Kerala Plus Two Electronics (DHSE) cheat sheet

Intrinsic silicon at 300 K has n_i ≈ 1.5 × 10^10 cm^-3; mass-action law: n·p = n_i^2.

For a diode, I = I_s(e^(V/(ηV_T)) − 1), with V_T ≈ 26 mV at room temperature and η = 1 for Ge, ≈ 2 for Si at low current.

Barrier potential: Si ≈ 0.7 V, Ge ≈ 0.3 V; a Ge diode conducts at lower forward voltage than Si.

Diode states: forward-biased when V_anode > V_cathode by more than the knee; reverse-biased below breakdown; Zener operates in controlled reverse breakdown.

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

A BJT is in active mode when the base-emitter junction is forward-biased and the base-collector junction is reverse-biased; saturation means both forward-biased.

JFET: I_D = I_DSS(1 − V_GS/V_P)^2 in the saturation region; a MOSFET's gate draws negligible steady current because of the oxide insulation.

Rectifier diode drop rule: subtract one diode drop (≈0.7 V Si) per conducting diode when estimating DC output from peak voltage.

Half-wave rectifier: V_dc = V_m/π ≈ 0.318V_m; ripple frequency = supply frequency f.

Full-wave (centre-tap or bridge) rectifier: V_dc = 2V_m/π ≈ 0.636V_m; ripple frequency = 2f.

Bridge rectifier uses four diodes and needs no centre-tapped transformer; two diodes conduct per half cycle, so total drop ≈ 1.4 V for Si.

Ripple factor: half-wave ≈ 1.21, full-wave ≈ 0.48; smaller ripple factor means better smoothing.

Ripple voltage for a capacitor filter: V_r ≈ I_dc/(f_r·C), where f_r is the ripple frequency; increasing C or f_r reduces ripple.

PIV: half-wave ≈ V_m; centre-tap full-wave ≈ 2V_m; bridge ≈ V_m (each diode blocks one peak).

Zener regulator: series resistor R_s = (V_in − V_Z)/(I_Z + I_L); the Zener must stay in reverse breakdown.

IC regulators: 78xx gives fixed positive output (7805 = +5 V), 79xx fixed negative; LM317 is adjustable via a resistor divider.

Transformer efficiency and regulation: % regulation = (V_no-load − V_full-load)/V_full-load × 100; lower is better.

CE amplifier: voltage gain A_v = −(R_C ∥ R_L)/r_e, where r_e ≈ 26 mV/I_E; the negative sign denotes 180° phase inversion.

Amplifier gain in decibels: A_dB = 20 log10(V_out/V_in) for voltage, 10 log10(P_out/P_in) for power.

Class A conducts 360°, Class B 180° per device, Class AB slightly more than 180°, Class C much less than 180°; efficiency rises from A to C.

Push-pull Class B maximum efficiency ≈ 78.5%; Class A maximum ≈ 25% (resistive load) or 50% (transformer-coupled).

Negative feedback: reduces gain by factor (1 + Aβ), increases bandwidth and input impedance, lowers distortion and output impedance.

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

RC phase-shift oscillator needs three RC sections giving 180° shift plus 180° from the amplifier; f = 1/(2πRC√6).

Colpitts uses a capacitive divider and Hartley an inductive divider in the tank; both are LC oscillators with f = 1/(2π√(LC)).

Op-amp ideal properties: infinite open-loop gain and input impedance, zero output impedance and zero offset; inverting gain = −R_f/R_in, non-inverting gain = 1 + R_f/R_in.

Boolean identities: A + A′ = 1, A·A′ = 0, A + AB = A, A + A′B = A + B (De Morgan: (A·B)′ = A′ + B′, (A + B)′ = A′·B′).

XOR: Y = A′B + AB′; output is 1 when inputs differ; XOR with 1 inverts, XOR with 0 passes through.

NAND and NOR are universal gates: any logic function can be built from either alone.

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

Binary-to-decimal: multiply each bit by 2^position; hexadecimal digit = 4 bits; octal digit = 3 bits.

Flip-flops: SR, JK (J = K = 1 toggles), D (Q follows D on clock edge), T (toggles when T = 1); a JK flip-flop removes the SR invalid state.

An n-bit ripple counter divides frequency by 2^n at its final stage; a MOD-N counter has N states and needs at least ⌈log2 N⌉ flip-flops.

Karnaugh map: group 1s in powers of two (1, 2, 4, 8), groups may wrap around edges, and each group eliminates the changing variable.

Combinational circuits have no memory (adders, multiplexers, decoders); sequential circuits use clocked storage elements (counters, registers).

AM: modulation index m = (V_max − V_min)/(V_max + V_min); m ≤ 1 avoids overmodulation and envelope distortion.

AM bandwidth = 2f_m; sidebands at f_c ± f_m; total AM power P_t = P_c(1 + m²/2), so maximum useful sideband power is one-third of total at m = 1.

FM: modulation index β = Δf/f_m; Carson's rule gives bandwidth ≈ 2(Δf + f_m).

FM has constant amplitude and better noise immunity than AM but needs more bandwidth; AM is simpler and cheaper to demodulate.

Sampling theorem: sample at f_s ≥ 2f_max to avoid aliasing; a reconstruction low-pass filter removes images.

Quantization noise in PCM improves about 6 dB per additional bit; SNR_dB ≈ 6.02n + 1.76 for a full-scale sinusoid.

Modulation types: AM, FM (analogue); ASK, FSK, PSK (digital); PAM, PWM, PPM (pulse).

Antenna length for a half-wave dipole ≈ λ/2, with λ = c/f (c = 3 × 10^8 m/s).

Propagation: ground wave follows the surface, sky wave reflects from the ionosphere (HF long distance), space wave is line-of-sight (VHF/UHF).

Microprocessor: CPU only, needs external RAM, ROM and I/O; microcontroller: CPU, memory, timers and I/O on one chip.

8051: 8-bit, 4 KB on-chip ROM, 128 bytes RAM, 4 register banks, two 16-bit timers, 5 interrupt sources, 32 I/O lines in four ports.

8051 special function registers: ACC (E0H), B (F0H), PSW (D0H), SP (81H), DPTR (82H/83H), P0–P3 (80H, 90H, A0H, B0H).

8051 reset vector is 0000H; interrupt vectors: external 0 = 0003H, timer 0 = 000BH, external 1 = 0013H, timer 1 = 001BH, serial = 0023H.

8051 machine cycle = 12 oscillator periods; with a 12 MHz crystal one machine cycle = 1 µs.

Instruction classes: data transfer (MOV), arithmetic (ADD, SUBB), logic (ANL, ORL, XRL), branching (SJMP, LJMP, JZ, DJNZ), bit operations (SETB, CLR, CPL).

Memory-mapped I/O shares the address space with memory; port-mapped I/O uses separate IN/OUT instructions (8085-style).

Embedded system characteristics: dedicated function, real-time constraints, limited resources, often programmed in C with register-level access.

Ammeter in series, voltmeter in parallel; an ideal ammeter has zero resistance and an ideal voltmeter infinite resistance.

A galvanometer becomes an ammeter with a low shunt: R_sh = I_g·R_g/(I − I_g); becomes a voltmeter with a high series multiplier: R_s = V/I_g − R_g.

CRO: time period = horizontal divisions × time/div; voltage = vertical divisions × volts/div; frequency = 1/period.

Lissajous figures: a 1:1 straight line means equal frequencies and zero phase; a circle means equal frequencies with 90° phase.

Digital multimeter accuracy is specified as ±(% reading + counts); counts are the last-digit uncertainty.

Multimeter loading effect: a low-impedance meter across a high-resistance circuit reads low; use a high-impedance instrument.

Continuity testing requires the circuit de-energised; a diode test on a DMM should show ≈0.5–0.7 V forward and open reverse for a good Si diode.

Oscilloscope probe compensation: adjust the trimmer until a 1 kHz square wave shows a flat top; a rounded or peaked top means over- or under-compensation.

Signal generator and function generator provide sine, square and triangular waveforms at calibrated amplitude and frequency for testing amplifiers.

Standard 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%.

Capacitor code 104 = 10 × 10^4 pF = 100 nF = 0.1 µF; 103 = 10 nF; 224 = 220 nF.

Breadboard rails: outer rails are supply buses, the central channel separates the two halves of each row; never bridge the channel with a single lead.

Soldering: use a 25–40 W iron, rosin-core solder, tin the tip, heat the joint then apply solder, and avoid cold or bridged joints.

Testing a BJT with a DMM: base-emitter and base-collector show a diode drop for NPN (red probe on base); collector-emitter should read open.

Project report structure: aim, components list, circuit diagram, working principle, observations, result and conclusion.

PCB layout basics: keep power and ground tracks wide, decouple ICs with 0.1 µF close to the supply pin, and avoid sharp 90° corners.

Safety: discharge filter capacitors before servicing a power supply; use an isolation transformer when working on mains-powered circuits.

Measurement discipline: record component tolerance, instrument range and least count with every reading, and repeat readings to check consistency.