FAQ
 
 Introduction

 The Woofer Tester can easily test a DVC woofer in any of its possible configurations. In general you should test the DVC in the same
 configuration that you plan to use it. The most common configurations are when two amplifiers are used or a single amplifier is used
 with the coils connected in series or parallel. Other options include connecting only one coil, or using the second coil for Thiele-
 Small parameter tuning.


 Theory

 Though we would like to think that the two coils in a DVC driver are identical, this is often not the case. For starters, one of the coils
 is often wrapped outside the other and will have a higher resistance due to the larger radii. This can be compensated with length.
 Bifilar windings are also used where the two wires are wound simultaneously, thus ensuring identical wire lengths. The main
 variation in this case will be the wire diameter that can often vary by as much as 5%. Luckily, most manufacturers take the time
 to take these effects into consideration. Nevertheless, knowing that the two coils can behave differently can open up some areas
 of discussion. For the purpose of this discussion, the two coils are assumed identical.

 From a 'terminal load' perspective, a few things are immediately evident. In the series-connect case, the resistance seen at the
 terminals doubles and the voice coil drive voltage is halved. The total power going into the driver is therefore Pser=V^2/2*R,
 or half that of a single driven coil. In the parallel connect case, the resistance seen at the terminals halves and the drive
 voltage 'V' across each coil remains constant. The total power going into the driver is therefore Ppar=V^2/(0.5R) or twice that
 of a single coil. But this does not tell us how the driver will respond, nor does it tell us anything about how the T/S
 parameters are affected. Two controversies are often discussed. The first is that the up/down cone motion orientation allows
 the suspension to sag under the influence of gravity. The second is that the nickels are merely 'stuck' to the cone by their
 own weight. Though convenient, these two questions should be addressed:

   Table 1. Series and Parallel Configuration

                Rterm    Power  Sensitivity db/V

   Single coil  Revc     1.0x   +0db       - not practical or used

   Series       2*Revc   0.5x   -3db

   Parallel     Revc/2   2.0x   +3db


 Mechanical and Thiele/Small Effects on Series and Parallel Connections

 It is easiest to assume a constant current and then consider how that current will divide and flow through each coil. Equations for
 the various driver parameters are then evaluated and a ratio determined. In the series-connect case, the applied current flows in
 series through both coils for a total wire length of 2*L. The force developed in each coil adds, so BL doubles. In the parallel
 connection case, the current in each coil is half, yet the total wire length is still L. BL therefore remains constant.

          Series     Parallel

   Icoil  constant   half

   Rterm  double     half

   BL     doubles    constant

   R      doubles    half

 What happens to Vas?

   Vas = 1000.0*(SpeedOfSound*SpeedOfSound)*AirDensity*(Sd*Sd)/Kms;

   >>>> No parameters are affected, Vas is constant

 What happens to Qes?

             Qes  = Revc*Kms/(BL^2*Fms*2.0*PI);                // Qe for single coil

     Series: Qes  = (2.0*Revc)*Kms/((BL*2)^2 * Fms * 2.0*PI);  // 1/2 Single Coil

   Parallel: Qes  = (0.5*Revc)*Kms/((BL*1)^2 * Fms * 2.0*PI);  // 1/2 Single Coil

      Ratio: 1.0

 What happens to Efficiency?

             Efficiency = 9.64e-10*(Fms^3)*Vas/Qes;       // Single Coil Efficiency

     Series: Efficiency = 9.64e-10*(Fms^3)*Vas/(0.5*Qes); // 2x Single Coil

   Parallel: Efficiency = 9.64e-10*(Fms^3)*Vas/(0.5*Qes); // 2X Single Coil

      Ratio: 1.0

 Comparing Series to Parallel

             BL     Revc   Q     Vas   dB/Watt  Sensitivity/Volt

   Series    Double Double Same  Same  Same      0 dB ref

   Parallel  Same   Half   Same  Same  Same     +6 dB ref

 Dual Amplifier Model

 When two amplifiers are connected, one to each voice coil, the effect is that of a parallel connection and is easy to evaluate.
 However, if only one channel is driven, the amplifier with no signal is effectively attempting to hold its output to 0V.
 This is the same as a short circuited coil. If the shorted coil then moves in the magnetic field, it will generate a voltage
 and current that opposes the direction of motion. The effect is that of damping or lowering of Qes and if the two coils are
 identical in every way, Qes will be roughly halved. The exact relationship can however become rather complicated since the
 bucking action depends on the electrical and mechanical phase angles, BL and R.

 Results

 The theoretical and practical results can be expected to differ slightly since exact coil matching is practically impossible.
 A certain amount of error can also be expected from the test itself. Complicating matters, the particular driver used in this
 example has a rather low Revc=1.6 ohms for each coil. When possible soldered connections, soldered connections were used to minimize clip resistance variation. As shown below, the results follow the theory reasonably well:

   Measured Data: Credence Dual Voice Coil 8" (dual 2 ohm)
Series Parallel Short1 Short2 Open1 Open2 Revc 3.2529 0.7976 1.5885 1.6111 1.6381 1.6149 ohms Fs 36.7213 36.9943 37.2960 37.3087 37.0022 37.0022 Hz Zmax 64.1066 16.4591 3.1522 3.0450 17.5385 16.9511 ohms Qes 0.4393 0.4347 1.0248 1.0903 0.8655 0.8876 Qms 8.2186 8.5355 1.0088 0.9705 8.4013 8.4293 Qts 0.4170 0.4136 0.5084 0.5135 0.7847 0.8030 Le 1.9055 0.4719 0.0967 0.0873 0.4967 0.4691 mH Diam 167.6400 167.6400 167.6400 167.6400 167.6400 167.6400 mm Sd 22072.1774 22072.1774 22072.1774 22072.1774 22072.1774 22072.1774 mm^2 Vas 21.0242 21.1961 20.4191 20.6009 20.9680 20.8463 L BL 10.2198 5.0480 4.7081 4.5755 5.1541 5.0682 N/A Mms 61.1358 59.7482 61.0224 60.4427 60.3725 60.7250 g Cms 307.2617 309.7747 298.4186 301.0759 306.4408 304.6619 uM/N Kms 3254.5542 3228.1521 3350.9971 3321.4211 3263.2732 3282.3271 N/M Rms 1.7163 1.6271 14.1756 14.6002 1.6707 1.6749 R mechanical Eff 0.2284 0.2380 0.0996 0.0946 0.1183 0.1147 % Sens 85.5877 85.7658 81.9846 81.7583 82.7303 82.5958 dB @1W/1m Sens 89.4959 95.7791 89.0055 88.7181 89.6178 89.5453 dB @2.83Vrms/1m Krm 4.429E-03 1.214E-03 4.824E-06 124.179E-09 1.214E-03 1.176E-03 ohms Erm 801.708E-03 792.678E-03 1.101E+00 1.402E+00 797.716E-03 791.900E-03 Kxm 32.300E-03 7.913E-03 46.932E-03 38.016E-03 8.419E-03 7.119E-03 Henries Exm 667.654E-03 668.905E-03 374.107E-03 394.508E-03 667.115E-03 682.511E-03
        Measured Data: Credence Dual Voice Coil 8"
        Both Coils Driven, Connected in Parallel

   DVC connected in series
                       Click Image to Enlarge


        Measured Data: Credence Dual Voice Coil 8"
        One Coil Driven, One Shorted

   DVC connected in series
                       Click Image to Enlarge

 Note:

 The impedance and phase differ significantly from the 'normal' series connection. This is caused by the shorted coil acting as an
 electromechanical damper. In this case, cone motion created by the driven coil creates a current in the second coil, which
 opposes motion. The extent to which this occurs depends on the BL, voice coil characteristics mass and suspension. The eventual
 impedance and phase of this 'bucking' action is much more complex to describe as the electrical and mechanical phase also
 becomes important.


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