Editing Thiele/Small parameters (section)

==Measurement notes—large signal behavior==
Some caution is required when using and interpreting T/S parameters. Individual units may not match manufacturer specifications. Parameters values are almost never individually taken, but are at best averages across a production run, due to inevitable manufacturing variations. Driver characteristics will generally lie within a (sometimes specified) tolerance range.  <math>C_{\rm ms}</math> is the least controllable parameter, but typical variations in <math>C_{\rm ms}</math> do not have large effects on the final response.<ref name="ComplianceScaling"/>

It is also important to understand that most T/S parameters are linearized small signal values. An analysis based on them is an idealized view of driver behavior, since the actual values of these parameters vary in all drivers according to drive level, voice coil temperature, over the life of the driver, etc. <math>C_{\rm ms}</math> decreases the farther the coil moves from rest. <math>Bl</math> is generally maximum at rest, and drops as the voice coil approaches <math>X_{\rm max}</math>. [[Electrical resistance#Temperature dependence|<math>R_{\rm e}</math> increases as the coil heats]] and the value will typically double by 270&nbsp;°C (exactly 266&nbsp;°C for Cu and 254&nbsp;°C for Al), at which point many voice coils are approaching (or have already reached) thermal failure.

As an example, <math>f_{\rm s}</math> and <math>V_{\rm as}</math> may vary considerably with input level, due to nonlinear changes in <math>C_{\rm ms}</math>. A typical 110-mm diameter full-range driver with an <math>f_{\rm s}</math> of 95&nbsp;Hz at 0.5 V signal level, might drop to 64&nbsp;Hz when fed a 5&nbsp;V input. A driver with a measured <math>V_{\rm as}</math> of 7&nbsp;L at 0.5&nbsp;V, may show a <math>V_{\rm as}</math> increase to 13&nbsp;L when tested at 4&nbsp;V. <math>Q_{\rm ms}</math> is typically stable within a few percent, regardless of drive level. <math>Q_{\rm es}</math> and <math>Q_{\rm ts}</math> decrease <13% as the drive level rises from 0.5&nbsp;V to 4&nbsp;V, due to the changes in <math>Bl</math>. Because <math>V_{\rm as}</math> can rise significantly and <math>f_{\rm s}</math> can drop considerably, with a trivial change in measured <math>M_{\rm ms}</math>, the calculated sensitivity value (<math>\eta_0</math>) can appear to drop by >30% as the level changes from 0.5&nbsp;V to 4&nbsp;V. Of course, the driver's actual sensitivity has not changed at all, but the calculated sensitivity is correct only under some specific conditions. From this example, it is seen that the measurements to be preferred while designing an enclosure or system are those likely to represent typical operating conditions. Unfortunately, this level must be arbitrary, since the operating conditions are continually changing when reproducing music. Level-dependent nonlinearities typically cause lower than predicted output, or small variations in frequency response.

Level shifts caused by resistive heating of the voice coil are termed [[power compression]].  Design techniques which reduce nonlinearities may also reduce power compression, and possibly distortions not caused by power compression. There have been several commercial designs that have included cooling arrangements for driver magnetic structures, which are intended to mitigate voice coil temperature rise, and the attendant rise in resistance that is the cause of the power compression.  Elegant magnet and coil designs have been used to linearize <math>Bl</math> and reduce the value and modulation of <math>L_{\rm e}</math>.  Large, linear spiders can increase the linear range of <math>C_{\rm ms}</math>, but the large signal values of <math>Bl</math> and <math>C_{\rm ms}</math> must be balanced to avoid dynamic offset.