Karnataka KSEAB II PUC Electronics and Hardware (Vocational) cheat sheet

Resistor colour code: Black 0, Brown 1, Red 2, Orange 3, Yellow 4, Green 5, Blue 6, Violet 7, Grey 8, White 9; Gold and Silver are multipliers ×0.1 and ×0.01 and also tolerance ±5% and ±10%.

Four-band resistor: band 1 and 2 are significant digits, band 3 is the decimal multiplier, band 4 is tolerance; a five-band part adds a third significant digit before the multiplier.

Series resistance: R_total = R1 + R2 + …; parallel resistance: 1/R_total = 1/R1 + 1/R2 + …, and two resistors in parallel give R1R2/(R1+R2).

Capacitor charge and current: Q = CV, i = C·dV/dt; capacitors in parallel add (C = C1 + C2), capacitors in series combine reciprocally.

Capacitive reactance Xc = 1/(2πfC); inductive reactance Xl = 2πfL; both are in ohms and depend on frequency, unlike resistance.

Impedance of a series RC circuit: Z = √(R² + Xc²), with phase angle φ = arctan(Xc/R); current leads voltage in a capacitive circuit.

Energy stored: capacitor W = ½CV², inductor W = ½LI²; an inductor opposes change of current, so its current cannot change instantaneously.

Standard E12 values include 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 and their decade multiples; a 4.7 kΩ ±5% part reads Yellow-Violet-Red-Gold.

A capacitor marked 104 is 10 × 10⁴ pF = 100 nF = 0.1 µF; the third digit is the number of zeros in picofarads.

Silicon barrier potential is about 0.7 V and germanium about 0.3 V in forward conduction; a silicon diode needs roughly 0.7 V before appreciable forward current flows.

Diode current equation: I = Is(e^(V/(nVt)) − 1), where Vt ≈ 26 mV at room temperature and n is 1 for germanium and about 2 for silicon at low currents.

Forward bias means anode positive with respect to cathode; reverse bias widens the depletion region and leaves only a small leakage current until breakdown.

Half-wave rectifier: Vdc = Vm/π ≈ 0.318Vm, ripple frequency equals supply frequency; full-wave centre-tap: Vdc = 2Vm/π ≈ 0.637Vm, ripple at twice supply frequency.

Bridge rectifier uses four diodes, needs no centre-tapped transformer, and conducts in diagonally opposite pairs on each half cycle.

PIV rating: half-wave ≈ Vm, centre-tap full-wave ≈ 2Vm, bridge ≈ Vm; choose a diode whose PIV and current ratings exceed these values.

Zener diode operates reverse-biased in breakdown as a shunt voltage regulator; series resistor drops the difference between input and Zener voltage.

A light-emitting diode emits when forward biased, with forward drop set by material: about 1.8–2.2 V for red, 3.0–3.4 V for blue and white.

A photodiode is reverse biased and its leakage current rises with illumination; a varactor diode acts as a voltage-controlled capacitance in tuning circuits.

NPN transistor conducts when base-emitter is forward biased (about 0.7 V) and collector-base is reverse biased; conventional current enters collector and base and leaves emitter.

Current relation: Ie = Ib + Ic, and dc current gain β = Ic/Ib; α = Ic/Ie = β/(β+1).

Operating regions: cutoff when Vbe < 0.7 V (acts as open switch), saturation when Vce ≈ 0.2 V (acts as closed switch), active region for amplification.

Load-line method: Vce = Vcc − Ic·Rc; the Q point is the intersection of the load line with the output characteristic.

Voltage-divider bias is the most stable common configuration because the base voltage is fixed by the divider and is nearly independent of β.

JFET is a voltage-controlled depletion device; with Vgs = 0 the channel is widest and Id = Idss, and pinch-off occurs at Vgs(off) = −Vp.

Shockley equation for JFET: Id = Idss(1 − Vgs/Vp)²; transconductance gm = 2Idss/|Vp| at Vgs = 0.

MOSFET gate is insulated by an oxide layer, so gate current is essentially zero; enhancement MOSFET needs Vgs above threshold Vth to conduct.

Transistor as a switch: choose Rb so that Ib ≥ Ic(saturation)/β(min), typically Ib = Ic/10 for hard saturation.

Common-emitter amplifier gives voltage gain and 180° phase inversion; common-collector (emitter follower) has gain near 1 and is used for impedance matching.

Mid-band voltage gain of a CE stage: Av = −(Rc ∥ RL)/re, where re ≈ 26 mV/IE in ohms at room temperature.

Decibel definitions: power gain in dB = 10 log(Pout/Pin); voltage gain in dB = 20 log(Vout/Vin); −3 dB corresponds to 0.707 of the output voltage.

Class A conducts over the full 360° cycle with maximum efficiency 25% (resistive load) or 50% (transformer-coupled); Class B conducts 180° and gives up to 78.5%.

Class AB reduces crossover distortion by keeping both devices slightly biased on; push-pull output stages normally use complementary transistor pairs.

Negative feedback reduces gain by the factor (1 + Aβ), widens bandwidth, lowers distortion, and raises or lowers input and output impedance depending on the sensing/feedback type.

Barkhausen criterion for oscillation: loop gain Aβ must be at least 1 and the total loop phase shift must be 0° or 360° at the oscillation frequency.

RC phase-shift oscillator uses three RC sections of 60° each with an inverting amplifier; f = 1/(2πRC√6) when all sections are identical.

Hartley oscillator uses a tapped inductor and Colpitts uses a capacitive divider; both are LC oscillators with f = 1/(2π√(LC)).

Crystal oscillator frequency is set by the quartz crystal's mechanical resonance, giving far better stability than RC or LC types.

Basic gates: AND outputs 1 only when all inputs are 1; OR outputs 1 when any input is 1; NOT inverts; NAND and NOR are the inverted forms of AND and OR.

XOR outputs 1 when inputs differ; XNOR outputs 1 when inputs are equal and is used as a 1-bit equality comparator.

NAND and NOR are universal gates because each can implement NOT, AND, OR and any other logic function when wired appropriately.

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

Number systems: binary 1011 = 11 decimal = B hexadecimal; each hex digit maps to exactly four binary bits.

Half adder: Sum = A ⊕ B, Carry = A·B; full adder adds a carry-in and can be built from two half adders plus an OR gate.

A multiplexer with n select lines routes 2ⁿ inputs to one output; a decoder with n inputs has 2ⁿ outputs, one active per input code.

Flip-flops are edge-triggered bistable storage elements; a JK flip-flop with J = K = 1 toggles on each clock edge, and a D flip-flop copies D to Q.

An n-bit ripple counter divides the clock by 2ⁿ and its output frequency halves at each stage; a shift register moves data one stage per clock.

Linear supply chain: transformer steps down ac, rectifier converts to pulsating dc, filter capacitor smooths, regulator holds a constant output.

Ripple factor: half-wave 1.21, full-wave 0.482, bridge 0.482; smaller ripple factor means better smoothing.

Filter capacitor sizing rule: C ≈ Iload/(f_ripple × Vripple), where f_ripple is 50 Hz for half-wave and 100 Hz for full-wave on a 50 Hz supply.

Three-terminal regulators: 78xx series gives positive fixed output (7805 = +5 V, 7812 = +12 V), 79xx gives negative output, and LM317 is adjustable.

A voltmeter is connected in parallel with the load and should have very high resistance; an ammeter is in series and should have very low resistance.

A moving-coil meter measures average dc and responds to current; a rectifier-type meter is used for ac, and a moving-iron meter reads rms.

Multimeter usage: select function and range above the expected value, connect common lead to ground, and never measure resistance in a live circuit.

Cathode-ray oscilloscope controls: time/div sets horizontal sweep, volts/div sets vertical scale, trigger stabilises the waveform, and probes are usually ×10.

A wheatstone bridge balances when R1/R2 = R3/R4; at balance the galvanometer shows zero deflection and the unknown arm can be calculated.

Solder alloy Sn63/Pb37 is eutectic with melting point 183 °C; lead-free SAC305 melts near 217–220 °C and needs a higher iron tip temperature.

Rosin flux removes oxide and improves wetting; it is non-corrosive, whereas acid flux is reserved for plumbing and must never be used on electronics.

A good solder joint is shiny, smooth, and concave, with the component lead wetted; a dull, ball-shaped or grainy joint indicates a cold joint.

Soldering iron tip temperature for tin-lead work is typically 300–350 °C; apply heat to the pad and lead together, then feed solder, and remove solder first.

Electrostatic discharge precautions: wear a grounded wrist strap, use an earthed iron and mat, and store CMOS devices in conductive foam.

Desoldering uses a solder sucker or desoldering braid; do not overheat pads, since prolonged heat above roughly 300 °C lifts copper tracks.

PCB assembly order: place low-profile parts first (resistors, diodes), then ICs and connectors; observe polarity marks on electrolytic capacitors, diodes and ICs.

Continuity testing with a multimeter confirms track integrity; a series lamp or current-limited supply is used when powering a board for the first time.

Hand tools: use a screwdriver whose tip matches the screw slot, diagonal cutters for trimming leads, and never use pliers as a hammer or on live circuits.

A microcontroller integrates CPU, RAM, flash program memory, timers, and I/O peripherals on one chip; a microprocessor needs external memory and peripherals.

8051 basics: 8-bit CPU, 4 kB on-chip ROM in the 8051, 128 bytes RAM, two 16-bit timers, 32 I/O lines in four ports, and a 12 MHz crystal gives 1 MIPS.

Arduino Uno uses the ATmega328P with 32 kB flash, 2 kB SRAM, 1 kB EEPROM, 14 digital I/O (6 with PWM) and 6 analogue inputs with a 10-bit ADC.

ADC resolution: with a 10-bit converter and 5 V reference, one step is 5/1024 ≈ 4.9 mV, and the digital value = (Vin/Vref) × 1023.

UART is asynchronous and uses start, data and stop bits with a baud rate; I²C uses two lines (SDA, SCL) with 7-bit addresses; SPI uses four lines with a chip-select.

Sensor types: thermistor changes resistance with temperature, LDR resistance falls with light, and LM35 gives 10 mV per °C as a linear analogue voltage.

PWM controls average power by varying duty cycle; an LED at 50% duty cycle on 5 V receives an average of 2.5 V, and PWM also drives motor speed.

A relay or transistor driver is needed when a microcontroller pin (typically 20–40 mA maximum) drives a load requiring more current.

Embedded program flow: initialise ports and peripherals, then loop reading inputs, processing, and writing outputs; interrupts allow time-critical events to pre-empt the main loop.

Resistor colour code: Black 0, Brown 1, Red 2, Orange 3, Yellow 4, Green 5, Blue 6, Violet 7, Grey 8, White 9; Gold and Silver are multipliers ×0.1 and ×0.01 and also tolerance ±5% and ±10%.

Four-band resistor: band 1 and 2 are significant digits, band 3 is the decimal multiplier, band 4 is tolerance; a five-band part adds a third significant digit before the multiplier.

Series resistance: R_total = R1 + R2 + …; parallel resistance: 1/R_total = 1/R1 + 1/R2 + …, and two resistors in parallel give R1R2/(R1+R2).

Capacitor charge and current: Q = CV, i = C·dV/dt; capacitors in parallel add (C = C1 + C2), capacitors in series combine reciprocally.

Capacitive reactance Xc = 1/(2πfC); inductive reactance Xl = 2πfL; both are in ohms and depend on frequency, unlike resistance.

Impedance of a series RC circuit: Z = √(R² + Xc²), with phase angle φ = arctan(Xc/R); current leads voltage in a capacitive circuit.

Energy stored: capacitor W = ½CV², inductor W = ½LI²; an inductor opposes change of current, so its current cannot change instantaneously.

Standard E12 values include 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 and their decade multiples; a 4.7 kΩ ±5% part reads Yellow-Violet-Red-Gold.

A capacitor marked 104 is 10 × 10⁴ pF = 100 nF = 0.1 µF; the third digit is the number of zeros in picofarads.

Silicon barrier potential is about 0.7 V and germanium about 0.3 V in forward conduction; a silicon diode needs roughly 0.7 V before appreciable forward current flows.

Diode current equation: I = Is(e^(V/(nVt)) − 1), where Vt ≈ 26 mV at room temperature and n is 1 for germanium and about 2 for silicon at low currents.

Forward bias means anode positive with respect to cathode; reverse bias widens the depletion region and leaves only a small leakage current until breakdown.

Half-wave rectifier: Vdc = Vm/π ≈ 0.318Vm, ripple frequency equals supply frequency; full-wave centre-tap: Vdc = 2Vm/π ≈ 0.637Vm, ripple at twice supply frequency.

Bridge rectifier uses four diodes, needs no centre-tapped transformer, and conducts in diagonally opposite pairs on each half cycle.

PIV rating: half-wave ≈ Vm, centre-tap full-wave ≈ 2Vm, bridge ≈ Vm; choose a diode whose PIV and current ratings exceed these values.

Zener diode operates reverse-biased in breakdown as a shunt voltage regulator; series resistor drops the difference between input and Zener voltage.

A light-emitting diode emits when forward biased, with forward drop set by material: about 1.8–2.2 V for red, 3.0–3.4 V for blue and white.

A photodiode is reverse biased and its leakage current rises with illumination; a varactor diode acts as a voltage-controlled capacitance in tuning circuits.

NPN transistor conducts when base-emitter is forward biased (about 0.7 V) and collector-base is reverse biased; conventional current enters collector and base and leaves emitter.

Current relation: Ie = Ib + Ic, and dc current gain β = Ic/Ib; α = Ic/Ie = β/(β+1).

Operating regions: cutoff when Vbe < 0.7 V (acts as open switch), saturation when Vce ≈ 0.2 V (acts as closed switch), active region for amplification.

Load-line method: Vce = Vcc − Ic·Rc; the Q point is the intersection of the load line with the output characteristic.

Voltage-divider bias is the most stable common configuration because the base voltage is fixed by the divider and is nearly independent of β.

JFET is a voltage-controlled depletion device; with Vgs = 0 the channel is widest and Id = Idss, and pinch-off occurs at Vgs(off) = −Vp.

Shockley equation for JFET: Id = Idss(1 − Vgs/Vp)²; transconductance gm = 2Idss/|Vp| at Vgs = 0.

MOSFET gate is insulated by an oxide layer, so gate current is essentially zero; enhancement MOSFET needs Vgs above threshold Vth to conduct.

Transistor as a switch: choose Rb so that Ib ≥ Ic(saturation)/β(min), typically Ib = Ic/10 for hard saturation.

Common-emitter amplifier gives voltage gain and 180° phase inversion; common-collector (emitter follower) has gain near 1 and is used for impedance matching.

Mid-band voltage gain of a CE stage: Av = −(Rc ∥ RL)/re, where re ≈ 26 mV/IE in ohms at room temperature.

Decibel definitions: power gain in dB = 10 log(Pout/Pin); voltage gain in dB = 20 log(Vout/Vin); −3 dB corresponds to 0.707 of the output voltage.

Class A conducts over the full 360° cycle with maximum efficiency 25% (resistive load) or 50% (transformer-coupled); Class B conducts 180° and gives up to 78.5%.

Class AB reduces crossover distortion by keeping both devices slightly biased on; push-pull output stages normally use complementary transistor pairs.

Negative feedback reduces gain by the factor (1 + Aβ), widens bandwidth, lowers distortion, and raises or lowers input and output impedance depending on the sensing/feedback type.

Barkhausen criterion for oscillation: loop gain Aβ must be at least 1 and the total loop phase shift must be 0° or 360° at the oscillation frequency.

RC phase-shift oscillator uses three RC sections of 60° each with an inverting amplifier; f = 1/(2πRC√6) when all sections are identical.

Hartley oscillator uses a tapped inductor and Colpitts uses a capacitive divider; both are LC oscillators with f = 1/(2π√(LC)).

Crystal oscillator frequency is set by the quartz crystal's mechanical resonance, giving far better stability than RC or LC types.

Basic gates: AND outputs 1 only when all inputs are 1; OR outputs 1 when any input is 1; NOT inverts; NAND and NOR are the inverted forms of AND and OR.

XOR outputs 1 when inputs differ; XNOR outputs 1 when inputs are equal and is used as a 1-bit equality comparator.

NAND and NOR are universal gates because each can implement NOT, AND, OR and any other logic function when wired appropriately.

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

Number systems: binary 1011 = 11 decimal = B hexadecimal; each hex digit maps to exactly four binary bits.

Half adder: Sum = A ⊕ B, Carry = A·B; full adder adds a carry-in and can be built from two half adders plus an OR gate.

A multiplexer with n select lines routes 2ⁿ inputs to one output; a decoder with n inputs has 2ⁿ outputs, one active per input code.

Flip-flops are edge-triggered bistable storage elements; a JK flip-flop with J = K = 1 toggles on each clock edge, and a D flip-flop copies D to Q.

An n-bit ripple counter divides the clock by 2ⁿ and its output frequency halves at each stage; a shift register moves data one stage per clock.

Linear supply chain: transformer steps down ac, rectifier converts to pulsating dc, filter capacitor smooths, regulator holds a constant output.

Ripple factor: half-wave 1.21, full-wave 0.482, bridge 0.482; smaller ripple factor means better smoothing.

Filter capacitor sizing rule: C ≈ Iload/(f_ripple × Vripple), where f_ripple is 50 Hz for half-wave and 100 Hz for full-wave on a 50 Hz supply.

Three-terminal regulators: 78xx series gives positive fixed output (7805 = +5 V, 7812 = +12 V), 79xx gives negative output, and LM317 is adjustable.

A voltmeter is connected in parallel with the load and should have very high resistance; an ammeter is in series and should have very low resistance.

A moving-coil meter measures average dc and responds to current; a rectifier-type meter is used for ac, and a moving-iron meter reads rms.

Multimeter usage: select function and range above the expected value, connect common lead to ground, and never measure resistance in a live circuit.

Cathode-ray oscilloscope controls: time/div sets horizontal sweep, volts/div sets vertical scale, trigger stabilises the waveform, and probes are usually ×10.

A wheatstone bridge balances when R1/R2 = R3/R4; at balance the galvanometer shows zero deflection and the unknown arm can be calculated.

Solder alloy Sn63/Pb37 is eutectic with melting point 183 °C; lead-free SAC305 melts near 217–220 °C and needs a higher iron tip temperature.

Rosin flux removes oxide and improves wetting; it is non-corrosive, whereas acid flux is reserved for plumbing and must never be used on electronics.

A good solder joint is shiny, smooth, and concave, with the component lead wetted; a dull, ball-shaped or grainy joint indicates a cold joint.

Soldering iron tip temperature for tin-lead work is typically 300–350 °C; apply heat to the pad and lead together, then feed solder, and remove solder first.

Electrostatic discharge precautions: wear a grounded wrist strap, use an earthed iron and mat, and store CMOS devices in conductive foam.

Desoldering uses a solder sucker or desoldering braid; do not overheat pads, since prolonged heat above roughly 300 °C lifts copper tracks.

PCB assembly order: place low-profile parts first (resistors, diodes), then ICs and connectors; observe polarity marks on electrolytic capacitors, diodes and ICs.

Continuity testing with a multimeter confirms track integrity; a series lamp or current-limited supply is used when powering a board for the first time.

Hand tools: use a screwdriver whose tip matches the screw slot, diagonal cutters for trimming leads, and never use pliers as a hammer or on live circuits.

A microcontroller integrates CPU, RAM, flash program memory, timers, and I/O peripherals on one chip; a microprocessor needs external memory and peripherals.

8051 basics: 8-bit CPU, 4 kB on-chip ROM in the 8051, 128 bytes RAM, two 16-bit timers, 32 I/O lines in four ports, and a 12 MHz crystal gives 1 MIPS.

Arduino Uno uses the ATmega328P with 32 kB flash, 2 kB SRAM, 1 kB EEPROM, 14 digital I/O (6 with PWM) and 6 analogue inputs with a 10-bit ADC.

ADC resolution: with a 10-bit converter and 5 V reference, one step is 5/1024 ≈ 4.9 mV, and the digital value = (Vin/Vref) × 1023.

UART is asynchronous and uses start, data and stop bits with a baud rate; I²C uses two lines (SDA, SCL) with 7-bit addresses; SPI uses four lines with a chip-select.

Sensor types: thermistor changes resistance with temperature, LDR resistance falls with light, and LM35 gives 10 mV per °C as a linear analogue voltage.

PWM controls average power by varying duty cycle; an LED at 50% duty cycle on 5 V receives an average of 2.5 V, and PWM also drives motor speed.

A relay or transistor driver is needed when a microcontroller pin (typically 20–40 mA maximum) drives a load requiring more current.

Embedded program flow: initialise ports and peripherals, then loop reading inputs, processing, and writing outputs; interrupts allow time-critical events to pre-empt the main loop.

Resistor colour code: Black 0, Brown 1, Red 2, Orange 3, Yellow 4, Green 5, Blue 6, Violet 7, Grey 8, White 9; Gold and Silver are multipliers ×0.1 and ×0.01 and also tolerance ±5% and ±10%.

Four-band resistor: band 1 and 2 are significant digits, band 3 is the decimal multiplier, band 4 is tolerance; a five-band part adds a third significant digit before the multiplier.

Series resistance: R_total = R1 + R2 + …; parallel resistance: 1/R_total = 1/R1 + 1/R2 + …, and two resistors in parallel give R1R2/(R1+R2).

Capacitor charge and current: Q = CV, i = C·dV/dt; capacitors in parallel add (C = C1 + C2), capacitors in series combine reciprocally.

Capacitive reactance Xc = 1/(2πfC); inductive reactance Xl = 2πfL; both are in ohms and depend on frequency, unlike resistance.

Impedance of a series RC circuit: Z = √(R² + Xc²), with phase angle φ = arctan(Xc/R); current leads voltage in a capacitive circuit.

Energy stored: capacitor W = ½CV², inductor W = ½LI²; an inductor opposes change of current, so its current cannot change instantaneously.

Standard E12 values include 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 and their decade multiples; a 4.7 kΩ ±5% part reads Yellow-Violet-Red-Gold.

A capacitor marked 104 is 10 × 10⁴ pF = 100 nF = 0.1 µF; the third digit is the number of zeros in picofarads.

Silicon barrier potential is about 0.7 V and germanium about 0.3 V in forward conduction; a silicon diode needs roughly 0.7 V before appreciable forward current flows.

Diode current equation: I = Is(e^(V/(nVt)) − 1), where Vt ≈ 26 mV at room temperature and n is 1 for germanium and about 2 for silicon at low currents.

Forward bias means anode positive with respect to cathode; reverse bias widens the depletion region and leaves only a small leakage current until breakdown.

Half-wave rectifier: Vdc = Vm/π ≈ 0.318Vm, ripple frequency equals supply frequency; full-wave centre-tap: Vdc = 2Vm/π ≈ 0.637Vm, ripple at twice supply frequency.

Bridge rectifier uses four diodes, needs no centre-tapped transformer, and conducts in diagonally opposite pairs on each half cycle.

PIV rating: half-wave ≈ Vm, centre-tap full-wave ≈ 2Vm, bridge ≈ Vm; choose a diode whose PIV and current ratings exceed these values.

Zener diode operates reverse-biased in breakdown as a shunt voltage regulator; series resistor drops the difference between input and Zener voltage.

A light-emitting diode emits when forward biased, with forward drop set by material: about 1.8–2.2 V for red, 3.0–3.4 V for blue and white.

A photodiode is reverse biased and its leakage current rises with illumination; a varactor diode acts as a voltage-controlled capacitance in tuning circuits.

NPN transistor conducts when base-emitter is forward biased (about 0.7 V) and collector-base is reverse biased; conventional current enters collector and base and leaves emitter.

Current relation: Ie = Ib + Ic, and dc current gain β = Ic/Ib; α = Ic/Ie = β/(β+1).

Operating regions: cutoff when Vbe < 0.7 V (acts as open switch), saturation when Vce ≈ 0.2 V (acts as closed switch), active region for amplification.

Load-line method: Vce = Vcc − Ic·Rc; the Q point is the intersection of the load line with the output characteristic.

Voltage-divider bias is the most stable common configuration because the base voltage is fixed by the divider and is nearly independent of β.

JFET is a voltage-controlled depletion device; with Vgs = 0 the channel is widest and Id = Idss, and pinch-off occurs at Vgs(off) = −Vp.

Shockley equation for JFET: Id = Idss(1 − Vgs/Vp)²; transconductance gm = 2Idss/|Vp| at Vgs = 0.

MOSFET gate is insulated by an oxide layer, so gate current is essentially zero; enhancement MOSFET needs Vgs above threshold Vth to conduct.

Transistor as a switch: choose Rb so that Ib ≥ Ic(saturation)/β(min), typically Ib = Ic/10 for hard saturation.

Common-emitter amplifier gives voltage gain and 180° phase inversion; common-collector (emitter follower) has gain near 1 and is used for impedance matching.

Mid-band voltage gain of a CE stage: Av = −(Rc ∥ RL)/re, where re ≈ 26 mV/IE in ohms at room temperature.

Decibel definitions: power gain in dB = 10 log(Pout/Pin); voltage gain in dB = 20 log(Vout/Vin); −3 dB corresponds to 0.707 of the output voltage.

Class A conducts over the full 360° cycle with maximum efficiency 25% (resistive load) or 50% (transformer-coupled); Class B conducts 180° and gives up to 78.5%.

Class AB reduces crossover distortion by keeping both devices slightly biased on; push-pull output stages normally use complementary transistor pairs.

Negative feedback reduces gain by the factor (1 + Aβ), widens bandwidth, lowers distortion, and raises or lowers input and output impedance depending on the sensing/feedback type.

Barkhausen criterion for oscillation: loop gain Aβ must be at least 1 and the total loop phase shift must be 0° or 360° at the oscillation frequency.

RC phase-shift oscillator uses three RC sections of 60° each with an inverting amplifier; f = 1/(2πRC√6) when all sections are identical.

Hartley oscillator uses a tapped inductor and Colpitts uses a capacitive divider; both are LC oscillators with f = 1/(2π√(LC)).

Crystal oscillator frequency is set by the quartz crystal's mechanical resonance, giving far better stability than RC or LC types.

Basic gates: AND outputs 1 only when all inputs are 1; OR outputs 1 when any input is 1; NOT inverts; NAND and NOR are the inverted forms of AND and OR.

XOR outputs 1 when inputs differ; XNOR outputs 1 when inputs are equal and is used as a 1-bit equality comparator.

NAND and NOR are universal gates because each can implement NOT, AND, OR and any other logic function when wired appropriately.

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

Number systems: binary 1011 = 11 decimal = B hexadecimal; each hex digit maps to exactly four binary bits.

Half adder: Sum = A ⊕ B, Carry = A·B; full adder adds a carry-in and can be built from two half adders plus an OR gate.

A multiplexer with n select lines routes 2ⁿ inputs to one output; a decoder with n inputs has 2ⁿ outputs, one active per input code.

Flip-flops are edge-triggered bistable storage elements; a JK flip-flop with J = K = 1 toggles on each clock edge, and a D flip-flop copies D to Q.

An n-bit ripple counter divides the clock by 2ⁿ and its output frequency halves at each stage; a shift register moves data one stage per clock.

Linear supply chain: transformer steps down ac, rectifier converts to pulsating dc, filter capacitor smooths, regulator holds a constant output.

Ripple factor: half-wave 1.21, full-wave 0.482, bridge 0.482; smaller ripple factor means better smoothing.

Filter capacitor sizing rule: C ≈ Iload/(f_ripple × Vripple), where f_ripple is 50 Hz for half-wave and 100 Hz for full-wave on a 50 Hz supply.

Three-terminal regulators: 78xx series gives positive fixed output (7805 = +5 V, 7812 = +12 V), 79xx gives negative output, and LM317 is adjustable.

A voltmeter is connected in parallel with the load and should have very high resistance; an ammeter is in series and should have very low resistance.

A moving-coil meter measures average dc and responds to current; a rectifier-type meter is used for ac, and a moving-iron meter reads rms.

Multimeter usage: select function and range above the expected value, connect common lead to ground, and never measure resistance in a live circuit.

Cathode-ray oscilloscope controls: time/div sets horizontal sweep, volts/div sets vertical scale, trigger stabilises the waveform, and probes are usually ×10.

A wheatstone bridge balances when R1/R2 = R3/R4; at balance the galvanometer shows zero deflection and the unknown arm can be calculated.

Solder alloy Sn63/Pb37 is eutectic with melting point 183 °C; lead-free SAC305 melts near 217–220 °C and needs a higher iron tip temperature.

Rosin flux removes oxide and improves wetting; it is non-corrosive, whereas acid flux is reserved for plumbing and must never be used on electronics.

A good solder joint is shiny, smooth, and concave, with the component lead wetted; a dull, ball-shaped or grainy joint indicates a cold joint.

Soldering iron tip temperature for tin-lead work is typically 300–350 °C; apply heat to the pad and lead together, then feed solder, and remove solder first.

Electrostatic discharge precautions: wear a grounded wrist strap, use an earthed iron and mat, and store CMOS devices in conductive foam.

Desoldering uses a solder sucker or desoldering braid; do not overheat pads, since prolonged heat above roughly 300 °C lifts copper tracks.

PCB assembly order: place low-profile parts first (resistors, diodes), then ICs and connectors; observe polarity marks on electrolytic capacitors, diodes and ICs.

Continuity testing with a multimeter confirms track integrity; a series lamp or current-limited supply is used when powering a board for the first time.

Hand tools: use a screwdriver whose tip matches the screw slot, diagonal cutters for trimming leads, and never use pliers as a hammer or on live circuits.

A microcontroller integrates CPU, RAM, flash program memory, timers, and I/O peripherals on one chip; a microprocessor needs external memory and peripherals.

8051 basics: 8-bit CPU, 4 kB on-chip ROM in the 8051, 128 bytes RAM, two 16-bit timers, 32 I/O lines in four ports, and a 12 MHz crystal gives 1 MIPS.

Arduino Uno uses the ATmega328P with 32 kB flash, 2 kB SRAM, 1 kB EEPROM, 14 digital I/O (6 with PWM) and 6 analogue inputs with a 10-bit ADC.

ADC resolution: with a 10-bit converter and 5 V reference, one step is 5/1024 ≈ 4.9 mV, and the digital value = (Vin/Vref) × 1023.

UART is asynchronous and uses start, data and stop bits with a baud rate; I²C uses two lines (SDA, SCL) with 7-bit addresses; SPI uses four lines with a chip-select.

Sensor types: thermistor changes resistance with temperature, LDR resistance falls with light, and LM35 gives 10 mV per °C as a linear analogue voltage.

PWM controls average power by varying duty cycle; an LED at 50% duty cycle on 5 V receives an average of 2.5 V, and PWM also drives motor speed.

A relay or transistor driver is needed when a microcontroller pin (typically 20–40 mA maximum) drives a load requiring more current.

Embedded program flow: initialise ports and peripherals, then loop reading inputs, processing, and writing outputs; interrupts allow time-critical events to pre-empt the main loop.

Resistor colour code: Black 0, Brown 1, Red 2, Orange 3, Yellow 4, Green 5, Blue 6, Violet 7, Grey 8, White 9; Gold and Silver are multipliers ×0.1 and ×0.01 and also tolerance ±5% and ±10%.

Four-band resistor: band 1 and 2 are significant digits, band 3 is the decimal multiplier, band 4 is tolerance; a five-band part adds a third significant digit before the multiplier.

Series resistance: R_total = R1 + R2 + …; parallel resistance: 1/R_total = 1/R1 + 1/R2 + …, and two resistors in parallel give R1R2/(R1+R2).

Capacitor charge and current: Q = CV, i = C·dV/dt; capacitors in parallel add (C = C1 + C2), capacitors in series combine reciprocally.

Capacitive reactance Xc = 1/(2πfC); inductive reactance Xl = 2πfL; both are in ohms and depend on frequency, unlike resistance.

Impedance of a series RC circuit: Z = √(R² + Xc²), with phase angle φ = arctan(Xc/R); current leads voltage in a capacitive circuit.

Energy stored: capacitor W = ½CV², inductor W = ½LI²; an inductor opposes change of current, so its current cannot change instantaneously.

Standard E12 values include 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 and their decade multiples; a 4.7 kΩ ±5% part reads Yellow-Violet-Red-Gold.

A capacitor marked 104 is 10 × 10⁴ pF = 100 nF = 0.1 µF; the third digit is the number of zeros in picofarads.

Silicon barrier potential is about 0.7 V and germanium about 0.3 V in forward conduction; a silicon diode needs roughly 0.7 V before appreciable forward current flows.

Diode current equation: I = Is(e^(V/(nVt)) − 1), where Vt ≈ 26 mV at room temperature and n is 1 for germanium and about 2 for silicon at low currents.

Forward bias means anode positive with respect to cathode; reverse bias widens the depletion region and leaves only a small leakage current until breakdown.

Half-wave rectifier: Vdc = Vm/π ≈ 0.318Vm, ripple frequency equals supply frequency; full-wave centre-tap: Vdc = 2Vm/π ≈ 0.637Vm, ripple at twice supply frequency.

Bridge rectifier uses four diodes, needs no centre-tapped transformer, and conducts in diagonally opposite pairs on each half cycle.

PIV rating: half-wave ≈ Vm, centre-tap full-wave ≈ 2Vm, bridge ≈ Vm; choose a diode whose PIV and current ratings exceed these values.

Zener diode operates reverse-biased in breakdown as a shunt voltage regulator; series resistor drops the difference between input and Zener voltage.

A light-emitting diode emits when forward biased, with forward drop set by material: about 1.8–2.2 V for red, 3.0–3.4 V for blue and white.

A photodiode is reverse biased and its leakage current rises with illumination; a varactor diode acts as a voltage-controlled capacitance in tuning circuits.

NPN transistor conducts when base-emitter is forward biased (about 0.7 V) and collector-base is reverse biased; conventional current enters collector and base and leaves emitter.

Current relation: Ie = Ib + Ic, and dc current gain β = Ic/Ib; α = Ic/Ie = β/(β+1).

Operating regions: cutoff when Vbe < 0.7 V (acts as open switch), saturation when Vce ≈ 0.2 V (acts as closed switch), active region for amplification.

Load-line method: Vce = Vcc − Ic·Rc; the Q point is the intersection of the load line with the output characteristic.

Voltage-divider bias is the most stable common configuration because the base voltage is fixed by the divider and is nearly independent of β.

JFET is a voltage-controlled depletion device; with Vgs = 0 the channel is widest and Id = Idss, and pinch-off occurs at Vgs(off) = −Vp.

Shockley equation for JFET: Id = Idss(1 − Vgs/Vp)²; transconductance gm = 2Idss/|Vp| at Vgs = 0.

MOSFET gate is insulated by an oxide layer, so gate current is essentially zero; enhancement MOSFET needs Vgs above threshold Vth to conduct.

Transistor as a switch: choose Rb so that Ib ≥ Ic(saturation)/β(min), typically Ib = Ic/10 for hard saturation.

Common-emitter amplifier gives voltage gain and 180° phase inversion; common-collector (emitter follower) has gain near 1 and is used for impedance matching.

Mid-band voltage gain of a CE stage: Av = −(Rc ∥ RL)/re, where re ≈ 26 mV/IE in ohms at room temperature.

Decibel definitions: power gain in dB = 10 log(Pout/Pin); voltage gain in dB = 20 log(Vout/Vin); −3 dB corresponds to 0.707 of the output voltage.

Class A conducts over the full 360° cycle with maximum efficiency 25% (resistive load) or 50% (transformer-coupled); Class B conducts 180° and gives up to 78.5%.

Class AB reduces crossover distortion by keeping both devices slightly biased on; push-pull output stages normally use complementary transistor pairs.

Negative feedback reduces gain by the factor (1 + Aβ), widens bandwidth, lowers distortion, and raises or lowers input and output impedance depending on the sensing/feedback type.

Barkhausen criterion for oscillation: loop gain Aβ must be at least 1 and the total loop phase shift must be 0° or 360° at the oscillation frequency.

RC phase-shift oscillator uses three RC sections of 60° each with an inverting amplifier; f = 1/(2πRC√6) when all sections are identical.

Hartley oscillator uses a tapped inductor and Colpitts uses a capacitive divider; both are LC oscillators with f = 1/(2π√(LC)).

Crystal oscillator frequency is set by the quartz crystal's mechanical resonance, giving far better stability than RC or LC types.

Basic gates: AND outputs 1 only when all inputs are 1; OR outputs 1 when any input is 1; NOT inverts; NAND and NOR are the inverted forms of AND and OR.

XOR outputs 1 when inputs differ; XNOR outputs 1 when inputs are equal and is used as a 1-bit equality comparator.

NAND and NOR are universal gates because each can implement NOT, AND, OR and any other logic function when wired appropriately.

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

Number systems: binary 1011 = 11 decimal = B hexadecimal; each hex digit maps to exactly four binary bits.

Half adder: Sum = A ⊕ B, Carry = A·B; full adder adds a carry-in and can be built from two half adders plus an OR gate.

A multiplexer with n select lines routes 2ⁿ inputs to one output; a decoder with n inputs has 2ⁿ outputs, one active per input code.

Flip-flops are edge-triggered bistable storage elements; a JK flip-flop with J = K = 1 toggles on each clock edge, and a D flip-flop copies D to Q.

An n-bit ripple counter divides the clock by 2ⁿ and its output frequency halves at each stage; a shift register moves data one stage per clock.

Linear supply chain: transformer steps down ac, rectifier converts to pulsating dc, filter capacitor smooths, regulator holds a constant output.

Ripple factor: half-wave 1.21, full-wave 0.482, bridge 0.482; smaller ripple factor means better smoothing.

Filter capacitor sizing rule: C ≈ Iload/(f_ripple × Vripple), where f_ripple is 50 Hz for half-wave and 100 Hz for full-wave on a 50 Hz supply.

Three-terminal regulators: 78xx series gives positive fixed output (7805 = +5 V, 7812 = +12 V), 79xx gives negative output, and LM317 is adjustable.

A voltmeter is connected in parallel with the load and should have very high resistance; an ammeter is in series and should have very low resistance.

A moving-coil meter measures average dc and responds to current; a rectifier-type meter is used for ac, and a moving-iron meter reads rms.

Multimeter usage: select function and range above the expected value, connect common lead to ground, and never measure resistance in a live circuit.

Cathode-ray oscilloscope controls: time/div sets horizontal sweep, volts/div sets vertical scale, trigger stabilises the waveform, and probes are usually ×10.

A wheatstone bridge balances when R1/R2 = R3/R4; at balance the galvanometer shows zero deflection and the unknown arm can be calculated.

Solder alloy Sn63/Pb37 is eutectic with melting point 183 °C; lead-free SAC305 melts near 217–220 °C and needs a higher iron tip temperature.

Rosin flux removes oxide and improves wetting; it is non-corrosive, whereas acid flux is reserved for plumbing and must never be used on electronics.

A good solder joint is shiny, smooth, and concave, with the component lead wetted; a dull, ball-shaped or grainy joint indicates a cold joint.

Soldering iron tip temperature for tin-lead work is typically 300–350 °C; apply heat to the pad and lead together, then feed solder, and remove solder first.

Electrostatic discharge precautions: wear a grounded wrist strap, use an earthed iron and mat, and store CMOS devices in conductive foam.

Desoldering uses a solder sucker or desoldering braid; do not overheat pads, since prolonged heat above roughly 300 °C lifts copper tracks.

PCB assembly order: place low-profile parts first (resistors, diodes), then ICs and connectors; observe polarity marks on electrolytic capacitors, diodes and ICs.

Continuity testing with a multimeter confirms track integrity; a series lamp or current-limited supply is used when powering a board for the first time.

Hand tools: use a screwdriver whose tip matches the screw slot, diagonal cutters for trimming leads, and never use pliers as a hammer or on live circuits.

A microcontroller integrates CPU, RAM, flash program memory, timers, and I/O peripherals on one chip; a microprocessor needs external memory and peripherals.

8051 basics: 8-bit CPU, 4 kB on-chip ROM in the 8051, 128 bytes RAM, two 16-bit timers, 32 I/O lines in four ports, and a 12 MHz crystal gives 1 MIPS.

Arduino Uno uses the ATmega328P with 32 kB flash, 2 kB SRAM, 1 kB EEPROM, 14 digital I/O (6 with PWM) and 6 analogue inputs with a 10-bit ADC.

ADC resolution: with a 10-bit converter and 5 V reference, one step is 5/1024 ≈ 4.9 mV, and the digital value = (Vin/Vref) × 1023.

UART is asynchronous and uses start, data and stop bits with a baud rate; I²C uses two lines (SDA, SCL) with 7-bit addresses; SPI uses four lines with a chip-select.

Sensor types: thermistor changes resistance with temperature, LDR resistance falls with light, and LM35 gives 10 mV per °C as a linear analogue voltage.

PWM controls average power by varying duty cycle; an LED at 50% duty cycle on 5 V receives an average of 2.5 V, and PWM also drives motor speed.

A relay or transistor driver is needed when a microcontroller pin (typically 20–40 mA maximum) drives a load requiring more current.

Embedded program flow: initialise ports and peripherals, then loop reading inputs, processing, and writing outputs; interrupts allow time-critical events to pre-empt the main loop.