5.4 Multi-Loop Arrays, Lead-In Cable & Pull-Box Splicing

5.4 Multi-Loop Arrays, Lead-In Cable & Pull-Box Splicing

1. Multi-Loop Arrays: Series vs. Parallel Calculations

When multiple detection loops are deployed in a single lane to cover a stop-bar zone, they can be wired in Series or Parallel configurations before terminating into the lead-in cable.

Mathematical Formulation

• Series Array: Inductances add directly: $L_{\text{series}} = L_1 + L_2 + \dots + L_n = \sum_{i=1}^n L_i$
• Parallel Array: Reciprocal addition: $\frac{1}{L_{\text{parallel}}} = \frac{1}{L_1} + \frac{1}{L_2} + \dots + \frac{1}{L_n} \implies L_{\text{parallel}} = \frac{L_1 \cdot L_2}{L_1 + L_2} \quad (\text{for } n=2)$

Sensitivity Impact Analysis

Consider two identical loops, each having baseline inductance $L = 120\ \mu\text{H}$. When a vehicle occupies Loop 1, it produces an inductance reduction $\Delta L = 1.2\ \mu\text{H}$ ($1.0%$ change on Loop 1):

1. In Series: $L_{\text{total}} = 120 + 120 = 240\ \mu\text{H}$ $\left( \frac{\Delta L}{L} \right)_{\text{system}} = \frac{1.2}{240} = 0.005 = 0.50\%$ System sensitivity drops by exactly half.
2. In Parallel: $L_{\text{total}} = \frac{120 \cdot 120}{120 + 120} = 60\ \mu\text{H}$ Equivalent inductance change across parallel branches: $\Delta L_{\text{eq}} = L_{\text{total}} - \frac{(L - \Delta L) \cdot L}{(L - \Delta L) + L} = 60 - \frac{118.8 \cdot 120}{238.8} = 60 - 59.7 = 0.3\ \mu\text{H}$ $\left( \frac{\Delta L}{L} \right)_{\text{system}} = \frac{0.3}{60} = 0.005 = 0.50\%$

Why Series Wiring is Strongly Preferred

While both configurations reduce single-loop sensitivity by $50%$, parallel wiring cuts total circuit inductance in half ($60\ \mu\text{H}$). If three loops were wired in parallel, total inductance would collapse to $40\ \mu\text{H}$—falling below the critical $50\ \mu\text{H}$ operating minimum of standard NEMA TS2 detector amplifiers! Furthermore, if one loop conductor breaks open in a parallel circuit, the system continues to run on the remaining loops at an altered inductance, masking the failure. In a series circuit, an open wire triggers an immediate cabinet loop-fault indicator, alerting technicians. Therefore, series wiring is standard engineering practice for stop-bar loop arrays.

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2. Lead-in Cables (IMSA 50-2) & Pull-Box Splicing Standards

IMSA Spec 50-2 Lead-In Cable Characteristics

The home-run connection between the roadside pull box and the cabinet detector rack utilizes IMSA Spec 50-2: a shielded, twisted-pair cable:

• Conductors: #14 AWG or #16 AWG stranded tinned copper, twisted at a minimum of 3 to 5 twists per foot.
• Shielding: Helically wrapped aluminum-polyester foil tape providing $100%$ electrostatic shielding coverage.
• Drain Wire: Continuous #16 AWG stranded or solid tinned copper drain wire in intimate electrical contact with the aluminum shield.
• Jacket: High-density polyethylene (HDPE), outdoor UV-rated and water-submersion resistant.
• Distributed Electrical Characteristics:
  • Distributed Inductance: $\approx 20\ \mu\text{H}$ per $1,000\text{ ft}$ ($0.02\ \mu\text{H/ft}$).
  • Distributed Capacitance: $\approx 25\text{ to } 35\text{ pF/ft}$.

Total Circuit Inductance Calculation

The total circuit inductance presented to the cabinet detector amplifier is the sum of the embedded loop array inductance plus the total lead-in cable inductance: $L_{\text{circuit}} = L_{\text{loops}} + \left( \text{Length}_{\text{lead-in}} \times 0.02\ \mu\text{H/ft} \right)$

Worked Engineering Example: Inductive Circuit Calculation

An intersection approach features two 6 ft x 6 ft stop-bar loops (each having 4 turns, with measured individual inductance $L_1 = 120\ \mu\text{H}$ and $L_2 = 120\ \mu\text{H}$) wired in series in the field pull box. The pull box is connected to the traffic signal cabinet via a 500-foot run of IMSA Spec 50-2 shielded lead-in cable.

Step 1: Calculate total loop array inductance: $L_{\text{array}} = L_1 + L_2 = 120\ \mu\text{H} + 120\ \mu\text{H} = 240\ \mu\text{H}$

Step 2: Calculate lead-in cable inductance: $L_{\text{lead-in}} = 500\text{ ft} \times \left( \frac{20\ \mu\text{H}}{1,000\text{ ft}} \right) = 500 \times 0.02\ \mu\text{H/ft} = 10\ \mu\text{H}$

Step 3: Calculate total circuit inductance: $L_{\text{total}} = L_{\text{array}} + L_{\text{lead-in}} = 240\ \mu\text{H} + 10\ \mu\text{H} = 250\ \mu\text{H}$ Result: $250\ \mu\text{H}$ sits squarely within the optimal $100 - 300\ \mu\text{H}$ amplifier tuning window.

Pull-Box Splice Enclosure Protocols

The electrical splice between the IMSA 51-5 loop wire tails and the IMSA 50-2 lead-in cable is the single most frequent failure point in traffic signal detection.

Pull Box Splice Detail
+-------------------------------------------------------------------------+
| IMSA 51-5 Loop Tails (Twisted >= 5 turns/ft)                           |
| --- Loop Wire 1 --+                                                     |
|                   | Soldered Western Union Splice                       |
| --- Loop Wire 2 --|-+                                                   |
|                   | |                                                   |
| IMSA 50-2 Lead-In | |                                                   |
| --- Conductor 1 --+ | Dual-Wall Adhesive-Lined Heat Shrink              |
| --- Conductor 2 ----+ or Gel-Filled Re-enterable Splice Kit             |
|                                                                         |
| --- Shield / Drain Wire ----> [CUT, TAPED & INSULATED - FLOATED!]        |
+-------------------------------------------------------------------------+
                                      | (No connection to earth in pull box)
                                      v
                           Cabinet End: DRAIN GROUNDED

Mandatory Splice Specifications

1. Tail Twisting: Loop lead-in tails exiting the pavement saw cut into the conduit must be twisted at a minimum rate of 5 to 6 twists per foot. Untwisted tails act as open magnetic receiver coils, picking up stray 60 Hz electrical noise from adjacent signal cables.
2. Conductor Splicing: Conductors must be mechanically joined using a Western Union splice or copper crimp sleeves, followed by thorough soldering using 60/40 rosin-core solder. Wire nuts, twist-on connectors, and push-in terminals are strictly forbidden.
3. Waterproof Sealing: Splices must be encapsulated using one of two approved methods:
   • Method A: A rigid transparent mold body injected with polyurethane or epoxy re-enterable potting resin.
   • Method B: Pre-filled silicone/gel-filled submersible splice enclosures, or heavy-wall cross-linked polyolefin heat-shrink tubing lined with thermoplastic hot-melt adhesive extending at least $2\text{ inches}$ beyond stripped jackets.
4. Single-Point Shield Grounding Rule: The aluminum shield and bare copper drain wire of the IMSA 50-2 cable must be insulated and floated (not connected to ground) in the field pull box. The drain wire is connected to earth ground ONLY inside the traffic signal cabinet at the detector rack ground busbar. Critical Warning: Grounding the shield at both the pull box and the cabinet establishes a Ground Loop. Potential differences between earth points drive circulating 60 Hz AC currents through the shield, inducing severe 60 Hz hum across the detector input that completely destabilizes loop tuning!