A Real Time Thiele-Small Measurement System
For The Woofer Tester Pro And Speaker Tester Systems

Understanding Real Time Measurements And how This Effects Results

The Woofer Tester Pro and Speaker Tester 'Snap TS' mode can be a useful real time mode for evaluating T/S parameters or making A/B tests against a known golden unit. Additionally, the high power testing capability of the WTPro often reveals fabrication issues that occur at higher drive levels.  As with any test, setup and result interpretation is important because this can either hide or reveal certain phenomena.  In any case when accuracy, stability and repeatability are important the more robust sine test is always preferred .  The information in this document should be helpful in understanding these concerns.

SnapTS Linear and Non-Linear Driver Effects to Consider

Q and Fs Ring Down Time

A damped oscillation will occur when an impulse force is applied to a mechanical resonator such as a loudspeaker. The time that it takes for the resulting oscillation to decrease from an initial level of Vo to Vf is T=-ln(Vf/Vo)*Q/(pi*Fs) where Q is the mechanical loss. For a loudspeaker Qts is typically understood to be the parallel combination of the mechanical and electrical losses, Qts=Qes||Qms. However, when the voice coil is not shorted or connected to a low output impedance amplifier there is no electromotive drag from the motor so Qes is not applied and Q=Qms. This condition also applies during the TS test because a constant current source is used and the output impedance is high. The consequence of this is that the ring down time is now much longer, and if this time is too long, it can affect the SnapTS real time measurements. Sine wave testing is immune to this effect because the test signal is applied for a much longer time, especially given how the search continually narrows.  The bottom line is that ring down time is a proportional to Qms/Fs.  A combination of both high Qms and low Fs being the worst case.  If this occurs, use a larger FFT by increasing the frame size.

Compression Effects - Why T/S Parameters Are Measured Using Small Signals

Several loudspeaker parameters are affected by temperature.  Voice coil heating is well known as this causes Re to change and can be directly entered or modified in many of the popular Thiele Small modeling software.  Note: The resistance of copper is directly proportional to absolute temperature (degrees Kelvin).

A less obvious, but actually a very large error contributor are changes in suspension stiffness due to temperature.  This relationship exists because the mechanical components that are used are often made from plastics and heat cured resins that continue to have strong temperature dependencies even when cured.  This effect goes beyond the initial break-in effect that tends to be a more or less permanent change.   What is not well documented is that as mechanical energy is absorbed (into mechanical impedance Rms), the suspension tends to warm and therefor soften, often quite dramatically.

When very small signals are used mechanical heating is far lower.  For this reason baseline models should be derived using the WT2 port.  Note: When the WT2 port is used in Sine mode, the extremely high precision provided is often enough to measure this compression effect even though the drive levels are very small.  The Woofer Tester Pro's HiZP port is simply an extension of this curve, often out to Xmax drive levels where the curve tends to turn around as the suspension (or motor) begins to bottom out.

Test Environment Noise Immunity

Though being able to measure drivers in a noisy environment can be solved by simply moving to a less noisy environment, eventually measurement limitations are likely to occur.  The interesting thing about a sine wave is that because it is a monotonic all of the driving energy is packed into one frequency.  On the input side it is also now possible to build a matched narrow band filter.  The effect is the same as using a larger signal and a very large FFT making truly 'small signal' conditions possible.

Motor and Suspension Non Linearity

Non linearity becomes increasingly important when testing at higher 'amplifier' drive levels with the WTPro.  In this case warming and stretching effects will cause the mechanical bias point to shift, often beyond the more simple example of reversing the leads and shifting the resonance.  Clearly not only has the resonance point changed, but so has the Q, BL and other parameters.  If a real time mode is used, eventually the impedance curve will even begin to distort.  This is because the resulting impedance curves are different for each extreme of the inward and outward stroke.  In this case an FFT real time mode is clearly not suitable while the sine test is far more likely to succeed.

FFT Results Averaging

Ultimately it is the shape of the impedance curve that determines the driver parameters.  However, given that FFT results are often noisy or sparse, averaging is often employed to produce a smooth curve.  Time averaging of several frames does not damage the data, but binning does.  Binning uses the neighboring bins as a group to produce a smooth curve.  This can however damage the shape of the curve and therefor effect Q (mainly by lowering the Fs peak).  Furthermore, if Fs does not align with the FFT bins, the actual peak is smeared into the adjacent bins.   These types of errors also increase as Fs decreases. The testers averaging options include selecting the octave width, and the number of desired outputs.  Ultimately this determines the number of bins that are averaged together.

DC Accuracy

The ADC used in the tester does not convert DC signals.  Therefor the DC bin of an FFT holds no useful information.  Like our sine test, the DC value must be interpolated from the next two lowest data points.  However, unlike the FFT that is restricted to the bin frequencies, the sine mode can measure any frequency.

Comparing SnapTS and Sine Mode Tests

The time to complete the QFs and Vas portions of the T/S test sweeps are given below. In both cases, additional setup time must also be considered when breaking in a driver (hours), or when the Vas portion of the test calls for adding a test mass (10~20 seconds), mounting the driver in a test box (minutes), measuring the suspension diameter (10 seconds), etc.

SnapTS Preferred Setup (results settle in 2~10 seconds)
  • Select LoZP or HiZP (WTPro only)
  • Select any Real Time signal. Use Impulse or Chirp for Low Frequency sensitivity
  • Enable input averaging (if needed)
  • Enable output averaging (if needed)
  • Set sampling rate to 48000 Hz
  • Set Frame Size from 8k-64k depending on the driver Fs and Q
  • Set low Frequency limit to 10, and high to 20k
  • 1/30th octave binning (or less) - Does not smear and lower the Zmax peak
  • Set 512 or more output points for smoother curves
  • Use dB/Ph filtering (not RI vectors)
  • If needed move to a quiet test area

Sine Mode Setup (QFs completes in ~1 minute, Vas in ~20 seconds)

  • Select LoZP or HiZP (WTPro only)
  • Select Sine test signal mode
  • Set sampling rate to 48000 Hz
  • Set frame size to 4k
  • Set buffers to 2
  • Set averaging to 2
  • Set Sweep Ratio to 1.3
  • Set Min Ratio to 1.001 (0.1% frequency accuracy)
  • Set low Frequency limit to 10, and high to 20k (or less for high L woofers)
  • Make adjustments as needed for curve smoothness, range etc.
Circuit and Signal Processing Back Ground

Real Time (Fast) and Swept Sine Impedance Curves

Traditionally Ohms law, R=V/I, is first learned with static DC voltages and current.  When AC circuits are considered, energy storage devices like capacitors and inductors cause the applied voltage and current to be out of phase.  The ratio V/I ratio is still used, but the V and I parts now must consider phase in the calculation.  In this case 'ohms' are now referred to as having 'reactive impedance', commonly referred to Z (and P for phase).  Since circuits are often made from more than one device, and capacitive and inductive energy storage is frequency dependent, the impedance curve relative to frequency is often complex.  Note: loudspeaker mechanical parameters such as mass and suspension stiffness store mechanical energy and are transposed as capacitors and inductors.

An impedance curve (a series of Z values at particular frequencies) can be generated in two ways.  The first is to apply a single frequency at each frequency of interest, measure the resulting voltage and current, and then compute the Z=V/I impedance ratio.  The second is to apply a complex signal that contains all of the frequencies of interest...all at one time.  An FFT is then used to convert the resulting complex voltage and current signals to frequency domain equivalents.  Since the amplitude and phase of V and I are now in matching frequency domain arrays, Z can be computed for each FFT bin frequency.  However, unlike the single sine method, and though this is a quicker method, a number of factors need to be considered when this technique is applied to a non-linear device such as a speaker.

FFT Frame Size and Resolution

Fourier Transform's are used to convert a sequence of time domain samples into frequency.  The highest frequency that can be defined (with aliasing) occurs when exactly two samples occur in one sine period.  This frequency is known as the Nyquist frequency or Nyquist rate, and is defined as Fn=Fs/2 where Fs is the sampling rate.  The lowest frequency that can be resolved occurs when one sine wave just fits the time sequence.   If for example a 48000 Hz sampling rate is used to capture a 32768 sample sequence, the elapsed time would be t=32768/48000, or  0.683 seconds and this would result in a minimum frequency of 1.464 Hz.  Another property of the FFT is that the minimum frequency is also the spacing between each adjacent frequency bin.  In the above case the available 'exact' frequencies would be 1.46, 2.92, 4.39...  If an analog  frequency falls between these points the energy is divided into the adjacent bins.  Additional math is needed to find the exact frequency and magnitude.  Note: FFT's are typically written for powers of 2 sizes for algorithmic reasons (2,4,8,16,...16384,32768,... etc.)

Signal Density of Real Time Signals

Depending on what needs to be measured, several test signal options are available for FFT real time mode testing.  For example, the impulse signal favors low frequency analysis while MLS is best used for high frequencies.  In any case what is important is that all of the frequencies of interest (each FFT bin) are represented.  Since these signals are obviously different in both time and in frequency, the energy density or spectrum and the phase become important.  Mathematically this is all sorted out when the V/I ratio is calculated.  What is less obvious is that the time and spectral energy density and the non-linear characteristics of a driver can result in differences when one signal is used as opposed to another.  A good example would be the impulse mode (actually modified triangle) where most of the energy is packed into a single edge.  In addition, the driver clearly moves inward or outward depending on the connection polarity.  As shown below this DC bias has generated two completely different impedance curves.  DC biases also occur, but to a lesser extent, in all of the other signal modes.  The only exception is the sine mode (and it even has a DC bias when it starts).

Drive Signals

The WT2 output is a true constant current source, which is very different from a faux (not quite real) constant current source that is created when a high value resistor is used inline with a voltage amplifier.  As an example the traditional method was to use an amplifier with a 1k series resistor.  In this case, the amplifier output was sufficiently large to achieve a measurable signal level, and as long as the measured impedance was not greater than say 100 ohms (10% of 1k) the error would be considered 'small enough'.  Note: Non amplified 'sound card' levels are considerably lower so its not uncommon to use an even smaller series resistor value in the 100-470 ohm range.

Note: The WTPro HiZP port is traditionally connected directly to an amplifier and constant current is simulated by adjusting the amplifier output level using one of the feedback modes.  An alternative would be to not use a feedback mode and instead add a large series resistor, just like the 'faux' constant current described above.  In this case the 0.5 ohm series resistor can also be increased to decrease the 5A current sensing range to something considerably less (use 5 ohms for a 500mA range).


SnapTS is ideal for quick real time evaluation of TS parameters. However, given its sensitivity to systematic errors, the modestly slower discrete tone 'sine mode' test is preferred when published or critical data is important.

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