Overview
After calibrating your TinySA using GPS, time standard broadcasts, or FM stations, you need to verify the calibration worked and characterize long-term performance.
This document provides: 1. Immediate verification procedures 2. Cross-checking against multiple references 3. Long-term stability testing 4. Temperature characterization 5. Uncertainty analysis
Immediate Verification (Post-Calibration)
Quick Check (5 minutes)
Purpose: Confirm calibration was applied correctly
Procedure:
- Re-measure calibration source:
- GPS 1PPS → Should read 1.000000 Hz (±0.001 Hz)
- CHU 7.850 MHz → Should read 7,850,000 Hz (±10 Hz)
-
FM 100.1 MHz → Should read 100,100,000 Hz (±100 Hz)
-
Check for improvement: ``` BEFORE calibration: CHU measured: 7,850,152 Hz Error: +152 Hz (+19.4 ppm)
AFTER calibration: CHU measured: 7,850,003 Hz Error: +3 Hz (+0.38 ppm) ```
- Verify correction was saved:
- Power cycle TinySA
- Re-measure
- Should still be accurate
Success Criteria: - ✓ Error reduced by >90% - ✓ Final error < 1 ppm (< 30 Hz @ 30MHz) - ✓ Calibration survives power cycle
Cross-Reference Validation (30 minutes)
Multiple Independent Sources
Purpose: Confirm calibration against different references
Procedure:
- GPS vs. WWV/CHU: ``` Method A (GPS):
- Measured 30MHz error: +5.2 ppm
- Applied correction: -5.2 ppm
Method B (CHU 7.850 MHz): - Measure CHU frequency - Calculate ppm error - Should read ±0.5 ppm of GPS result ```
- GPS vs. FM Broadcast: ``` After GPS calibration, measure FM station:
- Should read exact frequency (±1 ppm)
-
Example: 100.1 MHz → 100,100,000 Hz ±100 Hz ```
-
Multiple FM Stations:
Measure 3-5 different FM stations All should read exact frequency If one is off, that station is poorly calibrated
Acceptance Criteria
All methods should agree within: - GPS vs. Time Standard: ±0.1-0.5 ppm - GPS vs. FM Broadcast: ±1-2 ppm - FM vs. FM: ±0.5 ppm (same market)
Example Results (Good):
| Method | Error (ppm) | Agreement |
|---|---|---|
| GPS | +5.23 | Reference |
| CHU | +5.19 | ±0.04 ppm ✓ |
| FM 1 | +5.21 | ±0.02 ppm ✓ |
| FM 2 | +5.18 | ±0.05 ppm ✓ |
Example Results (Problem):
| Method | Error (ppm) | Agreement |
|---|---|---|
| GPS | +5.23 | Reference |
| CHU | +5.22 | ±0.01 ppm ✓ |
| FM 1 | +8.45 | ±3.22 ppm ✗ Bad station |
| FM 2 | +5.19 | ±0.04 ppm ✓ |
Short-Term Stability Test (1 hour)
Allan Deviation (Simplified)
Purpose: Measure frequency stability over short time scales
Equipment Needed: - GPS frequency counter (from construction guide) - TinySA 30MHz signal - Computer for logging
Procedure:
- Set up continuous measurement:
- GPS 1PPS gates TinySA 30MHz
- Measure every second
-
Log to file
-
Run for 1 hour (3600 measurements)
-
Calculate statistics: ```python import numpy as np import pandas as pd
# Load data data = pd.read_csv('frequency_log.csv') freq = data['Frequency_Hz'].values
# Calculate Allan deviation for τ = 1s expected = 30000000 y = (freq - expected) / expected # Fractional frequency
allan_1s = np.std(y) print(f"Allan deviation (1s): {allan_1s*1e6:.3f} ppm")
# Calculate for τ = 10s (average groups of 10) y_10s = [] for i in range(0, len(y)-10, 10): y_10s.append(np.mean(y[i:i+10])) allan_10s = np.std(y_10s) / np.sqrt(2) print(f"Allan deviation (10s): {allan_10s*1e6:.3f} ppm") ```
Typical Results
Good TCXO:
Allan deviation (1s): 0.1-0.5 ppm
Allan deviation (10s): 0.01-0.1 ppm
Allan deviation (100s): 0.005-0.05 ppm
Poor crystal:
Allan deviation (1s): 1-5 ppm
Allan deviation (10s): 0.5-2 ppm
Interpretation: - Lower = better - Should improve with longer averaging - If increases with time → drift problem - If flat → hitting measurement noise floor
Long-Term Stability Test (24 hours)
24-Hour Frequency Log
Purpose: Characterize drift, temperature effects, aging
Setup:
- Stable environment:
- Indoors, away from windows
- Minimize temperature swings
-
Avoid moving equipment
-
Continuous logging:
- Measure every 1-5 minutes
- Log frequency, temperature
-
Save to CSV file
-
Run for 24+ hours
Python Logging Script
import serial
import time
from datetime import datetime
ser = serial.Serial('/dev/ttyUSB0', 115200, timeout=1)
time.sleep(2)
log_file = open('24hr_stability.csv', 'w')
log_file.write('Timestamp,Frequency_Hz,Error_ppm,Temperature_C\n')
print("24-Hour Stability Test Started")
print("Logging every 60 seconds")
print("Press Ctrl+C to stop\n")
try:
while True:
line = ser.readline().decode('utf-8').strip()
if 'Frequency:' in line and 'Error:' in line:
# Parse frequency and error from Arduino output
# Example: "Frequency: 30000150 Hz Error: +5.000 ppm"
parts = line.split()
freq_hz = float(parts[1])
error_ppm = float(parts[4])
timestamp = datetime.now().isoformat()
log_file.write(f'{timestamp},{freq_hz},{error_ppm},25.0\n')
log_file.flush()
print(f'{timestamp}: {freq_hz} Hz ({error_ppm:+.3f} ppm)')
time.sleep(60) # Log every minute
except KeyboardInterrupt:
print("\n\nTest stopped by user")
log_file.close()
ser.close()
print("Generating report...")
# Generate summary
import pandas as pd
import matplotlib.pyplot as plt
df = pd.read_csv('24hr_stability.csv')
print("\n24-Hour Stability Report")
print("=" * 50)
print(f"Measurements: {len(df)}")
print(f"Mean frequency: {df['Frequency_Hz'].mean():.1f} Hz")
print(f"Std deviation: {df['Frequency_Hz'].std():.1f} Hz")
print(f"Min frequency: {df['Frequency_Hz'].min():.1f} Hz")
print(f"Max frequency: {df['Frequency_Hz'].max():.1f} Hz")
print(f"Peak-peak drift: {df['Frequency_Hz'].max() - df['Frequency_Hz'].min():.1f} Hz")
print(f"Mean error: {df['Error_ppm'].mean():.3f} ppm")
print(f"Error std dev: {df['Error_ppm'].std():.3f} ppm")
print("=" * 50)
# Plot
df['Timestamp'] = pd.to_datetime(df['Timestamp'])
plt.figure(figsize=(12, 8))
plt.subplot(2, 1, 1)
plt.plot(df['Timestamp'], df['Frequency_Hz'])
plt.ylabel('Frequency (Hz)')
plt.title('TinySA 30MHz Stability - 24 Hours')
plt.grid(True)
plt.subplot(2, 1, 2)
plt.plot(df['Timestamp'], df['Error_ppm'])
plt.ylabel('Error (ppm)')
plt.xlabel('Time')
plt.grid(True)
plt.tight_layout()
plt.savefig('24hr_stability.png', dpi=150)
print("\nPlot saved as: 24hr_stability.png")
Interpreting Results
Good Result:
Peak-peak drift: < 30 Hz (< 1 ppm)
Standard deviation: < 10 Hz (< 0.3 ppm)
Trend: Flat or slow linear drift
Temperature sensitivity: < 0.5 ppm/°C
Typical Result:
Peak-peak drift: 30-150 Hz (1-5 ppm)
Standard deviation: 10-50 Hz (0.3-1.7 ppm)
Trend: Follows temperature
Temperature sensitivity: 0.5-2 ppm/°C
Poor Result:
Peak-peak drift: > 300 Hz (> 10 ppm)
Standard deviation: > 100 Hz (> 3 ppm)
Trend: Erratic or large jumps
→ Possible crystal problem or loose connection
Temperature Characterization
Temperature Coefficient Measurement
Purpose: Quantify frequency vs. temperature relationship
Equipment: - Temperature sensor (DS18B20 or thermistor) - GPS frequency counter - Refrigerator and hair dryer
Procedure:
- Cold soak:
- Place TinySA in refrigerator
- Wait 30 minutes
-
Measure frequency at 5°C
-
Warm-up:
- Remove from fridge
- Measure frequency every 2 minutes
- Record temperature simultaneously
-
Until reaches room temp (20°C)
-
Heat test:
- Use hair dryer (gentle, low heat)
- Measure frequency every 2 minutes
- Record temperature
-
Up to 40°C (don't overheat!)
-
Cool-down:
- Turn off heat
- Measure as it cools
- Back to room temp
Data Analysis
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
# Load data
df = pd.read_csv('temperature_test.csv')
temp = df['Temperature_C'].values
error_ppm = df['Error_ppm'].values
# Linear fit
slope, intercept, r_value, p_value, std_err = stats.linregress(temp, error_ppm)
print("Temperature Coefficient Analysis")
print("=" * 50)
print(f"Temperature range: {temp.min():.1f} to {temp.max():.1f} °C")
print(f"Frequency range: {error_ppm.min():.2f} to {error_ppm.max():.2f} ppm")
print(f"Slope: {slope:.3f} ppm/°C")
print(f"R²: {r_value**2:.4f}")
print("=" * 50)
# Plot
plt.figure(figsize=(10, 6))
plt.scatter(temp, error_ppm, alpha=0.5, label='Measurements')
plt.plot(temp, slope*temp + intercept, 'r-', label=f'Fit: {slope:.3f} ppm/°C')
plt.xlabel('Temperature (°C)')
plt.ylabel('Frequency Error (ppm)')
plt.title('Crystal Temperature Coefficient')
plt.legend()
plt.grid(True)
plt.savefig('temperature_coefficient.png', dpi=150)
plt.show()
Typical Coefficients
| Crystal Type | Temp Coefficient | Frequency Change (0-40°C) |
|---|---|---|
| AT-cut (room temp) | -0.035 ppm/°C/°C | ±1-2 ppm |
| TCXO (cheap) | -0.5 to -2 ppm/°C | ±10-40 ppm |
| TCXO (good) | -0.1 to -0.5 ppm/°C | ±2-10 ppm |
| OCXO | -0.001 to -0.01 ppm/°C | ±0.02-0.2 ppm |
Temperature Compensation
Once you know TC, compensate manually:
Current temp: 35°C
Reference temp: 25°C
Temperature coefficient: -0.8 ppm/°C
ΔT = 35 - 25 = +10°C
Frequency shift = -0.8 ppm/°C × 10°C = -8 ppm
Apply correction: +8 ppm to compensate
Measurement Uncertainty Analysis
Sources of Uncertainty
GPS Method:
| Source | Uncertainty (ppm) | Notes |
|---|---|---|
| GPS 1PPS jitter | ±0.001 | Negligible |
| Counter resolution | ±0.00003 | 1 count in 30M |
| Temperature drift | ±0.1-1.0 | During measurement |
| Short-term noise | ±0.01 | Average multiple |
Total (RSS): ±0.1-1.0 ppm (dominated by temperature)
WWV/CHU Method:
| Source | Uncertainty (ppm) | Notes |
|---|---|---|
| Transmitter | ±0.00001 | Atomic clock |
| Ionosphere | ±0.01-0.1 | Doppler shift |
| Multipath | ±0.05-0.5 | Fading |
| Receiver | ±0.1-1.0 | Measurement |
Total (RSS): ±0.1-1.0 ppm
FM Broadcast:
| Source | Uncertainty (ppm) | Notes |
|---|---|---|
| Station accuracy | ±0.01-2.0 | GPS-locked vs. free |
| TinySA resolution | ±0.1-1.0 | At 100 MHz |
| Averaging | ±0.5 | Multiple stations |
Total (RSS): ±1-5 ppm (depends on station quality)
Reducing Uncertainty
- Average multiple measurements: ``` σ_average = σ / sqrt(N)
Example: Single measurement: ±1 ppm Average 10 measurements: ±0.32 ppm Average 100 measurements: ±0.1 ppm ```
- Temperature stabilization:
- Let equipment warm up 30+ minutes
- Measure in stable environment
-
Correct for temperature coefficient
-
Multiple methods:
- GPS (primary)
- WWV/CHU (verify)
- FM (quick check)
- All should agree within combined uncertainty
Acceptance Testing
Final Validation Checklist
Before considering calibration complete:
Immediate Checks: - [ ] Error reduced from >10 ppm to <1 ppm - [ ] Calibration survives power cycle - [ ] Verified against second independent source - [ ] No unexpected jumps or instabilities
Short-Term Checks (1 hour): - [ ] Frequency stable to ±0.5 ppm over 1 hour - [ ] No large temperature swings - [ ] Measurements repeatable
Long-Term Checks (24 hours): - [ ] Drift < 1 ppm over 24 hours - [ ] Temperature correlation understood - [ ] No sudden frequency jumps
Documentation: - [ ] Recorded calibration date - [ ] Noted calibration method - [ ] Documented temperature coefficient - [ ] Saved reference measurements - [ ] Planned re-calibration date (1 year)
Periodic Re-Calibration
When to Re-Calibrate
Mandatory: - After firmware update (may reset cal) - After opening case (may affect crystal) - After drop or impact - If measurements show >2 ppm error
Recommended: - Every 6-12 months (crystal aging) - After extreme temperature exposure - Before critical measurements
Optional: - Before each use (paranoid) - Monthly (if doing precision work)
Quick Cal Check
Don't need full re-calibration - just verify:
1. Measure GPS 1PPS or CHU
2. Note error
3. If < 1 ppm: OK, no action
4. If 1-3 ppm: Minor adjustment
5. If > 3 ppm: Full re-calibration needed
Documentation Template
Calibration Record
TinySA Calibration Record
=========================
Date: _____________
Operator: _____________
Method: [ ] GPS [ ] WWV/CHU [ ] FM [ ] Other:_______
Initial Error: _______ Hz (_______ ppm) @ 30MHz
Final Error: _______ Hz (_______ ppm) @ 30MHz
Reference Source(s):
1. __________________________
2. __________________________
3. __________________________
Measurements:
Before: _______ Hz
After: _______ Hz
Temperature During Cal: _______°C
Temperature Coefficient: _______ ppm/°C
Verification:
Method 1: _______ ppm error
Method 2: _______ ppm error
Agreement: ✓ / ✗
24-Hour Stability: _______ ppm p-p
Notes:
_____________________________________________
_____________________________________________
Next Calibration Due: _____________
Signature: _____________ Date: _____________
Troubleshooting Verification Failures
Problem: Large Discrepancy Between Methods
Example:
GPS shows: +5.2 ppm
CHU shows: +11.8 ppm
Difference: 6.6 ppm (too large!)
Possible causes: 1. GPS not locked (check 1PPS is blinking) 2. CHU propagation poor (multipath, fading) 3. Measurement error (recheck connections) 4. Temperature changed between measurements
Solution: - Re-measure with stable conditions - Use third method (FM) to arbitrate - Trust GPS if all other checks pass
Problem: Frequency Jumps
Example:
Measurement 1: 30,000,150 Hz
Measurement 2: 30,000,148 Hz
Measurement 3: 30,002,580 Hz ← Jump!
Measurement 4: 30,000,149 Hz
Possible causes: 1. Loose connection (intermittent) 2. Power supply noise 3. Counter overflow (if using 16-bit counter) 4. Software bug
Solution: - Check all connections - Add decoupling capacitors - Use 32-bit counter - Re-upload firmware
Problem: Temperature Sensitivity Too High
Example:
Measured TC: -5.2 ppm/°C
Expected: -0.5 to -2 ppm/°C
Possible causes: 1. Poor quality crystal 2. Aging crystal 3. Measurement error 4. Other temperature-sensitive component
Solution: - Re-measure carefully - Consider replacing crystal (if accessible) - Use tighter temperature control - Apply software compensation
Advanced Verification: Beat Frequency Method
Concept
Mix TinySA 30MHz with GPS-locked 30MHz reference, listen to beat note.
Setup:
GPS-locked 30MHz ──┐
├──→ Mixer ──→ Low-pass filter ──→ Audio amp ──→ Speaker
TinySA 30MHz ──────┘
Beat frequency = |f1 - f2|
If calibration perfect: - Beat frequency = 0 Hz (silence)
If error exists: - Beat frequency = error in Hz - Example: 150 Hz error → hear 150 Hz tone
Advantages: - Very sensitive (can hear 1 Hz difference) - Real-time monitoring - No counter needed
Disadvantages: - Requires building mixer circuit - Need GPS-locked 30MHz reference - Can't measure sign of error (only magnitude)
Summary
Verification Completed
✓ Immediate post-calibration check ✓ Cross-reference against multiple sources ✓ Short-term stability (1 hour) ✓ Long-term stability (24 hours) ✓ Temperature characterization ✓ Uncertainty analysis ✓ Acceptance testing ✓ Documentation
Key Metrics
Good Calibration: - Final error: < 1 ppm - Agreement between methods: < 0.5 ppm - 1-hour stability: < 0.5 ppm - 24-hour drift: < 1 ppm - Temperature coefficient: Known and compensated
Next Steps: - Use calibrated TinySA with confidence - Re-calibrate annually - Document all measurements
Your TinySA is now calibrated to atomic clock accuracy!