Unit 4 — Calibration Procedure and Calculations

TM-CAL-017 — Open Handout TM Chapters: Chapter 5, Appendix A ELOs: Execute calibration procedure; compute error and determine pass/fail Estimated time: 30 minutes

Step 1: Read the TM

Open TM-CAL-017. Read Chapter 5 and Appendix A completely.

Then come back here.

Chapter 5 — Calibration Procedure

  1. Transmit CW at calibrated power PW (measured at TX antenna feedpoint).
  2. Record received signal level Srx (dBm or dBμV/m) at known distance.
  3. Calculate expected E: E = √(30 × P × G) / d.
  4. If receive antenna is a calibrated dipole: received power Prx = E2 × Grx × λ2 / (480 π2).
  5. Compare expected vs. measured received level. Difference is receive antenna (or receiver) calibration error.
  6. Iterate at multiple distances (3 m, 5 m, 10 m) to verify 1/d falloff.

Appendix A — Formulas

Electric field (far field, from transmitted power)
E (V/m) = √(30 × P (W) × G) / d (m)

dBμV/m from V/m
E (dBμV/m) = 20 × log10(E × 106)

Effective aperture of half-wave dipole
Aeff = G × λ2 / (4π) = 1.64 × λ2 / (4π)

Received power from E field
Prx (W) = E2 × Aeff / (120π)

Key Formulas Summary

  • E (V/m) = √(30 × P (W) × G) / d (m)
  • E (dBμV/m) = 20 × log10(E × 106)
  • Aeff = G × λ2 / (4π) = 1.64 × λ2 / (4π)
  • Prx (W) = E2 × Aeff / (120π)

The Calibration Procedure

Chapter 5 specifies 6 calibration steps.

Calibration is a comparison: you apply a known reference value to the instrument under test and record what the instrument reads. The difference is the error. You then either: - Adjust the instrument until the error is within the acceptance criterion, or - Record the error as a correction factor to apply to future readings

Locate the acceptance criterion in Chapter 5 or Chapter 7.

Practice Problems

Work these before checking answers.

P4-1. The reference value is 10.000 V. Your instrument reads 10.043 V. (a) What is the error in volts? (b) What is the error as a percentage of the reference value? Show your work.

P4-2. Using the formula for % error: error% = (measured − reference) / reference × 100 Apply it to: reference = 100.0 kHz, measured = 99,985 Hz. (a) Error in Hz. (b) Error in %. (c) Error in ppm.

P4-3. The acceptance criterion in the TM is ±1%. Your measurement gives an error of +0.8%. Does it pass? State your reasoning.

Practice Problem Answers

P4-1. (a) 10.043 − 10.000 = +0.043 V (b) 0.043 / 10.000 × 100 = +0.43%

P4-2. (a) 99,985 − 100,000 = −15 Hz (b) −15 / 100,000 × 100 = −0.015% (c) −15 / 100,000 × 1,000,000 = −150 ppm

P4-3. +0.8% is within ±1%. PASS. State: "error = +0.8%; criterion = ±1%; result = PASS." Always cite the TM section for the criterion.

Self-Check Questions

SC4-1. How many steps does Chapter 5 specify for the calibration procedure?

SC4-2. What reference value(s) does Chapter 5 apply to the instrument under test?

SC4-3. State the calibration acceptance criterion from the TM. Cite the section.

SC4-4. Write the error formula from Appendix A. Include units.

SC4-5. If the instrument reads 2.3% high, is the error positive or negative? What does a positive error indicate?

Answer Key

SC4-1. Count the numbered steps in Chapter 5. (TM Ch. 5)

SC4-2. See Chapter 5 for the reference values applied. These are the known-good inputs used to check the instrument. (TM §5-1)

SC4-3. See TM Chapter 5 or Chapter 7. Copy the criterion exactly with units and section number.

SC4-4. See Appendix A. Write it exactly as shown.

SC4-5. Positive (instrument reads higher than reference). A positive error means the instrument over-reads — it reports a value higher than the true value. (TM App. A)

Checkpoint

Before proceeding, you must be able to: - State the calibration acceptance criterion without looking - Write the error formula from memory - Work a % error and ppm calculation correctly

→ Proceed to Unit 5