emccalc-core

A clean, zero-dependency JavaScript/TypeScript library for core Electromagnetic Compatibility (EMC) and Radio Frequency (RF) mathematical calculations.

🚀 This core engine powers the live web tools hosted at EMCCalc (emccalc.com).

Language: English | 简体中文

Features

• 7 Core Conversion Matrices: Seamlessly convert between all units for RF 50Ω System, Voltage, Current, Power, H-Field (Magnetic Field), Capacitance, and B-Field (Magnetic Flux Density).
• Wavelength & Resonance Calculators: Convert frequencies to wavelengths and calculate dipole/monopole resonance lengths.
• Antenna Factor Calculations: Convert electric field strengths based on receiver readings and antenna factors.
• Distance Extrapolation: Extrapolate electric field strengths at different testing distances (e.g., 3m to 10m).
• VSWR & Return Loss Matrix: Convert between VSWR, Return Loss, Reflection Coefficient, and Mismatch Loss.

Technical Reference: Mathematical Derivations

This library implements industry-standard formulas. Even if you are not using this package directly, you can use this section as a reference for your daily engineering calculations.

1. Decibel & Linear Conversions (Voltage, Current, Power & 50Ω System)

These are the standard formulas used for signal parameter conversions across different physical quantities:

A. RF 50Ω System (Power, Voltage & Current Link)

In a standard $50\ \Omega$ RF system, Power ($dBm$), Voltage ($dB\mu V$), and Current ($dB\mu A$) are directly related:

• $dB\mu V$ to $dBm$: $$dBm = dB\mu V - 107$$
• $dB\mu A$ to $dBm$: $$dBm = dB\mu A - 73$$
• $dB\mu A$ to $dB\mu V$: $$dB\mu V = dB\mu A + 34\ \ (\text{since } R = 50\ \Omega \Rightarrow 20\log_{10}(50) \approx 34\ dB)$$

B. Voltage

• $dB\mu V$ to $mV$: $$mV = 10^{\frac{dB\mu V - 60}{20}}\ \ \Longleftrightarrow\ \ dB\mu V = 20\log_{10}(mV) + 60$$
• $dBV$ to $V$: $$V = 10^{\frac{dBV}{20}}\ \ \Longleftrightarrow\ \ dBV = 20\log_{10}(V)$$
• $dBmV$ to $dB\mu V$: $$dB\mu V = dBmV + 60\ \ \Longleftrightarrow\ \ dBmV = dB\mu V - 60$$
• $\mu V$ to $dB\mu V$: $$dB\mu V = 20\log_{10}(\mu V)\ \ \Longleftrightarrow\ \ \mu V = 10^{\frac{dB\mu V}{20}}$$

C. Electric Current

• $dB\mu A$ to $mA$: $$mA = 10^{\frac{dB\mu A - 60}{20}}\ \ \Longleftrightarrow\ \ dB\mu A = 20\log_{10}(mA) + 60$$
• $mA$ to $dBmA$: $$dBmA = 20\log_{10}(mA)\ \ \Longleftrightarrow\ \ mA = 10^{\frac{dBmA}{20}}$$
• $\mu A$ to $dB\mu A$: $$dB\mu A = 20\log_{10}(\mu A)\ \ \Longleftrightarrow\ \ \mu A = 10^{\frac{dB\mu A}{20}}$$

D. Power

• $dBm$ to $mW$: $$mW = 10^{\frac{dBm}{10}}\ \ \Longleftrightarrow\ \ dBm = 10\log_{10}(mW)$$
• $W$ to $dBW$: $$dBW = 10\log_{10}(W)\ \ \Longleftrightarrow\ \ W = 10^{\frac{dBW}{10}}$$
• $\mu W$ to $dB\mu W$: $$dB\mu W = 10\log_{10}(\mu W)\ \ \Longleftrightarrow\ \ \mu W = 10^{\frac{dB\mu W}{10}}$$

2. Wavelength & Frequency Conversion

Electromagnetic wave propagation in free space or dielectric media follows: $$f \cdot \lambda = v = c \cdot VF$$

Where:

• $c \approx 299,792,458\ m/s$ (Speed of light in vacuum)
• $f$ is the frequency in Hertz ($Hz$)
• $\lambda$ is the wavelength in meters ($m$)
• $VF$ is the Velocity Factor of the medium ($0.01 \le VF \le 1.0$, $1.0$ in vacuum/free space)

Formulas (Frequency in $MHz$):

• Wavelength ($\lambda$): $$\lambda\ (m) = \frac{299.792458 \times VF}{f\ (MHz)}$$
• Dipole Antenna Length (1/2 Wave Resonance): $$L_{1/2}\ (m) = \frac{\lambda}{2} \approx \frac{150 \times VF}{f\ (MHz)}$$
• Monopole Antenna Length (1/4 Wave Resonance): $$L_{1/4}\ (m) = \frac{\lambda}{4} \approx \frac{75 \times VF}{f\ (MHz)}$$
• Max Shielding Aperture Leakage Size (1/20 Wave Limit): $$L_{leakage}\ (m) = \frac{\lambda}{20}$$

3. Antenna Factor & Field Strength Conversion

Antenna Factor ($AF$, in $dB/m$) is the ratio of the incident electric field strength ($E$, in $V/m$) to the voltage at the antenna terminals ($V_{rec}$, in $V$): $$AF = \frac{E}{V_{rec}}$$

In decibel units (standard receiver readings of $dB\mu V$): $$E\ (dB\mu V/m) = V_{rec}\ (dB\mu V) + AF\ (dB/m)$$

Convert to Linear Units ($V/m$):

$$E\ (V/m) = 10^{\frac{E\ (dB\mu V/m) - 120}{20}}$$

4. Field Strength Distance Extrapolation

When testing electromagnetic fields at different distances (e.g., standard limit translations between $3\ m$ and $10\ m$), we assume far-field free-space attenuation following the inverse-distance law ($20\ dB$ per decade): $$\frac{E_2}{E_1} = \frac{d_1}{d_2}$$

In decibels: $$E_2\ (dB\mu V/m) = E_1\ (dB\mu V/m) - 20 \log_{10}\left(\frac{d_2}{d_1}\right)$$

5. VSWR & Return Loss Matrix

Mismatch parameters describe how much RF energy is reflected back from a load (like an antenna or transmission line interface):

• Reflection Coefficient ($\Gamma$): $$\Gamma = \frac{VSWR - 1}{VSWR + 1}$$
• Return Loss ($RL$, in $dB$): $$RL = -20 \log_{10}(|\Gamma|)$$
• Mismatch Loss ($ML$, in $dB$): $$ML = -10 \log_{10}(1 - |\Gamma|^2)$$

6. Electromagnetic Field (E-Field & H-Field) Conversions

In the far-field region of free space, the ratio of the Electric Field ($E$, in $V/m$) to the Magnetic Field ($H$, in $A/m$) is constant and equal to the wave impedance of free space ($Z_0 \approx 120\pi \approx 377\ \Omega$): $$E = H \cdot Z_0 \approx H \cdot 377$$

In decibels: $$E\ (dB\mu V/m) = H\ (dB\mu A/m) + 20 \log_{10}(377) \approx H\ (dB\mu A/m) + 51.5$$

7. Magnetic Field (H-Field) to Magnetic Flux Density (B-Field)

In non-magnetic media (like air or vacuum), the Magnetic Flux Density ($B$, in Tesla) and Magnetic Field Strength ($H$, in $A/m$) are related by the permeability of free space ($\mu_0 = 4\pi \times 10^{-7}\ H/m$): $$B = \mu_0 \cdot H$$

Conversion to Decibel Units:

• To $dBpT$ (picoTesla, $1\ pT = 10^{-12}\ T$): $$B(dBpT) = H(dB\mu A/m) + 20 \log_{10}\left(4\pi \times 10^{-7} \times 10^{12}\right) - 120 = H(dB\mu A/m) + 1.9842 \approx H(dB\mu A/m) + 2$$ Hence: $$dBpT \approx dB\mu A/m + 2$$

• To $dB\mu T$ (microTesla, $1\ \mu T = 10^{-6}\ T$): $$dB\mu T \approx dB\mu A/m - 118$$

8. Magnetic Field Strength (H-Field) Decibel Conversions

Magnetic Field Strength $H$ is measured in Amperes per meter ($A/m$) in linear scale, and decibels microamperes per meter ($dB\mu A/m$) in logarithmic scale (referenced to $1\ \mu A/m = 10^{-6}\ A/m$):

• $A/m$ to $dB\mu A/m$: $$H(dB\mu A/m) = 20 \log_{10}\left(\frac{H(A/m)}{10^{-6}}\right) = 20 \log_{10}(H(A/m)) + 120$$ $$\Longleftrightarrow\ \ H(A/m) = 10^{\frac{H(dB\mu A/m) - 120}{20}}$$
• $dBmA/m$ to $dB\mu A/m$: $$H(dB\mu A/m) = H(dBmA/m) + 60$$
• $dB A/m$ to $dB\mu A/m$: $$H(dB\mu A/m) = H(dB A/m) + 120$$

9. Capacitance Unit Scale

Capacitance $C$ uses standard metric prefixes relative to the Farad ($F$). The conversions are purely linear:

• Millifarad ($mF$): $1\ mF = 10^{-3}\ F$
• Microfarad ($\mu F$): $1\ \mu F = 10^{-6}\ F$
• Nanofarad ($nF$): $1\ nF = 10^{-9}\ F$
• Picofarad ($pF$): $1\ pF = 10^{-12}\ F$
• Femtofarad ($fF$): $1\ fF = 10^{-15}\ F$

Installation

npm install emccalc-core

Usage

1. RF 50Ω System Conversion

import { convertRF50 } from 'emccalc-core';

// Convert 120 dBµV receiver reading under 50Ω to other units
const result = convertRF50(120, 'dbuv');

console.log(result);
/*
Output:
{
  dbm: 13,
  mw: 19.9526,
  dbuv: 120,
  mv: 1000,
  dbua: 86,
  ma: 20
}
*/

2. VSWR Conversion

import { calculateFromVswr } from 'emccalc-core';

// Convert a VSWR of 1.5 to return loss and mismatch loss
const mismatch = calculateFromVswr(1.5);
console.log(mismatch);
/*
Output:
{
  vswr: 1.5,
  returnLossDb: 13.9794,
  reflectionCoefficient: 0.2,
  mismatchLossDb: 0.177288
}
*/

Documentation

For interactive tools, standard limit databases (CISPR 25, EN 55032, ECE R10), and complete formula explanations, please visit the official web app:

• 🌐 EMCCalc - Online EMC Calculators (English)
• 🌐 EMCCalc - 中文电磁兼容单位换算速查网

License

This project is licensed under the MIT License.