Thiele-Small (TS) parameter testing is used to extract TS model parameters from various test points along the impedance and
 phase (ZP) curve of a driver. Traditionally, the Vas and Q extraction test begins with a measurement of the DC resistance 'Revc'.
 Free air mechanical system resonance frequency 'Fms' is found next followed by a test for the electrical Qes and mechanical Qms
 that define the shape of the resonance peak. Over the years, this test and the model it is based on, was first improved with the
 addition of an equivelent series inductance 'Le'. Though Le modeling was an improvement, it still had some short comings.
 More recently, the model has been extended in a way that models Le as a frequency dependent resistor 'Rem' and reactance 'Xem'.
 When this level of sophistication is used, the results are generally quite good, so it is recomended that Rem/Xem testing be used
 in all cases. Rem/Xem modeling is also integral to the previous tests, so the test for Rem/Xem is inserted after Revc and before
 the Fms test.

 The following steps illustrate how the tester measures Thiele-Small parameters:

 Step 1: Measure DC Voice Coil Resistance - Revc

 The software uses a special algorithm to measure and calculate Revc from the impedance and phase from test points at 1.0 and
 2.0 Hz. To calculate Revc, the algorithm looks at the real components and computes a slope and intercept for 0 Hz. Since the
 actual test points are AC signals, the voice coil is not actually DC biased, nor is it at rest. This overcomes certain mechanical
 limitations and at the same time allows the software to perform very narrow band filtering on the excitation signal even though
 the frequency is extremely low. No other TS test device is able to measure at these low frequencies and still provide full accuracy.
 Proper calibration of the tester is however important if extreme accuracy is desired.

 Step 2: Measure Frequency Dependent Rem and Xem

 There are two options menu setable methods for measuring Rem and Xem. Some experimentation may be required to achieve
 optimal results. In general, settings should follow these simple rules:
  • Set SweepHi as high as is practical - for example, 20 kHz
  • If clipping occurs, lower Idrive or SweepHi
  • For the single point mode, lower SweepHi if the phase is decreasing at SweepHi
 Rem/Xem from single point measurement method

 An Rem/Xem curve is made to fit such that it passes through Revc and a single measurement at SweepHi. This is fast and simple but
 the curve will only be guaranteed to pass through these two points. This might be a problem if phase is decreasing at SweepHi.

 Rem/Xem from Slope measurement method

 The software scans downward from SweepHi looking for a phase and Z-slope that are both positve. An Rem/Xem curve is then
 computed that will pass through these two points. This avoids the issue of a falling phase at SweepHi, but the curve might not fit
 particularly well for tweeters. This method tends to work exceptionally well with woofers. Just be aware that, at SweepHi, the
 impedance of some woofers can be very high causing the WT output to clip. The solution is simple, lower SweepHi or Idrive.

 Step 3: Measure Frequency of Mechanical System Resonance - Fms

 Traditionally, Fms was found using a voltmeter or oscilloscope and watching for a voltage peak. The problem with this solution is
 that the peak might be wide and the voltage vacillating, as the speaker transforms acoustic energy into voltage. Another problem
 with the original method is that the effects of Rem/Xem (or Le for the older generation model) were not considered skewing the
 results. The Woofer Tester overcomes these limitations by searching for the first zero phase-crossing to find Fms. This technique
 has several advantages:
  • The rate of phase change with frequency is greater than the rate of voltage change. The test is therefore more sensitive to
    changes in Fms and less sensitivity to noise.

  • Unlike other tools that interpret phase from impedance, the Woofer Tester actually measures phase

  • If the point of interest is passed during a frequency scan, the tester software will reverse direction and scan in the opposite
    direction with half of the original step ratio. This back and forth search continues until the terminal ratio is hit. The default
    terminal ratio is set to 0.1% but can be set to higher (or lower) precision.

  • The effects of Rem and Xem are taken into account during this test. The result is a 'bare' circuit model for the TS parameters.
    This leads to a higher degree of acuracy when it comes to extracting the remaining electrical and mechanical parameters

  • Rem/Xem effects are also simultaneously modeled using the Woofer Tester Simulator core. This feedback ensures that the
    final simulation is also more acurate.

  • Narrow-band, real-time digital lock-on filters are used to further reduce noise. These filters have complex (real and imaginary
    outputs) and are reconstructed for each frequency point to ensure that they are exactly centered on the frequency of interest.

 Step 4: Measure Resonance Peak Shape - Qes, Qms & Qts

 The height and width of the resonance peak indicates how well damped the speaker will be. This is known as the 'Q' or quality
 factor and indicates how well energy can be stored. Being 'electro-mechanical' a drivers total system Q (Qts) is broken
 down into electrical and mechanical components Qes and Qms respectively.  Equations for these parameters relate back to the
 peak amplitude impedance and Revc. From this an impedance is calculated where it is expected that the impedance peak will
 intercept at frequency points Fhi and Flo above and below the peak.

 Step 5: Finishing the Sweep

 At this point the basic TS parameters have been extracted.  The tester now continues its upward frequency sweep filling in
 data points until it hits the SweepHi limit.

 Step 6: Finding 'Le' at 1 kHz (Traditional Method)

 The tester changes frequency to 1 Khz and computes a value for Le. 1 kHz is used, because many inductor and capacitor testers
 (DVM testers) have standardized on this frequency. This measurement is supplied for comparison to other systems only.
 The Rem/Xem method is far more accurate.

 Step 7: Cleaning up the Graph (Optional)

 If you want to smoothen out the curves in your graphs, you can either change the sweep step ratio or go back and manually add
 datapoints. This is easily accomplished using the mouse when the 'set frequency with left moust button' option is enabled.
 Simply left click on the graph area to set the frequency, wait for the data to settle, and then right click to add that point
 to the data set. Clicking on the 'Calibrate' button begins the calibration process with a high frequency short circuit test.
 There will be a message reminding you to short the end of your test leads (at this point clip them together). Wait a moment
 for the data to stabilize and the message in the lower right should now read 'Pass'. Click 'Accept' or 'OK' to continue.
 This part of the calibration process measures residual signals due to resistance or internal signal path leakages. Data taken
 at this time is most important when measuring impedances that are close to zero ohms or when the current drive level is set
 very low.

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