Henromatic™: Inductor Network Synthesizer & Switch Fabric Engine

Henromatic™ Synthesizer & Hysteresis Resolver

Normal Synthesis

Inductors (n): 4

Engine Architecture:

Base Inductor Progression (L₁ … L_n): Quick Select:

Target Objective:

Singularity Stress Test:

Pareto States --

Game Fit --%

Fit NRMSE --%

BOM Cost $0.00

Span ΔL --

Min Step ΔL_min --

Max Gap ΔL_max --

Package Range --

Base Inductors & Required Packages: Seed Mode

Boundary Ranges & Switch Fabric

Log₁₀ Bounds (nH)

L_min: 10 nH

10¹

L_max: 100 μH

10⁵

Core Technology:

Tolerance:

Base DCR (Ω):

Switch Fabric Architecture:

Inductive Flyback & Commutation Protection: MBB Clamped

Switches:--

R_on:-- Ω

C_off:-- pF

State Sequence Scrubber & Switching Engine

State 1 / 1

Switch Sequentiality: 0% (Parallel)

Switch Toggles:ΔS = 0

Inductive Energy:-- μJ

Clamp Peak:-- V

Active Circuit Schematic (Crisp Single-Pixel Canvas): --

Inductors: 42×24px [Index Only]

✓

Pareto Selection Justification:

Canonical optimal selection: Lowest DCR copper loss, highest SRF resonance ceiling, and fewest toggled switches across equivalent inductance paths.

Y-Scale:

• Dark Line: Synthesized Pareto States • Shaded Area: Precision Tolerance Envelope [±P] • Stepped Amber Line: Minimum Core Footprint Area (mm²)

RL/RLC Filter Termination & Self-Resonant Frequency (SRF) Parameters:

R_load: Ω Test Freq (for Q): MHz

Electromagnetic Physics, Commutation Protection & Self-Resonance (SRF) Theory

Henromatic™ Electromagnetic Theory

Break-Before-Make (BBM) Arc Physics

$$v(t) = -L \frac{di}{dt} \to \infty, \quad E_m = \frac{1}{2} L I_0^2$$

The Inductive Commutation Hazard: An energized inductor enforces magnetic flux linkage continuity. Opening a contact instantaneously forces $di/dt \to -\infty$, producing hundreds to thousands of volts of flyback EMF. In air, this creates an electric arc sustaining a conductive plasma channel that pits relay contacts. In semiconductor switches, it triggers destructive avalanche punch-through.

Make-Before-Break (MBB) & TVS Clamping

$$i_L(t) = I_0 \, e^{-t/\tau_{\text{loop}}}, \quad \tau_{\text{loop}} = \frac{L_{\text{branch}}}{2 R_{\text{on}}}$$

Engineered Suppression Architecture: Henromatic applies Make-Before-Break (MBB) overlapping commutation where alternative shunt loops close before outgoing switches open, recirculating magnetic energy through switch on-resistance ($R_{\text{on}}$). Bidirectional TVS diodes across each node clamp AC/RF transients below switch breakdown ($V_{\text{clamp}} < V_{\text{BR}}$).

Core Saturation & Volumetric Growth

$$U_m = \frac{1}{2} \frac{B_{\text{sat}}^2}{\mu_0 \mu_r} \cdot \text{Vol}_{\text{core}}, \quad I_{\text{sat}} \propto \frac{B_{\text{sat}} \cdot A_e}{N \cdot \mu}$$

Ferromagnetic cores saturate above a critical flux density ($B_{\text{sat}} \approx 0.3\text{--}1.5\,\text{T}$). Handling higher inductance without saturating requires physical core volume and wire gauge: 0402 ($\le 100\,\text{nH}$) → 0603 ($\le 10\,\mu\text{H}$) → 1008 ($\le 100\,\mu\text{H}$) → 4040 ($\le 1\,\text{mH}$) → 1212 / Toroidal ($\le 10\,\text{mH}$).

Self-Resonance & Inversion

$$f_{\text{SRF}} = \frac{1}{2\pi \sqrt{L_{\text{eq}} C_{p,\text{total}}}}, \quad C_{p,\text{total}} = C_p + C_{\text{TVS}} + C_s$$

Turn-to-turn interwinding capacitance ($C_p$) plus protection junction capacitance ($C_{\text{TVS}}$) forms an intrinsic parallel resonant tank. Above $f_{\text{SRF}}$, inductive reactance collapses into capacitive reactance ($X_L \to X_C$). Henromatic's Pareto engine favors topologies that minimize $C_{p,\text{total}}$ to maintain maximum usable inductive bandwidth.