RF Engineering Calculator Suite

Impedance Matching & Transformations

L-Network Matching

Calculate series/parallel reactive components for impedance matching.

Formulas:

Q = √(R_high / R_low − 1)
X_series = R_low × Q · X_parallel = R_high / Q

L = X/(2πf) · C = 1/(2πfX)

Frequency (MHz)

Source Zs (Ω) — Real / Imag

Load Zl (Ω) — Real / Imag

Result

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Impedance ↔ Component

Convert between reactance (Ω) and component values (pF, nH).

Formulas:

X_C = −1/(2πfC) → C = 1/(2πf|X|)
X_L = 2πfL → L = X/(2πf)

Frequency (MHz)

Impedance (Ω) — Real / Imag

Capacitance (pF)

Result

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Parallel & Series Impedance

Combine two complex impedances in series or parallel.

Formulas:

Z_series = Z1 + Z2
Z_parallel = (Z1 × Z2) / (Z1 + Z2)

Z1 (Ω) — Real / Imag

Z2 (Ω) — Real / Imag

Result

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Series → Parallel Equivalent

Convert series R+jX to parallel equivalent Rp ∥ Xp, compute Y=1/Z.

Formulas:

R_p = |Z|²/Rs = Rs(1+Q²)
X_p = |Z|²/Xs
Q = |Xs|/Rs · Y = 1/Z

Frequency (MHz)

Series Z (Ω) — Rs / Xs

Result

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Unit Conversions

dBµV ↔ µV

Convert between voltage in dBµV and linear µV/mV/V.

Formulas:

dBµV = 20 × log₁₀(V_µV)
V_µV = 10^(dBµV/20)
dBmV = dBµV − 60 · dBV = dBµV − 120

dBµV

µV

Result

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dBm ↔ dBµV (50Ω)

Convert power (dBm) and voltage (dBµV) in a 50Ω system. Key offset: 107 dB.

Formulas:

P[dBm] = V[dBµV] − 107
V[dBµV] = P[dBm] + 107

0 dBm = 1mW → V=√(0.001×50) = 223.6mV = 107.0 dBµV

Power (dBm)

Voltage (dBµV)

Result

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Impedance ↔ Admittance

Convert between Z (Ω) and Y (Siemens).

Formulas:

Y = 1/Z = (R − jX)/(R² + X²)
Z = 1/Y

Z (Ω) — Real / Imag

Y (S) — Real / Imag

Result

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Wavelength & Beta

Compute wavelength, quarter-wave, and propagation constant.

Formulas:

λ = c × VF / f
β = 2π / λ [rad/m]

c = 299 792 458 m/s

Frequency (MHz)

Velocity Factor (0–1)

Result

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Power Analysis & Efficiency

PAE — Power Added Efficiency

Drain efficiency and PAE from RF output and DC consumption.

Formulas:

η = P_out / P_DC × 100%
PAE = (P_out − P_in) / P_DC × 100%
P_DC = V × I · Gain = P_out − P_in [dB]

Output Power (dBm)

Supply Voltage (V)

Supply Current (mA)

Input Power (dBm)

Result

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dBm ↔ Watts

Convert between dBm and linear power.

Formulas:

P[mW] = 10^(P[dBm]/10)
P[dBm] = 10 × log₁₀(P[mW])

Power (dBm)

Power (mW)

Result

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EMC & Field Strength Conversions

E-Field → EIRP (source power)

From a measured E-field at distance d, compute the EIRP of the source. Looks backward toward the transmitter.

Linear:

EIRP[W] = E²[V/m] × 4π × d²[m] / η₀

dB equivalent:

EIRP[dBm] = 20·log₁₀(E[µV/m] × d[m]) − 104.77

Constant breakdown (−104.77 dB):
µV/m → V/m (×10⁻⁶): −120 dB
4π factor: +10.99 dB
÷ η₀ = 377 Ω: −25.76 dB
W → mW (×1000): +30 dB
Total: −120 + 10.99 − 25.76 + 30 = −104.77 dB

η₀ = 377 Ω (free-space impedance)

E (µV/m)

E (V/m)

E (dBµV/m)

Distance d (m)

Result

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E-Field → Received Power (at DUT)

Power received by a DUT antenna in a known E-field. Looks forward toward the receiver. Used for ETSI immunity analysis.

Linear:

Pr[W] = E²[V/m] × G × λ²[m] / (4π × η₀) = S × Ae (S = E²/η₀ | Ae = Gλ²/4π)

dB (via Antenna Factor):

Pr[dBm] = E[dBµV/m] − AF[dB/m] − 107

AF [dB]: −29.8 + 20·log₁₀(f[MHz]) − G[dBi]
AF [linear]: 9.73/(λ√G)
−107 dB: dBµV/m→V/m (−120) + V→P/Z₀ (+13) + W→mW (+30)

E (dBµV/m)

E (V/m)

E (µV/m)

E (dBµV/m)

Frequency (MHz)

Antenna Gain (dBi)

Result

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EIRP → E-Field at Distance

From a known EIRP, compute E-field at a given distance. Inverse of EIRP formula.

Formula:

E = √(EIRP × η₀ / (4π × d²))
E[µV/m] = E[V/m] × 10⁶

Inverse of EIRP = E²×4πd²/η₀

EIRP (dBm)

Distance (m)

Result

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Antenna Factor (AF)

Links E-field in air to voltage at antenna port (50Ω). Essential for EMC measurements.

Formulas:

AF = E / V [m⁻¹]
AF[dB/m] = −29.8 + 20×log₁₀(f[MHz]) − G[dBi]
Measurement: E[dBµV/m] = P[dBm] + 107 + AF + L_cable

+107 converts dBm → dBµV in 50Ω

Frequency (MHz)

Antenna Gain (dBi)

Result

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FCC Part 15.209 Compliance

Check measured field against FCC limits. Normalizes to 3m and computes EIRP.

Method:

1. Normalize: E_3m = E_meas × (d/3)
2. Compare to band limit (µV/m @ 3m)
3. EIRP = E²_3m × 4π×9 / 377
Limits @ 3m: 30–88→100 · 88–216→150 · 216–960→200 · 960+→500 µV/m (−41.2 dBm)

Frequency (MHz)

Measured Field (µV/m)

Measured Field (dBµV/m)

Distance (m)

Result

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ETSI Immunity (EN 61000-4-3)

Power at DUT antenna during radiated immunity test. Also shows chamber source EIRP needed.

Formulas:

S = E²/η₀ [W/m²] · Ae = Gλ²/(4π) [m²]
Pr = S × Ae
Chamber EIRP @ 3m: E²×4π×9/η₀

EN 300 220 (LoRa) references EN 61000-4-3 at 3 V/m

Test E-Field (V/m)

Frequency (MHz)

DUT Antenna Gain (dBi)

Result

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Free Space Path Loss (FSPL)

Signal attenuation between isotropic antennas in free space.

Formula:

FSPL = (4πd/λ)²
FSPL[dB] = 20×log₁₀(d[m]) + 20×log₁₀(f[MHz]) − 27.55

Or: 20×log₁₀(d[km]) + 20×log₁₀(f[MHz]) + 32.45

Frequency (MHz)

Distance (m)

Result

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Universal Field Unit Converter

Type in any field value — all others update live.

Relationships:

V/m ↔ µV/m: ×10⁶ / ÷10⁶
dBµV/m = 20×log₁₀(µV/m)
S[mW/m²] = E²[V/m] / 377 × 1000

E-Field (V/m)

E-Field (µV/m)

E-Field (dBµV/m)

Power Density S (mW/m²)

Circuit Analysis

LC Resonance

Compute resonant frequency, or find L/C for a target.

Formulas:

f₀ = 1 / (2π√(LC))
Z₀ = √(L/C)

L = 1/(4π²f²C) · C = 1/(4π²f²L)

Frequency (MHz)

Inductance (nH)

Capacitance (pF)

Result

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Delta ↔ Y Transformation

Convert between delta (Δ) and star (Y) networks.

Formulas:

Δ→Y: Z1 = Zb×Zc/(Za+Zb+Zc)
Y→Δ: Za = (Z1Z2+Z2Z3+Z3Z1)/Z1

Za (Ω)

Zb (Ω)

Zc (Ω)

Result

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