Lumped-Element (LC) Directional Coupler Calculator

A directional coupler built from inductors and capacitors is far smaller than a λ/4 coupled line, which makes it a good fit for transmit power detection, ALC feedback and signal sampling below a few GHz. Enter the coupling factor, impedance and center frequency to get L, C and the coupling capacitor Cc.

Coupling Cf ≤ −15 dB4 ports: input / output / coupled / isolatedInductors in nH · capacitors in pFNarrowband power sampling

① Input parameters

Coupling factor CfdB Impedance ZoΩ Center frequency foMHz

Coupling is entered as a negative dB value (−20 dB couples about 1% of the power). The equations assume weak coupling; values above −15 dB are automatically changed to −15 dB.

② Results

Part	Description	Value
L	Series inductor, main and coupled line (2 each)	nH
C	Shunt capacitor at the midpoint (1 each)	pF
Cc	Coupling capacitor between the lines (2)	pF

Schematic

The main line (top) and coupled line (bottom) are identical. Blue = inductor, green = shunt capacitor, orange = coupling capacitor, gray = ground. All four ports see Zo.

Power split

How to use

Enter the coupling factor Cf in dB (negative, ≤ −15 dB), for example −20 dB.
Enter the system impedance Zo (normally 50 Ω) and the center frequency fo in MHz.
Press Calculate to get inductor L, shunt capacitor C and coupling capacitor Cc.
Fit four L, two C and two Cc as shown; connect the detector to the coupled port and terminate the isolated port with Zo.

Theory and formulas

On each line, two series inductors and a shunt capacitor at the midpoint behave as an artificial transmission line of impedance Zo. Small capacitors Cc between the line ends provide weak coupling: part of the main-line power appears at the coupled port while the contributions cancel at the isolated port.

ω = 2π · f_o
L = Z_o / ω
C = 1 / (ω · Z_o)
Cc = 10^{(Cf / 20)} · C

Coupling factor versus power: P_coupled / P_in = 10^Cf/10; −20 dB ≈ 1%, −30 dB ≈ 0.1%.

Design tips

A lumped coupler is narrowband. Directivity (isolation) is very sensitive to tolerance, so use matched, tight-tolerance (±2% or better) inductors and Cc from the same batch.
Cc is often only a fraction of a pF, so pad and trace parasitics are significant. Start with about 70–80% of the calculated value and fine-tune while measuring S31 and S41 on a network analyzer.
Choose high-Q RF inductors whose self-resonant frequency is well above fo, and connect parts with 50 Ω microstrip (see the microstrip calculator).
For an unequal power split, use the unequal-split Wilkinson divider.

FAQ

Why is the coupling limited to −15 dB or weaker?: The equations use a weak-coupling approximation: when Cc is much smaller than C, the main-line impedance is barely disturbed. Stronger coupling increases the mismatch and needs a full coupler synthesis.
What do I do with the isolated port?: Terminate it with a resistor equal to Zo (for example 50 Ω) to ground to keep the directivity. To measure reflected power as well, connect a second detector there.
How high in frequency can it be used?: Component self-resonance and parasitics limit lumped designs to roughly a few hundred MHz up to about 1–2 GHz. At higher frequencies a microstrip coupled-line coupler is preferred.

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