At last I have managed to sort out some of what is happening with this circuit.
Whilst easily measurable voltage and current amplitudes are important when driving a LS, so too are source impedance and current phase/group delay with respect to an original voltage waveform. I am not however in a position to relate driver current/voltage waveforms to the transduced sound waveform reaching our ears at a listening position.
This T-bass circuit does not just increase the LF amplitude, it improves the reproduction quality as well. Why ?
I have tested this circuit with mid-bass drivers having a Qts circa 0.4.
David above noted improvement via his drivers having a Qts of 0.23.
Reproduction quality improvement has not yet been checked/reported with a higher Qts LF driver (>0.7), though there is no reason why improvement should not be possible due to to the way in which waveform amplitude is increased below Fs, whilst output can be reduced by the circuit to counter an increase arising around Fs due to driver Qts. Hence reproduction quality with a B200 + Alpha-15A baffle combination is still likely to be improved, though would eat into a single Alpha's X.max limited capabilities.
A B200 + Alpha-15A can be matched using MJK's latest software, which I believe relies upon SS amplification. The LF response of this simple combination might be further extended by using a tube or current source amplier, but then the LF definition could suffer as a result of the Alpha's natural Q becoming less well controlled.
Here is a simulation circuit for looking back into the 'T'-bass component assembly from the viewpoint of a 6 ohm loudspeaker in order to examine the reactive nature of the effective source impedance being generated. From the outset this reactive nature was intentional in order to counter LF driver responses due to their own unavoidable natural reactivities.
(Other simulations will follow using an approximate equivalent LS circuit in order to more realistically examine electric current flow generated by the 'T'-bass when driven by a SS amplifier. It is not likely to work similarly if driven by a tube or SS current source amplifier, unless that tube amplifier is a push-pull triode or ultralinear tetrode type with global NFB.)
Transformer winding loss resistance does not change the shape of the the plots shown here because the impedance is a function of the C, L and R values chosen; however transformer resistance does reduce amplitude plots as the effective series resistance increases proportionately.
Transformer primary resistance can be countered by changing the resistor values in series with the C and L components, where all the values need to be adjusted to match individual driver+baffle+room installations anyway.
Transformer secondary resistance is likely to be small compared to LS driver resistance, with their series connected values added together anyway.
The reverse energised examination circuit is shown here;-
http://server6.theimagehosting.com/image.php?img=TB.imp.test.gifThe impedance and phase plots for the component values here;-
http://server6.theimagehosting.com/image.php?img=TB.impedance.gifThe three grey lines represent; top - 0.6 ohm; centre - 1.3 ohm; lower - 3.3 ohm.
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Below circuit resonance the 'T'-bass output impedance is due to the choke impedance, its resistance, plus series resistor and transformer winding resistance.
Here the summation tends towards 1.3 ohm by 10Hz.
The 'T'-bass gain when loaded with and matched to a LF driver system is approx 5dB, but the source impedance generated by this circuit is increased too.
Hence the LF SPL below driver resonance is increased more than might be expected due to circuit voltage gain plus an effective increase in the driver's Qes due to an increase in the driver's source impedance.
Another aspect relates to sub-resonant LF driver impedance. This rarely falls fully back to the nominal value below resonance - an aspect which further contributes to SPL losses during LF transduction efficiency. Thus the increased voltage drive provided by the 'T'-bass, even with its increased output impedance, provides a better amplifier/loudspeaker impedance match below an OB mounted driver's Fs.
Also, the load presented to an amplifier by the 'T'-bass circuit when driving an OB LF driver does not fall as low as might be expected due to any simplistic calculation of a 1:2 ratio transformer driving a nominal value resistor load.
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Close to driver resonance the 'T'-bass circuit output impedance increases - here to 3.3 ohm - a value which can be set by adjusting the C, L and all resistance values.
Even when the equalising impedance at the primary is adjusted to transform with unity output gain, the reproduced SPL can still be increased due to the raised 'T'-bass output impedance effectively increasing driver Qes. Yet current provided to the driver via the C+L+R tuning may be adjusted to reduce output at Fs, and thus counter the resonant energy storage within the driver which gives rise to increased SPL but degrades the drivers dynamic response.
'T'-bass throughput to low Qts drivers may thus be adjusted to match the driver and increase its LF output, yet it can also help to counter a high Qts driver resonance induced 'tonality' due to the driver's naturally resonant characteristics which arise in 'driver controlled time' and not 'music waveform controlled time'.
S we must not forget that where a driver has a higher Qes, or develops a higher Qes due to drive circuitry (type of amplifier, crossover, 'T'-bass etc.), then the driver's Qms can have an increased impact upon not only the SPL, but also the reproduction quality due to the effective increase in driver Qts. Whilst the 'T'-bass circuit is capable of increasing LF output, it is equally capable of allowing too high a proportion of LF 'gain' arising due to the increase of effective driver Qes/Qts at Fs, and the driver can be rendered incapable of transducing/reproducing cleanly - actually more like a driver in an undamped vented enclosure !
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Above the driver resonance, drive impedance tends towards 0.6 ohm.; this being the total resistance in series with the capacitor = R plus transformer winding resistances.
Here the circuit gain is unity (no step-up via the transformer) and the source impedance is close to normal, thus the SPL is not increased.
However a capacitor induced increase in dynamic first cycle current flow can counter first cycle loss due to a driver's natural impedance/mass induced dynamic loss.
Ordinary EQ cannot prevent this entirely natural loss of first cycle dynamic attack within a driver, nor indeed does this circuit, it does however compensate in a manner where the initial capacitor induced boost can be adjusted to match the loss during that first cycle.
See the current flow simulations in the post below.
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So the 'T'-bass circuit can increase LF output in two ways.
1) Below resonance it steps up the driving voltage.
2) Around resonance it allows the driver Qts to become increased.
It can also improve reproduction by linearising current flows which would otherwise remain reactively modified by driver characteristics if driven by either predominantly voltage or predominantly current source amplifiers, and it can compensate for dynamic loss within a driver.
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A low moving mass plus low Qts driver driver can reproduce more accurately because it subtracts, stores and releases less of the transduced waveform energy within its own electro-dynamically energised time frames, but this makes for a less SPL 'efficient' transducer on OB.
The 'T'-bass circuit allows low Qts drivers to run more like higher Qts drivers at lower frequencies only, and may be tuned for 'best' overall dynamic/SPL characteristics in a way which could not otherwise be achieved without much more powerful amplification, complex NFB circuitry and/or additional series/parallel driver loading components.
Cheers ......... Graham.