs in conductive foam.

Safety: isolate mains before working, use an RCD/ELCB, one hand rule for live measurements, and never exceed the meter's CAT rating.

PCB assembly order: lowest profile first - resistors and diodes, then ICs and transistors, then electrolytic capacitors and connectors.

Continuity testing with power off confirms track integrity; verify supply voltages at test points before inserting ICs.

Soldering iron wattage: 25–30 W for PCB work; tip temperature 300–350 °C for tin-lead solder, higher for lead-free.

Good solder joint is shiny and concave; a dull, ball-shaped joint indicates a cold joint (insufficient heat or contaminated surface).

Use rosin-core solder for electronics; acid flux is for plumbing and corrodes copper tracks. Clean the tip with a damp sponge.

Resistor value check: read colour bands from the end nearest the tolerance band; measure with a meter to confirm before soldering.

Electrolytic capacitors are polarised - the striped side is negative. Reversed polarity causes bulging, leakage, or explosion.

ESD protection: wrist strap with 1 MΩ resistor to ground, grounded mats, and store ICs in conductive foam.

Safety: isolate mains before working, use an RCD/ELCB, one hand rule for live measurements, and never exceed the meter's CAT rating.

PCB assembly order: lowest profile first - resistors and diodes, then ICs and transistors, then electrolytic capacitors and connectors.

Continuity testing with power off confirms track integrity; verify supply voltages at test points before inserting ICs.