Redcatt 81Find - The Saga continues

Now that we have tested our drivers parameters & the driver is loaded into Winisd, we cant start to work out our design.

Design considerations

Now we know some basic parameters which are important to us which is:

• Xmax

calculated as:  Voice coil winding height - Gap height / 2 which is,  12.5mm - 8mm = 4.5 & thus 4.5mm / 2 is  2.25mm. Though something to consider here is Redcatt quote 6mm peak to peak and I'm not sure but I would guess this is out to around 70% Bl means to peak. So we don't have much to work with here to help produce deep base, though we need to still look at the rest of the parameters! 

• Power Handling

Redcatt has provided power handling ratings in Aes / Program / Peak, I only care about the Aes value mostly as I personally believe that a speaker should never be pushed into power compression, this also keeps Xmax lower & gives more range to work with on the lower frequency range. Remember the more something moves the more it distorts due to nonlinearity. Our supplied power ratings are 200 Watts Aes, 400 Program & 800 Peak. 

• FS

Fs is a measure of a speakers resonance frequency, generally speakers with a low fs ranging between 30 to 50hz are indications they are potentially better at producing low deep bass. We can assume 50hz to 100Hz to be good woofer indicators that can play low but still generally might need a subwoofer, where compression drivers and dome tweeters might have an Fs between 800Hz to 3500hz which indicate ( Leave your answer in the comment section)  Redcatt gave a quoted figure of 80Hz I measured after conditioning for several hours 96Hz which is 15Hz difference!

• Sensitivity 

Redcatt defined the sensitivity being 94.68, Winisd give our values as USPL 98.16 & SPL which is 95.79, want to know the difference take our loudspeaker course here Crash course but im going to give it to you in any case lol

1. 1 Watt/1 Meter Sensitivity: This is the SPL measured at a distance of 1 meter from the speaker when 1 watt of power is applied into nominal impedance.
2. 2.83 Volts/1 Meter Sensitivity: This is the SPL measured at a distance of 1 meter from the speaker when 2.83 volts are applied which is is Z-min which is normally close to Re value.

An 8 ohm speaker nominal could have a Re value around 6 ohms and it can be higher or lower, we mostly care about the lesser impedance as this is what the amplifier could see and delivery some handsome extra watts that you never planned for.

To simplify this I'm going to round up to 95dB, this is much louder than you think for an example a vacuum is around 70 to 80dB, we are roughly 15 to 25dB louder. at this level of 95dB we have around 1 hour of listening and after this period we can start to suffer from hearing loss and fatigue. So please consider 1 watt is way louder than you think for the sake of your safety!

Winisd gives us a SPLmax value under the driver tab advance parameters of 115.80dB, lets compare. Using our log formula to derive how loud we can get with 200 watts Aes

Winisd SPL max 115.80dB

Sensitivity 1 watt 1 meter 118dB

Sensitivity 2.83 Volts 1 meter 121.17

Interesting we have 3dB increase to maximum spl using 200 watts as I giggle, I wonder if you find this to be interesting information in reference to 3 power ratings or am I just misguiding you lol.

Our sensitivity and loudness is looking great with our 200 watts but we don't have much in Xmax or a very deep fs, so its most likely best to keep away from tuning low I normally as a rule of thumb sit around 10Hz above the drivers Fs on tuning. In turn the lower we tune the quicker Xmax will peak. We could say that just by looking at these basic parameters we can see we not a sub woofer or a woofer and are hinting more at a mid range driver, this means we are most likely going to need a woofer that can handle below 150 to 100hz and deliver bass as deep as possible which for me if we can see 40hz we ok.

Design limitations in Winisd

Winisd is but a basic tool which is easy to understand, we cant do so many critical things say as VituixCad which has a learning curve of 1 zillion to a novice, so no baffle step calculation and other key factors.

Here we are taking the shortest root to victory or something being a speaker in a box, though this is still good enough to make things happen.

The driver has a very high Ebp so a vented might be the best option or we could go fancy and design a horn but that is beyond the scope of this project, I always reference a midrange and sometimes other speakers against a closed box as a reference point. Good habit or not it is one that I am fond of doing as it is a point to work around. We are using a Q of 0.707 for a flat response in our closed box and a nice gradual roll off, which looks like this in Winisd.

Don't worry if your graphs look different I explain how to change this in our crash course.

Now I'm going to add 2 more designs that are vented which is our Qb3 alignment and our "Boom Box" & compare this to our closed box, Navy Blue is our closed, green is our QB3 with Red being our Boom Box

Both of our bass reflex or vented enclosure play louder from about 300hz lets compare the points of F3 & F6 which is -3dB from "flat" and -6dB from flat for each of these designs.

Closed Box is -3dB @146.60Hz & -6dB @ 113.85Hz

QB3 Box is -3dB @ 71.14Hz & -6dB @ 65.6Hz

Boom Box is -3dB @90Hz & -6dB @ 79.69Hz

Our vented enclosures intersect around 108.45Hz and at this frequency they are both 6.5dB louder compared to our closed box, our Qb3 only starts to roll off at 84Hz give or take and if bass was a priority we can deduce that it will score in this order 1 being the best and 3 being the worst.

1. QB3 deepest bass
2. Boom Box best of both worlds
3. Closed box... not competing 

Now I want to automatically jump onto Xmax + power handling, I will keep adding watts reading the graph from right to left when the peak hits displacement. I know we are going to use a high pass filter on the lows so for not I'm not super concerned about the second peak which is out of control and well above Xmax which just means distortion!!

Here is what the graphs look like after completing this with each enclosure:

Power handling to Xmax approximation 

QB3  25 watt

Closed  25 watt

Boom Box 37 watt

This means on average at 100hz with these "watts" into our speaker we will have a loudness of:

QB3 100hz 110dB

Boom Box 100hz 110dB

Closed box 100hz 102dB

This gives us around 13.98dB increase in loudness with another 5dB to go according to winisd, why is this important simple...

We have not determined how far away the speakers are from us or we could say our listening position, which is IDK lol I have not considered the application yet which will influence the design choice and loudness required at distance.

Something to consider is Winisd is not considering crest factor its assuming everything is the same level like a sign wave which is -3dB to clipping or 0, popular or "pop music" music has around 6dB above and below  in peaks.

our constant 25 watts will reach out to 100 watts of our 200 watts and if we listen to music with higher dynamic range of say 9dB we reach out to 200 watts on those peaks with our average Rms still floating around 25 watts.

So long term 25 watts is looking healthy and we have tons of dynamic range without worrying if we are going to break anything with and spl average of 110db to 116db, this is 1/4 of the Aes power handling keeping us out of power compression for the most part.

400 watt amplifier 2 channel amplifier would be ideal here including some dynamic range.

Group delay consideration

Lower is better, remember group delay will increase as you go down in frequency.

When considering we could crossover between 80hz or 400Hz, design choice does not make of a difference at 400hz but around 200hz things start to change with a noticeable difference around 100hz. When you getting into speakers this is maybe not super important but understand it becomes important!

Impact on Audio Quality " Thanks Chat GPT" saving me 20 minutes of typing 

• Phase Distortion: When the group delay varies significantly across frequencies, it results in phase distortion. This means that different frequency components of the audio signal arrive at different times, leading to a smearing of the signal. This can degrade the clarity and sharpness of audio, making it sound unnatural or muddy.
• Temporal Smearing: Group delay variations can cause temporal smearing of transients, which are sudden, sharp sounds like drum hits or plucked strings. Proper alignment of transients is crucial for maintaining the attack and impact of these sounds. Excessive group delay can make transients sound less crisp.
  
• Localization and Imaging: Human perception of sound localization and imaging (i.e., the spatial placement of sounds) relies on the precise timing of sound waves reaching our ears. Variations in group delay can disrupt this timing, affecting the perceived spatial accuracy of the audio.
  
• Frequency Response and Fidelity: While a flat amplitude frequency response is desirable for high-fidelity sound, the phase response (and thus the group delay) also needs to be well-behaved. A system with a flat amplitude response but poor phase response can still sound bad due to the introduction of phase distortion.

Looking at our Max Spl

Our Qb3 drops out to 110dB and our boom box 113dB, you can chose to ignore this vs the normalized amplitude response. My personally take on this is flatter is better and lets leave that as is.

To conclude we know a rough loudness floating around 25 watts and we have looked at dynamic range and established a 400 watt amplifier into 8 ohms will work great, having a little more would be great but you could run the risk of generating the magic smoke.

One thing I do know is beyond any doubt the Redcatt 81Find is best used as a mid range speaker and a 3 way speaker system is inevitable!!

So a single enclosure could be a 15 or 12 inch to handle the lows in a single 3 way box or perhaps use the Redcatt more as a satellite along with a (sub), a 3 way box we can space the driver very close to one another which could help us with crossover networks  and the reverse with our satellite sub config.

Ok Satellite QB3 alignment I think will be the best go to for now,  this will most likely be a full dsp product giving us flexibility though this alignment is a much larger box vs the others  but it give me a little more wiggle room. 

Box dimensions are 27.67 liters with a tuning of 80.44Hz 

I'm now going to copy this project multiple times to review the response with some high pass filters, starting at 100hz with a 6dB per octave high pass and then a second / third & 4th order and so forth.

Black is no filter, you can see they all cross at 100Hz but the upper and lower end have a unique roll off rate & shape @ 100Hz we have a wavelength of is 3.43 meters, our half & quarter wave lengths are 1.715 meters & 0.857m. Knowing this helps indicate the max and minimum distance I want the Mid high to our woofer, ideally right on top of each other frame to frame is best! 

This means if I place a top hat on a 12" with a box height of say 60cm and we have a pole mount that is 1 meter high we are roughly around our half wavelength woofer to woofer, something to be conscious of for to many reasons to list here.

I can now establish our height roughly overall to some listening position which is going to be between 1.6 meters and 2 meters driver to driver give or take, this I can work with & if required we can always change the layout or add a secondary 12 to assist with the low end duty. The 12" I have on hand is the Redcatt 121FPW which might and I mean might just cut the low end on a single and I think will just fall shy with the double to give me the extra 10 to 20dB on the lows,

Looking at Xmax with all the drivers with each filter I can observe the cone displacement, to much displacement normally means more distortion as Bl drops and we experience non linearities, however we also want to keep things cool by letting the driver circulate some fresh air. If the driver is static we could experience heat build up and we don't want this.

Here is something is a fantastic read, its a long read but you might find this an incredible resource called The Science of String Instruments.pdf as the name suggestions it a compilation and a collection of work that look in great detail just how complex instruments are in nature and design.  Our mid range has a very large responsibility to handle from 100Hz to potentially as high as 3500hz, an easier way is to look at this in octaves which is a doubling of frequency and each time we do this we get another octave. 

100Hz to 200Hz is octave 1

200Hz to 400Hz is octave 2

400Hz to 800Hz is octave 3

800Hz to 1600hz is octave 4

1600Hz to 3200Hz is octave 5

Which covers a large portion of many instruments from Vocals / wind instruments / String instruments / Drums & keys and is critical range for the attack of many instruments and the 2nd and 3rd harmonics. Normally I would splurge out on an uber high end mid range speaker with staggeringly low distortion levels and cheap out on the woofer but here we doing things backwards a little. 

Adding the lows

Now I know first hand the Redcatt 121FPW is no subwoofer but it can indeed make bass, if we tune very low we drop in overall loudness if we tune high we gain back some loudness but the shear volume of air being pushed around from a single 12 vs a single 18 is massive. A dual 12" Shelf response to -3dB or - 6dB I is calling my name so lets load them up and have a look in Winisd

Green is our -3dB shelf, Red is our -6dB shelf.

Our -3dB shelf starts to roll of and hits -3dB around 63Hz with an F6 at 54Hz

Our -6dB shelf starts to roll off very early and hits - 3db @ 156Hz +- but hits an F6 at 45Hz or so which covers 90% if not more of all bass instruments.

Here is all the speakers combined at 1 Watt 1 meter

 Now here is our graph applying 10 Volts to each enclosure.

Our extended low frequency enclosure matches up rather nicely to the overall level of the 8" vs our -3d Shelf is certainly louder requiring less overall power to match the mid range. 

Flat is better - no no a house curve is better?

We want to be able to be flat and have enough power on our lows to be able to run 10 to 20dB louder which generally will start to creep up from 150hz or so, though this is preferential to you as a user!

Here is a picture from https://www.audiosciencereview.com from a member database with his house curve as an example, this type of tuning is common in Pa and theaters, though we don't know if we can do it yet so lets start throwing down some power to our 12s

We can just reach out 10dB at 40 volts, we would really need more speakers to do this correctly so our house curve target we might fall short as a potent dedicated dual 12" 121FPW compared to our 21 watts to our little 8".

The -6dB shelf response is also at Xmax, hmm what to do now?

With everything at 10 Volts all is good and maybe we revert or design to a multi way speaker rather than satellite and subwoofer,  good choice for this would be the B&C 12TBX 100 that's for sure.

Now I need to consider how loud do we really need to be at a distance of ( 25 meters ) 85dB is a nice level which is still loud & standing in front of the speakers we would produce around 113dB which is no rock concert but its far away from being soft.

So we are loud enough for small pubs and little gigs and have enough balls for a good home theater system, I'm sold as we are not crushing any speakers with huge amounts of power into thermal compression and we got them low frequency extensions.

Conclusion is -6dB shelf on the bottom end with 2 Redcatt 121Fpw 12" speakers paired with the Redcatt 81Find make a good enough match, lets make this happen

As this is now super long, I'm going to skip the part on my choice of port diameter and length with respect to port resonance and jump into the Cad work for the layout.

Our Low end section requires 100 liters tuned to 40hz & our little guy needs a volume of 27 liters tuned to 80hz or so, Next stop Part 5 - cad drawings, cutting & assembly!