Karnataka II PUC Electronics (KSEAB) cheat sheet

Intrinsic carrier concentration: n_i² = A·T³·exp(−E_g/kT); for silicon at 300 K, n_i ≈ 1.5×10¹⁶ m⁻³ and E_g ≈ 1.1 eV.

Mass-action law: n·p = n_i² in thermal equilibrium; doping one carrier type lowers the other proportionally.

Diode current: I = I_s(exp(V/ηV_T) − 1), with V_T = kT/q ≈ 26 mV at 300 K; η = 1 for Ge, ≈ 2 for Si at low currents.

Static resistance R_f = V_F/I_F and dynamic resistance r_d = ηV_T/I_D ≈ 26 mV/I_D for forward bias; r_d is large in reverse bias.

Barrier potential (knee) ≈ 0.7 V for Si and ≈ 0.3 V for Ge; reverse saturation current doubles roughly every 10 °C rise.

Half-wave rectifier: V_dc = V_m/π, ripple frequency f, ripple factor 1.21, efficiency ≈ 40.6%, PIV = V_m.

Full-wave (centre-tap) rectifier: V_dc = 2V_m/π, ripple frequency 2f, ripple factor 0.48, efficiency ≈ 81.2%, PIV = 2V_m.

Bridge rectifier: V_dc = 2V_m/π, ripple factor 0.48, PIV = V_m, no centre-tap needed; two diodes conduct per half cycle.

Zener regulator: series resistor R_s = (V_in − V_Z)/(I_Z + I_L); Zener conducts in reverse breakdown and holds V_Z nearly constant.

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

Active region: emitter-base junction forward biased, collector-base junction reverse biased; saturation has both forward biased, cut-off both reverse biased.

Transconductance g_m = I_C/V_T ≈ 38.5 mS per mA of collector current at 300 K; r_e = V_T/I_E.

BJT is a current-controlled device; FET is a voltage-controlled device with very high input impedance.

JFET drain current in saturation: I_D = I_DSS(1 − V_GS/V_P)²; pinch-off occurs when V_DS = V_GS − V_P.

MOSFET threshold: enhancement device conducts only when |V_GS| > |V_th|; depletion device conducts at V_GS = 0.

Regions of FET output characteristics: ohmic (triode) for small V_DS, saturation for V_DS beyond pinch-off, breakdown at high V_DS.

Leakage: I_CBO is collector-base leakage with emitter open; I_CEO = (1 + β)I_CBO; leakage roughly doubles per 10 °C rise.

Gain in decibels: A_dB = 20 log₁₀|A| for voltage or current, 10 log₁₀(P₂/P₁) for power; −3 dB point is the half-power frequency.

CE amplifier: voltage gain A_v = −β(R_C∥R_L)/r_in, input resistance ≈ βr_e, output phase inverted by 180°.

CC (emitter follower) gain ≈ 1, no phase inversion, high input and low output impedance - used as a buffer.

CB amplifier: gain ≈ α(R_C/r_e), no phase inversion, low input impedance, good high-frequency response.

Negative feedback: A_f = A/(1 + Aβ); desensitises gain, reduces distortion and noise, raises bandwidth by (1 + Aβ), changes input/output impedances.

Feedback topologies: series-shunt (voltage series) raises R_in and lowers R_out; shunt-shunt lowers both; series-series raises both; shunt-series raises R_out.

Class A conducts 360°, efficiency ≤ 25% (transformer-coupled ≤ 50%); Class B conducts 180°, efficiency ≤ 78.5%; Class AB reduces crossover distortion.

Gain-bandwidth product is constant for an op-amp: A_cl·f_cl = A_ol·f_unity; slew rate SR = 2πfV_m limits large-signal high-frequency output.

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

RC phase-shift oscillator: three RC sections give 180° shift, amplifier gives another 180°; f = 1/(2πRC√6) and minimum gain = 29.

Wien bridge oscillator: f = 1/(2πRC) with balanced arms; amplifier gain must be exactly 3 for sustained oscillation.

Hartley oscillator uses a tapped inductor and two capacitors; Colpitts uses a tapped capacitor and two inductors; both are LC oscillators.

Crystal oscillator: series resonance f_s = 1/(2π√(LC_s)) and parallel resonance slightly higher; very high Q gives excellent frequency stability.

Astable multivibrator has no stable state and free-runs as a square-wave generator; monostable has one stable state and produces a single pulse of width T = 1.1RC (555 timer).

Bistable multivibrator has two stable states and acts as a latch or flip-flop, changing state only on an external trigger.

555 astable frequency f = 1.44/((R₁ + 2R₂)C) with duty cycle (R₁ + R₂)/(R₁ + 2R₂).

Ideal op-amp: infinite open-loop gain, infinite input impedance, zero output impedance, infinite bandwidth, zero offset; virtual short V₊ = V₋ in linear negative feedback.

Inverting amplifier: A_v = −R_f/R_in; non-inverting amplifier: A_v = 1 + R_f/R₁; both set gain by external resistors only.

Voltage follower (A_v = 1) gives very high input impedance and very low output impedance - used for buffering and impedance matching.

Summing amplifier output V_o = −R_f(V₁/R₁ + V₂/R₂ + …); difference amplifier output proportional to (V₂ − V₁) when resistor ratios are matched.

Integrator: V_o = −(1/RC)∫V_in dt; differentiator: V_o = −RC·dV_in/dt; swap R and C between the two configurations.

Comparator compares inputs and saturates to ±V_sat; Schmitt trigger uses positive feedback with hysteresis V_H = 2V_sat·R₁/(R₁ + R₂).

IC 741 pin functions: 2 inverting input, 3 non-inverting input, 4 −V_EE, 6 output, 7 +V_CC; offset null on pins 1 and 5.

Active filters use op-amps with RC networks; first-order low-pass has cutoff f_c = 1/(2πRC) and roll-off 20 dB/decade (−6 dB/octave).

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

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

XOR: output 1 when inputs differ; Y = A′B + AB′; XOR with one input tied high gives the complement of the other input.

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

Flip-flops: SR has invalid state when both inputs are 1; JK removes it (toggles when J = K = 1); D stores input; T toggles on T = 1.

Counters: n flip-flops give modulus up to 2ⁿ; ripple counters are asynchronous, synchronous counters clock all flip-flops together.

K-map grouping uses powers of two (1, 2, 4, 8), wraps around edges, and favours the largest possible groups to minimise literals.

Number systems: binary-to-decimal by positional weights; hexadecimal groups 4 bits; 1's complement inverts bits, 2's complement adds 1 to 1's complement.

Modulation index for AM: m = V_m/V_c; percentage modulation = m×100; m > 1 causes overmodulation and envelope distortion.

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

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

Sampling theorem: f_s ≥ 2f_max to avoid aliasing; reconstruction uses a low-pass filter with cutoff at f_max.

Pulse modulation: PAM varies pulse amplitude, PWM varies width, PPM varies position; PCM quantises and encodes samples into binary words.

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

Antenna: half-wave dipole length ≈ λ/2, λ = c/f; propagation at VHF/UHF is mainly line-of-sight with space-wave propagation.

Modulation types: AM (envelope), FM (frequency deviation), PM (phase deviation); SSB transmits one sideband and saves power and bandwidth.

Half-wave and full-wave controlled rectifiers with SCRs: average output depends on firing angle α; full-wave average V_dc = (2V_m/π)cos α for a resistive load.

SCR turns on when anode is positive with respect to cathode and a gate pulse is applied; it latches on and turns off only when anode current falls below holding current.

Diac is a bidirectional trigger device; Triac conducts in both directions and is used for AC power control with phase-angle firing.

Power devices: SCR for high-power rectification, MOSFET for high-frequency switching, IGBT combines MOS input with bipolar output.

LED: forward-biased p-n junction emitting photons; colour set by band gap E_g ≈ hc/λ; must be current-limited by a series resistor.

Photodiode is reverse biased; photocurrent is proportional to illumination; solar cell operates in the fourth quadrant delivering power.

LDR resistance decreases as light intensity increases; used in light-activated switching and automatic street-light circuits.

Optocoupler pairs an LED with a phototransistor to transfer signals while providing electrical isolation between circuits.

Moving-coil (PMMC) meter responds to average value and measures DC; moving-iron responds to RMS and measures AC and DC.

Ammeter is connected in series and needs low resistance; voltmeter in parallel and needs high resistance; a shunt extends ammeter range, a multiplier extends voltmeter range.

CRO: time base sets horizontal sweep, vertical amplifier sets deflection sensitivity in V/div; frequency f = 1/T and peak voltage = (vertical divisions)×(V/div).

CRO measurement of phase and amplitude uses Lissajous figures: a straight line means 0° or 180°, a circle means 90°; ratio of intercepts gives phase angle.

Digital multimeter measures V, I, R and often continuity/diode test; input impedance is typically 10 MΩ, loading the circuit under test only slightly.

Rectifier-type and thermocouple-type meters extend AC measurement to higher frequencies; true-RMS meters read non-sinusoidal waveforms correctly.

Signal generator provides sine, square and triangular test signals; function generator frequency and amplitude are set independently.

Transducer converts a physical quantity (temperature, light, pressure) into an electrical signal; thermistor and LDR are common resistive transducers.