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C = ε₀ × εᵣ × A / d
Where:
| Material | Dielectric Constant (εᵣ) |
|---|---|
| Vacuum/Air | 1 |
| Teflon (PTFE) | 2.1 |
| Polyethylene | 2.3 |
| Paper | 3.5 |
| Glass | 7.5 |
| Mica | 6 |
| Ceramic (X7R) | 2500 |
| Ceramic (Y5V) | 14000 |
Parallel plate capacitance describes the ability of two conductive plates separated by a dielectric material to store electrical energy. The capacitance is determined by the formula C = ε₀ × εr × A / d, where ε₀ is the permittivity of free space (8.854 × 10¹² F/m), εr is the relative permittivity (dielectric constant) of the material between the plates, A is the overlapping area of the plates, and d is the separation distance between them. This fundamental model applies to all capacitor types, from tiny MLCC surface-mount components to large power factor correction capacitors. Increasing the plate area or dielectric constant raises capacitance, while increasing the separation lowers it.
Determine the overlapping area of the two parallel plates in square meters. For rectangular plates, multiply length by width. For circular plates, use A = πr². Only the area where both plates overlap contributes to capacitance.
Measure the distance between the two plates in meters. This is the thickness of the dielectric material. Smaller separation yields higher capacitance, but the dielectric must withstand the applied voltage without breakdown.
Look up the relative permittivity (εr) of the material between the plates. Common values range from 1 for air/vacuum to over 10,000 for high-K ceramics. The dielectric constant multiplies the base capacitance of an air-gap capacitor.
Compute C = (8.854 × 10¹²) × εr × A / d. Ensure all units are in SI (meters, farads). For multi-layer capacitors, multiply by the number of active layers (n − 1, where n is the total number of plates).
Every commercial capacitor is designed using parallel plate principles. Multi-layer ceramic capacitors (MLCCs) stack hundreds of thin plates to maximize capacitance in a small volume. Understanding this relationship guides engineers in selecting dielectric materials and optimizing dimensions.
Capacitive sensors use changes in plate area, separation, or dielectric to detect position, proximity, humidity, and pressure. Touchscreens, level sensors, and accelerometers all rely on measuring tiny capacitance changes based on the parallel plate model.
Parasitic capacitance between PCB traces and ground planes follows the parallel plate formula. Understanding this helps designers minimize unwanted coupling in high-speed digital circuits or intentionally create embedded capacitance in power planes.
| Material | εr (Dielectric Constant) | Breakdown (kV/mm) | Common Use |
|---|---|---|---|
| Vacuum / Air | 1.0 | 3 | Variable capacitors, tuning |
| Teflon (PTFE) | 2.1 | 60 | High-frequency, precision |
| Polypropylene | 2.2 | 50 | Film capacitors, audio |
| Polyester (Mylar) | 3.3 | 40 | General-purpose film caps |
| Paper | 3.5 | 16 | Legacy capacitors |
| Mica | 5 – 7 | 118 | RF, precision timing |
| Glass | 4 – 10 | 30 | High-reliability, military |
| Aluminum Oxide | 8.5 | 13 | Electrolytic capacitors |
| Tantalum Pentoxide | 26 | 10 | Tantalum capacitors |
| Ceramic (X7R) | 2,000 – 4,000 | 12 | MLCC decoupling, bypass |
| Ceramic (Y5V) | 10,000 – 15,000 | 10 | Bulk MLCC, non-critical |
The dielectric constant (εr) directly multiplies the capacitance of an equivalent air-gap capacitor. A material with εr = 10 produces 10 times more capacitance than air for the same plate area and separation. This is why high-K ceramics enable extremely high capacitance values in tiny packages.
The basic parallel plate formula assumes a uniform electric field between the plates, which is valid when the plate dimensions are much larger than the separation distance. Near the edges, the field "fringes" outward, adding a small amount of extra capacitance. For most practical capacitors where d is much less than A, fringe effects contribute less than 1–2%.
Multi-layer ceramic capacitors (MLCCs) stack many thin dielectric layers with alternating electrode plates. Each pair of adjacent plates acts as a parallel plate capacitor, and all pairs are connected in parallel. A 100-layer MLCC effectively has 99 parallel capacitors in one tiny package, multiplying the capacitance by 99 times.
The dielectric thickness is limited by its breakdown voltage. Each material has a maximum electric field strength (measured in kV/mm) it can withstand before conducting. A thinner dielectric gives more capacitance but reduces the maximum operating voltage. Modern MLCCs use dielectric layers as thin as 0.5 μm for low-voltage applications.
Yes, temperature changes the dielectric constant of most materials. Class 1 ceramics (C0G/NP0) have near-zero temperature coefficients, making them ideal for precision applications. Class 2 ceramics (X7R) can vary up to ±15%, and Class 3 (Y5V) can change by ±80% over their rated temperature range.
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