RFellow · operating reference

Understand the measurement. Use the right control.

Short, task-oriented explanations for the capabilities in RFellow today. Each topic states a working definition, the interpretation and the boundary of what the tool actually establishes.

Open RF workspace ↗17 focused topics · No RF file upload

01 · DATA IN

Touchstone import

An .s1p file describes one-port reflection; an .s2p file describes the four complex S-parameters of a two-port network at sampled frequencies.

RFellow workflow

Drop an .s1p or .s2p file or open the synthetic demo. RFellow reads the source locally and shows the actual file's reference impedance and sampled frequency range.

# MHz S MA R 50
900 0.10 30

Option-line meaning: frequency in MHz; S-data; magnitude/angle pairs; reference impedance 50 Ω. RI and DB are alternate complex-data formats. Unsupported/invalid variants must be rejected rather than guessed.

Do not infer The file does not prove that a VNA was calibrated, that the fixture was de-embedded, or that a source is trustworthy. Touchstone 2 keyword syntax, S3P/S4P and ZIP archives are not supported in this release. Unknown option tokens are rejected instead of guessed; max 10 MB and 250,000 sampled points per file.

02 · NETWORK DATA

S11 · S21 · S12 · S22

An S-parameter is a complex ratio of outgoing to incident traveling waves at a specified port and reference impedance.

b = S · a

b_{1} = S_{11} a_{1} + S_{12} a_{2}

b_{2} = S_{21} a_{1} + S_{22} a_{2}

Read the subscripts as output first, input second. The first digit identifies the port where the outgoing wave is observed; the second identifies the incident-wave port. S₂₁ therefore means Port 1 → Port 2, not the reverse. The a and b waves are complex, so each S-parameter carries both magnitude and phase.

How to read the sketch: every arrow is drawn from its own port's point of view. An a wave travels into the DUT and a b wave travels out of it. Both sides are shown in one physical left-to-right Port 1 → DUT → Port 2 orientation, even when the VNA source is moved to Port 2.

Drive Port 1 · forward measurementPort 2 terminated in Z₀ → a₂ = 0

PORT 1 · source

a₁incoming to DUT

b₁reflected from DUT

DUT
2-port

PORT 2 · load

b₂transmitted out

a₂ = 0matched termination

S_{11} = \frac{b_{1}}{a_{1}}

input reflection

S_{21} = \frac{b_{2}}{a_{1}}

forward transmission

Drive Port 2 · reverse measurementPort 1 terminated in Z₀ → a₁ = 0

PORT 1 · load

a₁ = 0matched termination

b₁transmitted out

DUT
2-port

PORT 2 · source

a₂incoming to DUT

b₂reflected from DUT

S_{12} = \frac{b_{1}}{a_{2}}

reverse transmission

S_{22} = \frac{b_{2}}{a_{2}}

output reflection

What happens on a real 50 Ω VNA?

Calibrate the VNA to the intended DUT reference planes, connect a two-port filter, and measure forward with Port 2 effectively matched to the same real Z₀ (normally 50 Ω). At a sample frequency, suppose S₁₁ = −20 dB magnitude and S₂₁ = −1.2 dB. Then |b₁/a₁| = 0.1: reflected incident-power fraction is 1%. Forward |b₂/a₁| ≈ 0.871: transmitted incident-power fraction is about 75.9% at the matched Port 2 reference. You have not measured an arbitrary ADC's delivered power or radiated antenna efficiency. Measure the reverse orientation to inspect S₁₂ and S₂₂.

Now connect the filter to an unmatched ADC input or a balun: the load can send a nonzero a₂ back toward the filter. If a₂ ≠ 0, b₁/a₁ alone is no longer the definition of S₁₁ for the original matched-port measurement, and b₂/a₁ alone is no longer S₂₁. Actual b₁ and b₂ follow both matrix terms, not just the single S₂₁ value. Model the full network and relevant impedances (or measure the assembled signal path) before asserting the ADC-pin Vpp.

Reference material

These wave directions and matched-port definitions follow Rohde & Schwarz ZNA User Manual, two-port S-parameters and Keysight's S-parameter measurement diagrams.

Common mistake S21 is not antenna radiation gain; S11 alone cannot prove antenna efficiency. A one-port file does not contain S21, S12 or S22.

03 · PLOT VALUE

Magnitude and dB

RFellow's magnitude plot shows the complex S-parameter's magnitude expressed in decibels.

G_{dB} = 20 \log_{10} | \frac{b}{a} |

G_{dB} = 10 \log_{10} (\frac{P_{2}}{P_{1}})

Why 20 rather than 10? With the same real reference impedance and correctly normalized traveling power waves, power is proportional to squared wave magnitude: P₂/P₁ = |b/a|². Hence 10 log₁₀(|b/a|²) = 20 log₁₀|b/a|. This does not mean 20log is the direct formula for a power ratio.

Half the powerP₂/P₁ = 0.5 → −3.0103 dB; corresponding wave-amplitude ratio √0.5 ≈ 0.7071.

Half the wave amplitude|b/a| = 0.5 → −6.0206 dB; corresponding power ratio = 0.25, or one quarter.

Absolute dBm is different

0 dBm = 1 mW absolute power; 0 dB is a ratio of 1. In the Tools page, dBm ↔ power uses 1 mW as the reference, whereas the other dB calculators distinguish power ratios (10log) from wave-amplitude ratios (20log).

Common mistake A −3 dB amplitude ratio is not half the voltage. Always name the quantity and reference conditions before converting dB into power or voltage.

04 · FORWARD PATH

Insertion loss

RFellow displays the negative of transmission magnitude in dB, so attenuation is shown as a positive loss.

IL = - 20 \log_{10} | S_{21} |

Worked reading

S21 = −1.2 dB on the magnitude plot corresponds to insertion loss = +1.2 dB. Use S12 to inspect the reverse path instead.

Limit This presentation is not necessarily an actual inserted system power penalty for arbitrary mismatched source/load conditions. An active stage may show a negative insertion-loss result (gain).

05 · REFLECTION

Return loss

RFellow shows return loss as a positive quantity for reflection magnitudes below unity.

RL = - 20 \log_{10} | Γ |

Worked reading

Γ = 0.1 gives RL = 20 dB, VSWR ≈ 1.222:1 and, for the specified single-port reference plane, reflected incident-power fraction |Γ|² = 1%. For an antenna, the other 99% is not necessarily radiated: it can include loss. Neither Γ phase nor complex input impedance can be reconstructed from return-loss magnitude alone.

Use the Return loss ↔ VSWR tool →

Common mistake “Higher return loss” normally means less reflection; the raw S11 magnitude in dB becomes more negative. Accepted power is not necessarily radiated antenna power.

06 · REFLECTION

VSWR

Voltage standing-wave ratio expresses reflection magnitude on a scale where a perfect match is 1:1.

VSWR = \frac{1 + | Γ |}{1 - | Γ |}

|Γ| = 0VSWR = 1:1; matched.

|Γ| = 1VSWR → ∞ at an ideal open/short.

RFellow display policy

When high/infinite values would make the trace unreadable, the VSWR chart can use a clearly labelled 20:1 display ceiling. Markers and hover retain the underlying value, including ∞.

Limit The graph ceiling is not a numerical clamp or PASS/FAIL threshold; do not infer actual VSWR from the clipped position alone.

07 · COMPLEX VALUE

Phase

The phase plot shows the argument of each complex S-parameter, in degrees.

φ = atan2 (Im S, Re S) \frac{180}{π}

Worked reading

A wrapped phase curve may jump from +179° to −179° without a real physical discontinuity. Use a consistent phase convention when comparing curves.

Current scope The current plotted phase is wrapped; do not imply that an unwrapped-phase control or a manually adjustable electrical-delay reference already exists.

08 · DERIVED VALUE

Group delay

Group delay is derived from the slope of unwrapped phase versus frequency, not from the vertical location of the phase plot.

τ_{g} = - \frac{1}{2 π} \frac{d φ}{d f}

RFellow workflow

Select a transmission S-parameter and Group delay. RFellow derives the result from sampled phase; the display unit adjusts to the magnitude of the time value.

Limit Differentiation amplifies noise, poor phase sampling and measurement floor artifacts. Group delay at or near vanishing transmission can be unreliable.

09 · IMPEDANCE VIEW

Smith chart and impedance

A Smith chart converts complex impedance into the reflection coefficient at a specified, positive real reference impedance. It makes constant-resistance and constant-reactance paths visible, helping engineers read mismatch, line transformations and the movement needed for a single-frequency match.

Interpretation

Chart center: Z = Z₀ (matched, Γ = 0). The leftmost perimeter point is a short (Z = 0); the rightmost is an open (|Z| → ∞). Positive reactance is above the horizontal axis; negative reactance is below. The diagram here is conceptual; use the interactive Smith lesson for a fully labelled grid.

z = \frac{Z}{Z_{0}}, Γ = \frac{z - 1}{z + 1}

Z = Z_{0} \frac{1 + Γ}{1 - Γ}

RL = - 20 \log_{10} | Γ |, VSWR = \frac{1 + | Γ |}{1 - | Γ |}

Step 1 · Normalize the loadDivide the complex load Z = R + jX by the chart reference Z₀. At 50 Ω, the load 25 + j25 Ω becomes z = 0.5 + j0.5. A resistance circle holds normalized r constant; a reactance arc holds normalized x constant.

Step 2 · Locate the reflection pointUse the intersection of the r = 0.5 resistance circle and x = +0.5 reactance arc. The point is Γ = −0.2 + j0.4: left of center and above the axis. A passive load (Re Z ≥ 0) lies on or inside the outer |Γ| = 1 circle.

Step 3 · Read mismatchFor the example, |Γ| ≈ 0.4472, return loss ≈ 6.99 dB and VSWR ≈ 2.618. These are quantities at the stated reference plane; a 50 Ω reference alone does not prove a 50 Ω physical load is connected.

Step 4 · Understand movementAdding a series L/C moves along a constant-resistance circle; adding a shunt L/C is easier in admittance coordinates (constant conductance). A lossless matched transmission line rotates Γ while preserving |Γ|. It does not itself eliminate mismatch.

Impedance versus admittance. In normalized form y = 1/z. The same physical reflection point can be read on an admittance grid rotated by 180° relative to the impedance grid. Positive susceptance describes capacitance; positive reactance describes inductance at positive frequency. Choosing the right grid avoids confusing series and shunt operations.

Try the worked Smith example

Set Z₀ = 50 Ω and Z = 25 + j25 Ω in the complex impedance ↔ Γ tool to verify Γ = −0.2 + j0.4. Then open Tools → Impedance ↔ Γ for the interactive resistance/reactance grids and load-to-source matching steps. Tools → Quick Match provides ideal one-frequency L/C matching candidates; it is already available, not a planned future solver.

Physical boundary The chart point alone says nothing about antenna gain, radiation efficiency, bandwidth or power handling. An ideal matching path is not a practical layout: frequency-dependent parasitics, losses, component tolerances and the actual reference plane must be verified. The diagram above is a concept sketch, not a calibrated Smith chart for geometry or signoff.

10 · REFERENCE PLANE

Reference impedance Z₀

S-parameters and the Smith-chart impedance conversion are defined relative to a specified reference impedance.

z = \frac{Z}{Z_{0}}

Worked reading

For a 50 Ω reference, a 50 + j0 Ω load maps to the chart center. With a 75 Ω reference the same 50 Ω load has Γ = −0.2 instead.

Current scope RFellow surfaces the file's Z₀, but the existing cascade engine requires equal real scalar Z₀ for both source networks. Merely changing labels is not a renormalization.

11 · MEASURE

Markers and deltas

A marker identifies a selected frequency; a delta reports the frequency and selected-trace value difference between two markers.

Δf · Δvalue

RFellow workflow

Add markers, give them names, lock selected identities if needed, and compare A/B with one or more deltas. Small glyphs identify trace positions; numerical readings sit outside the graph, with detailed measurement controls below it.

Limit A marker's requested frequency and the nearest source sample need not coincide. A delta is not inherently insertion loss or bandwidth; it inherits the selected parameter and metric.

12 · QUALIFY

Requirements and PASS/FAIL

A requirement evaluates selected measured samples against a named metric, frequency band, comparator and threshold.

Example · S21 IL ≤ 2 dBEvery available evaluated sample in the specified passband must satisfy the threshold to pass.

Example · S11 RL ≥ 15 dBHigher positive return loss corresponds to lower input reflection at the evaluated points.

RFellow workflow

Select a supported metric, comparator and frequency interval. The qualification panel evaluates the selected active DUT, reports the worst sampled point and counts how many measured samples were checked. Other loaded datasets are not independently qualified until selected.

Worked engineering example

At a sampled frequency, a measured insertion loss of 1.2 dB against a 2 dB maximum leaves 0.8 dB of positive margin. Measured return loss of 20 dB against a 15 dB minimum leaves 5 dB of positive margin. These are measured-point comparisons, not guarantees at unmeasured frequencies or about calibration uncertainty.

How to interpret the verdict: PASS requires every configured requirement to have usable samples and no measured violation within its entire declared sweep span. FAIL means an actual evaluated point violates a limit. INCOMPLETE means at least one required check could not be verified, for example an S21 criterion on an S1P file, a band outside the measured sweep, or a band with no usable samples. A FAIL remains a FAIL even if other checks are incomplete.

Limit PASS is sampled-point engineering qualification under the rule as defined—not certification or proof of behavior continuously between measurements. Missing band coverage is not a legitimate pass.

13 · COMBINE

Cascade two-port networks

RFellow models Stage 1 feeding Stage 2, including interstage reflections rather than simply adding S21 dB values.

RF IN→

Stage 1

→

Stage 2

→DERIVED

RFellow workflow

Load two .s2p files, select their physical order, then create the combined network. It appears as a new derived dataset alongside the originals.

Limit The current model requires matching scalar reference impedances and an overlapping frequency range; a calculated combined trace is not a substitute for measuring the assembled hardware.

14 · ENGINEERING CONTEXT

Reference plane, axes and trust

RFellow displays, compares and derives data from the supplied measurements; it does not establish whether the acquisition itself was valid.

VNA and fixturesCalibration, cable movement, port extensions and de-embedding determine what the source describes.

Frequency axisZoom/pan change what is visible—not the original measurements or their sampled frequencies.

Data identityA filename or future source fingerprint identifies data bytes, not measurement uncertainty or provenance.

High rejectionNoise floor and dynamic range limit meaningful interpretation of very small transmission.

Next step If results are consequential, retain calibration conditions, acquisition settings, fixture data and the original Touchstone file. RFellow engineering limits are not regulatory certification.

15 · RF POWER & VOLTAGE

RF power and signal voltage: dBm, RMS and Vpp

Power describes how much energy a signal delivers to an electrical load. Voltage describes how far that signal swings up and down. Converting between them requires two extra pieces of information: the resistance receiving the power and the shape of the waveform.

1. What does dBm mean?

0 dBm is 1 mW (one thousandth of a watt). Positive dBm values mean more than 1 mW; negative values mean less. dBm says nothing by itself about voltage or resistance. The same delivered power produces different voltages across different resistances.

P (W) = 0.001 × 10^dBm/10dBm = 10 log₁₀(P (W) / 0.001 W)

Why is 50 Ω so common in RF? RF cables, generators and measurement instruments often use 50 Ω as a standard reference. That does not mean every connected component has a physical 50 Ω resistor inside. For a power-to-voltage conversion, use the resistance that actually receives the stated power, not simply a number printed on an instrument.

Two meanings to keep separate An instrument's 50 Ω reference describes a measurement convention. A 50 Ω load is an electrical termination. They are not interchangeable.

2. From power to a voltage swing

For a steady sine wave, the voltage can be described in three ways: RMS is the effective voltage for power calculations, peak is the distance from the middle of the wave to its highest point, and Vpp (peak-to-peak) is the distance from the lowest point to the highest. The formulas below assume a known, purely resistive load and power measured at that load.

V_{RMS} = \sqrt{P R}

V_{pk} = \sqrt{2} V_{RMS}

V_{pp} = 2 \sqrt{2} V_{RMS} = 2 \sqrt{2 P R}

I_{RMS} = \frac{V_{RMS}}{R}

Optional: the mathematics behind the sine-wave formulas

Assume a single steady sinusoid across a fixed, positive, purely real resistance R, at one electrical measurement plane, with no DC offset. Let v(t) = Vpk sin(ωt + φ), i(t) = v(t)/R, and T = 2π/ω for nonzero angular frequency. Instantaneous resistive power is p(t) = v(t)i(t) = v(t)²/R by Ohm's law.

P_{avg} = \frac{1}{T} \int_{0}^{T} p (t) d t = \frac{{V_{pk}}^{2}}{R T} \int_{0}^{T} \sin^{2} (ω t + φ) d t

Use the trigonometric identity sin²θ = (1 − cos 2θ)/2. The antiderivative below includes both boundary terms: because 2ωT = 4π, the sine term at t=T equals its value at t=0. Their difference is zero for any starting phase φ.

\int_{0}^{T} \sin^{2} (ω t + φ) d t = [\frac{t}{2} - \frac{\sin (2 ω t + 2 φ)}{4 ω}]_{0}^{T} = \frac{T}{2}

P_{avg} = \frac{{V_{pk}}^{2}}{2 R} = \frac{{V_{RMS}}^{2}}{R} = \frac{{V_{pp}}^{2}}{8 R}

The RMS definition independently gives VRMS = Vpk/√2; for a centered sine wave Vpp = 2Vpk. Substituting both identities yields the displayed equalities. Dimensional check: volts squared divided by ohms is watts.

Scope Delivered average real power, not power merely available at the generator. The RMS/Vpp factors require a single undistorted sine wave into a known real load. Unmatched sources, noise, multiple tones or clipped waveforms require different assumptions and a clearly defined measurement point.

Reverse the same chain when a specification provides Vpp: divide Vpp by 2√2 to find RMS voltage, square it, and divide by the load resistance to find watts. Compare that result with 1 mW to express it in dBm. This voltage is measured across the load; it is not necessarily the value shown on a generator.

V_{RMS} = \frac{V_{pp}}{2 \sqrt{2}}

P = \frac{{V_{pp}}^{2}}{8 R}

P_{dBm} = 10 \log_{10} (\frac{{V_{pp}}^{2}}{8 R \times 1 mW})

For the same delivered power, Vpp grows with √R: doubling the resistance from 50 Ω to 100 Ω multiplies Vpp by √2 (about 1.414). That does not mean changing the impedance of a real generator automatically preserves its delivered power; that is a different calculation covered below.

Same delivered power across two different real loads · sine wave
Delivered power	50 Ω · Vpp	100 Ω · Vpp
−20 dBm · 0.01 mW	0.06325 Vpp	0.08944 Vpp
0 dBm · 1 mW	0.63246 Vpp	0.89443 Vpp
−10 dBm · 0.1 mW	0.20000 Vpp	0.28284 Vpp
10 dBm · 10 mW	2.00000 Vpp	2.82843 Vpp

Waveform limitation These RMS↔Vpp factors apply to a single undistorted sine wave. For multitone signals, modulated RF, noise or clipped/peaky waveforms, average power and Vpp require the waveform's crest factor; Vpp cannot be inferred from dBm alone.

3. Single-ended and differential voltage

Voltage is always measured between two points. Single-ended voltage is measured from a signal to its return, often ground. Differential voltage is measured between two signal wires.

Single-ended

Signal ── ● RReturn ── ●

Vpp is the complete voltage swing between the signal and the return.

Differential

Signal + ● ─┐ RSignal − ● ─┘V_diff = V+ − V−

Vpp is the swing between the two wires. With a balanced signal, each wire swings half the differential Vpp around their shared midpoint.

For a real 100 Ω resistor across two wires, the power formula uses the voltage across that resistor and R = 100 Ω. The common-mode voltage, V_CM, is a separate DC level.

Safety A grounded oscilloscope probe is not a differential probe. Use a safe measurement setup for floating signals.

4. Source power and delivered power can differ

A generator has internal resistance. Its stated power can describe what is available to a matching load. A different load receives a different voltage and may receive less power. The formulas below describe the simple resistive case.

V_{TH,RMS} = 2 \sqrt{P_{available} R_{S}}

V_{load,RMS} = V_{TH,RMS} \frac{R_{L}}{R_{S} + R_{L}}

P_{delivered} = \frac{{V_{load,RMS}}^{2}}{R_{L}}

Example: 0 dBm available from a 50 Ω source

Into a matching 50 Ω load, the source delivers 1 mW at about 0.632 Vpp.

With a 100 Ω load connected directly, it delivers about 0.889 mW at 0.843 Vpp. If a full 1 mW is delivered to 100 Ω, the voltage is 0.894 Vpp instead.

Cables, matching networks and other components can change the result. The simple divider is an introductory model, not a complete RF analysis.

Measurement note A high-impedance scope can show nearly twice the voltage expected for a matched 50 Ω load. Confirm the actual load and instrument display settings.

5. A simple example: 0 dBm delivered to 50 Ω

0 dBm means 1 mW. Across an actual 50 Ω resistance, a sine wave has 0.224 V RMS, 0.316 V peak, and 0.632 Vpp. If the same 1 mW is delivered to 100 Ω, the voltage is 0.894 Vpp instead. These are load voltages, not guaranteed generator display readings.

Open the power and Vpp calculator in Tools

6. Before converting

Confirm where power is delivered, the actual load resistance, the two points defining voltage, and whether the waveform is a clean sine wave. Generator settings and load power are not always equal. Cables and matching networks can change the result.

16 · PHYSICAL LENGTH

Frequency, wavelength & velocity factor

Translate RF frequency into free-space wavelength, approximate propagation length in a uniform cable or line, a quarter wavelength, and period. This is a local RF planning calculator, not a replacement for a stackup or measured propagation model.

λ_{0} = \frac{c}{f}, λ_{medium} = VF \times \frac{c}{f}, c = 299792458 m/s

Velocity factor (VF) is phase velocity divided by free-space light speed for the assumed uniform, nondispersive medium. For the supported cable/line approximation, 10⁻⁶ ≤ VF ≤ 1 in this calculator (a practical numerical bound, not a universal law). The nominal value depends on the dielectric and line geometry. Frequency in hertz is essential to the SI equation: multiply the MHz input by 10⁶ before dividing c by frequency.

Worked RF line

At 100 MHz, free-space λ₀ is 2.99792458 m. With VF = 0.66, the estimated wavelength along the medium becomes 1.97863022 m; a quarter wavelength is about 0.49465756 m. A 100 MHz period is 10 ns. The calculator also shows one-way delay in ns per meter. The electrical lengths apply only where VF is appropriately characterized at the working frequency.

Why quarter wave?In an ideal uniform transmission line, a quarter of the propagation wavelength corresponds to a 90° phase advance at that frequency. Electrical connectors, opens, fringing, and terminations may shift an actual built design.

Phase velocity ≠ always group velocityIf the line is dispersive, VF may depend on frequency and pulse/group delay is not necessarily the one-frequency phase delay. A waveguide may have a phase velocity above c; this limited VF calculator intentionally does not model that case.

Limit Use the actual cable datasheet or PCB stackup and EM model for physical cut lengths or timing signoff; do not assume all media share VF = 0.66 or that a nominal factor captures connectors and frequency variation.

Open frequency ↔ wavelength in Tools ↗

17 · IDEAL SINGLE-FREQUENCY MATCH

Quick Match · ideal L network

Quick Match synthesizes ideal, lossless two-reactance L-network candidates that transform one passive complex load Z = R + jX to a real positive target resistance at one entered frequency.

Network equations. A series element adds reactance in ohms (Ω); a shunt element adds susceptance in siemens (S). Angular frequency is ω = 2πf, with f in hertz. The same L or C has opposite reactive signs in impedance and admittance.

Z^{'} = Z + j X_{s}

Y^{'} = \frac{1}{Z} + j B_{p}

X_{L} = ω L, X_{C} = - \frac{1}{ω C}

B_{C} = ω C, B_{L} = - \frac{1}{ω L}

Direction matters. RFellow reports every topology in load → source order. “Series → shunt” means add the series L/C at the load, then the shunt L/C toward the source; “shunt → series” is the reverse order. Every candidate is numerically re-applied to the original load and must terminate at the entered real target resistance.

25 Ω to 50 Ω at 1 GHz

The ideal core returns the two dual series-then-shunt solutions: series L with shunt C, and series C with shunt L. These are mathematically valid alternatives, not a recommendation that one is physically better.

Open Quick Match in Tools ↗

Model boundary A one-point ideal L match does not establish bandwidth, component Q/ESR, tolerance, package/layout parasitics, power handling, antenna radiation efficiency, gain, pattern or range. Purely reactive R = 0 and active negative-resistance loads are outside this bounded contract. Use measured-band data and real component models before practical signoff.