Measuring Re, Fs, Fc, Qes, Qms, Qts, Qtc, Vas, Cms, Sd

To measure these parameters, you will need the following equipment:

1. Voltmeter
2. Audio signal generator
3. Frequency meter
4. Powerful (at least 5 watts) 1000 ohm resistor
5. Precise (+- 1%) 10 ohm resistor
6. Wires, clips and other rubbish to connect it all into a single circuit.

Of course, this list is subject to change. For example, most oscillators have their own frequency scale and a frequency counter is not necessary in this case. Instead of a generator, you can also use a computer sound card and appropriate software capable of generating sinusoidal signals from 0 to 200 Hz of the required power.

Scheme for measurements

Calibration

First you need to calibrate the voltmeter. To do this, instead of the speaker, a resistance of 10 ohms is connected and by selecting the voltage supplied by the generator, it is necessary to achieve a voltage of 0.01 volts. If the resistor is of a different value, then the voltage should correspond to 1/1000 of the resistance value in ohms. For example, for a calibration resistance of 4 ohms, the voltage should be 0.004 volts. Remember! After calibration, it is IMPOSSIBLE to adjust the output voltage of the generator until all measurements are completed.

Finding Re

Now, by connecting a speaker instead of a calibration resistance and setting a frequency close to 0 hertz on the generator, we can determine its direct current resistance Re. It will be the voltmeter reading multiplied by 1000. However, Re can also be measured directly with an ohmmeter.

Finding Fs and Rmax The speaker during this and all subsequent measurements must be in free space

The resonant frequency of a speaker is found from its peak impedance (Z-characteristic). To find it, smoothly change the frequency of the generator and look at the readings of the voltmeter. The frequency at which the voltage on the voltmeter will be maximum (a further change in frequency will lead to a voltage drop) will be the main resonance frequency for this speaker. For speakers larger than 16cm in diameter, this frequency should be below 100Hz. Do not forget to write down not only the frequency, but also the readings of the voltmeter. Multiplied by 1000, they will give the speaker impedance at the resonant frequency, Rmax, needed to calculate the other parameters.

Finding Qms, Qes and Qts These parameters are found by the following formulas:

As you can see, this is a sequential finding of additional parameters Ro, Rx and measurement of previously unknown frequencies F₁ and F₂. These are the frequencies at which the speaker impedance is Rx. Since Rx is always less than Rmax, then there will be two frequencies - one is slightly less than Fs, and the other is somewhat larger. You can check if your measurements are correct with the following formula:

If the calculated result differs from the previously found by more than 1 hertz, then you need to repeat everything from the beginning and more accurately. So, we have found and calculated several basic parameters and can draw some conclusions based on them:

1. If the resonant frequency of the speaker is above 50Hz, then it has the right to claim to work as a midbass at best. You can immediately forget about the subwoofer on such a speaker.
2. If the resonant frequency of the speaker is higher than 100 Hz, then this is not a low-frequency speaker at all. You can use it to reproduce mid frequencies in XNUMX-way systems.
3. If the Fs/Qts ratio of a speaker is less than 50, then that speaker is designed to operate exclusively in closed boxes. If more than 100 - exclusively for working with a phase inverter or in bandpasses. If the value is between 50 and 100, then you need to carefully look at other parameters - what type of acoustic design the speaker tends to. The best way to do this is to use special computer programs that can graphically simulate the acoustic output of such a speaker in different acoustic design. True, in this case, one cannot do without other, no less important parameters - Vas, Sd, Cms and L.

Finding Sd

This is the so-called effective radiating surface of the diffuser. For the lowest frequencies (in the piston action zone), it coincides with the design one and is equal to: .

Radius R in this case, it will be half the distance from the middle of the width of the rubber suspension on one side to the middle of the rubber suspension on the opposite side. This is due to the fact that half the width of the rubber suspension is also a radiating surface. Please note that the unit of this area is square meters. Accordingly, the radius must be substituted into it in meters.

Finding the speaker coil inductance L

This requires the results of one of the readings from the very first test. You will need the impedance (impedance) of the voice coil at a frequency of about 1000 Hz. Since the reactive component (XL) is separated from the active Re by an angle of 900, we can use the Pythagorean theorem: .

Since Z (coil impedance at a certain frequency) and Re (coil DC resistance) are known, then the formula is converted to

Having found reactance XL at frequency F, we can calculate the inductance itself using the formula:  

Vas measurements

There are several ways to measure equivalent volume, but two are easier to use at home: the "Added Mass" method and the "Added Volume" method. The first of them requires several weights of a known weight from materials. You can use a set of weights from pharmacy scales or use old copper coins of 1,2,3 and 5 kopecks, since the weight of such a coin in grams corresponds to the face value. The second method requires an airtight box of known volume with an appropriate speaker hole.

Finding Vas by the method of additional mass

First you need to evenly load the cone with weights and again measure its resonant frequency, writing it as F's. It must be lower than Fs. It is better if the new resonant frequency is less by 30% -50%. The weight of the weights is taken to be approximately 10 grams per inch of cone diameter. Those. for a 12" head, you need a weight of about 120 grams. Then you need to calculate Cms based on the results obtained using the formula:

,

where М - mass of added weights in kilograms. Based on the results You(m3) is calculated by the formula:

Finding Vas by the Added Volume Method

It is necessary to hermetically fix the speaker in the measuring box. It is best to do this with the magnet outward, since the speaker does not care which side it has volume on, and it will be easier for you to connect the wires. And there are fewer extra holes. The volume of the box is indicated as Vb. Then you need to take measurements Fc (resonant frequency of the speaker in a closed box) and, accordingly, calculate Qmc, Qec и Qtc. The measurement technique is completely similar to that described above. Then the equivalent volume is found using the formula:

With almost the same results, you can use a simpler formula:

The data obtained as a result of all these measurements is sufficient for further calculation of the acoustic design of a low-frequency link of a sufficiently high class. But how it is calculated is a completely different story ...

Please note that the above technique is only valid for measuring speakers with resonant frequencies below 100Hz, at higher frequencies the error increases.

Publication: cxem.net

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