Unit 1 — Theory of Operation

TM-CAL-011 — Open Handout TM Chapter: Chapter 2 ELOs: Understand how the reference standard generates or maintains its reference value; identify key specifications Estimated time: 20 minutes

Step 1: Read the TM

Open TM-CAL-011. Read Chapter 2 — Theory of Operation completely.

Then come back here.

Chapter 2 Content

2-1. RC EXPONENTIAL RESPONSE

Time constant definition
τ = R × C

Voltage at time t (charging)
V(t) = Vsupply × (1 − e−t/τ)

Time to reach 63.2% of supply
t63% = τ = R × C

10–90% rise time
tr = 2.197 × τ

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.

NOTE: Resistor types: use 0.1% metal film or better. See TM-CAL-008. Avoid wirewound in AC circuits due to inductance.

Why Theory Matters for Calibration

You cannot calibrate what you do not understand. Theory tells you: - What the instrument or standard is supposed to do — so you recognize when it is not doing it - What the sources of error are — so you know which ones your calibration procedure addresses - What the limits of the calibration are — so you know when to stop and call it good

If a calibration measurement produces a surprising result, theory is where you look first.

Self-Check Questions

SC1-1. In one sentence, state the operating principle of the RC TIME-CONSTANT STANDARD as described in Chapter 2.

SC1-2. What does Chapter 2 identify as the primary source(s) of measurement error or uncertainty?

SC1-3. What key specification(s) (accuracy, range, resolution) does the TM state for this standard?

SC1-4. What safety precaution does §1-3 specify? State it exactly.

SC1-5. What references does §1-2 cite? List at least two.

Answer Key

SC1-1. See TM §2-1. Compare your sentence to the first substantive paragraph of Chapter 2.

SC1-2. See Chapter 2. Look for language about error sources, uncertainty, drift, or limiting factors.

SC1-3. See Chapter 2. Look for numbers with units: %, ppm, Hz, Ω, dB.

SC1-4. See TM §1-3. Copy the safety text exactly.

SC1-5. See TM §1-2. The references list is there.

Checkpoint

Before proceeding, state without looking: - The operating principle of the RC TIME-CONSTANT STANDARD - The primary error source(s) - At least one key specification with its value

→ Proceed to Unit 2