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A Discussion of the Behavior of Capacitor Blocked Supertweeters
Spoiler Alert
This web page is a somewhat detailed technical discussion intended for those who care about technical detail. For those that do not, here is the short story: 
It is clear that a capacitor blocked supertweeter behaves in a very decent way. It works as intended, and may result in significant benefits to the listener.
A Quick Peek at the Calculated Results
The table below provides a quick summary of calculated results of the combined electrical output of the Altec N800F crossover circuit with an added supertweeter circuit. These results reflect only on the performance of the crossover, not an entire system. The computed results above 10 kHz may be up to 3 dB high because the model may not accurately deal with the way in which the pressure waves of the tweeter and supertweeter combine. Here is the table summarizing the combined electrical response of the crossover woofer, tweeter, and supertweeter outputs:

Case                                                       50 Hz     600 Hz    1500 Hz   15 kHz  
2-way, no supertweeter                     0 dB       +1.5 dB      0 dB         0 dB 
16 Ohm Supertweeter Cases:    
0 dB Supertweeter attenuation        0 dB       +1.5 dB      0 dB         +3 dB      
3 dB Supertweeter attenuation        0 dB        +1.5 dB     0 dB          +2 dB             

6 dB Supertweeter  attenuation        0 dB        +1.5 dB     0 dB          +1 dB
8 Ohm Supertweeter Case:
0 dB Supertweeter attenuation        0 dB         +1.5 dB     0 dB         +1 dB


Introduction
A popular way to add a supertweeter to a loudspeaker system is to block lower frequencies from the supertweeter and to parallel the supertweeter off the input to a loudspeaker or to parallel the supertweeter off the tweeter. It is common to use an L-pad to allow the effect of the supertweeter t0 be adjusted. This is an easy, inexpensive, and gentle way to bring in the effect of the supertweeter without truncating the high frequency response of the tweeter. This technique is often used in DIY systems and sometimes used in commercially offered systems. I regularly use this technique with my Altec Altec A7-500-8 Voice Of The Theatre speakers and like the additional space and sparkle provided by the supertweeter.

What is the Effect of a Capacitor Blocked Supertweeter on Individual and Combined Response Curves?

This is a great question, and one I have never seen asked or addressed, with two exceptions. I have asked and addressed the question. Also, one of my customers recently asked the question. Let's get started by looking at a circuit diagram for the Pete Riggle version of the 16 Ohm Altec N800F crossover with the addition of a capacitor blocked and L-pad controlled supertweeter.​

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Important Note: The circuit diagram below shows the supertweeter piggy-backed off of the tweeter. The idea behind this arrangement is that the user would adjust the supertweeter relative to the tweeter, after which adjusting the tweeter level would handle the entire treble adjustment. This was a reasonable idea, but I have found that the supertweeter sounds clearer if it is driven directly from the amplifier + input of a single amplifier crossover or driven from the treble amplifier + input of a biampable crossover. Until I make time to publish a modified circuit diagram, here is the change that is needed: Disconnect the supertweeter switch from terminal 2 of the tweeter L-pad and reconnect the switch to the power amplifier + input of the crossover for a single amplifer installation, or to the treble power amplifier + input of a biampable crossover.
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Note that the woofer and tweeter filters are second order networks. These networks were designed to be used with 16 Ohm drivers, but also work quite well with any combination of 8 Ohm and 16 Ohm drivers. You will see that the supertweeter circuit is piggybacked off the tweeter L-pad and that it includes a toggle switch to engage or disengage the supertweeter, and a 1 microfarad capacitor that passes high frequencies but reduces output of a 16 Ohm supertweeter by about 3 dB at 10 kHz and continues to fall at 6 dB/octave for lower frequencies. Note that in the computations below the woofer is assumed to be 12 dB less sensitive than the tweeter, the tweeter and supertweeter are assumed to have equal sensitivity, and the tweeter L-pad is set to attenuate the tweeter by 6 dB.

Computed Response Curves
I have developed models using the SPICE electrical engineering program that allow me to calculate the electrical response curves of the crossover network that give an idea of what the crossover does for the individual and combined driver response curves. The calculated electrical response curves show only the effect of the crossover network. The curves can be interpreted as driver and combined response curves assuming a perfect room, perfect
time aligned coaxial drivers acting as resistive loads, no cabinet effects, perfect electronics, and  a perfect measuring technique. Realize that actual drivers and conditions will add their own variations to the response curves. In the figures that follow the solid lines are frequency response. The dotted lines are phase response.

Calculated 2-way response, 16 Ohm Resistive Loads
The computed response curves in the figure immediately below show the woofer and tweeter electrical outputs, and the effective combined electrical output of a 2-way N800F circuit crossover with 16 Ohm resistive loads representing the woofer and tweeter. The red curve is the woofer. The green curve is the tweeter. The blue curve is the combined response of the woofer and tweeter. Crossover is in the vicinity of 1100 Hz. The response is reasonably flat with a 1.5 dB bump in response at 700 Hz.
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Calculated Response, 16 Ohm loads, 2-Way Plus Capacitor Blocked Supertweeter Unattenuated Relative to the Tweeter.
The response curves below show the results with the same network as in the above figure, plus a capacitor blocked 16 Ohm resistance representing a supertweeter piggybacked off the tweeter. The blue-green curve is the woofer electrical output. The dark blue curve is the tweeter electrical output. The green curve is the supertweeter electrical output. The red curve represents the combined electrical output of the woofer, the tweeter, and the supertweeter. The woofer sensitivity is set 12 dB below the tweeter sensitivity. The supertweeter sensitivity matches that of the tweeter. The tweeter L-pad reduces the tweeter output by 6 dB relative to the woofer. The supertweeter L-pad is turned all the way up, for no attenuation of the supertweeter relative to the tweeter.

If we call the combined response zero dB at 50 Hz, the combined response will be 1.5 dB at 600 Hz, 0 dB at 1500 Hz, and +3 dB at 15 kHz.

It is noteworthy that at frequencies where the supertweeter curve is many dB  below the tweeter curve, it nonetheless adds substantially to the combined response. Note that at very high frequency, the blocking capacitor essentially disappears, pulling the tweeter and supertweeter response curves together. Note that engaging the supertweeter circuit has caused a droop in the tweeter high frequency response, but that that droop has been more than made up for by the contribution of the supertweeter.

Also, consider the following: Because the supertweeter and the tweeter are most likely not coaxial and time aligned, they may combine to provide a lift of only 3 dB, instead of the 6 dB shown, in which case the combined response at 15 kHz may be 0 dB, versus the 3 dB shown.


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Calculated Response, 16 Ohm loads, 2-Way Plus Capacitor Blocked Supertweeter Attenuated 3 dB Relative to the Tweeter.
The response curves below show the results with the same network as in the above figure, plus a capacitor blocked 16 Ohm resistance representing a supertweeter. The woofer sensitivity is 12 dB below the tweeter and supertweeter sensitivity. The tweeter L-pad reduces the tweeter output by 6 dB relative to the woofer. The supertweeter L-pad is turned 3 dB down relative to the tweeter.

If we call the response zero dB at 50 Hz, the response will be 1.5 dB at 600 Hz, 0 dB at 1500 Hz, and +2 dB at 15 kHz.
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Calculated Response, 16 Ohm loads, 2-Way Plus Capacitor Blocked Supertweeter Attenuated 6 dB Relative to the Tweeter.
The response curves below show the results with the same network as in the above figure, plus a capacitor blocked 16 Ohm resistance representing a supertweeter. The woofer sensitivity is 12 dB below the tweeter and supertweeter sensitivity. The tweeter L-pad reduces the tweeter output by 6 dB relative to the woofer. The supertweeter L-pad is turned 6 dB down relative to the tweeter.

If we call the response zero dB at 50 Hz, the response will be 1.5 dB at 600 Hz, 0 dB at 1500 Hz, and +1 dB at 15 kHz.


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​Calculated Response, 16 Ohm Woofer and Tweeter, 8 Ohm Capacitor Blocked Unattenated Supertweeter

The response curves below show the results with the same network as in the above figure, but with a capacitor blocked 8 Ohm resistance representing a supertweeter. The woofer sensitivity is 12 dB below the tweeter and supertweeter sensitivity. The tweeter L-pad reduces the tweeter output by 6 dB relative to the woofer. The supertweeter L-pad is set full up, for 0 db attenuation relative to the tweeter.

If we call the response zero dB at 50 Hz, the response will be 1.5 dB at 600 Hz, 0 dB at 1500 Hz, and +1 dB at 15 kHz.
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Summary of the combined response results
The following table summarizes the combined response results:
Case                                                       50 Hz     600 Hz    1500 Hz   15 kHz  
2-way, no supertweeter                     0 dB       +1.5 dB      0 dB         0 dB 
16 Ohm Supertweeter Cases:    
0 dB Supertweeter attenuation        0 dB       +1.5 dB      0 dB         +3 dB      
3 dB Supertweeter attenuation        0 dB        +1.5 dB     0 dB          +2 dB             

6 dB Supertweeter  attenuation        0 dB        +1.5 dB     0 dB          +1 dB
8 Ohm Supertweeter Case:
0 dB Supertweeter attenuation        0 dB         +1.5 dB     0 dB         +1 dB


Because of the way the tweeter and supertweeter pressure waves combine when the origin is not coincident, the computed and tabulated combined response results with the supertweeter may be 3 dB lower than shown.

Concluding this discussion of the results, it is clear that a capacitor blocked supertweeter behaves in a very decent way!


What Happens above the Tweeter Fall-off Frequency
In a 3 way system, we can count on the supertweeter to make a full contribution out to the upper end of its response band. That is not the case with a capacitor blocked supertweeter. When we study the curves shown above, and imagine a steep drop off of the tweeter at perhaps 12 kHz, we see that above the tweeter fall-0ff frequency a properly set up capacitor blocked supertweeter will end up about 6 dB below the 0 dB baseline. This may be beneficial to those who hear out beyond the tweeter fall-off frequency, but we should not imagine that the supertweeter will perform at full effect above the tweeter fall-off frequency. On the other hand, those of us who have lost the top octave of our hearing, this paragraph may be academic.

Why Use a Supertweeter?
One could argue that the calculated response curves show little advantage to using a supertweeter. The main argument for using a supertweeter is for increased dispersion in the frequencies that the supertweeter can play, above perhaps 5 kHz. The effect of a supertweeter is clearly audible, and in many cases beneficial. 


An Example of a Good and Inexpensive Supertweeter
Worth looking into is the Selenium (branded JBL) ST400 BLK bullet supertweeter. Prices change. I bought my pair delivered from Parts Express for $126 USD. These tweeters are reasonably flat from 6 to 15 kHz. They are about 111 dB/w/m sensitive. Dispersion is decent out to about 10 kHz. It is so very difficult to find a high sensitivity tweeter with good dispersion above 10 kHz.
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​Here is a URL for the Selenium Supertweeters:

https://www.parts-express.com/pedocs/specs/264-450--st400blk-spec-sheet.pdf

Currently the Selenium ST400BLK supertweeters are available for $130 per pair, including shipping, from Amazon. Here is a URL:

https://www.amazon.com/Selenium-ST400-Super-Tweeter-Black/dp/B0049U4EBS/ref=sr_1_3?crid=22GEV7073MGQE&keywords=selenium+st400&qid=1651877300&sprefix=selenium+st%2Caps%2C183&sr=8-3
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​___________________________________________________________________________​ 
                                                                  
Pete Riggle Audio
                             2112 S. Olympia Street, Kennewick WA 99337, USA
                      shop phone: 509 582 4548      email: [email protected]
                          VTAF™ Trademarked.  U.S.Patent No. 7630288.
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