MEASURING THIELE-SMALL DRIVER PARAMETERS Qes, Qms, Qts
Determination of Thiele-Small (TS) "small-signal" driver parameters using a constant voltage method is explained.  Here we describe two approaches, the first uses the 4-wire method and the second uses the dedicated hardware/software package CLIO operated under constant voltage test conditions.  The constant voltage method means exactly that, the TS parameters are determined under conditions where the voltage applied to the device under test ("DUT") is constant over the complete range of frequencies examined.  Note that either method may be used to determine the impedance modulus  (the impedance as a function of frequency) of ANY reactive component within the audio frequency spectrum including capacitors, inductors, networks and cables.

CAUTION - THE FOLLOWING MEASUREMENT METHODS REQUIRE A VOLTAGE FROM AN AMPLIFIER TO BE APPLIED TO THE DUT. IT IS POSSIBLE TO INADVERTANTLY APPLY THE FULL RATED VOLTAGE OF THE AMPLIFIER TO EITHER THE DUT OR TEST EQUIPMENT RESULTING IN AN OPEN VOICE COIL, DESTROYED METER OR DAMAGED NETWORK.  IT IS ALSO POSSIBLE TO SHORT THE AMPLIFIER.  LABEL ALL CONNECTIONS (+, GND, AMP +).   

Test equipment:
1. Basic audio amplifier (voltage source) capable of providing a low distortion, 0-5V signal between 10-1000Hz.  
2. Audio frequency wave generator (sinusiodal signal source).  If TTL output equipped, use to trigger frequency counter.
3. Frequency counter capable of 0.1Hz resolution and adjustable triggering  
4. Digital AC/DC multimeter capable 1mV and 0.01 Ohm resolution (voltage drop and resistance of source resistor, respectively)
5. Analog or Digital AC meter capable of 0.1V resolution (amplifier voltage)
6. A non-inductive, 5-10W, 8 Ohm resistor (source resistor).
7. Optional: phase meter (network analysis) or oscilloscope (loudspeaker analysis).

The TS parameters are derived directly from the impedance modulus of the driver operating within the bandwidth that captures the response at the moving mass free-air resonance, Fs.  The 4-wire method makes this task straightforward requiring only five measurements to be taken.  We have created an Excel spreadsheet named 4-wire constant voltage TS that sequences the tasks and performs the calculations required to derive the driver Quality factors Qes, Qms and Qts.  A schematic of the setup shown below.  Note that the schematic shown is from a functioning SPICE model of a loudspeaker in series with a source resistor driven by a sinusoidal AC voltage source with a maximum output of 3Vrms.  Drive signal voltages with magnitudes between 0.5-1.0V are reasonable for woofers.  The analysis, to be valid, assumes the magnetic force acting on the coil is uniform, regardless of coil position.











Procedure
1.    Measure DC resistance of source resistor, Rs, and driver voice coil, Re. Input both values in spreadsheet.
2.    Place source resistor in loop, apply amplifier voltage and set voltage level, Vs (for example 0.5 Vrms).  Input value in spreadsheet.
3.    Adjust the sine wave generator to a frequency near the specification value of Fs. Adjust until the voltage drop measured
       across the source resistor is a minima, Vm.  Exact value of Fs occurs at Vm. Input measured Vm and Fs values in spreadsheet.
4.    To establish the values of Fh and Fl, adjust the sine wave generator to a frequency below Fs that exhibits a source resistor voltage
       drop equivalent to the spreadsheet parameter, Vr.  Input the value in spreadsheet as Fl (= frequency low).  Repeat the procedure for
       the frequency above Fs that exhibits a source resistor voltage drop equivalent to the spreadsheet parameter, Vr.  Input the value in
       the spreadsheet as Fh (= frequency high).
5.    Once Fh and Fl meet check requirements, the values of Qms, Qes and Qts are known at the drive signal selected.