The hexadecimal series configuration uses a single-pole, 16-position (hex 0-F) rotary switch to select one of 16 discrete series components. For precision bench loads, programmable current limiters, or selectable voltage dividers, this topology eliminates the cumulative contact resistance and complex equivalent-resistance math inherent in binary DIP switch arrays. By routing current through a single mechanical wiper rather than multiple series/parallel switch contacts, you guarantee predictable, repeatable resistance values down to the milliohm.
The Hexadecimal Series Topology: Nodes and Architecture
In a standard hexadecimal series resistor network, the 16 discrete resistors are arranged in a star or fan topology around the rotary switch. This is fundamentally different from a binary weighted network (like an R-2R ladder) or a parallel DIP switch array where multiple resistors are active simultaneously.
A 4-position DIP switch set to parallel selection requires you to calculate the equivalent parallel resistance for all 16 combinations. Worse, mechanical DIP switches exhibit contact resistance (typically 50mΩ to 100mΩ per pole). When current flows through multiple DIP contacts in series or parallel, that contact resistance compounds unpredictably, destroying precision at low-ohm values. The hexadecimal series topology uses a single rotary wiper, ensuring exactly one mechanical contact is in the primary current path regardless of the selected position.
Node Labels and Routing
- V_IN: The common input node tied to one leg of all 16 resistors.
- R1 through R16: The discrete series elements (mapped to Hex 0 through Hex F).
- SW_0 to SW_F: The 16 stator terminals on the rotary switch.
- SW_COM (Wiper): The common rotating contact that bridges the selected stator terminal to the output.
- V_OUT: The switched output node connected directly to SW_COM.
Current enters at V_IN, passes through exactly one resistor (R_n), enters the switch at stator SW_n, crosses the wiper contact, and exits at V_OUT via SW_COM.
Behavior Matrix: Failure Modes at the Extremes
When designing for the bench or industrial environments, you must understand what happens when a single element fails. Because the hexadecimal series topology isolates each path, failures are strictly localized to the selected position.
| Failure Event | Affected Position(s) | Circuit Behavior & Measurement | System Consequence |
|---|---|---|---|
| Resistor R5 Opens | Hex 4 only | Infinite resistance (Open Circuit) at Hex 4. All other positions measure normally. | Loss of one specific step; no damage to downstream load. |
| Resistor R5 Shorts | Hex 4 only | Resistance drops to ~50mΩ (wiper contact resistance + wire trace) at Hex 4. | Massive current spike if V_IN is an unregulated supply; potential wiper melting. |
| Switch Wiper (SW_COM) Fails Open | All 16 positions | Infinite resistance across all settings. | Total system failure; load loses power entirely. |
| Wiper Contact Degrades (High Resistance) | All positions (variable) | Measured resistance = R_n + degradation (e.g., +2Ω to +10Ω). | Severe precision loss at low-ohm settings; negligible error at high-ohm settings. |
| Adjacent Stator Short (SW_5 to SW_6) | Hex 4 and Hex 5 | Selecting Hex 4 or Hex 5 places R5 and R6 in parallel. | Yields an unintended intermediate resistance value; no catastrophic failure. |
Design Walkthrough: 16-Step Precision Current Limiter
Let’s design a practical hexadecimal series network: a 16-step selectable current limiter for a 12V DC test rail. We want 16 linearly spaced current steps from 10mA (Hex F) to 160mA (Hex 0). According to SparkFun's resistor guidelines, selecting the right tolerance and material is critical for thermal stability in current-limiting applications.
Calculating the Resistor Values
Using Ohm’s Law (R = V / I), we calculate the required resistance for each of the 16 hexadecimal positions. We will select the nearest standard 1% E96 series values to ensure you can actually buy these off the shelf.
| Switch Pos (Hex) | Target Current | Calculated R (Ω) | Nearest 1% E96 Value | Actual Current @ 12V |
|---|---|---|---|---|
| 0 | 160 mA | 75.0 | 75.0 Ω | 160.0 mA |
| 1 | 150 mA | 80.0 | 80.6 Ω | 148.9 mA |
| 2 | 140 mA | 85.7 | 86.6 Ω | 138.6 mA |
| 3 | 130 mA | 92.3 | 93.1 Ω | 128.9 mA |
| 4 | 120 mA | 100.0 | 100 Ω | 120.0 mA |
| 5 | 110 mA | 109.1 | 110 Ω | 109.1 mA |
| 6 | 100 mA | 120.0 | 121 Ω | 99.2 mA |
| 7 | 90 mA | 133.3 | 133 Ω | 90.2 mA |
| 8 | 80 mA | 150.0 | 150 Ω | 80.0 mA |
| 9 | 70 mA | 171.4 | 174 Ω | 69.0 mA |
| A | 60 mA | 200.0 | 200 Ω | 60.0 mA |
| B | 50 mA | 240.0 | 243 Ω | 49.4 mA |
| C | 40 mA | 300.0 | 301 Ω | 39.9 mA |
| D | 30 mA | 400.0 | 402 Ω | 29.9 mA |
| E | 20 mA | 600.0 | 604 Ω | 19.9 mA |
| F | 10 mA | 1200.0 | 1.21 kΩ | 9.9 mA |
Power and Material Selection
The maximum power dissipation occurs at the highest current setting (Hex 0, 160mA). P = I²R = (0.16)² × 75 = 1.92W. A standard 1/4W or 1/2W axial resistor will instantly overheat and drift, or fail open. For the lower resistance values (Hex 0 through Hex 5), you must use 2W or 3W wirewound or metal oxide resistors. For Hex 6 through Hex F, 1/2W metal film is sufficient. As noted in Analog Devices' guidelines on resistor selection, metal film provides superior thermal stability and lower noise compared to carbon composition, which is critical when maintaining a tight current tolerance.
Breadboard Testing and Verification Protocol
Before soldering this network into a permanent enclosure or PCB, you must validate the switch contact resistance and the physical layout on a solderless breadboard. High-current paths on breadboards are notorious for voltage drops due to poor spring-clip tension.
- Prep the Switch: Solder 18 AWG solid-core pigtails to the SW_COM (wiper) and all 16 stator pins of your rotary switch. Do not rely on breadboard clips to grip bare switch terminals.
- Seat the Resistors: Insert the 16 resistors into the breadboard. Connect one leg of every resistor to a common heavy-gauge bus wire (this will be V_IN). Connect the other leg of each resistor to the corresponding switch stator pigtail.
- Measure Contact Baseline: Set your multimeter to the lowest ohms range (typically 200Ω or 4-wire mode if available). Short your probes to establish your lead resistance baseline. Measure across SW_COM and the active stator pin before adding resistors. A healthy rotary switch should read between 0.02Ω and 0.05Ω.
- Validate the Extremes: Connect V_IN and V_OUT to your DMM. Dial to Hex 0 (160mA target). Record the resistance. Dial to Hex F (10mA target). Record the resistance. Ensure the measured values match your E96 table within 1% plus the 0.05Ω contact offset.
- Thermal Sweep: Inject 12V at Hex 0. Monitor the lowest-value resistor with a thermal camera or IR thermometer for 60 seconds. If the resistor body exceeds 80°C, your breadboard clips are adding series resistance and generating heat, or the resistor wattage rating is insufficient. Move to a soldered perfboard for high-current validation.
Decision Path: Finalizing Your Switch and Resistor Specs
Selecting the exact hardware for a hexadecimal series network depends entirely on your current and precision requirements. Use the decision matrix below to lock in your Bill of Materials (BOM).
| Design Constraint | If True... | If False... |
|---|---|---|
| Is max current > 500mA? | Require switch with >1A contact rating; use 16 AWG wiring. | Standard 250mA signal switch is acceptable. |
| Is precision tolerance < 1% required? | Use metal foil or precision wirewound resistors; require 4-wire Kelvin switch. | Standard 1% metal film (CMF series) is adequate. |
| Will the switch be adjusted while powered (Hot Switching)? | Require "Make-Before-Break" (MBB) switch contacts to prevent arcing/open-circuit spikes. | Standard "Break-Before-Make" (BBM) is safer and cheaper. |
The Concrete BOM Pick
For a standard 12V bench load operating under 250mA where precision is 1% and hot-switching is avoided (you turn off the supply before turning the knob), terminate your design with this exact hardware:
- The Switch: Grayhill 56A16-01-1-AJN. This is a 16-position, 1-deck, break-before-make rotary switch rated for 200mA at 115VAC (which safely translates to ~1A at 12VDC resistive loads). It features a 30-degree index angle, perfectly mapping to 16 discrete hex steps.
- The Resistors: Vishay Dale CMF55 series (1/2W, 1%, 100ppm/°C) for positions Hex 6 through Hex F. For positions Hex 0 through Hex 5, use Vishay Dale CW005 5W wirewound resistors to handle the thermal load without drifting.
By committing to this specific hexadecimal series topology and hardware set, you eliminate the guesswork of parallel equivalent math and ensure your bench load behaves exactly as the schematic dictates, step after step.
