Introduction to Electronics Engineering: Capacitors Study Guide

Core Fundamentals of Capacitors

• Basic Definition: A capacitor is a passive electronic component consisting of an insulating layer (known as the dielectric) placed between two conductive plates.

• Capacitance ($C$): The ability or capacity of a component to accumulate and store electric charge ($Q$).

• SI Unit: The fundamental unit of capacitance is the Farad ($F$).

• Common Sub-Units:

  • Microfarad ($\mu F$ or $mF$): $10^{-6}\,F$

  • Nanofarad ($nF$): $10^{-9}\,F$

  • Picofarad ($pF$): $10^{-12}\,F$

• Schematic Symbols:

  • EU Style (Standard Non-Polarized): Displayed as two equal, parallel straight line segments.

  • US Style (Standard Non-Polarized): Displayed as one straight vertical plate and one curved vertical plate.

  • Polarized Capacitor: Denoted with explicit positive ($+$) marking on the positive plate.

  • Variable Capacitor: Standard capacitor symbol overlaid with a diagonal arrow pointing upward and to the right.

Physical Construction and Charging Dynamics

• Physical Layer Structure:

  • Plate 1: First conductive plate.

  • Plate 2: Second conductive plate.

  • Dielectric Material: An insulating layer positioned directly between Plate 1 and Plate 2.

  • Current Flow Restriction: Because the dielectric material is a non-conductive insulator, no direct electric current flows through the interior of the capacitor.

• Mechanism of Capacitor Charging:

  • When connected to a direct current ($DC$) voltage source $V_C$, the negative terminal repels free electrons in the conductor toward Plate A, while the positive terminal attracts free electrons away from Plate B.

  • Because the insulating dielectric prevents electron conduction across the central gap, electrons accumulate on Plate A (making it negatively charged with $-Q$) and leave Plate B electron-deficient (making it positively charged with $+Q$).

  • This charge accumulation creates a potential difference (voltage) across the two plates.

  • Charging continues until the potential difference across the capacitor equals the supply voltage ($V_C$).

• Sequential Stages of Charging and Discharging:

  1. Uncharged State: Switch $S$ is open; no potential difference across plates A and B ($0\,V$).

  2. Charging Phase: Switch $S$ is closed; a $10\,V$ battery induces electron flow, charging Plate A negative and Plate B positive until the voltage across the capacitor reaches $10\,V$.

  3. Charge Retention: When disconnected from the battery, the accumulated electrostatic charges remain stored on the plates, maintaining the full $10\,V$ output potential without requiring an active external power source.

  4. Discharging Phase: Shorting the capacitor terminals creates a return path, causing accumulated electrons on Plate A to flow back to Plate B until both plates return to electrical neutrality ($0\,V$).

Functional Characteristics and Operational Parameters

• Voltage and Charge Relationship: Increasing the applied voltage proportionally increases the total quantity of charge accumulated on the conductive plates.

• Electric Field Generation: Accumulation of charges on the opposing plates creates an electrostatic electric field spanning through the dielectric medium.

• Maximum Voltage Rating and Dielectric Breakdown:

  • Every physical capacitor has a maximum rated operating voltage explicitly marked on its body.

  • Exceeding this voltage threshold forces dielectric breakdown, transforming the insulator into a conductor and resulting in permanent component damage.

• Filtering Characteristics: Capacitors block Direct Current ($DC$) while allowing Alternating Current ($AC$) to pass, making them essential elements in electronic filtering circuits.

• Primary Design Specifications: Any capacitor is fundamentally specified by:

  1. Its capacitance value ($C$).

  2. Its maximum operating voltage rating ($V_{max}$).

Key Mathematical Equations and Relationships

• Capacitance of a Parallel Plate Capacitor:     \n    C = \frac{\epsilon A}{d}\n         or     \n    C = \frac{\epsilon_r \epsilon_0 A}{d}\n    

  • $C$ = Capacitance in Farads ($F$)

  • $A$ = Surface area of one plate

  • $d$ = Separation distance between conductive plates

  • $\epsilon$ = Absolute permittivity of dielectric material

  • $\epsilon_0$ = Permittivity of free space ($8.854 \times 10^{-12}\,F\,m^{-1}$)

  • $\epsilon_r$ = Relative permittivity (dielectric constant)

• Stored Electric Charge:     \n    Q = C \times V\n    

  • $Q$ = Accumulated charge in Coulombs ($C_{oulomb}$)

  • $C$ = Capacitance in Farads ($F$)

  • $V$ = Voltage across capacitor terminals in Volts ($V$)

• Capacitive Reactance ($X_C$):     \n    X_C = \frac{1}{2 \pi f C}\n    

  • $X_C$ = Opposing force to AC current flow in Ohms ($\Omega$)

  • $f$ = Frequency of the AC signal in Hertz ($Hz$)

  • $C$ = Capacitance in Farads ($F$)

Classification and Types of Fixed Capacitors

Fixed capacitors are categorized based on the specific dielectric material utilized in their construction.

Mica Capacitors

• Construction: Stacked sheets of mica dielectric layered between tin-foil plates. Alternate tin-foil strips connect together to form one terminal plate, and the remaining strips connect to form the opposite terminal.

• Capacitance Range: Small values ranging from $10\,pF$ to $5000\,pF$

• Voltage Rating: High voltage capabilities ranging from $500\,V$ to $20\,kV$

Paper Capacitors

• Construction: Two long rolls of tin foil serving as conductive plates, separated by a thin paper dielectric sheet, rolled tightly into a compact cylinder with leads connected to each foil roll.

• Capacitance Range: Medium values ranging from $0.001\,\mu F$ to $1.0\,\mu F$

• Voltage Rating: Range from $200\,V$ to $1600\,V$

Film Capacitors

• Construction: Similar to paper capacitors, but replacing paper with a thin plastic film dielectric.

• Sub-Classifications:

  • Foil Type: Employs physical sheets of metal foil (aluminum or tin) as conductive plates.

  • Metalized Type: Formed by vacuum-spraying a thin layer of metal (aluminum or zinc) directly onto the plastic film. Metalized types are significantly smaller than foil types.

• Physical Formats: Available in box-type and cylindrical molded enclosures.

• Capacitance Range: $100\,pF$ to $100\,\mu F$

• Voltage Rating: $50\,V$ to $600\,V$

Ceramic Capacitors

• Construction: Utilizes ceramic material as the dielectric with thin metal films deposited onto it as plates.

• Disk Type: Silver film is deposited on opposite faces of a ceramic disk.

• Tubular Type: Offered in cylindrical ceramic tubes ranging from $0.5\,pF$ to $1600\,pF$

• Overall Capacitance Range: $1\,pF$ (or lower) up to $1\,\mu F$

• Voltage Rating: High voltage capability from $500\,V$ to $20\,kV$

Electrolytic Capacitors

• Polarity: Polarized components requiring strict adherence to positive ($+$) and negative ($-$-) terminal markings during circuit installation.

• Sub-type 1: Aluminum Electrolytic Capacitor:

  • Anode ($+$): Formed by an aluminum foil.

  • Dielectric: A thin aluminum oxide layer ($Al_2O_3$) grown on the anode surface.

  • Cathode ($-$-): Paper soaked in a liquid electrolyte solution, backed by a secondary cathode aluminum foil lead connection.

  • Packaging: Foils are tightly rolled into a compact cylindrical cartridge housed inside an aluminum can with the negative side clearly marked.

  • Capacitance Range: $1\,\mu F$ to $6800\,\mu F$

  • Voltage Rating: $10\,V$ to $450\,V$

• Sub-type 2: Tantalum Capacitors:

  • Anode ($+$): Formed from pure tantalum metal covered with a thin oxide dielectric film. Positive terminal is explicitly marked.

  • Cathode Types:

    • Solid Tantalum: Dipped in chemical solutions and baked to form a manganese dioxide ($MnO_2$) cathode layer.

    • Wet Tantalum: Uses a liquid electrolyte filled within its outer protective casing.

  • Key Advantage: Offers a substantially larger capacitance ($C$) per unit physical volume compared to aluminum types.

  • Capacitance Range: $0.047\,\mu F$ to $330\,\mu F$

  • Voltage Rating: $6\,V$ to $50\,V$

Variable Capacitors

• Air Capacitors (Ganged Capacitors):

  • Construction: Formed from two intermeshed sets of semi-circular metal plates using ambient air in the gap space as the dielectric.

  • Stator: Stationary assembly of parallel metal plates connected together.

  • Rotor: Movable assembly of parallel metal plates connected to a rotating central control shaft.

  • Operation: Turning the central shaft changes the total overlapping area between the rotor and stator plates.

  • Maximum Capacitance: Achieved when the overlapping physical plate area between stator and rotor is maximized.

  • Capacitance Range: $10\,pF$ to $400\,pF$

  • Voltage Rating: $400\,V$ (at an air gap distance of $0.02\,\text{inches}$)

Decoding Capacitance Values and Identification Schemes

Scheme 1: Direct Value Printing

• For physically large capacitors, capacitance and maximum operating voltage ratings are printed directly onto the outer casing (e.g., $6800\,\mu F$, $50\,V$).

• Units indicated directly: mF or uF ($\mu F$), pF ($pF$), V ($V$), kV ($kV$).

Scheme 2: Numerical Digit Codes (2 or 3 Digits)

• Two Whole Digits: Read value directly in picofarads ($pF$). Example: 47 = $47\,pF$

• Three Whole Digits:

  • 1st Digit = First significant digit

  • 2nd Digit = Second significant digit

  • 3rd Digit = Multiplier ($10^n$ where $n$ is the 3rd digit), evaluated in picofarads ($pF$)

• Multiplier Value Lookup Table:

  • 0 = $\times 1$

  • 1 = $\times 10$

  • 2 = $\times 100$

  • 3 = $\times 1000$

  • 4 = $\times 10,000$

  • 5 = $\times 100,000$

  • 6, 7 = Not used

  • 8 = $\times 0.01$

  • 9 = $\times 0.1$

• Decimal Numbers: Values written with decimal points are read directly in microfarads ($\mu F$). Example: 0.0033 = $0.0033\,\mu F$

Scheme 3: Tolerance Letter Markings

When numbers are followed by an alphabetic letter, the letter specifies the component tolerance rating:

• A: $\pm 0.05\,pF$

• B: $\pm 0.1\,pF$

• C: $\pm 0.25\,pF$

• D: $\pm 0.5\,pF$

• E: $\pm 0.5\%$

• F: $\pm 1\%$

• G: $\pm 2\%$

• H: $\pm 3\%$

• J: $\pm 5\%$

• K: $\pm 10\%$

• L: $\pm 15\%$

• M: $\pm 20\%$

• N: $\pm 30\%$

• P: $-0\%, +100\%$

• S: $-20\%, +50\%$

• W: $-0\%, +200\%$

• X: $-20\%, +40\%$

• Z: $-20\%, +80\%$

Note: If no tolerance letter is specified on the body, standard baseline tolerance Z ($-20\%, +80\%$) is assumed.

Scheme 4: Embedded Alphabetical Characters

• Letter R Placement: Replaces the decimal point for picofarad values. Example: 4R1 represents $4.1\,pF$.

• Letters p, n, u Placement: Specifies both unit prefix (p = picofarad, n = nanofarad, u = microfarad) and decimal location.

  • n61 = $0.61\,nF$

  • 5u2 = $5.2\,\mu F$

• Combined Voltage and Capacitance Code (e.g. 1A253):

  • Prefix 1A indicates maximum operating voltage rating.

  • Suffix 253 indicates capacitance ($25 \times 10^3\,pF = 25,000\,pF = 25\,nF$).

• Voltage Letter Codes:

  • 1H = $50\,V$

  • 2A = $100\,V$

  • 2T = $150\,V$

  • 2D = $200\,V$

  • 2E = $250\,V$

  • 2G = $400\,V$

  • 2J = $630\,V$

Worked Numerical Code Calculations

• Problem 1: Calculate parameters for marking 472M

  • Capacitance: $47 \times 10^2\,pF = 4700\,pF$

  • Tolerance: M = $\pm 20\%$

  • Capacitance Range: $4700\,pF \pm 20\%$ ($3760\,pF$ to $5640\,pF$

• Problem 2: Calculate parameters for marking 0.0033Z

  • Capacitance: $0.0033\,\mu F$

  • Tolerance: Z = $-20\%, +80\%$

  • Capacitance Range: $0.0033\,\mu F - 20\%$ to $0.0033\,\mu F + 80\%$ ($0.00264\,\mu F$ to $0.00594\,\mu F$

• Problem 3: Calculate parameters for marking 189K

  • Capacitance: 3rd digit 9 multiplier is $0.1 \rightarrow 18 \times 0.1\,pF = 1.8\,pF$

  • Tolerance: K = $\pm 10\%$

  • Capacitance Range: $1.8\,pF \pm 10\%$ ($1.62\,pF$ to $1.98\,pF$

Capacitor Color Coding Schemes

E.I.A. Color Code Chart (Values in MMF / pF)

Molded Mica Capacitors (6-Dot Color Code)

• First Dot Requirement: The top-left dot is ALWAYS white, identifying the component as a molded mica capacitor.

• Reading Direction: Indicated by an arrow stamped on the body or standard reading layout:

  • Top row (left-to-right): White identifier, 1st Digit (A), 2nd Digit (B).

  • Bottom row (right-to-left): Multiplier (C), Tolerance (D), Class (disregard).

5-Band Capacitor Color Code Format

• Band 1: 1st Digit (in $pF$)

• Band 2: 2nd Digit (in $pF$)

• Band 3: Multiplier

• Band 4: Tolerance

• Band 5: Operating Voltage Rating

• Examples:

  • Brown-Black-Orange-Black-Red: $10 \times 10^3\,pF = 10,000\,pF = 10\,nF$, $\pm 20\%$, $100\,V$

  • Yellow-Violet-Orange-White-Red: $47 \times 10^3\,pF = 47,000\,pF = 47\,nF$, $\pm 10\%$, $250\,V$