And when 4th-order Linkwitz–Riley (LR4) filters are used, the knees are much less sharp than those based on BW3 filter transfer functions. The XSim4 simulation of an ideal loudspeaker built from LR4 filter transfer functions is shown below. Here the drivers are assumed to be coincident, and the midrange is connected with positive polarity, the same as the other two drivers.
The step response associated with the above frequency response curve is shown below, also computed using XSim4. This looks quite different to the step responses based on the BW3 and LR2 systems. The reason for that is that the second peak is dominated by the output from the midrange, and the midrange is connected with positive polarity, the same as the other drivers. Note that the tweeter response dies away most quickly, followed by the midrange response, and then the woofer response. It needs to be kept in mind that we are dealing with driver frequency ranges that differ by many octaves, hence the clearly distinct features of the step response function.
The acoustic sound pressure asymptotes to zero, as when the drivers stop moving, there is no output, even though the woofer will have a constant physical displacement (e.g., similar to what happens when we connect a 9V battery to a woofer).
The step response over a longer time scale, 40ms instead of 10ms, is shown below. By the 40ms mark, the transient responses of the tweeter and midrange drivers would have decayed away to more or less be zero, while the woofer is still oscillating away and producing acoustic output.
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If anyone is curious as to what a "perfect" minimum-phase loudspeaker's step response might look like, a simulation has been put together to showcase its behavior. This perfect loudspeaker consists of a single "driver". Its low-frequency response is modelled as a 4th-order Butterworth (B4) high-pass filter with a 35Hz cut-off frequency. Its high-frequency response is modelled as a 2nd-order Butterworth (B2) low-pass filter with a 25kHz cut-off frequency.
The frequency response function of this "perfect" loudspeaker is shown below.
The step response of the above "perfect" loudspeaker is shown below.
The frequency response function of this "perfect" loudspeaker is shown below.
The step response of the above "perfect" loudspeaker is shown below.
Hi, I think your Step Response looks excellent.
And looks to be maybe more of a 3rd order than second, or perhaps a mixture of third and second among the two xovers.
The only way to evaluate acoustic Step response that makes sense to me, is vs what a perfect Step response looks like electrically. We know that can't be beat acoustically.
Here's a 3-way electrical Step, with 400Hz and 2.3kHz xovers, using second order LR's on both.
Here's same but with 4th order LR's.
Both of those LR Steps represent perfect time alignment...(as well as perfect mag and phase)
Witwald shows what a perfect electrical BW3 looks like in #500, which as you can see falls kind of in between LR12 and LR24, perhaps leaning more to LR12.
The greater the phase rotations introduced from higher order xovers, the more degradation we have to see in the best step than can be realized.
Because we simply can't get a better finished-speaker acoustic step response than perfect electrical sims (without bring in phase correction ala FIR or some other technique)
Again, good looking acoustic step you have there, Mr Jim ! 🙂
Shows how much midrange is making it back through the cone without a lot of attenuation too.
If possible, nearfield measurements should be taken with only one driver/way connected. With a ready-made commercial speaker this might be impossible.
Jim said: "Next we look at the woofer and PR responses separately. In this case, these are the near field responses without the low pass filter"
I collected some Klippel scans here https://www.diyaudio.com/community/...field-measurements.416261/page-2#post-7791600
Jim said: "Next we look at the woofer and PR responses separately. In this case, these are the near field responses without the low pass filter"
I collected some Klippel scans here https://www.diyaudio.com/community/...field-measurements.416261/page-2#post-7791600
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When I made the NF scans of the woofer and PR, I was driving the woofer without passive network. I measured the woofer first, then the PR.
Yes, from 200 Hz up there is a good bit of output from the PR, but how much of that is actual radiation from the PR cone, and how much of it is spillover from the woofer which is located just 25 cm above it? It is difficult to achieve true isolation between the two low frequency sound sources, as @stv has shown us.
What would be the lower limit of sound transmission through the PR diaphragm? Sound transmission through 3/4" plywood is about -20 dB in this frequency range, so I think it would be unreasonable to expect the PR to outperform the cabinet wall. If we assume I have no spillover in my PR NF scan (perfect isolation), then it would seem that this PR is providing about -15 dB sound transmission. Compared to -20 dB for a solid plywood wall, this is reasonable, and actually better than I would have expected.
This uncertainty carries over into the simulation. In the above plot (post #505), we can see that the combined merged woofer+PR response from 200 Hz to 1000 Hz is about 1 dB higher than the woofer alone. This is valid if the PR NF scan represents the true radiation from the PR. But if the PR NF scan in this range is mostly spillover from the woofer, then the combined merged woofer+PR response is 1 dB too high. The truth is probably somewhere in the middle. I can't think of an analytical or empirical solution to this problem... Which underscores the importance of the subjective voicing process.
j.
Yes, from 200 Hz up there is a good bit of output from the PR, but how much of that is actual radiation from the PR cone, and how much of it is spillover from the woofer which is located just 25 cm above it? It is difficult to achieve true isolation between the two low frequency sound sources, as @stv has shown us.
What would be the lower limit of sound transmission through the PR diaphragm? Sound transmission through 3/4" plywood is about -20 dB in this frequency range, so I think it would be unreasonable to expect the PR to outperform the cabinet wall. If we assume I have no spillover in my PR NF scan (perfect isolation), then it would seem that this PR is providing about -15 dB sound transmission. Compared to -20 dB for a solid plywood wall, this is reasonable, and actually better than I would have expected.
This uncertainty carries over into the simulation. In the above plot (post #505), we can see that the combined merged woofer+PR response from 200 Hz to 1000 Hz is about 1 dB higher than the woofer alone. This is valid if the PR NF scan represents the true radiation from the PR. But if the PR NF scan in this range is mostly spillover from the woofer, then the combined merged woofer+PR response is 1 dB too high. The truth is probably somewhere in the middle. I can't think of an analytical or empirical solution to this problem... Which underscores the importance of the subjective voicing process.
j.
I finally found the time to do an outdoor ground plane measurement. Rain was on the horizon, so I had to move quickly. The nearest wall was 19.5 ft away, so I had resolution to below 30 Hz.
Here is a comparison of low frequency system response. The solid black line is the ground plane measurement. The dashed blue line is the VituixCad simulation of the woofer + passive radiator, along with whatever contribution the midrange driver makes below 300 Hz. The two near field responses are merged using a ratio of their areas (Sd), and the NF responses are adjusted using a 2-pi to 4-pi transfer function that VituixCad calculates with the diffraction tool.
For me, this is the final validation that the low frequency response of the woofer + PR + cabinet is correct and is being modelled correctly. This system has an anechoic F3 of 51 Hz, F6 of 35 Hz, and F10 of 30 Hz.
Now that I have a valid low frequency 4-pi measurement, I can merge it with the long gate far field system measurement I made in post #471.
I am rather pleased with the agreement. I have achieved very good agreement in the past with DSP controlled active systems, but I was skeptical that I would achieve such close agreement between simulation and measured response with a fully passive system.
j.
Here is a comparison of low frequency system response. The solid black line is the ground plane measurement. The dashed blue line is the VituixCad simulation of the woofer + passive radiator, along with whatever contribution the midrange driver makes below 300 Hz. The two near field responses are merged using a ratio of their areas (Sd), and the NF responses are adjusted using a 2-pi to 4-pi transfer function that VituixCad calculates with the diffraction tool.
For me, this is the final validation that the low frequency response of the woofer + PR + cabinet is correct and is being modelled correctly. This system has an anechoic F3 of 51 Hz, F6 of 35 Hz, and F10 of 30 Hz.
Now that I have a valid low frequency 4-pi measurement, I can merge it with the long gate far field system measurement I made in post #471.
I am rather pleased with the agreement. I have achieved very good agreement in the past with DSP controlled active systems, but I was skeptical that I would achieve such close agreement between simulation and measured response with a fully passive system.
j.
Looks Like the passive crossovers and equalization turned out well.
Good Job!
Thanks DT
Thanks ! I have been doing some listening the last few days, both casual listening while I organize and clean my shop, and dedicated serious listening. I will have more to say about the sound later, but for now I satisfied with the voicing. I am not planning any changes to the filter network.
For clarity, this is the crossover filter, as it was built. Voicing is controlled by the tweeter series resistor and the 25R midrange parallel resistor.
On the good news side, the on-axis response is +/- 1.4 dB from 100 to 10k. The Predicted-In-Room (PIR) response is +/- 1.25 dB from 600 to 7k. Overall, pretty good performance for modest cost drivers in a simple box with a passive filter.
On the less than good news side, the one aspect of frequency response/directivity which I would improve if I could is the range from 1.5k - 3k. The PIR response has a 1.5 dB rise in this region, and the power response has a 2 dB rise. This does not seem to be audibly noticeable (yet), but it would be nice if these two curves were flat in this region.
j.
On the good news side, the on-axis response is +/- 1.4 dB from 100 to 10k. The Predicted-In-Room (PIR) response is +/- 1.25 dB from 600 to 7k. Overall, pretty good performance for modest cost drivers in a simple box with a passive filter.
On the less than good news side, the one aspect of frequency response/directivity which I would improve if I could is the range from 1.5k - 3k. The PIR response has a 1.5 dB rise in this region, and the power response has a 2 dB rise. This does not seem to be audibly noticeable (yet), but it would be nice if these two curves were flat in this region.
j.
@Juhazi brought up the topic of phase matching and physical alignment.
For this design, I chose the tweeter to be the design axis, since it is about ear level for a person sitting in a typical chair. The tweeter and the midrange have a phase offset over a broad range. The tweeter phase is about 40 degrees ahead of the midrange.
However, if I move the design axis down to be level with the midrange driver, I get a nearly perfect phase alignment.
Design axis is in line with midrange
The difference in response is insignificant as we can see in this plot. Dashed is the original on tweeter asxis, and solid line is on midrange axis
Now the interesting thing is that I can easily adjust my chair to be in line with the midrange or the tweeter. So far, I have not been able to tell the difference, but I will keep listening.
j.
I think that your example showcases the intrinsic ability of the Linkwitz–Riley filter topology to tolerate phase errors through the crossover region. The loudspeaker system was designed to be listened to on the tweeter axis. In VituixCAD the default listening distance is 2000mm. At this distance, switching to the midrange for the purpose of the listening axis, we are not all that many degrees off-axis from the original design axis.
@hifijim, what is the listening distance from the loudspeaker to your ears when seated in the chair?
@hifijim, what is the listening distance from the loudspeaker to your ears when seated in the chair?
Verticals of my LR2 4-way speaker at 1,2m (inroom reflections included, notice scales!) When listening, my ears are 5-10 deg below 0-axis. Mid is a 18cm tall planar with rather high vert. directivity itself.
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Looking forward to your thoughts on the midrange. As mentioned earlier in the thread, there haven't been many builds or reviews and the ones I have found I don't really trust.
I am listening in my shop, and the distance varies. 2 m is probably about average.