201509091413文章剪影--Symmetry and Asymmetry (對稱與不對稱)

前些日有網友曾詢問在下關於非線性失真上對稱與不對稱的問題,在此將一點點基本相關資訊剪影以茲分享,若有興趣者可再自行深入探析學習,其屬電聲領域,深入處尤為非線性失真的電聲領域。

Symmetry and Asymmetry

非線性參數最明顯的特點就是曲線的對稱特性。製作精良的揚聲器應該有對稱的Kms(x) 和 Bl(x)曲線。在正向或負向的較大沖程時,懸掛系統將因被拉伸及展開的支撐部件限制住,音圈也將會離開磁氣隙。對稱的曲線通常會產生三次及其它奇次階失真成分,如下圖所示。如果非線性系統是穩定的,就不會產生任何直流偏移或是其它偶次失真分量。如果一個揚聲器有著音圈卷幅和磁氣隙等長的磁路結構,且採用了懸掛系統較軟的設計,那麼整個系統將變得不穩定。

非線性特性的曲線形狀與奇偶次失真成分產生的關係

 

其它的非線性特性,比如不帶短路環的揚聲器單元的電感值、多譜勒效應、或者是波形畸變等,都有著明顯的不對稱特性,要改善電感的不對稱特性稍微有些困難,要消除波形的畸變,那就是不可能的了。不對稱的非線性特性主要是產生偶次失真。然而,由於這些非線性特性通常都是反饋回路的一部分(可以用一個非線性的微分方程來描述系統的特性),奇次失真分量也可以由偶次失真分量與基波分量相乘而產生得到。

 

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Low-frequency drive units test

 

Examples:

woofer, subwoofer

Applications:

home, automotive, multimedia and professional

Particularities:

Low frequency drive units are operated below and above the fundamental resonance frequency (usually below 500 Hz) by using a crossover with a low-pass characteristic. Most low frequency drive units contain a moving coil assembly using an electro-dynamical motor principle. The electrical, mechanical and thermal behavior of the drive unit at fundamental resonance frequencies can be described by equivalent network comprising lumped elements with linear and nonlinear parameters. The linear parameters comprise the Thiele-Small parameters, visco-elastic parameters (creep factor) and electrical parameters describing the lossy inductance at higher frequencies. The dominant nonlinearities are the force factor Bl(x), stiffness Kms(x) or compliance Cms(x) and inductance L(x) versus displacement x and the inductance L(i) varying with the input current i. Thermal parameters describe the heating of the coil, the heat transfer to the pole tips, magnet and ambience considering conduction, radiation and convection cooling. 

Critical issues:

  • Maximal peak displacement
  • High dc displacement (coil is shifted out of the gap)
  • Motor instability (bifurcation, jumping effect)
  • Thermal power handling
  • Rocking modes and circumferential modes
  • Intermodulation distortion caused by Le(x) and Bl(x)


Standards:

  • IEC Standard IEC 60268-5 Sound System Equipment, Part 5: Loudspeakers
  • IEC Standard IEC62458 Sound System Equipment – Electroacoustic Transducers - Measurement of Large Signal Parameters
  • AES2-1984 AES Recommended practice Specification of Loudspeaker Components Used in Professional Audio and Sound Reinforcement

 

 

 

Most relevant Measurements 

Linear lumped parameters
(resonance frequency, Q-factors, Thiele/Small, creep, inductance)

Effective radiation area Sd

Loudspeaker nonlinearities
(Bl(x), Kms(x), L(x) , L(i))

Single-valued nonlinear parameters
(X
max , XBl , XC , Voice coil offset Xoffset , Suspension asymmetry AKms)

Thermal parameters
(thermal resistances, time constants, capacities, air convection parameter)

Irregular loudspeaker defects
(Rub & Buzz, loose particles, wire beat, bottoming, air leakage noise)

Air leakage noise localization ok
(position of modulated noise source)

On-axis sound pressure amplitude response
(sensitivity, mean SPL, effective frequency range )

Directional characteristics
(directivity index, coverage angle, radiation angle, polar radiation measurement)

Sound power response

Phase response
(minimal-phase, excess-phase)

Group time delay response
(total, minimal phase)

Time-frequency analysis
(Wigner, cumulative decay spectrum, sonagraph, wavelet, …)

Nonlinear harmonic distortion
(THD, THD+N, components)

Equivalent harmonic input distortion

Intermodulation distortion
(difference-tone and sum-tone IMD)

Amplitude intermodulation distortion (AMD)
(modulation of the fundamental)

Sinusoidal burst measurement

Thermal and nonlinear compression
(fundamental, harmonics versus voltage)

Voice coil displacement
(peak, bottom, dc component, Xmax)

HI-2 distortion

Multi-tone distortion

Accelerated life test, power test
(durability, parameter variation, maximal input power)

Voice coil temperature

Distortion in reproduced audio signal
(contribution of Bl(x), Cms(x), Le(x), Le(i))

Auralization

3D-geometry scanning

Shape of the surface
(scanning geometry)

Distributed mechanical parameters
(mechanical vibration scanned on radiator’s surface)

Modal analysis
(natural frequencies, shape of modal vibration, modal loss factor)

Accumulated acceleration level (AAL)

Decomposition into radial and circumferential mode (indicating rocking mode)

 

 

 

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Passive Loudspeaker Systems test

 

 

Examples:

drive units with crossover in enclosure

Applications:

home, automotive, multimedia and professional

Particularities:

Passive loudspeaker systems use an external power amplifier and are usually operated over the entire audio band. The transfer behavior of each drive unit (woofer, midrange, tweeter) can be described by an equivalent network model using lumped elements which are valid at the corresponding resonance frequency. The linear, nonlinear and thermal parameters of the model can be measured by using a new identification technique monitoring voltage and current at the loudspeaker terminals only. In addition to the mechanical and electrical parameters of drive units (see tweeter, woofer), there are a few acoustical parameters describing the port resonance of a vented enclosure, nonlinear resistance of the air in the port and the ratio of the air and suspension compliances. Small leakages in the enclosure which do not affect the electrical input impedance may cause audible air noise. This can be detected more reliably by using a sensitive noise demodulation technique. Parasitic vibration of the grill, handle or any other part of the enclosure may cause impulsive distortion similar to the irregular Rub & Buzz defects found in the drive unit. The sound pressure response on-axis and off-axis, sound power response and other directivity characteristics can be measured in the near field under arbitrary conditions or in the far field under anechoic condition. The acoustical characteristics can also be predicted by FEA and BEA using the mechanical distributed parameters of the loudspeaker drive units measured by a laser scanning technique and the geometry of the enclosure. Thermal model and the parameters valid for a single drive unit measured in free air may describe approximately the coil temperature and the cooling process in vented box systems. If the drive unit is mounted in a sealed enclosure, the thermal resistance Rtm describing the heat transfer between magnet and ambience is much higher than in free air.

Design Challenges:

  • Optimal selection of drive units (woofer, tweeter)
  • Optimal design of the vented enclosure (alignment, port noise)
  • Crossover design and time alignment
  • Thermal power handling


Most important characteristics:

  • SPL frequency response (1 m, 1 W on-axis)
  • Mean SPL in a effective frequency range (1m, 1W on-axis)
  • Long-term maximal input power
  • Maximal short-term sound pressure level (SPL) in stated frequency band (1s, 1m, on-axis)
  • Maximal long-term SPL in stated frequency band (1 min, 1m, on-axis)
  • Impedance curve (rated impedance)
  • Total harmonic distortion
  • Intermodulation distortion
  • Impulsive distortion (Rub & Buzz) at maximal short-term SPL in stated band
  • Sound power response or directivity index


Critical Issues:

  • Rub & Buzz, loose partials in the drive unit
  • Parasitic vibration of the grill
  • Air leakage noise
  • Hard limiting of the suspension (large values of weighted harmonics HI-2 distortion)
  • Excessive modulation distortion (motor instability, Bl(x) and L(x) asymmetries)
  • Acoustical cancellation effects (negative directivity index)


Standards:

  • IEC Standard IEC 60268-5 Sound System Equipment, Part 5: Loudspeakers
  • IEC Standard IEC62458 Sound System Equipment – Electroacoustic Transducers - Measurement of Large Signal Parameters
  • AES2-1984 AES Recommended practice Specification of Loudspeaker Components Used in Professional Audio and Sound Reinforcement
  • AES56-2008 AES standard on acoustics – Sound source modeling – Loudspeaker polar radiation measurement
  • CEA-2034, Standard Method of Measurement for In -Home Loudspeakers

 

 

Most relevant Measurements 

Linear transducer parameters

(resonance frequency, Q factors, T/S, creep, inductance, tuning resonance and quality factor of the port)

Nonlinear parameters

Electrical impedance

Thermal parameters

Rub & Buzz and other irregular defects

On-axis SPL amplitude response

(sensitivity, mean SPL, effective frequency range )

Group time delay response

(total, minimal phase)

Phase response

(minimal-phase, excess-phase)

Directional characteristics

(directivity index, coverage angle, radiation angle, polar radiation measurement)

Sound power response

Input voltage

(rated noise voltage, short-term maximum voltage, long-term maximum power)

Input power

(rated noise voltage, short-term maximum voltage, long-term maximum power)

Nonlinear harmonic distortion

(THD, components)

Intermodulation distortion (IMD)

Amplitude intermodulation distortion (AMD)

(modulation of the fundamental)

Thermal and nonlinear compression

(fundamental, harmonics)

Peak displacement

DC displacement

Sinusoidal burst measurement

HI-2 distortion

Multi-tone distortion

Time-frequency analysis

(Wigner, cumulative decay spectrum, sonagraph, wavelet, …)

Accelerated life test, power test

(durability, parameter variation)

Coil temperature

Rated noise power

Distortion generated by dominant nonlinearities

Bl(x), Cms(x), Le(x), Le(i) in reproduced audio signal

Distributed mechanical parameters

(cone vibration, geometry)

Accumulated acceleration level (AAL)

Modal analysis and decomposition techniques to find circumferential, radial components and rocking modes

Radiation analysis

(sound pressure on-axis and off-axis, directivity index, sound power response)

Auralization

 

 

==========================================================================================

 

Active Loudspeaker Systems test

 

Examples:

transducers in enclosure with built-in power amplifier

Applications:

home, automotive, multimedia, professional, telecommunication

Particularities:

 

Active loudspeaker systems use an internal power amplifier and additional analogue and digital electronics for digital audio streaming, DA conversion, limiting, crossover, gain attenuation and loudspeaker control (protection and linearization). The electrical terminals of the transducers (e.g. tweeter and woofer) are usually not accessible for the assessment of the final product. Therefore, the evaluation of an active loudspeaker system has only access to mechanical or acoustical output signal monitored by using a microphone or a laser sensor. Contrary to drive units and passive loudspeaker systems, the nonlinearities cannot be measured directly by using a nonlinear system identification technique. However, measurement of harmonic and intermodulation distortion and other meaningful nonlinear symptoms (e.g. dc displacement) may give meaningful indications about the physical cause. Small leakages in the enclosure generating audible air noise can reliably be detected by using a sensitive noise demodulation technique. Parasitic vibration of the grill, handle or any other part of the enclosure may cause impulsive distortion similar to the irregular Rub & Buzz defects found in the drive unit. The sound pressure response on-axis and off-axis, sound power response and other directivity characteristics can be measured in the near field under arbitrary conditions or in the far field under anechoic conditions. The acoustical characteristics can also be predicted by FEA and BEA using the mechanical distributed parameters of the loudspeaker drive units measured by laser the scanning technique and the geometry of the enclosure. Measurements of the fundamental response at multiple input levels reveal the compression of the fundamental and distortion components caused by nonlinearities and the heating of the voice coil. This data may be used to predict the voice coil temperature and to define the maximal sound pressure output for different stimuli.

Challenges in the design:

 

  • Optimal selection of drive units (woofer, tweeter)
  • Optimal design of the vented enclosure (alignment, port noise)
  • Crossover design and time alignment
  • Thermal power handling
  • Thermal and mechanical protection
  • Additional equalization
  • Rub & Buzz, vibration of the grill, air leakage noise

 


Most important characteristics:

 

  • Maximal short-term sound pressure level (SPL) in stated frequency band (1s, 1m, on-axis)
  • Maximal long-term SPL in stated frequency band (1 min, 1m, on-axis)
  • Harmonic distortion at short-term maximal SPL in stated band
  • Intermodulation distortion at maximal short-term SPL in stated band
  • Impulsive distortion (Rub & Buzz) at maximal short-term SPL in stated band
  • Small signal sound pressure frequency response (magnitude and group delay at 1m, on-axis)
  • Sound power response or directivity index

 


Critical Issues:

 

  • Rub & Buzz, loose partials in the drive unit
  • Parasitic vibration of the grill
  • Air leakage noise
  • Hard limiting of the suspension (large values of weighted harmonics HI-2 distortion)
  • Excessive modulation distortion (motor instability, Bl(x) and L(x) asymmetries)
  • Acoustical cancellation effects (negative directivity index)

 


Standards:

 

  • IEC Standard IEC 60268-5 Sound System Equipment, Part 5: Loudspeakers
  • IEC Standard IEC62458 Sound System Equipment – Electro-acoustic Transducers - Measurement of Large Signal Parameters
  • AES2-1984 AES Recommended practice Specification of Loudspeaker Components Used in Professional Audio and Sound Reinforcement
  • AES56-2008 AES standard on acoustics – Sound source modeling – Loudspeaker polar radiation measurement
  • CEA-2034, Standard Method of Measurement for In -Home Loudspeakers
  • CEA-2019, Testing and Measurement Methods for Audio Amplifiers
  • CEA-CEB19, Recommended Loudspeaker Safety Practices
  • CEA-2006-A, Testing & Measurement Methods for Mobile Audio Amplifiers
  • CEA-2031, Testing and Measurement Methods for Mobile Loudspeaker Systems,
  • ITU-R Recommendation BS. 775-2: Multi-channel stereophonic sound system with and without accompanying picture. International Telecommunication Union (ITU), 2006
  • ITU-R Recommendation BS. 1116: Method for subjective assessment of small impairments in audio systems including mulitchannel sound systems. International Telecommunication Union (ITU), 1997
  • IEEE Standard 269 IEEE Standard Methods for Measuring Transmission Performance of Analog and Digital telephone Sets, Handsets, and Headsets
  • IEEE Standard 1329 Standard Method for Measuring Transmission Performance of Speakerphones
  • IEEE Standard 1652 Standard for the Application of Free Field Acoustic Reference to Telephony Measurements

 

 

Most relevant Measurements 

Rub & Buzz and impulsive distortion

Far field sound pressure on-axis

(sensitivity, mean SPL, effective frequency range)

Directional radiation characteristics

(directivity index, coverage angle, radiation angle, polar and balloon plots, sound power response)

Phase response

(minimal-phase, excess-phase, polarity)

Group time delay response

(total, minimal phase)

Time-frequency analysis

(Wigner, cumulative decay spectrum, sonagraph, wavelet, …)

Nonlinear harmonic distortion

(THD, THD+N, components)

Equivalent harmonic input distortion

Intermodulation distortion

(difference-tone and sum-tone IMD)

Amplitude intermodulation distortion

(AMD, temporal variation of the fundamental)

Thermal and nonlinear compression

(fundamental, harmonics versus voltage)

Sinusoidal burst measurement

HI-2 distortion

Multi-tone distortion

Distributed mechanical parameters

(mechanical vibration scanned on radiator's surface )

Modal analysis

(natural frequencies, shape of modal vibration, modal loss factor)

3D-geometry scanning

Accumulated acceleration level (AAL)

Decomposition into radial and circumferential mode (indicating rocking mode)

 

 

 

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