Unit 4 — Calibration Procedure and Calculations

TM-CAL-001 — 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-001. Read Chapter 5 and Appendix A completely.

Then come back here.

Chapter 5 — Calibration Procedure

CAUTION: If calibrating the frequency counter's internal oscillator (TCXO/OCXO), refer to the counter manufacturer's manual. Some counters require internal adjustment access; incorrect adjustment can degrade accuracy.

5-1. DIRECT CARRIER METHOD (PREFERRED)

This method measures the received carrier directly with the frequency counter. It requires a receiver with a BFO output or accessible IF/detector output.

  1. Tune receiver to 10.000 MHz (best daytime signal) or 5.000 MHz (night).
  2. Switch receiver to CW or USB mode. Zero-beat the carrier: the audio beat note approaches zero Hz as receiver VFO aligns with the carrier.
  3. Measure the receiver VFO frequency at zero-beat. This equals 10.000000 MHz (within ±5 Hz for consumer receivers, ±100 Hz for older equipment).
  4. If the counter shows 10.000100 MHz at zero-beat, the counter's reference is high by 10 Hz at 10 MHz = 1 ppm high.
  5. Apply correction: freqtrue = freqdisplayed × (1 − errorppm/106).
  6. Repeat on 5.000 MHz and 15.000 MHz to verify consistency.
  7. Record result in calibration log.

5-2. AUDIO BEAT NOTE METHOD

If direct carrier access is not available, beat the carrier against a known oscillator and count the beat note frequency.

  1. Connect a 10 MHz signal generator (or GPSDO output) to one input of a signal mixer or the RF input of a second receiver.
  2. Receive WWV on the first receiver.
  3. Mix the two signals; the difference frequency (beat note) is the error between your oscillator and WWV.
  4. Count the beat note with the frequency counter. Any non-zero reading is the error of your signal generator at 10 MHz.
  5. Error in ppm = beatHz / 10 (at 10 MHz reference).

Appendix A — Formulas

A-1. FREQUENCY ERROR

Parts-per-million error
errorppm = (fmeasured − fnominal) / fnominal × 106

Correction factor
ftrue = fdisplayed × (1 − errorppm / 106)

Hz error from ppm (10 MHz)
errorHz = errorppm × 10 (at 10 MHz)

A-2. PROPAGATION DELAY

One-way propagation delay (ionospheric, approximate)
delay ≈ 3.3 ms per 1000 km

NOTE: Propagation delay affects phase and timing measurements only. For frequency calibration, the Doppler shift from a quasi-static ionosphere averages to zero over 30 seconds or more. Time-of-day synchronization requires propagation delay correction; frequency calibration does not.

Key Formulas Summary

  • errorppm = (fmeasured − fnominal) / fnominal × 106
  • ftrue = fdisplayed × (1 − errorppm / 106)
  • errorHz = errorppm × 10 (at 10 MHz)

The Calibration Procedure

Chapter 5 specifies 12 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

An error criterion found in Chapter 5: 1 ppm. Confirm the exact criterion in the TM.

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