**7. Abnormal distortion**

Loudspeaker defects such as voice coil rubbing, mechanical vibrations of loose parts, air turbulences, and other irregular nonlinear dynamics that are neither intended nor considered in the design can generate particular distortion that can significantly degrade the audio quality. A loudspeaker generating abnormal distortion, usually called "rub & buzz" should not be shipped to a customer!

Modern measurement techniques exploit unique features of abnormal distortion. Time-analysis applied to a distorted single-tone stimulus reveals a complex fine structure comprising spikes, transients, and noise-like patterns [29]. Contrary to the harmonic and intermodulation distortion discussed in Section 6, the abnormal distortions cover the entire audio band. However, they have a low RMS value, are usually close to the noise floor, and thus require a near-field measurement. Spherical wave expansion or averaging over multiple periods removes the random features of the abnormal distortion.

The IEC standard 60268–21 [11] recommends a chirp stimulus at varying excitation frequency *f*<sup>e</sup> and a high-pass tracking filter with a cut-off frequency *f*<sup>c</sup> > *n*co*f*<sup>e</sup> to separate the abnormal distortion in the measured sound pressure signal *p*(*t*). The factor *n*co for the cut-off frequency *f*<sup>c</sup> (typical value *n*co = 10) depends on the excitation frequency *f*e, the transducer type, and properties of potential defects. The optimal value for *n*co can be determined by maximizing the crest factor **C**ID(**r**) defined according to IEC 60268–21 [11] as the ratio between peak and RMS values of the high-pass filtered signal *p*ID as:

$$\mathbf{C\_{ID}(r)} = \mathbf{10lg} \left( \frac{\mathbf{MAX}\_t^{t+T} \left| p\_{\rm ID}(t, \mathbf{r}) \right|^2}{\frac{1}{T} \int\_t^{t+T} p\_{\rm ID}(t, \mathbf{r})^2 dt} \right) d\boldsymbol{B} \tag{33}$$

The crest factor *C*ID(**r**) is independent of the spectral energy but describes the impulsiveness of the abnormal distortion considering the phase relationship between the spectral components. A high crest factor is a unique symptom of abnormal distortion, while the crest factor of the fundamental, regular nonlinear distortions or electronic noise is typically below 12 dB.

This fact initiated the measurement of the impulsive distortion (ID) defined in IEC 60268–21 as a peak level in decibel as

$$L\_{\rm ID}(f\_{\rm e}, \mathbf{r}\_k) = 20 \lg \left( \frac{\mathbf{M} A X\_t^{t+T} |p\_{\rm ID}(t, \mathbf{r}\_k)|}{p\_{\rm ref}} \right) dB \tag{34}$$

Using a peak found over a period length *T* in the nominator in Eq. (33) and normalized by reference sound pressure *p*ref. This peak level *L*ID(*f*e,**r***k*) is a helpful metric for finding the most critical excitation frequency *f*ID and a scanning point **r**ID ∈ Sr at the nearest position to the source (e.g., rattling), generating impulsive distortion with **C**ID(*f*) > 12 dB. The maximum value found under the condition

$$L\_{\rm IDmax} = L\_{\rm ID} \left( f\_{\rm ID}, \mathbf{r}\_{\rm ID} \right) = \max\_{\forall f\_{\varepsilon}} \left( \max\_{\forall \mathbf{r}\_k \in S\_{\mathbf{r}}} \left( L\_{\rm ID} \left( f\_{\varepsilon}, \mathbf{r}\_k \right) \right) \middle| \mathbf{C}\_{\rm ID} (f) > 12 dB \right) \tag{35}$$

is the basis for calculating the maximum impulsive distortion ratio (IDR) defined according to IEC 60268–21 [11] as

$$L\_{\rm IDR} = L\_{\rm ID} \left( f\_{\rm ID}, \mathbf{r}\_{\rm ID} \right) - L\_{\rm REF} \tag{36}$$

*Modeling and Testing of Loudspeakers Used in Sound-Field Control DOI: http://dx.doi.org/10.5772/intechopen.102029*

using a reference sound pressure level LREF measured at the standard evaluation point (on axis, *r* = 1 m) or a scanning point **r***<sup>k</sup>* generating the largest SPL value:

$$L\_{\rm REF} = 10 \lg \left( \frac{1}{T p\_{\rm ref}^2} \mathbf{MAX} \int\_t^{t+T} p(t, \mathbf{r}\_k)^2 dt \right) dB \tag{37}$$

Those metrics compared with meaningful limits for passing or failure are essential for the quality control of loudspeakers in manufacturing and maintenance.
