RAVENFORGE

Signal & Transduction Research Log

A03 — Magnetic Pickups as RLC Systems

Reading a distributed electromagnetic transducer through a first-order equivalent network while separating DCR, Z(f), resonance and Q

1. Research question — How far can we say “a pickup is an RLC circuit”?

A01 defined the magnetic pickup as an electromechanical transducer between mechanical and electrical domains, and A02 treated pickup position and spatial harmonic sampling. A03 asks a narrower question: how much of the passive pickup’s terminal electrical behavior can be represented by R, L and C, and what boundaries prevent that model from being confused with the complete physics of the transducer?

Horton & Moore and Lemarquand & Lemarquand model the source mechanism: a moving ferromagnetic string perturbs the magnet/string field and the resulting flux variation produces EMF by Faraday induction [1,2]. Paiva et al. and the technical treatments of Lemme and Zollner address pickup-position coloration, linear resonant filtering and terminal electrical behavior as another layer [3–5]. A03 therefore deliberately separates the source model from the terminal equivalent model.

Figure 1. Separation of electromagnetic source and terminal equivalent circuit.

RavenForge schematic. The R–L–C network is a first-order lumped approximation and does not represent every distributed winding or loss branch.

2. First-order equivalent circuit — separate the voltage source from terminal impedance

A widely used first-order model consists of an induced source eₛ(t), series winding resistance Rₛ and equivalent inductance Lₛ, with the distributed winding capacitance collapsed into a shunt capacitance Cₚ across the branch [4,5]. With the source set to zero, terminal impedance can be written as:

Zpu(ω) = [ 1 / (Rₛ + jωLₛ) + jωCₚ ]⁻¹

This is a lumped approximation for one topology. A real winding is a distributed network of turn-to-turn and layer-to-layer capacitances, while conductive magnetic components such as steel poles, blades, keepers and baseplates introduce eddy-current loss and frequency-dependent apparent inductance. Fitted R/L/C values are therefore engineering descriptors over a stated band, not immutable “true material constants” that replace raw Z(f).

3. Resonance — do not merge self resonance, impedance peak and transfer peak

The lossless LC relation f₀ = 1/(2π√LC) is useful intuition, but real pickups contain winding resistance and additional losses. More importantly, the resonance condition depends on what quantity is being maximized or zero-crossed. For the (R+jωL)∥C topology, the zero of imaginary admittance and the maximum of |Z| are not generally identical at finite R. A03 therefore does not promote one closed-form expression as a universal pickup-resonance formula.

The safer practice is to name the measured criterion directly: `fZ,max = frequency of maximum |Z(f)| under the stated fixture`, `fφ0 = terminal phase zero-crossing`, and `fH,max = peak of magnetic-excitation→voltage transfer response`. They are related but not assumed identical. Once pots, cable capacitance and input impedance are attached, another loaded response emerges; that is the detailed subject of A04.

Figure 2. Separating resonance criteria in complex Z(f) and magnetic transfer H(f).

Conceptual only, not measured data. In real pickups, losses and measurement topology can move each peak or zero-crossing.

4. DCR — useful manufacturing information, not a universal output/tone metric

DC resistance follows R = ρl/A and therefore depends directly on total conductor length, cross-sectional area, resistivity and temperature. NIST copper data demonstrate significant temperature dependence around room temperature [6,7]. Even the same pickup changes DCR with temperature, so comparative data should include measurement temperature.

Within a controlled pickup family—same bobbin, wire gauge, magnetic structure and winding method, with turn count as the main changed variable—DCR can proxy wire length/turn count. Across pickups with different AWG, bobbin dimensions, lead length, packing and magnetic circuits, however, statements such as “17 kΩ is hotter/darker than 9 kΩ” are not physically sufficient. DCR does not directly encode magnet-to-string coupling or transfer sensitivity.

5. Inductance and distributed capacitance — record the conditions behind the number

The ideal-solenoid relation L ∝ μN²A/l provides directional intuition but a guitar/bass pickup is not a closed magnetic circuit. Leakage, fringing, pole/blade/core permeability, steel hardware and coil shape all matter, and eddy-current/magnetic losses can make the apparent inductance reported by an LCR meter depend on frequency and equivalent-series/parallel mode [2,5]. “L = 5 H” alone is therefore incomplete.

Capacitance is likewise not one physical capacitor. The winding contains distributed turn-to-turn, layer-to-layer, coil-to-core/cover, lead and fixture capacitances. A single Cₚ is an equivalent fitted parameter for a low-order model. It is physically plausible that scatter winding changes average capacitive coupling, but pickup-specific controlled peer-reviewed evidence remains weak. RavenForge treats this as a measurement hypothesis rather than an established universal law.

6. Turns and wire gauge — output is not the only thing that changes

In Faraday-law intuition, induced EMF may rise with turn count N. In a real winding, increasing N also lengthens wire and raises R, generally increases L, and changes distributed capacitance, coil dimensions and fill. Turn count is therefore not an independent “hotness knob.”

Batchelor et al. built Strat-style test coils spanning 5,000–12,000 turns and 42/44 AWG and used a frequency-response analyser to show resonance behavior changing with turns and wire gauge [8]. The currently verified publication status is an arXiv preprint. Its impedance-peak magnitude must not be generalized as if it were identical to moving-string output sensitivity. It is useful evidence that turns/gauge alter Z(f), not a universal predictor of playing output.

Figure 3. Causal map showing how added turns alter several electrical and geometric variables at once.

Qualitative RavenForge working model. Effect sizes require measurement for each pickup architecture.

Figure 4. Why equal DCR does not guarantee equal frequency-dependent impedance.

Illustrative curves. A single “10 kΩ” value does not determine L/C/Q or the actual transfer response.

7. Magnetic circuit, metal parts and eddy-current loss

Rather than translating magnet names directly into adjectives such as warm, bright or aggressive, A03 separates their causal routes. Permanent-magnet flux and string coupling primarily affect the source term, while permeability and conductivity of poles, blades, cores, steel hardware, baseplates and covers can alter L(f), loss and Q [2,5].

Lemme’s technical measurements report commercial pickup examples in which the presence or absence of a metal casing changes resonance/Q [4]. The engineering implication is to record conductivity, permeability, thickness, geometry and electrical continuity and then measure Z(f), rather than memorizing a tone adjective by material name. Nickel silver cannot be assumed to be perfectly “electrically transparent.”

8. Z(f) versus H(f) — an impedance test is not an output test

Complex terminal impedance Z(f) is a network property obtained by electrically probing the pickup terminals. Magnetic-excitation→output transfer Hmag→V(f), by contrast, describes how an external magnetic perturbation becomes output voltage. The curves are related but they are not the same physical quantity.

Horton/Moore and Lemarquand illuminate source geometry and nonlinearity [1,2], while Lemme describes a practical pickup-analyser method that excites the pickup with a transmitting coil rather than a moving string [4]. RavenForge should therefore record Z(f) sweeps and H(f) measurements as separate channels.

9. Active pickups are a separate architecture class

Powered pickups such as EMG and Fishman Fluence combine an internal transducer with active electronics that shape output impedance and voice/transfer behavior. The EMG 40-TW-X official sheet specifies 2 kΩ output impedance, while Fishman Fluence Bass Soapbar specifies 9.4 kΩ output impedance and current draw [9,10]. These are complete-output architecture values, not equivalents of passive-coil DCR/L/C.

Passive high-impedance pickups and powered/active pickups should therefore not be ranked on one DCR–L–C–Q scale. Shared comparison should instead use architecture class, transduction topology, output/source impedance, transfer behavior, required interface/load, noise, and headroom/current where applicable.

Figure 5. Architecture boundary between passive high-Z and powered/active pickups.

Shared functions can be compared, but passive-coil RLC metrics are not applied directly to the complete active output.

10. Evidence matrix — what can A03 legitimately claim?

11. RavenForge Pickup Characterization Protocol

The purpose of A03 is not to accumulate more spec-sheet numbers but to establish a common measurable language. Bench testing should avoid the absolute word “unloaded” and instead state the fixture input impedance/capacitance as a specified high-impedance condition. Perfect zero loading does not exist; lead and fixture parasitics are part of the measurement system.

Figure 6. RavenForge pickup electrical & transfer characterization workflow.

Z(f) and H(f) are measured as separate channels while fixture compensation, fit residuals and repeatability are preserved.

12. RavenForge comparison frame — placing Delano / Turner / Herrick / Nova beside EMG / Fishman

13. A03 / A04 / A05 / C-log boundary

14. Current conclusion — expand pickup specification from “one kΩ number” to a frequency-dependent system

A03 establishes the RavenForge minimum description as `architecture + source mechanism + complex Z(f) + measurement condition + magnetic transfer H(f)`, not DCR alone. R/L/C are useful first-order descriptors but do not replace distributed winding or loss mechanisms.

Accordingly, “higher DCR,” “larger inductance,” or “higher Q” are not independent quality rankings. Model voice starts with the B02 Sonic Brief, then A02 pickup coordinate, A03 pickup electrical architecture, A04 load and A05 interface are separated and recombined through prototype data.

15. Next research — variables passed to A04

References

[1] Horton, N. G.; Moore, T. R. “Modeling the magnetic pickup of an electric guitar.” American Journal of Physics 77(2), 144–150 (2009). DOI: 10.1119/1.2990663.

[2] Lemarquand, G.; Lemarquand, V. “Calculation Method of Permanent-Magnet Pickups for Electric Guitars.” IEEE Transactions on Magnetics 43(9), 3573–3578 (2007). DOI: 10.1109/TMAG.2007.891671.

[3] Paiva, R. C. D.; Pakarinen, J.; Välimäki, V. “Acoustics and Modeling of Pickups.” Journal of the Audio Engineering Society 60(10), 768–782 (2012).

[4] Lemme, H. E. W. “The Secrets of Electric Guitar Pickups.” Technical article / guitar-electronics reference; updated 2026. Includes first-order pickup electrical models, measurement methods and resonance tables.

[5] Zollner, M. Physik des Magnettonabnehmers. Selbstverlag, Regensburg (2022), 287 pp. Technical monograph; pickup impedance, loss and equivalent-network treatment.

[6] Matula, R. A. “Electrical resistivity of copper, gold, palladium, and silver.” Journal of Physical and Chemical Reference Data 8(4), 1147–1298 (1979). DOI: 10.1063/1.555614.

[7] U.S. Bureau of Standards. Circular No. 31, Copper Wire Tables, 3rd ed. Resistance conversion at 20 °C and temperature coefficient ≈ 0.00393 K⁻¹ for standard copper wire calculations.

[8] Batchelor, C.; Gooding, J.; Marriott, W.; Chalashkanov, N.; Tucker, N.; Margetts, R. “Guitar Pickups I: Analysis of the Effect of Winding and Wire Gauge on Single Coil Electric Guitar Pickups.” arXiv:2409.19782 (2024). Preprint; peer-review status not verified.

[9] EMG Pickups. 40-TW-X installation/specification sheet, model 40-TW-X. Official manufacturer documentation; output impedance 2 kΩ for cited modes.

[10] Fishman. Fluence Bass Soapbar 5-String Pickups official specifications. Output impedance 9.4 kΩ; current draw and voice peak-frequency data for the cited model.

[R1] RavenForge / Signal & Transduction Research Log A01. “From Mechanical Vibration to Electrical Signal.” 2026.09.05.

[R2] RavenForge / Signal & Transduction Research Log A02. “Pickup Position and Harmonic Sampling.” Verified revision, 2026.09.06.

[R3] RavenForge / Design Methodology Research Log B02. “Voicing Before Specification.” 2026.09.08.