A08 — Coil Topology

Defining Series, Parallel, and Split as source reconfiguration

2026-10-06 · v0.9 · Literature / equation / terminology verification complete · RavenForge specimen bench validation pending

1. Research question and boundary

This entry does not ask which wiring “sounds better.” It asks:

Paiva, Pakarinen, and Välimäki analyze magnetic pickups as frequency-dependent systems involving pickup position, sensing width, equivalent-circuit resonance, loading, and pickup combinations [1]. A08 therefore does not treat DCR or a tone adjective as a complete description of pickup state.

2. Evidence tags

3. A coil switch reconfigures the source

LIT A magnetic pickup is not fully represented by one ideal voltage source. Even a first-order model requires induced EMF E_i(f), winding resistance R_i, and self-inductance L_i for coil i. A real pickup also introduces mutual inductance, distributed capacitance, magnetic/core losses, and eddy-current effects [1,2].

The boundary seen by the downstream circuit can be written in Thevenin form:

MODEL This boundary model makes the key point: a topology switch can change E_TH(f) and Z_TH(f) before the volume pot, tone network, cable, buffer, or amplifier input. A08 therefore treats Series/Parallel/Split as source reconfiguration, not merely as a post-source tone switch.

4. Matched coupled-coil first-order model

MODEL The following equations are not product specifications. They define a first-order baseline for two electrically identical coils that generate the same string-induced EMF, are symmetrically coupled, use a fixed dot/sign convention in the signal-aiding direction, and initially neglect distributed capacitance and losses.

Series, signal-aiding

Parallel, signal-aiding

Beller's humbucking-pickup patent explicitly describes the ideal matched-coil relation in which a parallel connection yields a combined impedance one half that of an individual coil [4]. In a real pickup, however, E₁(f) and E₂(f) need not be exactly equal because sensing position, winding, and magnetic structure can differ [1].

The sign of mutual inductance depends on terminal and dot convention. The +M above means signal-aiding coupling for the selected current/reference directions. A different convention can reverse the algebraic sign, so polarity and lead definitions must be documented with the equations.

5. Series — not “always +6 dB”

MODEL In the equal-EMF open-circuit baseline, the two source voltages add, producing a 2:1 voltage ratio to one coil, or about 6.02 dB. But Series also changes source resistance and effective inductance. Once a real load is connected, the output ratio becomes frequency-dependent. “Series = always +6 dB” is therefore not a valid product rule.

PENDING Broadband level difference, resonant peak, and transient difference for a RavenForge specimen remain unquantified until bench measurement.

6. Parallel — not merely a quieter Split

PAT MFR Both coils remain in the signal path in Parallel. Beller explicitly describes a parallel humbucking implementation [4], while four-conductor humbucker documentation shows Series, Parallel, and single-coil states as distinct wiring configurations [7].

Even if Parallel and Split happen to show a similar open-circuit level under a particular condition, that does not make them electrically equivalent sources.

7. Split taxonomy — record A/B and termination together

The word “Split” alone does not fully define the circuit. A08 records at least two axes.

MODEL The following equation is restricted to the isolated-split first-order case in which one surviving coil is the useful source:

PENDING A shunted/shorted unused winding can carry induced current and can reflect a load into the surviving coil through mutual coupling. It is therefore not assumed to be identical to the isolated equation above. The magnitude of the difference is handed to complex-impedance measurement on the specimen.

8. Partial / resistive split — residual-coil topology

MFR Manufacturer wiring material also shows applications in which the contribution of one coil is blended rather than simply removed [7]. If a finite resistor or blend control leaves part of the second coil electrically involved, the circuit is not the same as a hard split.

INFER RavenForge records this as a separate Residual-Coil / Partial-Split topology. The label is an internal engineering taxonomy for traceability, not a claim that the phrase is an industry standard. A08 deliberately does not prescribe one universal “correct” resistor value.

9. Resonance and loading — do not turn an ordering into a law

A simplified lumped model can use:

MODEL If effective capacitance were held fixed across topology, the change in effective inductance would suggest a direction for resonance movement. Real reconnection, however, can also change effective/distributed capacitance, damping, mutual coupling, and loss conditions. Kotiuga specifically addresses distributed winding capacitance and the limitations of overly simple lumped representations [2]. Controlled experimental pickup work also shows that turn count and wire gauge affect resonance and peak behavior [8].

PENDING “Series → Split → Parallel always produces progressively higher resonance” is therefore not a verified A08 law. Topology-specific resonance ordering remains a hypothesis to test on the same specimen under a defined load.

Every measurement records volume/tone resistance, tone capacitance, cable capacitance, input impedance, and buffer/bypass state. When source topology changes, the same downstream component cannot be assumed to create the same proportional effect.

10. Hum cancellation — not exclusive to Series

PAT Seth Lover's original patent describes the humbucking principle in which interference-induced components from two coils are cancelled while string-induced musical signal is made additive [3]. Beller's later patent explicitly implements the same noise-cancellation / musical-signal-addition goal with the two coils connected in parallel [4].

Under the required magnetic/electrical polarity, sufficient matching, and the relevant interference field, both Series and Parallel can be hum-cancelling. Conventional one-coil Split generally gives up the original pair's two-coil cancellation mechanism. This statement does not exclude a surviving split coil from participating in a new hum-cancelling combination with another suitably arranged pickup or coil.

PENDING Actual hum attenuation in dB for a RavenForge specimen is measured only after field strength, orientation, bandwidth, background, and repeatability are controlled.

11. Split A/B also carries a spatial-sensing hypothesis

LIT Pickup position and sensitivity width contribute to the sampled string-harmonic response [1]. In a side-by-side dual-coil structure, the two coils do not occupy exactly the same longitudinal coordinate.

INFER Selecting which physical coil survives can therefore change the sensing region as well as the electrical source. A08 records this as a mechanism-supported hypothesis. The actual spectral effect size between Split A and Split B remains PENDING; no tonal ranking is assigned before measurement.

12. Coil split ≠ coil tap

MFR Manufacturer technical documentation distinguishes coil splitting from coil tapping. Splitting disables or suppresses one coil of a multi-coil pickup to obtain one-coil operation; tapping selects an intermediate connection in a winding and changes the active number of turns [6]. RavenForge documentation does not use the two terms as synonyms.

13. RavenForge design rules and SKAÐI application

MFR DELANO classifies the THE XTENDER 5 HE/S, currently considered in the SKAÐI design, as a dual coil humbucker [9]. DELANO also publishes separate four-conductor series/parallel wiring documentation [10]. A08 does not infer that DELANO has published topology-specific DCR, inductance, resonance, output delta, or hum-attenuation values for the exact THE XTENDER 5 HE/S specimen.

PENDING SKAÐI's intended Series/Parallel option is therefore not frozen as a “fat/bright mode.” The exact lead version and real onboard load/buffer boundary must be fixed first; bench measurement then determines whether the two states remain sufficiently distinct and useful.

14. Claim-by-claim evidence matrix

15. Bench-validation handoff

The follow-up experiment uses the same pickup specimen for every topology. Manufacturing variation between different samples must not be folded into the topology effect.

Listening comparison follows only after the electrical dataset is frozen and a level-matching rule has been declared. Loudness difference is not silently re-labeled as topology character.

16. Current conclusion and next research

The conclusion of A08 v0.9 is not “Series is strongest and Parallel is brightest.” It is that changing coil connection changes the pickup-source boundary before the tone circuit begins. The size and musical usefulness of that difference must be measured at the actual instrument load boundary.

The regular research sequence now continues, as announced in L13, to L04 — Epistemology of Craft. A08 is promoted to a measured v1.0 only after Coil Topology Bench Validation. The experiment code remains unassigned pending C-series namespace normalization.

References

Internal research lineage

A08 v0.9 separates literature evidence, analytical models, engineering inference, and pending measurement. No unpublished specimen value is presented as measured fact.