A diode is a semiconductor device that allows current to flow in one direction only. It is made of a p-n junction that conducts when forward-biased and blocks current when reverse-biased. Diodes are essential in rectification, voltage regulation, switching, signal modulation, and many other electronic applications.

When a diode is forward-biased (positive voltage on the anode relative to the cathode), current flows once the voltage exceeds the threshold or forward voltage drop:

I ≈ I₀ * (e^(Vd / (n * Vt)) - 1)

Where:

• I = diode current
• I₀ = reverse saturation current
• Vd = voltage across the diode
• n = ideality factor (typically 1–2)
• Vt = thermal voltage (~26 mV at 300K)

A diode’s schematic symbol shows the direction of conventional current flow (from anode to cathode). The cathode is marked with a stripe on physical diodes.

• Forward Voltage Drop (Vf): The voltage required to turn on the diode (≈0.7 V for silicon, ≈0.3 V for germanium, ≈0.2 V for Schottky).
• Reverse Breakdown Voltage (Vz): The voltage at which reverse current rapidly increases.
• Reverse Recovery Time (trr): The time needed for a diode to stop conducting after switching off.
• Maximum Forward Current (If): The highest continuous forward current rating.

Click an example to expand. Only one will show at a time.

• Half-Wave Rectifier
  Half-Wave Rectifier

  A single diode allows only the positive half-cycles of an AC signal to pass, converting AC to pulsed DC.

  
  // Simple half-wave rectifier simulation
  float Vin = 10.0 * sin(phase); // AC input
  float Vout = (Vin > 0.7) ? Vin - 0.7 : 0.0;
  Serial.println(Vout);
              

• Zener Voltage Regulation
  Zener Voltage Regulation

  A Zener diode maintains a constant voltage across its terminals when reverse-biased beyond its breakdown voltage.

  
  // Simple zener regulator model
  float Vin = 12.0;
  float R = 220.0; // series resistor
  float Vz = 5.1;
  float Iz = (Vin - Vz) / R;
  Serial.println(Iz);
              

• Schottky Fast Switching
  Schottky Fast Switching

  Schottky diodes have low forward voltage (~0.2 V) and are ideal for high-speed switching circuits.

  
  // Example forward voltage comparison
  float Vf_silicon = 0.7;
  float Vf_schottky = 0.2;
  float efficiency_gain = (Vf_silicon - Vf_schottky) / Vf_silicon * 100.0;
  Serial.println(efficiency_gain); // ~71% less drop
              

• LED Forward Bias
  LED Forward Bias

  LEDs emit light when forward-biased. The current must be limited by a resistor.

  
  // LED current-limiting resistor
  float Vs = 5.0;
  float Vf = 2.0;
  float If = 0.02; // 20 mA
  float R = (Vs - Vf) / If; // 150 Ω
  Serial.println(R);
              

• Photodiode Current
  Photodiode Current

  Photodiodes generate a current proportional to the light intensity.

  
  // Photodiode model
  float lightIntensity = 100.0; // arbitrary units
  float sensitivity = 0.5; // µA per lux
  float Iphoto = lightIntensity * sensitivity; // µA
  Serial.println(Iphoto);
              

• Varactor Tuned Oscillator
  Varactor Tuned Oscillator

  A varactor diode acts as a voltage-controlled capacitor, tuning the frequency of an LC oscillator.

  
  // Varactor capacitance example
  float Vbias = 5.0;
  float C0 = 50e-12; // 50 pF
  float Vj = 0.7;
  float m = 0.5;
  float Cvar = C0 / pow(1 + Vbias / Vj, m);
  Serial.println(Cvar);
              

• Gunn Diode Oscillator
  Gunn Diode Oscillator

  Gunn diodes generate microwave oscillations by negative differential resistance in a semiconductor without a p-n junction.

  
  // Gunn diode frequency approximation
  float domainTransitTime = 1e-12; // s
  float f = 1 / domainTransitTime; // 1 THz
  Serial.println(f);
              

Capacitors are passive electronic components that store energy in an electric field. They resist changes in voltage, filter signals, and smooth power supplies. Capacitors are widely used in electronics for timing, coupling, decoupling, energy storage, and voltage regulation.

The Farad (F) is the SI unit of capacitance, representing the ability to store one coulomb of charge per volt. One coulomb (C) is the charge transferred by a current of one ampere in one second.

// Q = C × V
// Example: A 100 µF capacitor charged to 5 V
// Q = 100e-6 × 5 = 0.0005 C = 0.5 mC
      

Electrolytic Capacitors

Polarized capacitors with high capacitance per volume. Ideal for power supply filtering and bulk energy storage. Advantages: high capacitance, low cost. Disadvantages: limited lifetime, polarized, higher ESR.

Tantalum Capacitors

Polarized capacitors with stable capacitance and low leakage. Advantages: compact, reliable. Disadvantages: expensive, can fail short-circuit if overvolted.

Ceramic Capacitors

Non-polarized, stable, low ESR, used for decoupling and high-frequency applications. Advantages: small, reliable, cheap. Disadvantages: low capacitance, voltage coefficient effects.

Film / Foil Capacitors

Non-polarized, excellent stability, low loss. Advantages: high voltage ratings, precise, long life. Disadvantages: larger size, more expensive than ceramics.

Polymer Capacitors

Electrolytic replacement with low ESR and longer life. Advantages: better performance at high frequencies, low ESR, temperature stable. Disadvantages: cost higher than standard electrolytics.

Other Types

Supercapacitors: extremely high capacitance for energy storage. Mica capacitors: stable and precise. Glass capacitors: high voltage, low loss. Each type chosen based on application requirements.

Capacitors are represented in schematics as two parallel lines for non-polarized types, or one straight line and one curved line for polarized types. Physically, they can appear as small ceramic disks, electrolytic cylinders, or large can-style capacitors in power circuits.

// Example symbols
// Non-polarized:  ─| |─
// Polarized:      ─| (─
      

Capacitors use numerical or color codes to indicate capacitance values, typically in picofarads (pF). A common three-digit code uses the first two digits as significant figures and the third as a multiplier.

Capacitors are manufactured in standard E-series (E6, E12, E24, etc.), similar to resistors and inductors. Typical tolerances range from ±20% for electrolytic capacitors to ±1% for precision film capacitors.

// Example: 100 nF capacitor
// Electrolytic ±20% → actual range 80 nF to 120 nF
// Film ±5% → actual range 95 nF to 105 nF
      

A resistor is a passive electronic component that limits or regulates the flow of electric current in a circuit. It is one of the most fundamental components in electronics, used in nearly every device to control voltage, current, and signal levels. Resistors obey Ohm’s Law, which defines the relationship between voltage, current, and resistance.

Ohm’s Law

Ohm’s Law states that the voltage across a resistor is directly proportional to the current flowing through it, given by:

  

Ohm’s Law relationships:

1) Voltage (V)
   V = I × R

   Example:
   I = 0.02 A
   R = 470 Ω

   V = 0.02 × 470
   V = 9.4 V


2) Current (I)
   I = V / R

   Example:
   V = 5 V
   R = 1000 Ω

   I = 5 / 1000
   I = 0.005 A = 5 mA


3) Resistance (R)
   R = V / I

   Example:
   V = 12 V
   I = 0.1 A

   R = 12 / 0.1
   R = 120 Ω
  
    
    

Where: V = Voltage across the resistor (Volts), I = Current through the resistor (Amperes), R = Resistance (Ohms, Ω).

Rearranging this formula allows you to calculate any one of the three quantities if the other two are known.

Axial lead resistors use colored bands to encode their electrical resistance value. This system allows a quick visual identification without the need for printed numbers. The colors are standardized and correspond to digits, multipliers, tolerance, and sometimes temperature coefficient.

The color bands are read from left to right (usually the bands closest to an end). The meaning of each band depends on the total number of bands:

• 3-band resistors: First two bands = significant digits, third band = multiplier, tolerance is often 20% (assumed).
• 4-band resistors: First two bands = significant digits, third = multiplier, fourth = tolerance.
• 5-band resistors: First three bands = significant digits, fourth = multiplier, fifth = tolerance.
• 6-band resistors: Like 5-band, plus sixth band = temperature coefficient in ppm/K.

How to decode a resistor:

1. Identify the number of bands and locate the tolerance band (often gold or silver) to determine orientation.
2. Read the significant digits from the first 2 or 3 bands.
3. Apply the multiplier from the next band to calculate the resistance value.
4. Use the tolerance band to understand the possible variation of the resistor value.
5. If present, use the temperature coefficient band to understand how resistance changes with temperature.

Example: A 4-band resistor with colors Red, Violet, Yellow, Gold:

• Red (2) + Violet (7) → 27
• Yellow multiplier = ×10,000 → 27 × 10,000 = 270,000 Ω = 270 kΩ
• Gold tolerance = ±5%

Understanding the resistor color code is fundamental in electronics as it allows you to quickly identify resistor values, verify components, and calculate circuit tolerances without relying on printed numbers.

Value: 4.7 kΩ ±5%

Value: 12.4 kΩ ±1%

Value: 10.0 kΩ ±0.5%, 10 ppm/K

Values repeat for each decade (×10ⁿ). Blank cells indicate that the value does not exist in that E-series.

Resistors are passive electronic components designed to oppose the flow of electric current. Different resistor constructions are optimized for accuracy, stability, power dissipation, noise performance, and environmental robustness. The sections below describe the most commonly encountered resistor types and their practical characteristics.

Carbon composition resistors are made from a mixture of carbon powder and an insulating binder. The resistance value is determined by the ratio of carbon to binder.

These resistors typically have wide tolerances (±10% to ±20%) and generate significant electrical noise. However, they can withstand short, high-energy surge currents better than most modern types, which is why they are sometimes used in pulse or surge-prone circuits.

Carbon film resistors use a thin carbon layer deposited on a ceramic substrate. The resistance is adjusted by cutting a helical groove in the film.

Compared to carbon composition resistors, carbon film types offer improved tolerance (typically ±5%), better stability, and lower noise. They are commonly used in general-purpose and low-cost electronic circuits.

Metal film resistors replace the carbon layer with a thin metal alloy film. This construction provides excellent precision and long-term stability.

Typical tolerances range from ±1% down to ±0.1%, and temperature coefficients can be as low as 10 ppm/°C. These properties make metal film resistors ideal for analog signal paths, measurement circuits, and precision voltage references.

Wirewound resistors are constructed by winding a resistive wire, typically nickel-chromium alloy, around a ceramic core.

They are capable of handling significantly higher power levels than film resistors and offer very high accuracy. However, the wire winding introduces inductance, which can limit their use in high-frequency applications.

Variable resistors allow the resistance value to be adjusted mechanically. A potentiometer has three terminals and functions as an adjustable voltage divider, while a trimmer resistor is intended for infrequent calibration adjustments.

These components are widely used for volume controls, sensor calibration, bias adjustment, and user-configurable settings.

When current flows through a resistor, electrical energy is converted into heat. The amount of heat generated per second is the power dissipated by the resistor.

For reliability, a resistor should normally be rated for at least twice the calculated power dissipation.

The following examples demonstrate how resistor-related formulas are applied in real circuits using step-by-step calculations.

A transistor is a semiconductor device used to amplify or switch electrical signals and power. They are the building blocks of all modern electronic systems, from simple audio amplifiers to complex microprocessors.

Transistors generally operate in three regions: Cutoff (off), Saturation (fully on), and Active (amplification). The core equations depend on the transistor type.

Schematic symbols distinguish between NPN/PNP for BJTs and N-channel/P-channel for FETs.

Click an example to expand. Only one will show at a time.

• BJT as a Switch
  BJT as a Switch

  When driven into saturation by a small base current, the BJT acts as a closed switch between collector and emitter.

  
  // MCU control of a BJT switch
  void setSwitch(bool on) {
    digitalWrite(BASE_PIN, on ? HIGH : LOW);
  }
              

• BJT Current Amplifier
  BJT Current Amplifier

  In the active region, the BJT amplifies a small AC base current into a larger collector current.

  
  // Simple BJT gain simulation
  float beta = 100.0;
  float Ib_mA = 0.5;
  float Ic_mA = beta * Ib_mA; // 50 mA
  Serial.println(Ic_mA);
              

• MOSFET PWM Dimming
  MOSFET PWM Dimming

  High-speed PWM switching of a MOSFET allows efficient control of power to a load like a motor or lamp.

  
  // PWM dimming with N-channel MOSFET
  void setBrightness(int level) {
    analogWrite(GATE_PIN, level); // 0–255
  }
              

• Darlington Pair Current Gain
  Darlington Pair Current Gain

  Two BJTs connected as a Darlington pair multiply their gains (β_total ≈ β1 * β2).

  
  // Total gain of Darlington pair
  float beta1 = 100.0;
  float beta2 = 120.0;
  float total_gain = beta1 * beta2; // 12,000
  Serial.println(total_gain);
              

Thyristors are a class of semiconductor devices used primarily for high-power switching. They act as bistable switches, conducting when their gate receives a current pulse and continuing to conduct until the voltage across the device is reversed or the current drops below a threshold.

The Silicon Controlled Rectifier (SCR) was first proposed by William Shockley in 1950 and developed by GE in 1957. Thyristors replaced bulky mercury-arc rectifiers and thyratron tubes, enabling efficient control of large AC currents in industrial and consumer applications.

This pseudocode demonstrates triggering a TRIAC at different phase angles to control AC power:

// Simple AC phase control pseudocode
void loop() {
  int phaseAngle = readPotentiometer(); // 0 to 180 degrees
  waitForZeroCrossing();
  delayMicroseconds(angleToTime(phaseAngle));
  pulseGate(); // Trigger TRIAC
}
      

An Operational Amplifier is a high-gain electronic voltage amplifier with differential inputs (inverting and non-inverting) and usually a single-ended output. Op-Amps are fundamental building blocks for analog circuits including amplifiers, filters, integrators, and oscillators.

The concept of an Op-Amp originated in the 1940s for analog computers, performing mathematical operations like addition, subtraction, integration, and differentiation. Early devices were vacuum-tube based, but modern IC Op-Amps (like the 741, LM324) became popular in the late 1960s. They provide very high input impedance, low output impedance, and large open-loop gain.

The most common configurations are:

• Inverting amplifier
• Non-inverting amplifier
• Low-pass filter
• High-pass filter

Click a configuration below to open a calculator for gain or cutoff calculations:

• Inverting Amplifier Gain
  Inverting Amplifier Calculator

  Gain formula: Gain = -Rf / Rin

  Rin (Ω):
  Rf (Ω):

  Calculate Gain

  Gain:

• Non-Inverting Amplifier Gain
  Non-Inverting Amplifier Calculator

  Gain formula: Gain = 1 + Rf / Rin

  Rin (Ω):
  Rf (Ω):

  Calculate Gain

  Gain:

• Low-Pass Filter Cutoff
  Low-Pass Filter Calculator

  Cutoff frequency formula: f_c = 1 / (2π R C)

  R (Ω):
  C (F):

  Calculate Cutoff Frequency

  f_c: Hz

• High-Pass Filter Cutoff
  High-Pass Filter Calculator

  Cutoff frequency formula: f_c = 1 / (2π R C)

  R (Ω):
  C (F):

  Calculate Cutoff Frequency

  f_c: Hz

Analog Integrated Circuits (ICs) are semiconductor devices designed to process continuous voltage or current signals. Unlike digital ICs, analog ICs operate on a continuous range of values and are essential in signal conditioning, amplification, timing, and sensing applications.

Analog ICs emerged in the 1960s with the rise of monolithic integrated circuits. Early ICs were primarily for audio, instrumentation, and voltage regulation. Over the decades, ICs for oscillators, voltage references, filters, comparators, and power management have become ubiquitous in electronic systems.

The following are widely used analog IC types outside of operational amplifiers:

An inductor stores energy in a magnetic field created by current flowing through a coil. It resists changes in current, producing a voltage proportional to the rate of change.

Fundamental relationship:

Inductance is measured in henries (H). Practical values typically fall in:

• µH — RF and fast-switching converters
• mH — audio, filters, small power converters
• H — chokes and energy storage

Inductance is measured in henries (H). For practical inductors:

• 1 H = 1000 mH
• 1 mH = 1000 µH
• 1 µH = 0.001 mH = 0.000001 H

Calculate the inductance of an air-core coil:

• Diameter = 20 mm → radius r = 0.01 m
• Length = 20 mm → l = 0.02 m
• Turns N = 38

Calculation:

Area A = π × r² = π × 0.01² ≈ 3.1416×10⁻⁴ m²
L = μ₀ × N² × A / l = (4π×10⁻⁷) × 38² × 3.1416×10⁻⁴ / 0.02 ≈ 2.847×10⁻⁵ H
L ≈ 28.5 µH

Same coil, ferrite rod with μᵣ = 400:

Calculation:

L = μ₀ × μᵣ × N² × A / l = 2.847×10⁻⁵ × 400 ≈ 0.0114 H
L ≈ 11,400 µH

E-Core inductors use a ferrite E-shaped core to concentrate magnetic flux. Inductance depends on the number of turns, core cross-section, core length, permeability, and any air gap present. Adding a gap lowers the effective permeability and decreases inductance but increases linearity.

Formula: L = μ₀ × μᵣ × N² × A / l

Example: 38 turns, cross-section A = 32 mm², magnetic path length l = 48 mm, μᵣ = 2000

μ₀ = 4π × 10⁻⁷ H/m
μᵣ = 2000
N = 38
A = 32 × 10⁻⁶ m²
l = 0.048 m

L = (4π×10⁻⁷ × 2000 × 38² × 32×10⁻⁶) / 0.048
L ≈ 0.00242 H
L ≈ 2420 µH
      

Formula (air gap dominates): L = μ₀ × N² × A / g

Example: 38 turns, same cross-section A = 32 mm², air gap g = 0.5 mm = 0.0005 m

μ₀ = 4π × 10⁻⁷ H/m
N = 38
A = 32 × 10⁻⁶ m²
g = 0.0005 m

L = (4π×10⁻⁷ × 38² × 32×10⁻⁶) / 0.0005
L ≈ 1.16 × 10⁻⁴ H
L ≈ 116 µH
      

Notice that introducing a small air gap drastically reduces the inductance compared to the ungapped core.

Understanding the relationships between units:

• 1 H (Henry) = 1000 mH (millihenry)
• 1 mH = 1000 µH (microhenry)
• 1 H = 1,000,000 µH

Example: 2.42 mH = 2420 µH

RF electronics deal with high-frequency alternating currents used for wireless communication. Components at these frequencies behave differently due to parasitic effects and the speed of light.

Encoding information into a carrier wave.

• AM: Amplitude Modulation.
• FM: Frequency Modulation.
• PM: Phase Modulation.

• Antennas: Transduce between EM waves and currents.
• Mixers: Combine frequencies to shift signals.
• Filters: Select specific frequency bands.

Electronic circuits require stable and predictable voltage. A power supply converts raw electrical energy into a usable form for microcontrollers, sensors, and actuators.

Simple, quiet, and produces very clean output by dissipating excess voltage as heat.

• Pros: Low noise, low cost, simple.
• Cons: Inefficient, requires heatsinks for large voltage drops.
• Example: 7805 (5V regulator).

Uses high-frequency switching and inductors to convert voltage with high efficiency.

• Buck: Steps voltage down.
• Boost: Steps voltage up.
• Buck-Boost: Can do both.