flowchart TD
Model["Declared physical model<br/>and independent coordinates"] --> Operation["Transform, reduce,<br/>quantize, solve, or fit"]
Operation --> Result["Result in a declared<br/>basis and normalization"]
Boundary["Ports, environment,<br/>and approximation"] --> Operation
Result --> Observable["Named observable<br/>and allowed interpretation"]
Source["Primary model support<br/>and page derivation"] -. "scope of the claim" .-> Operation
Knowledge
Look up physical concepts, modeling methods, assumptions, and source support.
Use this catalog when you know the quantity or operation you need. For a connected introduction, choose a Learning Path. Every node separates a physical model, a mathematical operation, and the observable that can actually be reported.
Variables, phase, and stored energy
- Symbol conventions: which qualifiers identify topology, basis, channel, and processing?
- Dynamics conventions: which signs, units, frames, and time-evolution rules apply?
- One LC in every language: how do energy, resonance, admittance, and oscillator amplitude relate?
- Gauge-invariant phase: which branch phase is observable?
- Fluxoid quantization: what does a loop quantize, and why can applied flux remain continuous?
- Josephson current, energy, and inductance: when is a cosine element different from its linearized inductance?
Circuit and quantum models
- Physical circuit coordinates: which nodes, reference, branch maps, and open operator belong to the physical model?
- Lagrangian, Hamiltonian, and quantization: which conservative energies and independent coordinates support the Legendre transform?
- Normalization: which scaling is canonical, local, or merely a residual scale?
- Cosine and anharmonicity: how does a classical nonlinear energy change a quantum spectrum?
- SQUID tunability: what changes with asymmetry, loop inductance, and bias?
- Inductive coupling: how do signed mutual inductance, self inductance, and dimensionless coupling relate?
- Zero exchange and residual ZZ: why are exchange cancellation and conditional transition shifts different outcomes?
Fields and distributed lines
- Field-extracted C and L: what energy, basis, and reference does an extraction represent?
- RLGC matrices: what belongs to conductors, modes, or a particular matrix representation?
- Telegrapher model: what does a uniform distributed line predict?
- Matrix-to-pi lowering: what is approximated, and where do the endpoint half shunts go?
- Resonator estimate: what does a quarter-wave estimate or local equivalent LC mean?
Open response and observation
- Port references: what is a wave reference, a physical load, or a reference plane?
- Node and line flux to input-output: how does a physical attachment produce waves and radiative rates?
- Multimode scattering: how do internal dynamics, emission, direct propagation, and repeated reflections combine?
- Poles, zeros, and residues: which feature belongs to internal dynamics, interference, or one response projection?
- Decay, linewidth, and Q: how do amplitude decay, energy decay, complex poles, and spectral widths differ?
- Network trace views: what can an S, Y, or Z trace and its processing actually constrain?
- Vector fitting and passivity: what can a rational response fit establish, and why is a scalar transmission not a complete passive network?
- Finite-order response and chain realizations: which internal realization preserves the declared response?
Reduction and nonlinear methods
- Coordinate transforms: how do variables and power-conjugate maps change together?
- Schur/Kron reduction: what is eliminated under the stated boundary condition?
- Termination compensation: which proven shunt may be subtracted without deleting a physical load?
- Harmonic balance: what periodic question does the finite Fourier solve answer?
Engineering uses and decisions
- System objectives and trade-offs: which owner defines a goal, quantity, weight, or threshold?
- Charging-energy targeting and local reduction: when does a static charging-energy estimate differ from dynamic capacitance or decay?
- Human-reviewable report export: which evidence must remain inspectable when a report leaves its producer?
- Potential individual-filter footprint: which generic design questions are still open?
Follow a relationship, not just a title
The relationship map scrolls horizontally when needed; its labels remain readable rather than shrinking to the page width.
A mathematical operation transforms or estimates a declared object. It does not create physical ownership by itself. A fitted pole, an internal diagonal root, a Hamiltonian coefficient, and a measured trace are different results even when their units coincide.
For source identity, supported scope, source-device examples, or unresolved bibliographic notes, use References. For contributions, citation categories, and review-state meanings, use the Authoring Guide. Package APIs, version-specific behavior, and private project evidence stay with their source owners; see package documentation.