Quarter-wave resonator calculation online. Calculation of the design of a quarter-wave resonator. Calculation using hornresp ver.1 program

Hornresp - A program for calculating a horn, as well as a QW (Quarter-Wave Resonator) which is gaining popularity.

Calculation using hornresp ver.1 program

Open Hornresp, if not, you can download the current version of the program here - http://hornresp.net. The calculation will be carried out using the example of a DD Audio 512b D4 subwoofer speaker. We go to the manufacturer’s website and find all the parameters necessary for the calculation

1. Create a new project using the Add button.

• We remove parameters that are not required for calculating the frequency factor.
• In the Comment line you can give a name to the project and save it later.

2. We begin work by entering vehicle parameters:

• SD– effective speaker area. If the manufacturer has not indicated the exact area, enter the average value for your caliber. For a 12-inch speaker this is 480 sq.cm.
• Cms– rigidity of the dynamics mechanics. Double-click on the value of the cms parameter, agree that you have entered the correct diffuser area and enter vas speaker - the equivalent volume.
• mmd– displacement mass. Double-click on the mmd parameter value and agree that you have entered the correct value for the diffuser area and correctly calculated the mechanical stiffness. Enter fs – the resonant frequency of the speaker.
• Re– DC resistance. If the manufacturer does not specify this parameter, re is usually slightly lower than the speaker impedance. For 4 ohm speakers the value will be 3.6-3.8. For double coils the value is in parallel or series connection.
• Bl– motor power. Double-click on the value of the bl parameter and agree that the entered parameters re and cms are correct. We introduce the resonant frequency and qes – electrical quality factor.
• Rms– mechanical resistance. Double-click on the value of the rms parameter and agree that we have correctly calculated the stiffness of the speaker. We enter the resonant frequency and qms - mechanical quality factor.
• Le– inductance. If the manufacturer has not indicated the exact value, enter the unit.

3. Set the length, as well as the areas of the beginning and exit of the tunnel:

• We remove unnecessary areas by entering zeros. Leave only one line (S1, S2, Con)
• S1– area of ​​the beginning of the tunnel.
• S2– tunnel exit area. The output area is usually equal to 1 – 2Sd speakers, depending on the purpose (quality/volume).
• Con– length of the quarter-wave tunnel.

4. We begin modeling our CV:

• Tools – Loudspeaker Wizard. (Ctrl+E)
• We see a schematic view of our tunnel. The speaker is on the wall with a dead end and is marked with a red line.
• System volume – design volume in liters.

• To view the frequency response graph in the bottom line, select – Response\Horn S1 – S2\Combined.
• Put a tick Show Baseline– overlaying a graph with changed parameters on the original graph. We change the area value and see the changes.

• In the first column we select Displacement– calculated stroke of the speaker diffuser. Here you can see the diffuser stroke at a given power and the tuning frequency of the housing.

Instructions for calculating CV ver.2

So let's begin! I know perfectly well what types of designs there are for low-frequency speakers (I’m talking about the most common ones) - closed box, bass resonator, 4th and 6th order band pass, and the quarter-wave resonator, which is currently gaining enormous popularity. But…
Not long ago, while walking through the vastness of the World Wide Web, I came across a new Tiv - megaphone(well, new to me at least). And then the search for all kinds of information began: calculation methods, drawings, results and reviews. The more I searched, the more I became convinced that there was no such volume as, say, about CV. I looked at the beloved D2 website and couldn’t find anything specific.
I, of course, understand that there are people who designed the horn several years ago, but nevertheless I believe that at this time the number of interested people is high and continues to grow.
Having gained enough information over several months of studying, I will try to describe the method for calculating the horn. I often come across comments where one writes that the mouthpiece is “flat”, another that it is a waste of time, effort and money. Let's figure it out together:
The horn is essentially a bass reflex box, to which is adjacent a port that expands in certain proportions and of a certain length. The horn plays a wide range of frequencies, sometimes 30-100 Hz. (we won’t talk now about the pros and cons of this or that design) and has high efficiency. It is necessary to calculate the horn for a specific speaker and design a box for a specific trunk. Under no circumstances should you take just any drawing and then say that the megaphone is nonsense.
Let's start: we have. for example, a Kick PRO 300 speaker and we want a horn for it.
First we need a program. I used Hornresp and you can download it from here
OK! We downloaded it, opened it and see this window:

There is no need to be scared by a large number of values ​​and numbers, let’s look at them now. To start working you need to press the button Add in the picture below it is highlighted with a red oval.

We clicked, now our windows have become active. We continue to work with the data highlighted below in the picture

Sd is the effective area of ​​the speaker. The average value for a 12″ speaker is 480 cm2. Enter the number 480 in this field
Cms- this is the rigidity of the suspension mechanics. We are not afraid if we do not have such a meaning. We double-click in the window with numbers, a small window appears where the program asks in non-Russian words whether we have entered the effective area value correctly. We agree with her and enter the value in the new window that appears vas our speaker and click OK.
mmd- mass of movement. Again, don’t be afraid if this value doesn’t exist. As in the previous parameter, double-click on the value. We agree that we entered the area correctly and calculated the stiffness correctly, and at the end in the empty line we enter the resonant frequency of the speaker Fs
Re- DC resistance. Famous manufacturers indicate this figure. But if we do not have such a value, then for 4 ohm speakers this value will be slightly less than the speaker resistance and equal to 3.6-3.8. We choose anyone from this limit.
Bl- motor power. Double-click on this window and agree that you have entered the parameters correctly Re and Cms. In the last window we enter Qes- electrical quality factor.
Rms- this is mechanical resistance. Again, double-click on the window and agree that the speaker stiffness and resonant frequency have been entered correctly. At the end we put Qms- value of the mechanical quality factor parameter.
Le- inductance. If the manufacturer has not specified this parameter, set it to 1.
So, the input of unchanged speaker parameters is completed, let's move on to the next stage. Any horn has a pre-horn chamber. So let's do:

We will work with those parameters that are circled in red in the pictures above. Title boxes Vrc, Fr, Lrc, Tal we make zero ones, i.e. put 0 there. Vtc- and this is already the volume of our pre-horn chamber. Where can I get it from? - elementary, this is the recommended volume of FI, which even non-genuine manufacturers indicate. We are not afraid to make mistakes here, I will try to explain further, I think you will understand. So the recommended volume for my example speaker is 42.48 liters. When entering into the program, this value must be multiplied by 1000, i.e. We enter 42480.
Atc- a parameter, in our case, that does not affect the calculation, therefore, so that the program does not swear, we will set it to 1000.
Congratulations! We filled in the parameters of the speaker and pre-horn camera. What else do we need? oh yes! the most important thing is the horn itself. Well, in the pictures below the red rectangle highlights the parameters with which we will work.

Let's look carefully! We only need to leave S1, S2, Con, and in the remaining columns of this section there should be zeros, if this is not the case, enter 0 manually :)
S1- cross-sectional area of ​​the beginning of the horn. Those. this is the area of ​​the hole through which the pre-horn chamber communicates with the horn itself.
S2- cross-sectional area of ​​the horn output.
Ideally, the output area is 1.5-2 times the effective area of ​​the speaker, and the optimal ratio of the areas of the beginning and end of the horn is 1:3. But we can play with these parameters, I’ll explain later, so I set the values ​​to 250 and 800, respectively.
Con- horn length. If in the CV we adjusted the length to a certain setting, then here please do not confuse us, here we will change the length to get to the desired setting. Based on theory, people's reviews and personal experience, I want to say that it is better to make the horn length within the range of 150-180 cm. I set it to 150 to begin with.
Well, HURRAY! Entering the parameters is completed, let's move on.

Click Tools - Loudspeaker Wizard.

And we see a schematic representation of our horn (highlighted with a red rectangle), and underlined in yellow System volume- this is the volume of our speaker. Now let's look at the schematic graph of the frequency response. To do this, in the lower left corner let's put Response

What kind of graph is this? What kind of cardiogram? Patience my friends!
Let's check the box next to it Show Baseline- so we can see the overlay of graphs when we change the parameters. and we'll also deliver Combined as in the picture below

We did it, the schedule changed to this

We see that with these parameters, our din’s setting is set to 40 Hz and it will play up to 100-105 Hz. Never mind that there is a failure in this area; practice has shown the opposite. I don’t even know how to explain it, maybe the program represents something wrong, or I don’t understand it correctly! :) The higher the graph, the louder the shout, but the less the crowd, then who cares what’s more interesting.
For example, the setting is too high for me - 40 Hz. I start playing with the parameters of the pre-horn chamber, cross-section and port length. those. change them and I can already see how it is reflected in the chart. By manipulating the horn length I was able to lower the tuning to around 32-33 Hz.

This suits me and I click Save.
Now I know the setting of my horn (calculated), I know its volume, the volume of the pre-horn chamber, I know the cross-sectional areas of the beginning and exit of the horn, as well as its length, and now I can start modeling the box.
When playing with cross-sectional areas, try to maintain an area ratio of 1:3.
I tried to make the technique as accessible to you as possible, so don’t be too hard on yourself. In general, friends, try it, experience is built only on experiments!
If anyone is interested, stay with us, next there will be a short article on modeling horns.
Thank you all for your attention!

Then I found a free sub at my place and decided to put it in a car. If the sub is no good, then we make the best box and according to all the laws. Thanks to Xynkin for the BZ, referring to him I assembled this box. In general, the sub is 5″, so it was also possible to create a mesh for it from 16 Hertz.

The main advantages of CV are:
- low level of group delays, precision bass processing and detail;
- smooth and wide range of reproduced frequencies; with the right approach, the frequency response can easily handle both the upper bass and the lowest bass;
- high efficiency, with the same power you get a return that is on average 20-40% higher than that of bass reflexes or bandpasses, and a closed box that is 150-300% higher.
A classic quarter-wave resonator is a tunnel of a certain length and a certain cross-sectional area, and that’s all. It is surprisingly simple in calculations and, given the availability of free space, it is also simple to manufacture.
The figure shows a tunnel with a circular cross-section, but in practice, in the vast majority of cases, a square cross-section of the same area is used.

The CV is calculated as follows. The cross-sectional area of ​​the tunnel depends on the caliber of the subwoofer and is calculated using the following formula.
Tunnel = 1.5*(3.14*((Dsubwoofer/2)^2)).
Simply put, the cross-sectional area of ​​the tunnel is equal to one and a half area of ​​the subwoofer.
The diameter of the speaker is measured: for a round speaker, the diameter of the diffuser is from the middle to the middle of the suspension. And if the speaker is square, then you need to measure the length of one of its sides.

Approximate subwoofer data:
4″ - 100 sq.cm
5″ - 125 sq.cm
6″ - 200 sq.cm
8″ - 300 sq.cm
10″ - 500 sq.cm
12″ - 750 sq.cm
15″ - 1000 sq.cm
18″ - 1600 sq.cm

The length of the tunnel determines the CV setting. The following simple formula is used:
Ltunnel = (343/Fb)/4, where Fb is the desired tuning frequency, the result in meters.
You should never try to tune any resonator, be it a HF or a simple FI, to a frequency below the speaker's resonance frequency. This will lead to a sharp decrease in output, loss of damping and possible destruction of the speaker at high powers, there are plenty of examples of this.

In my case, calculating the frequency response, tuned to 45 Hz, for a subwoofer with a caliber of 5″ (13cm). Tunnel = 1.5*(3.14*((13/2)^2)) = 200 sq.cm. Ltunnel = (343/45)/4 = 1.9 meters. In order to fit a tunnel of this length into the trunk, it must be rolled up.

HF is essentially a comb filter, it amplifies frequencies at 1/4, 3/4, 5/4 and so on and attenuates frequencies at 2/4, 4/4, 6/4 of the wavelengths for which it was designed. Very As a rule, the resonance of the second mode is strongly pronounced, i.e. 3/4 of the wavelength. In order to compensate for this effect, the speaker is placed not at the very beginning of the pipe, but in the side wall of the pipe at a distance of 1/3 of the length from the beginning of the pipe. Due to this displacement, an additional standing wave is formed in the pipe which neutralizes this surge in the frequency response, reducing the unevenness of the frequency response in this area to 1-2 dB.

The first and main misconception. Turns must be rounded. This is not entirely true; roundings affect the character of the bass and the final tuning of the body (more on this below). Without rounding, the bass is softer and a little smeared. Tracks with low peaks will play better and deeper. With rounding, the bass becomes precise and fast; rounding is a must for faster music.
The second thing many people don’t think about. The fillets will reduce the length of the tunnel and the setting will increase accordingly. How much depends on the number of rounded turns. Usually it is 2-3 Hz

In addition to the constant-section CV, there are 2 more types, namely, expanding and tapering. Differences in calculations will appear in the length and dimensions of tunnels and boxes, respectively.
Tapering, diverging and constant-section CV:
The most universal is, of course, a labyrinth with a constant cross-section, the calculation of which does not pose any problems. The narrowing CV is a tunnel that gradually narrows from 3 speaker areas at the beginning to 1.5 at the exit. With the same setting, it will be shorter than the labyrinth, with a constant cross-section. Considered the most musical. It has minimal delays, high accuracy and bass development. The only disadvantages are that it is more difficult to calculate and takes up more space. HF with an expanding tunnel has maximum efficiency, but the bass quality is noticeably worse. Mainly used in SPL systems

In general, I make the HF tapering by smoothing the corners and installing the speaker at 1/3 of the length of the tunnel. Exactly 1 meter of carpet was enough to cover the box, it turns out like this.

“It’s also a resonator - an organ pipe, it’s also a transmission line”

Quarter wave (QW) in simple words

Do not be alarmed by the clutter of these words, we will not delve into the theoretical foundations of the quarter-wave resonator or quarter-wave resonator here, as it is usually called. Let's consider this type of design from the user's point of view, because CV has important advantages and few disadvantages.

In short, a quarter wave is a tunnel of a certain length and cross-sectional area; there are no separate concepts of body and port, as we are used to. If there is free space, it is very simple to calculate and does not have any special difficulties in manufacturing.

Main advantages of CV:

• reduced degree of group delay, well-developed bass and detail, sometimes exceeding a closed box;
• wide and smooth - if the approach is correct, the upper and lower bass can be easily mastered;
• increased level of efficiency, 20–40% more than that of bass reflexes or bandpasses and 150–300% than that of a closed box.

Just a cheater building - that's how it is! There is only one minus, but a significant one - the large volume of the box.

In other words, if you don’t mind space, then the HF will be the best choice for subwoofer design.

ChV calculation

The cross-sectional area of ​​the port depends on the size of the speaker.

In words it means that the cross-sectional area of ​​the port is one and a half effective area subwoofer.

It is important to know that the effective area (Sd) is not calculated based on the standard size (10″, 12″, etc.), it is always smaller since the basket and part of the suspension do not participate in the radiation. Manufacturers often indicate this value in the documentation, but if there is no data, you can use the table:

Effective subwoofer area by size

Sd — effective subwoofer area, cm²;

Where D - diameter in centimeters, taken through the center from the middle of the suspension.

For a square subwoofer, calculating the area is even simpler - you need to square the length of one side.

Effective area of ​​subwoofers

Accordingly, the port area is calculated as follows:

— cross-sectional area of ​​the port, cm²;

The CV setting depends on the length of the port and is calculated as follows:

Facebook – desired tuning frequency, Hz

The optimal range is 35–45 Hz, no one forbids setting it low, if you like infra, lower the setting.

Calculation example

For example, let's calculate the frequency response with a setting of 38 Hz for a 12-inch (30 cm) speaker.

S port = 1.5 * 480 (from the table for 12″) = 720 cm²

In order for the box to fit into the car, the port is rolled up.

Types of CV

Above we analyzed the calculation for a quarter-wave of constant cross-section, but there are also tapering and expanding tunnels.

If sound quality comes first for you, then make a HF with a tapering design. It is larger and more complex to manufacture, but the result is a bass that is accurate, fast and deep. This case is suitable for systems focused on sound quality! Unlike the classic direct HF port, the port is made to gradually taper from 3 Sd to 1.5 Sd at the outlet.

The expanding port will give the highest efficiency and volume due to the humpback.

A tapering port will be shorter than the opening for the same setting. See the table for calculated data:

Port length depending on the type of CV

Which speaker is suitable for HF

The table below shows the experience-tested characteristics of speakers for HF, the closer to them, the better the sub fits this design (Fs and Qts are of paramount importance).

An HF box or quarter-wave resonator is a hollow box made of any furniture material. The design is used for a subwoofer and allows for deeper sound with a harmonious spectrum. Such branded devices are quite expensive, but the box can be assembled independently from scrap materials. This is exactly what we will discuss in our review.

Purpose, design and principle of operation of the CV box

The design of the HF box is aimed at modulating the sound flow. The effect of sound transmission and reflection is used. Thanks to the special housing design, sound harmonization is achieved. This is especially noticeable at low frequencies and when installing a subwoofer. With the appropriate dimensions, the HF box will make the bass sound quite loud, bright, but unusually deep.

Subwoofer box

Purpose and use

In a certain context, this device can be compared to an analog-type sound processor. Now that the purpose is clear, let’s now look at the design, operating principle and calculations. The proposed solution is especially in demand among motorists who want to install high-quality sound on used cars; with some effort, it will not be inferior to expensive audio systems.

So, in the technical understanding, the FM box, as implied by the name, is a resonator. We are talking about a hollow structure with the help of which sounds of a given frequency are reproduced. One of the functions of the resonator is to enhance audio sound. Such a device in the car will allow you to listen to loud music, provide musical accompaniment in nature, or use it for commercial purposes, for example, for scoring weddings and celebrations. The most popular solution is a box for a 12-inch speaker.

Operating principle

With a resonator, another example of which is box for CV, motorists may be familiar in a completely different area. For example, it is used as a functional element of a muffler. In this case, the hollow structure has its own characteristics and another purpose.

From a technical point of view, a resonator is an oscillatory system that accumulates vibrations due to frequency resonance. Typically, the design involves “working” with a limited set of frequency characteristics. Depending on the design, resonators of cumulative and instantaneous action differ.

The storage resonator accumulates external energy by reducing the frequency of internal oscillations. In a mathematical context, any resonator design whose oscillation frequency is greater than the oscillation frequency of the external influence is cumulative. This happens whether the diameter is 10 or 12 inches, but you need to choose a different volume.

Instantaneous action implies the correspondence of the internal oscillatory force in period to external oscillations. Such resonators increase the sound power due to thermal absorption of the surrounding space, shifting the frequency at the input power - changes due to an increase in the playback interval.

The common CV box has a rectangular shape with partitions resembling a caterpillar in arrangement. The appearance will depend on the speaker and its features, size - 10″ or 12 inches. At the moment, you can find drawing diagrams for any frequency device and make a resonator at no extra cost. It will differ slightly from the brand name.

You can make a resonator in a mini version. This solution is shown in the figure.

To obtain drawings of CV boxes 10, 12 and 15″ you can use a search engine or our resonator database or a calculation program. The easiest way is to search by type of speaker and required volume. For example, a 12″ CV box can be implemented in several versions, depending on the technical features described and demonstrated below.

How to calculate a resonator for the Urals yourself?

First of all, we note that the main material for making this audio device is multi-layer moisture-resistant plywood. The speaker input is sized according to the selected model. The volume and design will depend on the technical tasks: interior features, required power and other features.

The figure shows that the direction of the port and other parameters also influence the design. Sometimes drivers, after making calculations, are concerned that the dimensions are very large compared to the available space in the cabin, so they recommend a design that is suitable for this task.

Other housing options

The photo shows an example of the calculation of the HF box, but in total the cross-sectional area of ​​the tunnel is taken into account (for example, 10″ or 12″), depending on the caliber of the subwoofer, for example, Machete m10d2.

Use the Quarter Wave Box calculation program. You will only need to enter the speaker parameters and box volume. Otherwise you will have to make the drawings yourself.

To do this, use ready-made recommendations - a table with subwoofer sizes for 10, 12 inches and others. The cells show the volume that needs to be taken as a basis to achieve certain audio parameters. A “tuning” is also selected depending on the machine owner’s preferences and frequency. The box can be designed for two or more speakers, they can be different 10″ or 15″.

The proposed variations demonstrate some solutions for organizing a car interior media system that are available for self-production. With a little effort, you will get a high-quality sound system in your car for your new Machete m10d2 or Ural, taking into account the features of your interior and preferences.

In this article we will not delve into the theory quarter-wave resonator or in common parlance - a quarter wave (QW), but let's look at things from the everyday point of view of an ordinary user. This type of design used for a subwoofer has both advantages and disadvantages, although there are not many of the latter.

The main advantages of CV are:

• low level of group delays, accuracy of bass processing and detail sometimes even higher than a closed box;
• smooth and surprisingly wide range of reproduced frequencies; with the right approach, the frequency response can easily handle both the upper bass and the very bottom;
• high efficiency, with the same power you get a return that is on average 20-40% higher than bass reflexes or bandpasses, and a closed box that is 150-300% higher.

Agree, this is just a great bonus even for the best subwoofer.

However, there are also disadvantages:

• occupies a decent part of the trunk, if not all of it;
• quite demanding when choosing a speaker, weak magnetic systems, low linear travel and a heavy moving part - all this is not for HF, however, you will not find this among DD subwoofers;
• Contraindicated for use with powers 2 or more times higher than the rated power of the subwoofer.

In a nutshell, if you don’t mind space, the HF will be the best design choice for a subwoofer. So, a classic quarter-wave resonator is a tunnel of a certain length and a certain cross-sectional area, and that’s all. It is surprisingly simple in calculations and, given the availability of free space, it is also simple to manufacture. Figure 1 shows a schematic diagram of the operation of the CV, where the red line indicates the estimated length of the tunnel. The figure shows a tunnel with a circular cross-section, but in practice, in the vast majority of cases, a square cross-section of the same area is used.

The CV is calculated as follows. The cross-sectional area of ​​the tunnel depends on the caliber of the subwoofer and is calculated using the following formula. Tunnel = 1.5*(3.14*((Dsubwoofer/2)^2)). Simply put, the cross-sectional area of ​​the tunnel is equal to one and a half area of ​​the subwoofer. The length of the tunnel determines the CV setting. The following simple formula is used: Ltunnel = (343/Fb)/4, where Fb is the desired tuning frequency, the result in meters. We recommend using settings from 34 to 47Hz; we consider 39-41Hz to be the optimal and most universal setting.

An example of calculating the frequency response, tuned to 40Hz, for a subwoofer with a caliber of 12″ (30cm). Tunnel = 1.5*(3.14*((30/2)^2)) = 1060 sq.cm. Ltunnel = (343/40)/4 = 2.14 meters. For convenience, the tunnel length (L) is depicted in all our drawings with a red line. As we can see, the length of the straight CV is about 2 meters; this is of course not acceptable for a car and is not used in practice. In order to fit a tunnel of this length into the trunk, it must be rolled up. The figure below shows classic tunnel collapse schemes. We calculated, chose the most convenient form of folding, completed the drawing using simple geometric constructions and calculations, and that’s it, you can cut and enjoy the magnificent bass!

For those of our users for whom sound quality is especially important, we recommend using a tapered, folded HF. It is much more complex to manufacture and larger in volume, but the result is certainly impressive - the bass is uniquely fast, accurate and deep. This type of case will perform well in sound quality competitions. The difference with the classic HF is that the tunnel smoothly narrows from 3 woofer areas at the beginning to 1.5 at the output at the end. Traditional designs for a tapered rolled CV are shown in the figure below.

Surely, after preliminary calculations, you are all worried about this question: “the dimensions of the housing are too large for the desired setting, what will happen if the cross-sectional area is reduced...?” The answer to this question is simple - when the cross-sectional area is reduced down to 0.75 of the area of ​​the woofer, all the advantages of the frequency response gradually disappear. On even smaller cross-sectional areas of the tunnel, unpleasant jet noise appears. With a tunnel area of ​​less than 0.5, the jet noise will probably be audibly louder than the bass. I think that now it has become clear to many what CV is and why it is so discussed. Build your own unique bass rigs and share your impressions!

based on materials from the site www.digitaldesigns.ru