⚙️ ENGINEER LEVEL: Measurement and Analysis
Thiele-Small Parameter Measurement
Professional driver design requires accurate T/S parameter measurement.
Equipment needed: - Precision LCR meter or audio analyzer - Known test mass (typically 10-20g) - Signal generator - Precision resistor (0.1% tolerance) - Stable power supply
Measurement procedure:
1. Measure DC resistance (Re):
Direct measurement with ohmmeter. Typical values 75-85% of nominal impedance.
2. Free-air resonance (Fs):
Method A: Impedance sweep - Sweep frequency from 10-200 Hz - Measure impedance vs. frequency - Peak impedance occurs at Fs - Record impedance at Fs (Z_max)
Method B: Added mass - Measure Fs normally (F₁) - Add known mass (Madd) to cone - Measure new resonance (F₂) - Calculate: Fs = F₁, Mms = M_add / [(F₁/F₂)² - 1]
3. Mechanical Q (Qms):
From impedance curve:
Q_ms = F_s × Z_max / (R_e × √((Z_max/R_e)² - 1) × ΔF)
Where ΔF is bandwidth between points where Z = Z_max/√2
4. Electrical Q (Qes):
Added resistance method: - Measure Fs with known series resistance (Radd) - Measure new resonance (Fnew) - Calculate from frequency shift
Formula:
Q_es = Q_ms × [R_e / (R_test + R_add - R_e)]
Where R_test is measured impedance at new resonance.
5. Moving mass (Mms):
From added mass measurement:
M_ms = M_add / [(F₁/F₂)² - 1]
6. Compliance (Cms):
From mass and resonance:
C_ms = 1 / [(2π × F_s)² × M_ms]
Units: meters/Newton
7. Equivalent compliance volume (Vas):
V_as = ρ₀ × c² × S_d² × C_ms
Where: - ρ₀ = 1.21 kg/m³ - c = 343 m/s - S_d = effective piston area (m²)
8. Verify total Q (Qts):
Q_ts = (Q_es × Q_ms) / (Q_es + Q_ms)
Typical measurement accuracy: - Re: ±2% - Fs: ±1% - Q: ±10% - Vas: ±15% - Xmax: ±20% (mechanical measurement)
Importance of accuracy:
Small parameter variations significantly affect enclosure design: - 10% error in Qts → 15% error in optimal enclosure volume - 10% error in Vas → 10% error in enclosure volume - 15% error in Fs → enclosure tuned to wrong frequency
Amplifier Distortion Analysis
Types of distortion:
1. Harmonic Distortion:
Non-linear transfer function creates harmonics of input frequency.
THD measurement:
Input: 1 kHz sine wave
Output contains: - Fundamental: 1 kHz - 2nd harmonic: 2 kHz - 3rd harmonic: 3 kHz - 4th harmonic: 4 kHz - etc.
THD = √(V₂² + V₃² + V₄² + ...) / V₁
Often expressed in % or dB:
THD (dB) = 20 × log₁₀(THD)
Examples: - 0.01% = -80 dB (excellent) - 0.1% = -60 dB (very good) - 1% = -40 dB (acceptable)
Harmonic spectrum analysis:
2nd harmonic dominant: - "Musical" distortion - Octave above fundamental - Less objectionable - Typical of Class AB near clipping
3rd harmonic dominant: - "Harsh" distortion - Musical fifth above octave - More objectionable - Typical of Class D, crossover distortion
High-order harmonics: - Very unpleasant - Indicates severe non-linearity - Sign of poor design or damage
2. Intermodulation Distortion (IMD):
Two tones create sum and difference frequencies.
Test signal: Two tones (e.g., 60 Hz + 7 kHz)
Distortion products: - 6940 Hz (7000 - 60) - 7060 Hz (7000 + 60) - 6880 Hz (7000 - 2×60) - 7120 Hz (7000 + 2×60) - etc.
SMPTE IMD test: - 60 Hz + 7 kHz at 4:1 ratio - Measure sidebands around 7 kHz
IMD% = (Sideband level / 7 kHz level) × 100%
CCIF IMD test (twin-tone): - Two closely spaced high frequencies (e.g., 19 kHz + 20 kHz) - Measure difference frequency (1 kHz) - More revealing of high-frequency non-linearity
3. Transient Intermodulation Distortion (TIM):
Slew-rate limiting creates distortion on complex transient signals.
Not easily measured with steady-state tones.
Indication of TIM: - High negative feedback amplifier - Limited slew rate - Harsh sound on complex material - Measures well with simple tests but sounds poor
4. Crossover Distortion:
Class AB and Class B amplifiers can have distortion at zero-crossing point.
Causes: - Insufficient bias current - Mismatched output transistors - Thermal drift
Measurement: - Low-level sine wave (<1W) - Look for "steps" or discontinuity at zero crossing - Shows as high 3rd harmonic
Modern quality amplifiers: <0.01% at all power levels
Speaker Frequency Response Measurement
Required equipment: - Measurement microphone (calibrated) - Audio interface - Measurement software (REW, ARTA, SoundEasy) - Powered amplifier - Anechoic environment or gating (outdoor measurement)
Measurement types:
1. On-axis frequency response:
Setup: - Microphone at 1 meter, on speaker axis - Far-field measurement (distance > 3× driver diameter) - Low background noise - Stable temperature
Stimulus: - Swept sine wave (20 Hz - 20 kHz) - Pink noise - MLS (Maximum Length Sequence)
Analysis: - Plot magnitude vs. frequency - Note peaks and dips - Check rolloff slopes - Measure -3 dB points
Typical results: - Tweeter: 2 kHz - 20 kHz - Midrange: 300 Hz - 5 kHz - Midbass: 60 Hz - 500 Hz - Subwoofer: 25 Hz - 150 Hz
2. Off-axis response:
Measure at 15°, 30°, 45°, 60° horizontal and vertical angles.
Polar plots show: - Dispersion pattern - Beaming (narrowing at high frequency) - Directivity
Good speaker: - Wide dispersion at low frequencies - Controlled narrowing at high frequencies - Smooth polar response
Poor speaker: - Irregular polar pattern - Severe beaming - Sudden changes in directivity
3. Impedance vs. frequency:
Procedure: - Measure impedance from 10 Hz - 20 kHz - Note resonance peak - Check for anomalies
Interpretation: - Peak = resonance frequency (Fs) - Height = Q factor indication - Multiple peaks = mechanical issues - Sharp dips = problem
4. Distortion vs. frequency/level:
Measure THD at various: - Frequencies (sweeps) - Power levels (1W, 10W, 50W, etc.)
Typical THD for quality speaker: - <1% at rated power, midband - <3% at rated power, extremes - Rises toward frequency extremes
Component Comparison Database Example
Comparative analysis framework:
Example: Three midrange amplifiers
| Specification | Amp A | Amp B | Amp C |
|---|---|---|---|
| Price | $299 | $449 | $799 |
| Channels | 4 | 4 | 4 |
| RMS Power @ 4Ω | 75W × 4 | 100W × 4 | 125W × 4 |
| RMS Power @ 2Ω | 120W × 4 | 150W × 4 | 200W × 4 |
| CEA-2006 | No | Yes | Yes |
| THD @ rated | <1% | <0.1% | <0.05% |
| SNR | 95 dB | 100 dB | 110 dB |
| Frequency Response | 20-20k ±1dB | 10-50k ±0.5dB | 5-100k ±0.1dB |
| Input Sensitivity | 0.2-4V | 0.2-6V | 0.2-8V |
| Crossover | 12dB/oct | 24dB/oct | 36dB/oct variable |
| Class | D | AB | AB |
| Size (in) | 9×7×2 | 11×9×2.5 | 14×11×3 |
| $/Watt @ 4Ω | $1.00 | $1.12 | $1.60 |
| Value Rating | ★★★★☆ | ★★★★☆ | ★★★☆☆ |
| Performance Rating | ★★★☆☆ | ★★★★☆ | ★★★★★ |
Analysis:
Amp A: Best value for money, adequate specifications, Class D efficiency, but non-CEA rated suggests real power is lower (estimate 50-60W actual).
Amp B: Good balance of price/performance, honest CEA rating, excellent THD, Class AB for purists, best overall value.
Amp C: Ultimate performance, extremely low distortion, audiophile-grade, high cost, worth it only for serious enthusiasts.
Recommendation: - Budget/efficiency: Amp A - Best overall: Amp B ← Winner for most users - No-compromise: Amp C