================================================================================ TM-VCAP-SCH-004 Rev A SLIDING PVC PIPE VARIABLE CAPACITOR — CONSTRUCTION Coaxial Plunger-Type Air/Polymer Dielectric ================================================================================ 1. OPERATING PRINCIPLE ======================= A coaxial capacitor is formed by two concentric cylindrical conductors separated by a thin dielectric layer. Capacitance is proportional to the overlap length: C(x) = ε₀ × εᵣ × 2πa / d × x = K × x (K in pF/mm; x = insertion depth in mm) This is the THIN-SHELL approximation, valid when d << a (gap << radius). The formula is the circumferential parallel-plate equation "unwrapped." Physical analogy: Area A = 2πa × x (cylindrical shell area for length x) C = ε₀εᵣA/d (same as flat plate, but area is curved shell) 2. CROSS-SECTION VIEW (PIPE-HF DESIGN, 1/2" PVC) =================================================== OUTER SLEEVE (3D-printed PETG or flexible vinyl) ┌─────────────────────────────────────────────────────┐ │ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ │ ← PETG/vinyl wall │ ◄══════════════ copper foil tape inside ══════════► │ ← OUTER CONDUCTOR │ ┌─────────────────────────────────────────────────┐ │ │ │ ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ │ │ ← polymer dielectric film │ │ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ │ │ ← copper foil tape │ │ ═════════════════════════════════════════════ │ │ ← PVC pipe wall │ │ AIR CORE │ │ │ │ (inner pipe hollow) │ │ │ │ ═════════════════════════════════════════════ │ │ │ │ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ │ │ ← copper foil tape │ │ ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ │ │ ← polymer dielectric film │ └─────────────────────────────────────────────────┘ │ │ ◄══════════════ copper foil tape inside ══════════► │ │ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ │ └─────────────────────────────────────────────────────┘ LEGEND: ▓▓ = copper foil tape (conductor) ░░ = polymer dielectric film (Kapton, OHP, PTFE tape) ══ = PVC pipe wall (insulator, structural) KEY DIMENSIONS (PIPE-HF): ┌─────────────────────────────────────────────────────┐ │ Inner PVC pipe OD: 21.34 mm (1/2" Schedule 40) │ │ Copper foil on pipe: +0.10 mm → 21.54 mm │ │ Polymer dielectric: +0.13 mm → 21.80 mm (Kapton) │ │ Outer sleeve ID: ~22.0 mm (0.2mm clearance) │ │ Outer foil (inside sleeve): applied before sleeve │ │ Conductor radius a: 10.77 mm │ │ Dielectric gap d: 0.13 mm │ │ C per mm: ~17.7 pF/mm │ └─────────────────────────────────────────────────────┘ 3. SIDE VIEW — PLUNGER ASSEMBLY (MANUAL VERSION) ================================================= INSERTION DEPTH x ←──────────────→ ┌────────────────────────────────────────────────────────────────┐ │ FIXED END CAP OUTER SLEEVE (stationary) OPEN END │ │ (3D print) ┌───────────────────────┐ (guide) │ │ ┌──────┐ │▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓│ ┌─────┐ │ │ │ T₂ ├──────────┤ outer conductor foil ├──────────┤guide│ │ │ │(outer│ │▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓│ │bushing│ │ │term.)│ └─────────────┬─────────┘ └──┬──┘ │ │ └──────┘ │ │ │ │ INNER PIPE (slides) │ │ │ │ ════════════════════╪════════════════════════╪═══→│ │ ░░░░░░░░░░░░░░░░░░░│ poly dielectric film │ │ │ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓│ copper foil on inner │ │ │ ══════════════════════════════════════════════════→│THUMB │ ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓│ copper foil on inner │ │KNOB │ ░░░░░░░░░░░░░░░░░░│ poly dielectric film │ │ │ ════════════════════════════════════════════════════ │ ↑ ↑ │ │ T₁ (inner) scale marks on inner pipe │ │ terminal (mm and pF scale) │ └────────────────────────────────────────────────────────────────┘ ← C_min C_max → (inserted 0mm) (inserted x_max mm) POSITION SCALE: Engrave or mark on INNER PIPE at: 0, 10, 20, 30, 50, 75, 100, 125, 150mm Label with corresponding pF: 0, 177, 354, 531, 885, 1328, 1770, 2213, 2655 pF (for PIPE-HF: K = 17.7 pF/mm; mark at x_min alignment point on sleeve edge) 4. CONSTRUCTION SEQUENCE — INNER PIPE PREPARATION =================================================== Step 1 — Clean inner pipe surface: Wipe 1/2" Schedule 40 PVC pipe with IPA. Ensure no mold release agent, printing inks, or grease. Step 2 — Apply copper foil tape: Use 0.1mm copper foil tape (self-adhesive, conductive adhesive type). Wrap helically with 50% overlap, length = max_depth + 30mm extra. Burnish flat with fingernail tool; eliminate air bubbles. Ensure NO copper extends past one end — leave 15mm bare for thumb knob. At wire-end: leave 25mm copper tab extending beyond pipe end for terminal. Step 3 — Apply polymer dielectric: For KAPTON (preferred): wrap single layer helically; overlap 2mm. For OHP transparency: cut strip, width = π × pipe_OD + 5mm (one wrap + overlap). Secure with one small piece of scotch tape at start and end. For PTFE tape: wrap 8 tight turns for 0.61mm total thickness. CRITICAL: No wrinkles or folds. Smooth completely — wrinkles = voltage hotspots. Step 4 — Check dielectric: Before inserting into sleeve: use ohmmeter — must read >10 MΩ between copper foil on pipe and any metal tool pressed against outer dielectric surface. Step 5 — Apply guide strips (for 3D-printed sleeve): Optional: apply 3× strips of 3mm PTFE tape on pipe end as low-friction glide pads. Position at 0°, 120°, 240° around circumference. 5. CONSTRUCTION SEQUENCE — OUTER SLEEVE PREPARATION ===================================================== Option A — 3D-Printed PETG Sleeve (TM-VCAP-ENC-006): Print sleeve per OpenSCAD file. Sand ID smooth (220 grit). Apply copper foil tape to INSIDE before assembly (cannot reach after): Cut one strip = π × sleeve_ID width × sleeve_length. Press into sleeve; burnish edge with rod. Verify: ohmmeter continuity along full length of sleeve foil. Option B — Flexible Vinyl Sleeve (for PIPE-QRP, no 3D printing): Use 1" garden soaker hose or vinyl tubing, ID = 20mm (relaxed). Clean inside surface. Cut to max_depth + 40mm. Turn inside-out. Apply copper foil tape in section = max_depth mm. Turn right-side-out. Sleeve will stretch slightly when inner pipe is inserted. ADVANTAGE: Self-centering, no clearance gap, consistent contact. Option C — Rolled Sheet Capacitor (flat-plate variant): Instead of round pipe: use flat PVC sheet 60×(max_depth+30)mm as inner plate. Copper foil on both faces of a polymer sheet. Slides into PVC channel (cut from flat PVC sheet). Uses formula: C(x) = ε₀ × εᵣ × W × x / d (W = width, x = depth, same formula) 6. ELECTRICAL CONNECTIONS =========================== TERMINAL T₁ (inner pipe / moving conductor): Solder flexible wire (18 AWG) to the copper foil tab at the far end of inner pipe. Wire must be LONG enough to allow full insertion without tension. Use coiled flexible hookup wire to maintain flexibility. IMPORTANT: As inner pipe moves, the wire curls/uncoils — plan for this. TERMINAL T₂ (outer sleeve / fixed conductor): Solder wire directly to copper foil on inner surface of sleeve, accessible through slot in end cap or via foil tab that extends past sleeve end. HV ISOLATION: At voltages >500V: use ceramic standoffs for wire routing. Keep T₁ and T₂ wires separated by ≥ V_work/2kV × 10mm spacing in air. For PIPE-HF-HV (7.3kV working): separate by ≥ 37mm in air. Insulate thumb knob from inner pipe with PTFE sleeve if >200V expected. 7. MOTORIZED VERSION — LEAD SCREW DRIVE ========================================= M6 × 1.0mm threaded rod drives inner pipe via 3D-printed nut adapter. Motor and rod are collinear with inner pipe: [NEMA14 motor]──[shaft coupler]──[M6 threaded rod]──[nut in inner pipe end cap] | | fixed to slides inner outer sleeve end cap pipe axially Travel per motor revolution: 1.0mm (M6 × 1.0 pitch) At 1/8 microstepping (1600 µsteps/rev): 0.000625 mm/µstep ΔC per µstep (PIPE-HF): 0.000625 × 17.7 = 0.011 pF/µstep Limit switches: micro-switch at x=0 (min insertion) and x=max_depth (fully inserted) Position sensing: count motor steps from home (no separate encoder needed) Verify with pot on lead screw shaft if missed steps are a concern. See TM-VCAP-FW-001 config.h, CAP_DRIVE_MODE = LINEAR for firmware configuration. 8. CALIBRATION ================ 1. Mark "ZERO" line on inner pipe where it exits sleeve at minimum insertion. 2. Slowly insert inner pipe to x=10mm; measure C with LCR meter at 1 kHz. 3. Verify: measured C ≈ C_min + K × 10mm (from TM-VCAP-CAL-005 table). 4. If C/mm is low: dielectric wraps may have air gaps — re-wrap more tightly. 5. If C/mm is high: check for tube deformation creating areas of reduced d. 6. Record calibrated K in NVS via `SETC PIPE_K ` command. ================================================================================ END TM-VCAP-SCH-004 ================================================================================