Calculate the volumetric power density generated in a dielectric material under an RF or microwave field.
Common: 13.56, 27.12, 915, 2450 MHz
Voltage gradient across the material
Relative permittivity of the material
Dissipation factor of the material
Calculation Results
Power Density (W/m³)–
Power Density (W/cm³)–
Loss Factor (ε")–
Understanding Dielectric Heating Physics
Dielectric heating (also known as RF heating or microwave heating) is a process in which a radio frequency (RF) alternating electric field heats a dielectric material. Unlike conventional heating which relies on conduction from the surface inward, dielectric heating generates heat volumetrically within the material itself. This occurs due to dipole rotation, where polar molecules align and rotate with the rapidly changing electric field, creating molecular friction and heat.
This calculator determines the Power Density ($P_d$), which represents the amount of heat energy generated per unit volume per second. This metric is crucial for engineers designing industrial dryers, plastic welders, and microwave processing equipment.
The Power Density Formula
The power dissipated per unit volume in a dielectric material is calculated using the following equation:
P = 2 · π · f · ε₀ · εᵣ' · tan(δ) · E²
Where:
P = Power density (Watts per cubic meter, W/m³)
f = Frequency of the applied field (Hertz, Hz)
ε₀ = Permittivity of free space ($8.854 \times 10^{-12}$ F/m)
εᵣ' = Dielectric constant (Relative permittivity)
tan(δ) = Loss tangent (Dissipation factor)
E = Electric field strength (Volts per meter, V/m)
Note: The product of the dielectric constant and the loss tangent ($\epsilon_r' \cdot \tan\delta$) is often referred to as the Dielectric Loss Factor ($\epsilon"$).
Key Parameters Explained
1. Frequency (f)
The frequency dictates how often the electric field polarity reverses. Higher frequencies (like 2450 MHz in microwaves) cause molecules to oscillate faster, generally generating more heat. Industrial applications often use specific ISM bands such as 13.56 MHz, 27.12 MHz, or 915 MHz.
2. Electric Field Strength (E)
The voltage gradient across the material is the most dominant factor because power density is proportional to the square of the electric field ($E^2$). Doubling the voltage across the material results in a four-fold increase in heating power. This is usually measured in Volts per centimeter (V/cm) in industrial settings.
3. Material Properties (Dielectric Constant & Loss Tangent)
Not all materials heat equally. Materials with a high loss tangent (like water or PVC) heat very efficiently. Materials with a very low loss tangent (like PTFE or polyethylene) are transparent to RF energy and do not heat up significantly. This property allows for selective heating, where wet areas dry out while dry areas stop heating.
Common Applications
RF Welding: Joining polar plastics like PVC using pressure and RF energy.
Industrial Drying: Drying textiles, ceramics, or food products evenly from the inside out.
Microwave Heating: Rapid heating of food or chemical reactions.
Wood Gluing: Curing adhesives in composite wood manufacturing.
How to Use This Calculator
To estimate the heating rate:
Enter the operating Frequency in MHz.
Enter the Electric Field Strength in V/cm (Voltage applied / distance between electrodes).
Input the material's Dielectric Constant.
Input the material's Loss Tangent.
The tool will output the power density in both Watts per cubic meter and Watts per cubic centimeter.
function calculateDielectricHeat() {
// 1. Get Input Values
var freqMHz = document.getElementById('dh_frequency').value;
var eFieldVcm = document.getElementById('dh_efield').value;
var dielectricConst = document.getElementById('dh_dielectric_constant').value;
var lossTangent = document.getElementById('dh_loss_tangent').value;
// 2. Validate Inputs
if (freqMHz === "" || eFieldVcm === "" || dielectricConst === "" || lossTangent === "") {
alert("Please fill in all fields to calculate power density.");
return;
}
// Convert strings to numbers
var f_mhz = parseFloat(freqMHz);
var E_vcm = parseFloat(eFieldVcm);
var eps_r = parseFloat(dielectricConst);
var tan_delta = parseFloat(lossTangent);
if (isNaN(f_mhz) || isNaN(E_vcm) || isNaN(eps_r) || isNaN(tan_delta)) {
alert("Please enter valid numerical values.");
return;
}
if (f_mhz <= 0 || E_vcm < 0 || eps_r <= 0 || tan_delta < 0) {
alert("Values must be positive numbers.");
return;
}
// 3. Define Constants and Convert Units for Physics Formula
// Formula: P = 2 * pi * f * eps_0 * eps_r * tan_delta * E^2
// Convert Frequency to Hz
var f_hz = f_mhz * 1000000;
// Convert E-Field from V/cm to V/m
// 1 V/cm = 100 V/m
var E_vm = E_vcm * 100;
// Permittivity of free space (F/m)
var eps_0 = 8.854187817e-12;
// Calculate Loss Factor (eps_double_prime)
var loss_factor = eps_r * tan_delta;
// 4. Calculate Power Density (Watts per cubic meter)
// P = 2 * π * f * ε₀ * ε" * E²
var powerDensityWm3 = 2 * Math.PI * f_hz * eps_0 * loss_factor * Math.pow(E_vm, 2);
// Convert to Watts per cubic centimeter (W/cm³)
// 1 m³ = 1,000,000 cm³
var powerDensityWcm3 = powerDensityWm3 / 1000000;
// 5. Display Results
var resultDiv = document.getElementById('dh_results');
resultDiv.style.display = 'block';
// Formatting numbers with commas and fixed decimals
document.getElementById('res_pd_m3').innerHTML = powerDensityWm3.toLocaleString(undefined, {
minimumFractionDigits: 2,
maximumFractionDigits: 2
});
// For W/cm³, we might need more precision if value is small
document.getElementById('res_pd_cm3').innerHTML = powerDensityWcm3.toLocaleString(undefined, {
minimumFractionDigits: 4,
maximumFractionDigits: 6
});
document.getElementById('res_loss_factor').innerHTML = loss_factor.toFixed(4);
}