Difference between revisions of "THD Sweep Measurement"

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THD Sweep Measurement (view source)

Revision as of 15:31, 15 April 2026

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→‎THD Formulas
Tag: Manual revert
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== THD Formulas ==
= THD Formulas ==


=== THD Percentage (DC1) ===
=== THD Percentage (DC1) ===


<math>
'''Formula:'''
\text{THD\%} = \frac{\sqrt{H_2^2 + H_3^2 + \cdots + H_9^2}}{H_1} \times 100
 
</math>
<code>THD(%) = (√(H2² + H3² + ... + H9²) / H1) × 100</code>


Where:
Where:
* <math>H_1</math> = Fundamental amplitude
* H1 = Fundamental amplitude (1st harmonic)
* <math>H_2, H_3, \ldots, H_9</math> = Harmonic amplitudes
* H2, H3, ..., H9 = Harmonic amplitudes (2nd to 9th)
* √ = Square root


'''Example:''' If H1 = 1.0 V and harmonics RMS = 0.05 V, then THD% = 5%
'''Plain English:'''
Take the sum of squares of all harmonics, take the square root, divide by fundamental, multiply by 100.
 
'''Example:'''
* H1 (fundamental) = 1.0 V
* H2 = 0.02 V
* H3 = 0.01 V
* H4 = 0.01 V
* (all others = 0)
 
Calculation:
* Harmonics RMS = √(0.02² + 0.01² + 0.01²) = √0.0006 = 0.0245 V
* THD% = (0.0245 / 1.0) × 100 = '''2.45%'''


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=== THD in Decibels (DC2) ===
=== THD in Decibels (DC2) ===


<math>
'''Formula:'''
\text{THD}_{\text{dB}} = 20 \log_{10}\left(\frac{\sqrt{H_2^2 + H_3^2 + \cdots + H_9^2}}{H_1}\right)
 
</math>
<code>THD(dB) = 20 × log₁₀(√(H2² + H3² + ... + H9²) / H1)</code>
 
Or from THD%:
 
<code>THD(dB) = 20 × log₁₀(THD% / 100)</code>


Or equivalently:
Where:
* log₁₀ = Base-10 logarithm
* All H values same as above


<math>
'''Plain English:'''
\text{THD}_{\text{dB}} = 20 \log_{10}\left(\frac{\text{THD\%}}{100}\right)
Calculate the ratio of harmonics to fundamental, take log base 10, multiply by 20.
</math>


'''Example:''' THD% = 5% → THD dB = -26 dB
'''Example from above:'''
* Ratio = 0.0245 / 1.0 = 0.0245
* log₁₀(0.0245) = -1.611
* THD(dB) = 20 × (-1.611) = '''−32.2 dB'''
 
Or: THD(dB) = 20 × log₁₀(2.45 / 100) = 20 × (−1.611) = '''−32.2 dB'''


---
---


=== Conversion Reference ===
=== Quick Conversion Table ===


{| class="wikitable"
{| class="wikitable"
|-
|-
! THD % !! THD dB
! THD Percentage !! THD in dB !! Quality Rating
|-
| 0.5% || −46 dB || Excellent (pro audio)
|-
| 1% || −40 dB || Very Good
|-
|-
| 1% || -40 dB
| 3% || −30 dB || Good
|-
|-
| 3% || -30 dB
| 5% || −26 dB || Acceptable
|-
|-
| 10% || -20 dB
| 10% || −20 dB || Fair
|-
|-
| 30% || -10 dB
| 30% || −10 dB || Poor
|-
|-
| 100% || 0 dB
| 100% || 0 dB || Unusable
|}
|}


'''Rule:''' Lower dB = better (more negative = less distortion)
'''Key Rule:''' The more negative the dB value, the better the quality. A 10 dB improvement = 10× reduction in distortion.


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{| class="wikitable"
{| class="wikitable"
|-
|-
! Output !! Formula !! Range
! Output Channel !! Measurement !! Formula !! Typical Range
|-
| DC1 || THD % || (Harmonics RMS / H1) × 100 || 0 to 100%
|-
| DC2 || THD dB || 20 × log₁₀(ratio) || −200 to 0 dB
|-
| DC3 || Frequency || Sweep frequency at current point || 0 to 40 kHz
|}
 
---
 
=== Coherence Between DC1 and DC2 ===
 
The two THD channels always maintain mathematical coherence. Given DC1 value (THD%), you can always calculate DC2:
 
<code>DC2(dB) = 20 × log₁₀(DC1(%) / 100)</code>
 
'''Example:'''
* If DC1 displays 5.5%
* Then DC2 = 20 × log₁₀(0.055) = 20 × (−1.26) = '''−25.2 dB'''
 
This relationship is guaranteed by the software mathematics.
 
---
 
=== Implementation Details ===
 
The software measures '''9 harmonics''' (H1 through H9):
 
{| class="wikitable"
|-
! Harmonic !! Frequency (1 kHz example) !! Typical Amplitude
|-
| H1 (Fundamental) || 1.000 kHz || 1.0 V (reference)
|-
| H2 || 2.000 kHz || 0.1 V (typical)
|-
| H3 || 3.000 kHz || 0.05 V (typical)
|-
|-
| '''DC1 (THD %)''' || <math>\text{THD\%}</math> || 0 - 100%
| H4 || 4.000 kHz || 0.03 V (typical)
|-
|-
| '''DC2 (THD dB)''' || <math>20 \log_{10}(\text{ratio})</math> || -200 to 0 dB
| H5 || 5.000 kHz || 0.02 V (typical)
|-
|-
| '''DC3 (Frequency)''' || <math>f_{\text{sweep}}</math> || 0 - 40000 Hz
| H6-H9 || 6-9 kHz || Progressive decrease
|}
|}
For sweep frequencies other than 1 kHz, all frequencies scale proportionally.
---
=== Why Two Formats (% and dB)? ===
'''THD %:'''
* Easier to understand for non-technical users
* Direct representation: "5% distortion"
* Useful for product specifications
'''THD dB:'''
* Logarithmic scale: easier to see small differences
* Standard in audio/RF engineering
* Used in all standards and specifications
* Better for comparing measurements at different levels
Both represent the same information, just in different scales.
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