UNCLASSIFIED
TM-CAL-011
RC TIME-CONSTANT STANDARD
Precision RC Circuit for Oscilloscope Timebase Calibration
Table of Contents
CHAPTER 1 — GENERAL INFORMATION
1-1. SCOPE
This manual covers construction and use of precision RC time-constant circuits as time and frequency calibration references for oscilloscopes and time-interval counters. With GPS-disciplined timing and C0G/NP0 capacitors, time constant accuracy of ±0.1% is achievable.
CHAPTER 2 — THEORY OF OPERATION
2-1. RC EXPONENTIAL RESPONSE
Time constant definitionτ = R × C
Voltage at time t (charging)V(t) = Vsupply × (1 − e−t/τ)
Time to reach 63.2% of supplyt63% = τ = R × C
10–90% rise timetr = 2.197 × τ
| R (Ω) | C | τ | f−3dB | Notes |
|---|---|---|---|---|
| 1k | 100 nF | 100 μs | 1592 Hz | Scope timebase ref |
| 1k | 1 μF | 1 ms | 159.2 Hz | Easy to measure |
| 10k | 100 nF | 1 ms | 159.2 Hz | Low current |
| 100k | 10 nF | 1 ms | 159.2 Hz | Very low current |
2-2. COMPONENT STABILITY
Capacitor types for precision RC standards:
- C0G/NP0: TC = 0 ±30 ppm/°C. Best choice for precision RC standards.
- X7R: TC = ±15% over temperature. Not acceptable for standards.
- Polystyrene: TC ≈ −120 ppm/°C. Very stable, good for audio range.
- Mica: TC ≈ ±50 ppm/°C. Good, but large and expensive.
NOTEResistor types: use 0.1% metal film or better. See TM-CAL-008. Avoid wirewound in AC circuits due to inductance.
CHAPTER 3 — MATERIALS AND CONSTRUCTION
3-1. BILL OF MATERIALS
| Qty | Item | Specification |
|---|---|---|
| 2 | Metal film resistor | 1kΩ 0.1%, for R1 and verification R |
| 2 | C0G/NP0 capacitor | 100 nF ±1%, 50 V |
| 1 | GPS 1PPS source | See TM-CAL-002 |
| 1 | SPDT signal switch | Low leakage, for step-function drive |
| 1 | BNC connectors | Input and output |
CHAPTER 4 — ASSEMBLY PROCEDURES
- Solder 1kΩ resistor and 100 nF C0G capacitor in series on small PCB. Mount cap vertically to minimize stray capacitance to ground.
- Connect output across capacitor to BNC output connector.
- Connect input (drive side of resistor) to BNC input connector via signal switch.
- Keep lead lengths short (<15 mm) to minimize stray inductance and capacitance.
- Mount in small shielded enclosure. Ground the enclosure.
- Connect switch control line to GPS 1PPS output for step-function generation.
CHAPTER 5 — CALIBRATION PROCEDURE
- Set oscilloscope timebase to 200 μs/div (2 ms full screen).
- Apply a step function to the RC input (switch from 0V to +5V at GPS 1PPS).
- Display the exponential charge curve on scope.
- Measure time for output to reach 63.2% of +5V = 3.16 V. This is τ.
- Compare measured τ against calculated: τ = R × C = 1000 × 100×10−9 = 100 μs.
- Error ppm = (measured τ − calculated τ) / calculated τ × 106.
- If error exceeds ±500 ppm: remeasure R and C with 4-wire method.
- The RC standard then calibrates the scope: adjust scope timebase until displayed τ matches calculated value.
CHAPTER 6 — TUNING AND ADJUSTMENT
NOTEThe RC standard is not adjustable post-construction. Select R and C with measured values. Calculate τtrue = Rmeas × Cmeas using measured component values as the reference, not nominal values.
CHAPTER 7 — VERIFICATION
- Verify calculated τ by oscilloscope cursors at two time-constant multiples: at 2τ, V = 86.5% of supply. Both measurements should be consistent.
- Cross-check: apply 1 kHz square wave to RC input. Measure −3 dB frequency with NanoVNA. f−3dB = 1/(2πτ) = 1/(2π×100μs) = 1592 Hz.
- Log: R measured, C measured, τ calculated, τ measured, scope timebase error %.
APPENDIX A — CALCULATIONS AND FORMULAS
Time constantτ = R × C
−3 dB frequencyf−3dB = 1 / (2πτ)
10–90% rise timet10-90 = 2.197 × R × C
Scope timebase error from measured vs. expected τerror% = (tscope − tcalculated) / tcalculated × 100%
APPENDIX B — EXAMPLE RESULTS
| R (meas) | C (meas) | τ (calc) | τ (scope) | Error | f-3dB (NanoVNA) |
|---|---|---|---|---|---|
| 999.8 Ω | 100.2 nF | 100.18 μs | 100.0 μs | −0.18% | 1589 Hz (calc 1589) |