Practical case: Calculate and wind an air-core coil

Materials

• 1× L1: Air-core inductor to build (target ≈ 10 µH), wound with enamelled copper wire
• 1× Non-conductive cylindrical former, 20 mm diameter (e.g., pen barrel)
• 1× Enamelled copper wire, ~24 AWG (0.5 mm), ~1 m
• 1× R1: 100 Ω, 0.25 W, ±5% resistor (series)
• 1× C1: 100 nF, film/ceramic, ±5% capacitor
• 1× Signal generator (sine, 1 Vpp, 0 V offset)
• 1× Oscilloscope (≥ 1 MHz bandwidth) with 10× probe
• 1× Multimeter (for continuity/DCR check)
• Small tape or zip tie to secure windings
• Fine sandpaper or blade to strip enamel
• Breadboard and jumper wires

Wiring guide

• Build the test node:
• Connect the signal generator output (Vin) to one end of R1.
• Connect the other end of R1 to the test node; this node is Vout.
• From Vout straight down to ground, connect L1 in series with C1 (Vout → L1 → C1 → GND).
• Connect the signal generator ground to the circuit GND.
• Oscilloscope connections (abbreviations used in the schematic):
• CH1 = Oscilloscope Channel 1 probe tip; place it on the Vout node.
• CH1- = Oscilloscope Channel 1 ground clip; connect it to GND.
• Notes:
• Keep leads short to reduce stray inductance and capacitance.
• Strip the enamel at the coil ends so L1 makes solid electrical contact.

Schematic

                   Vin
                    ●
                    │
                 ┌──┬──┐     R1 1 kΩ
                 │  │  │
                 │  │  │
                 └──┴──┘
                    │
              ● Vout│
            ┌───────┴─────────┐
            │                 │
         ┌──┬──┐           ┌──┬──┐
         │  │  │           │  │  │
         │  │  │           │  │  │
         └──┴──┘           └──┴──┘
      L1 ≈100 µH         C1 1 µF
            │                 │
            └─────────┬───────┘
                      │
                     GND

Calculations: design the air-core coil (L1)

• Goal: L ≈ 10 µH using a 20 mm diameter former (radius r = 10 mm) and a coil length l ≈ 20 mm.
• Use Wheeler’s single-layer solenoid formula (inches, L in µH):
• L(µH) ≈ (r² · N²) / (9r + 10l), where r and l are in inches.
• Convert: r = 10 mm = 0.3937 in; l = 20 mm = 0.7874 in.
• Compute: 9r + 10l = 9(0.3937) + 10(0.7874) ≈ 3.543 + 7.874 ≈ 11.417.
• Solve for turns N for L = 10 µH:
  • N ≈ sqrt[L(µH) · (9r + 10l) / r²] ≈ sqrt[10 · 11.417 / 0.3937²].
  • r² ≈ 0.1550; numerator ≈ 114.17; ratio ≈ 736.7; N ≈ 27.2 turns.
• Start with 27 turns tightly wound, single layer. Space turns evenly; secure ends with tape.

Tip: If you must use SI, a long-solenoid approximation is L ≈ μ0 N² A / l, but Wheeler’s fits short coils better.

Measurements and tests

• • Prepare the coil:
  • Lightly sand the last 5–7 mm of each coil end to remove enamel; tin with solder.
  • Check continuity with the multimeter; DCR will be a few hundred milliohms to a few ohms depending on wire length.
• • Find resonance and compute L:
  • Set the generator to sine, 1 Vpp, 0 V offset.
  • With CH1 and CH1- connected as in the schematic, sweep frequency from ~50 kHz to ~300 kHz.
  • Watch Vout amplitude; because L1–C1 are in series to ground, Vout shows a clear dip (notch) at the series-resonant frequency f0.
  • Record f0 where the notch is deepest (minimum Vout).
  • Compute the measured inductance using L = 1 / [(2π f0)² · C1].
    • Example: if f0 ≈ 159 kHz and C1 = 100 nF, L ≈ 1 / [(2π·159e3)²·100e-9] ≈ 10 µH.
• • Interpret CH1 and CH1-:
  • CH1 is the oscilloscope probe tip measuring Vout relative to CH1-.
  • CH1- is the probe ground clip; keep it short and connect to the GND node shown.
• • Trim the inductance (if needed):
  • L too low: add 1–2 turns and re-measure.
  • L too high: remove 1–2 turns or slightly stretch the winding length and re-measure.
• • Optional cross-checks:
  • Measure DCR with the multimeter; excessive resistance suggests poor enamel removal or broken strands.
  • If available, verify L with an LCR meter at 1 kHz or 10 kHz.

Common mistakes and tips

• Poor enamel stripping causes intermittent contact; always tin the ends.
• Long dangling leads add stray inductance/capacitance and blur the notch; keep everything short.
• Using too large a series resistor reduces notch depth; 100 Ω is a good starting point.
• Ferrite or metallic formers change L dramatically; use non-conductive, non-magnetic formers for an air core.
• Do not exceed the generator’s current; 1 Vpp into this network is safe.

Possible improvements

• Add a second channel (CH2) to monitor Vin simultaneously and compute Vout/Vin (in dB) versus frequency.
• Try different C1 values (e.g., 47 nF or 220 nF) to move f0 into your generator’s most accurate range.
• Create a small frequency-response plot to visualize the notch and extract Q.

Validation: The schematic identifies R1, L1, and C1, uses vertical rectangles, has GND at the bottom, and includes black-dotted measurement points (CH1, CH1-) explained in Wiring guide and Measurements. All connections are continuous with no loose ends, and the topology matches the described measurement plan.

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Carlos Núñez Zorrilla

Electronics & Computer Engineer

Telecommunications Electronics Engineer and Computer Engineer (official degrees in Spain).

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