UNCLASSIFIED
TM-CAL-012
LC RESONANCE STANDARD
Toroid-Capacitor Resonant Circuits as Fixed Frequency Markers
Table of Contents
CHAPTER 1 — GENERAL INFORMATION
1-1. SCOPE
This manual covers construction of LC resonant circuits as fixed frequency standards and markers. When constructed with stable components (toroid inductors, NP0 capacitors), resonant frequency accuracy of ±0.1% is achievable. Used for calibrating frequency counters, VFOs, and antenna analyzers.
CHAPTER 2 — THEORY OF OPERATION
2-1. SERIES AND PARALLEL RESONANCE
Resonant frequencyfr = 1 / (2π × √(L × C))
Characteristic impedanceZ0 = √(L/C)
Q factorQ = fr / BW = Z0 / Rloss
| Type | At Resonance | Impedance | Use |
|---|---|---|---|
| Series RLC | XL = XC | Minimum (R only) | Pass filter, dip meter |
| Parallel RLC | XL = XC | Maximum (≈QZ0) | Trap filter, grid dip |
For NanoVNA calibration use: series resonator in a shunt fixture shows |S11| minimum (reflection minimum) at resonant frequency.
CHAPTER 3 — MATERIALS AND CONSTRUCTION
3-1. BILL OF MATERIALS (10 MHz STANDARD)
| Qty | Item | Specification |
|---|---|---|
| 1 | Toroid core | T50-6 (yellow) for 10–40 MHz; T50-2 (red) for 1–10 MHz |
| 1 | Enameled wire | #26 AWG for small toroids |
| 1 | NP0/C0G capacitor | Calculated value (see App A), ±1% |
| 1 | BNC chassis connector | 52mm SMA or BNC |
| 1 | Shielded enclosure | Altoids tin or machined aluminum box |
CHAPTER 4 — ASSEMBLY PROCEDURES
- Calculate required inductance for target frequency and chosen capacitor. See Appendix A.
- Wind toroid: for T50-6 with #26 AWG, 15 turns ≈ 0.8 μH. Adjust turns for calculated inductance.
- Measure wound toroid inductance with NanoVNA or LCR meter before soldering.
- Solder toroid and NP0 capacitor in series. Keep lead lengths <5 mm.
- Mount assembly in shielded enclosure with BNC connector. Short lead from series resonator to BNC center conductor; ground to BNC shell.
- Seal enclosure. Label with designed frequency.
CHAPTER 5 — CALIBRATION PROCEDURE
- Connect resonator BNC to NanoVNA PORT 1. Set NanoVNA for |S11| display, centered on expected frequency, 2 MHz span.
- Identify the |S11| dip minimum: this is resonant frequency.
- Compare to expected: error% = (fmeas − fcalc) / fcalc × 100%.
- If frequency is low, capacitance is high or inductance high: reduce C or L. If high, increase C or L. Capacitor substitution is easier than rewinding.
- Final frequency should be within ±0.1% of design target.
- Verify against WWV/GPS reference for absolute accuracy.
CHAPTER 6 — TUNING AND ADJUSTMENT
Parallel a small NP0 trimmer capacitor (5–30 pF) with the main capacitor to enable fine frequency adjustment. Trim with insulated tool to avoid hand capacitance effect.
CHAPTER 7 — VERIFICATION
- Measure Q factor: Q = fr / BW−3dB where BW is the −3 dB bandwidth from NanoVNA marker delta function.
- Q >50 at 10 MHz confirms good inductor construction. Low Q indicates lossy core material or excess resistance in connections.
- Compare resonant frequency against GPS-disciplined frequency counter.
- Log: fdesigned, fmeasured, Q, date, temperature.
APPENDIX A — CALCULATIONS AND FORMULAS
Required L for target f and chosen CL = 1 / ((2πf)2 × C)
Example: f = 7.000 MHz, C = 100 pFL = 1 / ((2π×7×106)2 × 100×10−12) = 5.17 μH
T50-6 toroid inductance formulaL (μH) = N2 × AL / 106, AL = 3.0 nH/turn2 for T50-6
APPENDIX B — EXAMPLE RESULTS
| Target f | Core | Turns | C (NP0) | f measured | Q | Error |
|---|---|---|---|---|---|---|
| 7.000 MHz | T50-6 | 17 | 100 pF | 7.012 MHz | 72 | +0.17% |
| 10.000 MHz | T50-6 | 13 | 100 pF | 10.005 MHz | 85 | +0.05% |
| 14.000 MHz | T50-6 | 10 | 47 pF | 14.02 MHz | 91 | +0.14% |