rftools -- RF coil calculators

Data entry

Rigorous, ephemeral RF-coil calculators for the bench

Three calculators, each calling the real rfcoil library (no reimplemented physics):

Loop L/R — self-inductance, skin-effect resistance, unloaded Q, distributed-cap sizing and critical array overlap from rfcoil.geometry, with the closed-form ~1% validation shown alongside the numeric result.
Resonance & Tuning — tuning C for your target frequency (default 127.74 MHz / 3T), verified via a real rfcoil.network.Network sweep, plus DESIGN.md's analytic tolerance-quadrature model and a Monte Carlo yield against your loaded bandwidth.
Z↔S — impedance/S conversion at arbitrary complex per-port reference impedance via rfcoil.renorm, with power reflection and preamp noise-mismatch penalty reported side by side, never a single S11.

Zero storage. This app has no database and writes no files. Every number you enter is used to compute a response and then discarded — nothing you submit is logged, cached, or persisted anywhere. Access logging is disabled at the server.

Loop inductance & resistance

Loop diameter mm

Conductor

Diameter / width mm

Material Frequency MHz

Shared across every tab (see the frequency bar above) — editing it here updates it everywhere.

Coil target / match impedance Z_target

This coil's own target impedance (default 50Ω, always editable — never assumed). Single source of truth: sizes C_match/L_match on the Coil Network tab and the match report on Resonance & Tuning — entered once, here, as a coil design parameter.

R + jX ohm

+ j

= |Z|∠θ

Ω ∠ °

Advanced Proximity factor (measured multiplier, 1.0 = optimistic) Polygon segments Cap junction count N, set by

Max electrical length per segment Cap junction count (N)

Max electrical length per cap segment deg

Derived (read-only): resulting minimum cap junction count N.

N = --

Cap junction count N

Derived (read-only): resulting electrical length per segment.

deg/segment = --

Compute critical array overlap Coil-R source (how the coil series resistance is determined)

Capacitor ESR ohm/cap

Copper/skin loss is computed; capacitor ESR is not -- rfcoil has no dielectric-loss model, so this is a user-entered per-cap figure at the shared frequency (default 0.3Ω, a documented planning estimate for a high-Q RF chip/porcelain cap plus its solder joints -- see calc_loop.py's CAP_ESR_OHM_DEFAULT docstring). Summed over every physical series cap in the ring: each junction's own split N (Coil Network tab's per-junction voltage-split control -- the single source of truth, no global split figure here), plus one more for the match cap.

ATC (Kyocera-AVX) 100B Series porcelain Superchip multilayer capacitors, Document TDS-RFM-0006 Rev 2 -- ESR digitized from the vendor's own "ESR vs. Capacitance" chart (150/500/1000 MHz curves, 1.0–51 pF and 56–1000 pF panels). REFUSE-EXTRAPOLATE outside that digitized range (including the 51–56 pF gap between the two chart panels, and frequencies outside 150–1000 MHz -- rftools' own 127.74 MHz 3T default is below it and will be refused).

Passive Plus (PPI) 0603N EIA Low-ESR High-Q multilayer capacitors, Document PPI0603NDATA010324RevA -- ESR digitized from the vendor's own "ESR vs. Frequency" chart for the catalog values 3/5.6/10/15/27/100 pF. Your value is snapped to the nearest catalog value (flagged if not exact). REFUSE-EXTRAPOLATE outside that value's own plotted frequency window (rftools' own 127.74 MHz 3T default is below every 0603N catalog value's plotted start and will be refused -- use 1111C/P instead at 127.74 MHz).

Passive Plus (PPI) 1111C/P Traditional High-Q (≥10,000) Low ESR multilayer capacitors, Document PPI1111CPDATA060123RevA -- ESR digitized from the vendor's own two "ESR vs. Frequency" charts for the catalog values 3.3/6.8/10/33/68/100/150/180/330/470/680/1000 pF. Your value is snapped to the nearest catalog value (flagged if not exact). Unlike 0603N, this DOES cover rftools' own 127.74 MHz 3T default for 11 of the 12 catalog values -- each curve's own plotted data starts between ~130-280 MHz (not the chart's 100 MHz axis start), so a request within 2x of that start is served by a flagged, bounded log-log extrapolation from the curve's own two nearest real points (see "extrapolated" in the result); REFUSE-EXTRAPOLATE beyond that 2x window (including 3.3 pF at 127.74 MHz -- its data starts at 279.8 MHz, a 2.19x gap) or outside the chart's own 100-2000 MHz axis.

Unloaded Q (free value, no upper limit -- rejected if ≤0)

Loaded Q (guidance ~40-60; the default match source)

Two related Q inputs. Unloaded Q sets the coil's INTRINSIC (unloaded) reference R directly from a user-supplied UNLOADED Q via R = ωL / Q (L = loop inductance at f0) -- a peer alternative to ESR/ATC/Passive Plus/Rs for the coil's intrinsic R (same closed form, just user-supplied instead of computed from conductor+cap-ESR). A real assembled coil's unloaded Q is dominated by solder-joint/board/connector/proximity losses this tool cannot model, so the conductor+cap-ESR model can honestly compute several hundred for a good chip-cap build while a real bench coil measures lower -- typically ~140-150, HIGHER for a genuinely high-Q build (not clamped/capped to that range; only rejected if ≤0). Loaded Q (guidance ~40-60, sample/patient in place) gives R_loaded = ωL / Q_loaded -- the coil's real loaded operating resistance and the DEFAULT source that sizes the match (C_match/L_match). Which source actually feeds the match is your choice below (Match resistance source); loaded is the default. rfcoil has no sample/tissue-loss model, so Loaded Q is a user-supplied planning figure, not clamped to any range.

Rs ohm (intrinsic series resistance, entered directly)

Sets the coil's INTRINSIC (unloaded) reference R directly, in ohms -- a peer alternative to ESR/ATC/Passive Plus/Q (skip the model entirely and enter a bench-measured or known series resistance). Rejected if ≤0. This Rs value is also selectable as the match resistance source below.

Which source's R sizes the match (C_match/L_match): pick it with the "use for match" radio inside each source's tab above (one group, exactly one selected across all tabs; default Loaded Q). Compute the Loop tab to populate each source's R. Sources that can't be computed for the current inputs (e.g. a vendor cap value/frequency outside its digitized datasheet range, or a Q/Rs value not yet entered) are shown disabled with the reason.

Tuning cap value pF (computed, per physical cap -- not hand-entered)

Tuning cap value = -- pF

The physical tuning cap value fed to the vendor ESR lookup is COMPUTED, never hand-entered: per-junction net capacitance C_each = N × C_total (N from the "Cap junction count N" control above, C_total from the Resonance & Tuning tab's tuning C -- the same C_each the Coil Network tab's board/component values use), then scaled by each junction's own split N (Coil Network tab -- the single source of truth for voltage split; there is no global split field here) to arrive at the per-PHYSICAL-cap value -- the same identity calc_split.py uses for the Coil Network tab's per-junction split. Run the Loop tab (for N), the Resonance & Tuning tab (for C_total), and the Coil Network tab (for each junction's split) at least once so all three are in the shared workspace; the computed value here always reflects the last of each, same pattern as the independent Loaded Q input above.

Enter loop geometry and compute.

Resonance & tuning

Loop inductance nH

Loop resistance ohm (matched-source R for verification)

Target frequency MHz

Shared across every tab (see the frequency bar above) — editing it here updates it everywhere.

L tolerance %

C tolerance %

Stray capacitance pF (footprint/pads, always adds) Loaded Q (sets bandwidth = f0/Q)

Q loaded = 50 (default -- run the Loop calc's independent Loaded Q input to carry its value here instead; single source of truth, not re-entered here).

Monte Carlo Trials Distribution

Match report (vs shared target impedance)

At verified resonance the loop's reactance is ~0, so its terminal Z is just the loop resistance above. Reported against the shared target/match impedance (Loop L/R tab, Z_target) — never a hardcoded 50 Ω.

include preamp noise-mismatch panel

Fmin dB

Rn ohm

|Gamma_opt|

angle(Gamma_opt) deg

z0_ref for Gamma_opt ohm

Enter loop L/R and compute.

Z↔S converter

Ports Convention

Coil-side impedance matrix Z & reference z0

Preamp noise parameters (optional) include noise-mismatch panel

Source Z seen by preamp (usually = Z11 above) ohm

+ j

Fmin dB

Rn ohm

|Gamma_opt|

angle(Gamma_opt) deg

z0_ref for Gamma_opt ohm (vendor data, real)

Preamp actual Zin (optional, informational only) include preamp Zin panel

Preamp Zin ohm

+ j

Reference z0 ohm

Enter an impedance and compute.

System model — live from the shared workspace above

Coil network

Interactive schematic of the loop element: exactly N junctions (from the Loop calc), each with its own split tuning/decouple cap(s) and optional PIN-diode blocking network. Exactly one junction, chosen below, is also the match -- it carries one additional match cap (target Z from the Loop L/R tab) in series with its own caps.

Compute the Loop tab (for the cap junction count N) and the Resonance & Tuning tab (for the tuning C) first, then return here.

Loop shape Circle Octagon

L_block ESR source Manual Coilcraft Q

Coilcraft 132 Series air-core fixed RF inductors, Document 114 -- each junction's own computed L_block is snapped to the nearest 132-series catalog part and its datasheet ESR (guaranteed-min Q at that part's own 25/50 MHz test frequency) used in place of a manual Q. REFUSE-EXTRAPOLATE if L_block or the shared frequency falls outside that part's sourced range.

Drag to pan · scroll to zoom

Junctions

Match junction launch

What the match junction hands off to. Both paths keep the three DESIGN.md impedances distinct (coil source Z; preamp Γopt/Fmin/Rn noise target; preamp actual Zin/coax Z0 for power match) and report power reflection and noise-mismatch penalty side by side.

Preamp on coil Coax

L_match ESR source

Manual Coilcraft

L_match series ESR ohm (0 = ideal/lossless, the prior behaviour)

Coilcraft 132 Series air-core fixed RF inductors, Document 114. L_match is solved first (ideal reactance), then snapped to the nearest 132-series catalog part (14.0–709 nH) and its own datasheet ESR (guaranteed-min Q at that part's OWN test frequency, 25 or 50 MHz) is added as a real series R -- REFUSE-EXTRAPOLATE if your design frequency is more than 2× away from that test frequency, or L_match falls outside the catalog range.

Coax / cable runs (T-line model)

Model real coax lengths in the receive chain with rfcoil.tline's transmission-line ABCD. The input-side and output-side runs are two INDEPENDENT physical pieces of coax and can both be modeled at once. Each reports the impedance transform through its own cable, reflection Γ / VSWR against its own line Z0, and phase + loss over its own length.

Input side: Coil → Amp Model a cable after the coil, feeding the amplifier input (Coax launch only — terminated by the coil's matched source Z)

Physical length m

Velocity factor (v_p/c)

Cable Z0 ohm (blank = coax Z0)

Loss dB/m (0 = lossless)

or electrical length deg @ f0 (optional — overrides length×VF for phase; e.g. 90 = quarter-wave, 180 = half-wave)

Output side: Amp → Output Model coax on the amplifier's output (both launch modes — terminated by the system target Z)

Physical length m

Velocity factor (v_p/c)

Cable Z0 ohm (blank = coax Z0)

Loss dB/m (0 = lossless)

or electrical length deg @ f0 (optional — overrides length×VF for phase; e.g. 90 = quarter-wave, 180 = half-wave)

Whichever junction is toggled as the match (Junctions panel) carries one additional match cap C_match, in series with its own tuning/decouple caps, sized jointly with L_match from the coil source Z and the target Z above. The same L/C pair both noise-matches the coil to the preamp and decouples the preamp's low Zin into a high series loop impedance. Feed is single-ended, bridging C_match's own two terminals only: HOT via L_match to the preamp's + input, RETURN to preamp ground.

Preamp noise parameters (Γopt / Fmin / Rn)

Fmin dB

Rn ohm

|Gamma_opt|

angle(Gamma_opt) deg

z0_ref for Gamma_opt ohm (vendor data, real)

Preamp actual Zin (deliberately low, transformed for decoupling) Zin ohm

+ j

Whichever junction is toggled as the match carries one additional match cap C_match, in series with its own tuning/decouple caps, sized jointly with L_match from the coil source Z and the target below. Feed is single-ended, bridging C_match's own two terminals only: HOT via L_match to the coax center pin, RETURN ties to the coax shield.

Coax Z0 ohm (default 50 — fully editable, never assumed)

no impedance transformation — coil connects directly to the coax match to the shared target Z (Loop L/R tab) when set — uncheck to match to the coax Z0 line instead. (On by default so a specified target impedance is honored, never silently matched to 50.)

Computing...