TOOL 04 / AT THE LOAD

VSWR & Impedance

See the reflection, the match and the power accepted by the load.

Load & reference

ONE REFERENCE PLANE

Known quantity

Real reference impedance Z₀ (Ω)

50 Ω and 75 Ω are common. Use any real, positive 1e-6–1e9 Ω value. All inputs refer to the same load plane and operating frequency.

Termination

Resistance R (Ω)

Reactance X (Ω)

Passive R ≥ 0. R and |X|: zero, or 1e-6–1e9 Ω. +X inductive; −X capacitive. A pure reactance accepts no net real power.

Forward power at the load plane

Forward travelling-wave power

Power unit

Average power: zero in linear units, or 1e-30–1e30 W. This is forward wave power at this plane, not the transmitter's available power.

Display precision

Dot decimals and scientific notation. Changing a unit reinterprets its value. Changing the known quantity loads an example for that mode.

Reflection & power

PASSIVE LOAD

VOLTAGE STANDING WAVE RATIO

—: 1

Reflection magnitude—|Γ| · voltage-wave ratio

Return loss—dB · larger means less reflection

Mismatch loss—dB · reduction in accepted power

Reflected power—% of forward power

Accepted power—% of forward power

Reference Z₀: —
Load ZL: —
Complex Γ · real / imaginary: — / j—
Γ phase (degrees): —

Power at the same reference plane; dBm reference is 1 mW
Power	W	dBm
Forward	—	—
Reflected	—	—
Delivered / accepted	—	—

Equations & assumptions

SHOW THE WORK

Complex impedance and scalar mismatch

ZL = R + jX · Z₀ real and positive

Γ = (ZL − Z₀) / (ZL + Z₀) · ρ = |Γ|

VSWR = (1 + ρ) / (1 − ρ)

Return loss = −20 log₁₀(ρ)

Mismatch loss = −10 log₁₀(1 − ρ²)

Complex mode calculates Γ with phase from R + jX. Scalar inputs determine ρ and power fractions; they cannot recover phase or a unique impedance, except at a perfect match. For example, both 25 Ω and 100 Ω in a 50 Ω system give 2:1 VSWR, with opposite Γ signs.

Return loss is positive here. A VNA log-magnitude S₁₁ reading is its negative. Return loss describes reflection; it is not insertion loss and must not be subtracted from forward dBm as a cable attenuation.

Travelling waves at one plane

P_reflected = P_forward × ρ²

P_delivered = P_forward × (1 − ρ²)

P_forward = P_reflected + P_delivered

P_delivered [dBm] = P_forward [dBm] − ML

Assumes sinusoidal steady state, a passive one-port (R ≥ 0), a real positive reference impedance and powers at the same reference plane. The equivalent VSWR is for a lossless line with this real characteristic impedance. Impedance must apply at the frequency of interest; this tool does not extrapolate it.

Delivered power is net real power accepted by the load. It says nothing about radiation efficiency, load heating distribution, source foldback, a lossy feeder or multiple source/load reflections. No source mismatch, complex Z₀, active negative resistance, matching network or cable interaction is modelled. Tool 03's matched insertion-loss estimates remain separate.

Fixed reference anchors · 50 Ω system

Load / case	\|Γ\|	VSWR	RL dB	ML dB	Reflected
50 + j0 Ω	0	1:1	∞	0	0%
100 + j0 Ω or 25 + j0 Ω	1/3	2:1	9.542425	0.511525	11.1111%
50 + j50 Ω	√0.2	2.618034:1	6.989700	0.969100	20%
20 dB return loss	0.1	1.222222:1	20	0.043648	1%
Open / short / pure reactance	1	∞:1	0	∞	100%

Boundaries, numerical limits & verification

At a match, Γ = 0 with undefined phase, VSWR = 1, RL = ∞ and ML = 0. At an open, Γ = +1; at a short, Γ = −1 (180°). Both have infinite VSWR, RL = 0 and ML = ∞. A pure reactance also reflects all real power but has its own Γ phase. An open is a distinct ideal limit, not an enormous finite R value.

Scalar VSWR: 1–1e15 or ∞. |Γ|: zero or 1e-30–1. Reflected power: zero or 1e-28–100%. RL and ML: zero or 1e-30–600 dB or ∞. Infinity is accepted only for VSWR and the two dB inputs. Numerical limits are inclusive and are not equipment ratings.

IEEE-754 double precision; display choices are 3, 6 or 9 significant figures, including losses and power levels. Both reflected and accepted fractions are retained to avoid cancellation near endpoints. Derived powers may reach 1e-90 W, beyond Tool 01's input range. A zero wave power displays −∞ dBm. No display rounding feeds back.

Invalid mismatch or reference inputs clear dependent results while keeping valid forward power. Invalid power keeps mismatch results usable. Inactive inputs are ignored; calculator inputs are not saved or uploaded by this app. Calculation checks cover reference values, units and numerical boundaries, with separate high-precision comparisons.

Primary references checked 24 October 2026: Keysight reflection measurements · Keysight Γ / impedance equation · Rohde & Schwarz 1GP77, §8, pp. 22–24. Reference links require internet; calculations run in your browser after the page loads.