The Thiele-Small Parameters window is used to calculate the parameters for a drive unit from measurements of its impedance. To calculate all the parameters two measurements are required, one in "free air" and a second with either mass added to the cone or with the unit in a sealed (air tight!) enclosure (ideally with a volume a little less than the expected Vas). Note that the drive unit must be rigidly supported during the measurements, and ideally mounted vertically (i.e. so that the cone is firing horizontally as it would be in a typical loudspeaker installation). Some pre-conditioning of the unit with signals at medium levels helps to stabilise the behaviour and suspension compliance and reduce memory effects in the suspension from periods of storage or lack of use. Quiet conditions are important for good measurements, drive units act as microphones and pick up noise and vibration, affecting the results. The measurements should be made up to 20kHz so that the lossy inductance of the voice coil can be accurately modelled, and the impedance calibration step should be carried out before making measurements.

To show the results of a TS parameter calculation a small bass-midrange drive
unit was measured. It has an effective cone area of 137cm^{2}. The plots below
show the impedance measurements made in free air and then with a mass of 5g added
to the cone. REW determines whether the secondary measurement is from a sealed box
or added mass by looking at the resonant frequency, which is lower than free air for
added mass and higher for a sealed box. A least squares fit of an
electrical model of the drive unit impedance is carried out on the
free air measurement to determine the model parameters. Another least squares fit is
carried out on the secondary measurement to determine the modified motional parameters
and the TS parameters are then calculated.

To calculate the TS parameters the two measurements are selected and the required values are entered:

- the DC resistance of the voice coil (R
_{DC}) in ohms. Accurate measurement of low resistances is unfortunately not easy (see footnote), but the impedance model REW uses can easily compensate for a DC resistance which is slightly lower than the actual, so it is recommended to err on the low side - the effective area in square centimetres, most driver data sheets include an effective area figure but if this is not available REW can calculate the figure for you given the effective diameter, which is the diameter of the cone plus a proportion of the surround, typically 1/3 to 1/2, just click the calculator icon on the left hand side of the effective area box
- the air temperature in degrees Celsius
- the air pressure in millibar
- the volume of the sealed box in litres, or, if the second measurement was made with an added mass, the additional mass in grammes

The *Calculate Parameters* button is then clicked, with the following results.

The first column of results in the bottom of the window show the loudspeaker
resistance R_{E}, which is generally a little higher than the DC resistance;
the minimum impedance Z_{min} after the peak and the frequency f_{min} at which it occurs;
f_{3}, which is the frequency at which the impedance has increased to sqrt(2)*Zf_{min};
the inductance at f_{3}; the effective diameter and the effective area. The
second column shows the resonant frequency f_{S}; the mechanical (Q_{MS}),
electrical (Q_{ES}) and total (Q_{TS}) Q-factors and the F_{TS}
figure (f_{S}/Q_{TS}). These parameters can also be calculated for any
single measurement, without requiring a secondary measurement to be selected. The
L_{P} figure and the M_{MS}, C_{MS}, R_{MS}, V_{AS},
Bl and Eta (efficiency) figures in the third column can only be calculated using both measurements.

The "Compensate for leakage losses" and "Compensate for Air Load" check boxes are
only applicable for sealed box measurements, they take into account the leakage loss of
the sealed box (which would be shown as Q_{l} at the bottom of the first column
of results) and the air mass load due to the sealed box. These compensations use the
Carrion-Isbert method described by Claus Futtrup in the documentation for his *Driver
Parameter Calculator* application at http://www.cfuttrup.com/

The results can be copied to the clipboard by right-clicking on the results area,
or written to a text file using the *Write Parameters to File* button. When writing
to file the separator between values, labels etc is as defined in the File -> Export
menu.

REW uses a driver impedance model that incorporates elements that cater for Frequency-Dependent Damping. The model is described in detail in the paper by Thorborg, Tinggaard, Agerkvist & Futtrup, "Frequency Dependence of Damping and Compliance in Loudspeaker Suspensions" J. Audio Eng. Soc., vol. 58, pp. 472-486 (June 2010). The diagram below shows the components of the model.

The model is split into two parts. The part at the right hand side models the motional
impedance due to the movement of the driver, with parameters R_{ES},
C_{MES}, L_{CES} and Λ_{ES}. This part reproduces the peak
seen in the impedance plot. It differs from the classical model by the addition of a
frequency-dependent resistance omega*Λ_{ES} in parallel with L_{CES}. Note
that the FDD model R_{ES} value is higher than that of the classical model due to
the effect of omega*Λ_{ES}, which acts in parallel with R_{ES}.

The other part of the model deals with the blocked electrical impedance of the driver.
It is based on a model developed by Thorborg and Unruh, described in “Electrical Equivalent Circuit
Model for Dynamic Moving-Coil Transducers Incorporating a Semi-Inductor,” J. Audio Eng.
Soc., vol. 56, pp. 696–709 (Sept 2008). That model begins with a drive unit resistance
R_{E} which is the DC resistance R_{DC} followed by a small additional
resistance dR which models the resistance contribution due to eddy currents. It is followed by
a series inductance L_{EB} and then a parallel combination of an inductance L_{E},
a semi-inductance K_{E} and a resistance R_{SS}. L_{E} represents the
inductance of the part of the voice coil located inside the motor gap. L_{EB} represents
the part of the coil outside the motor gap.
The semi-inductance K_{E} has an impedance that varies with the square root of
omega*j. It models the effects of eddy currents and skin depth in the pole piece.
The parallel combination of L_{E} and K_{E} models the transition of the coil's
behaviour from largely that of a conventional inductor at low frequencies to a semi-inductor
at high frequencies. The R_{SS} component models the effect of electrically conductive
material in the magnet system, to be described in the paper by Thorborg and Futtrup "Electrodynamic
Transducer Model Incorporating Semi-Inductance and Means for Shorting AC Magnetization",
JAES Volume 59 Issue 9 pp. 612-627 (Sept 2011). The parameter values REW determines may be
modified if desired and the effect on the modelled impedance and phase traces viewed on the
graph, but the TS parameters which have been calculated will not be altered.

The plot below shows the modelled impedance traces (darker red and dashed) overlaying the measured values.

When TS parameters have been calculated the derived and simulated motional and blocked impedance magnitudes and phases can be plotted in addition to the total impedance traces. The simulated traces are produced using the model parameter values, the derived traces are produced by subtracting the model values from the measured values (for example, derived motional impedance is produced by subtracting the modelled blocked impedance from the total measured impedance).

As frequency-dependent component values are not supported by many circuit
simulators REW also calculates values for an alternative blocked impedance model using
two parallel resistor-inductor pairs in series, labelled R2-L2 and R3-L3, and the
conventional R_{ES}, C_{MES}, L_{CES} motional impedance model
without the frequency-dependent damping. The values of these components are shown in the
"Simplified Model" box. This diagram shows the simplified model components.

Accurate measurement of low resistances is challenging, LCR meters that are in calibration may have a suitable range and give good results. If you do not have access to a calibrated LCR meter an alternative is to get an accurate measurement of a higher value resistor, perhaps 50 ohm or so, or purchase a very high precision resistor (such as a Vishay bulk foil part) and form a voltage divider with a DC source, the reference resistor and the driver. A decent multimeter can provide accurate voltage measurements, measuring the voltage across the driver and the voltage across the reference resistor allows the driver resistance to be determined from (ref resistor) * (driver voltage) / (ref resistor voltage).