Кроссовер для акустики калькулятор

Javascript® Electronic Notebook
by Martin E. Meserve
2nd Order Active Filters, Low-Pass/High-Pass

This page contains two calculators. The first calculator can be used to aide in the design of 2nd Order Low-Pass and High-Pass Active Filters . It uses the equations that are listed below the calculator. This maked it flexible when specifying the requirements.

The second calculator, while similar to the first calculator, is based on Tables and uses a Scale Factor to calculate the components. While the same filter types can be designed, the Gain is limited to the available table entries, which is usually Gains of 2 and 10 for 2nd order filters.

The drawings on the right show the Ideal and Realizable filter responses for 2nd Order Low-Pass and High-Pass Active Filters .

The frequency ω_C is the cutoff frequency. This is the point at which the amplitude equals 1/ √ 2 = 0.707 times its maximum value.

The Low-Pass filter, left side, has a single passband, 0 < ω < ω_C , and a single stopband, ω > ω_C . So signals below ω_C are passed without attenuation and signals above ω_C are attenuated.

The High-Pass filter, right side, has a single passband, ω > ω_C , and a single stopband, 0 < ω < ω_C . So signals above ω_C are passed without attenuation and signals below ω_C are attenuated.

The flat response in the passband is a feature of a Butterworth response. A Chebishev response would have Ripple in the passband. The calculators provide selectable passband ripple of 0.1 dB, 0.5 dB, and 1.0 dB.

There are two configurations, Multiple Feed Back (MFB) and Voltage Controlled Voltage Source (VCVS) . Each configuration allows for Butterworth and Chebishev response characteristics.

Both MFB and VCVS configurations contain a minimal number of circuit elements, have low output resistance, and are convenient for cascading with other stages. While the MFB has better stability than VCVS , the VCVS configuration is capabile of relatively high gains, and is relatively easy to adjust the characteristics. The MFB configuration provides «inverting» gain, whereas the VCVS configuration provides «non-inverting» gain.

2nd Order Low-Pass/High-Pass Filter Calculater — Equation Method

Filter Type
Low-Pass
High-Pass

Configuration
MFB
VCVS

Characteristics

Gain

Cutoff
Hz

Res. Tol.

C ≅ xxx
yyy

Gain

Cutoff
Hz

Res. Tol.

C_A/C_B ≅ xxx

Use SVC
Yes No

Another method for determining filter components is the Table method. It is intended to be a quick method, as long as your needs are simple. While you could certainly make a set of tables to handle any Gain figure, published tables for 2nd Order filters are usually only available for Gains of 2 and 10. Initially a Scale Factor ( SF ) is calculated using SF = 500/(PI×F₀×C) where F₀ is the filter cut-off frequency and C is the initial capacitance, in uF

On the left side of the calculator is a selection panel. Start by selecting the Filter Type (Low-Pass or High-Pass), Configuration (MFB or VCVS), and Response Characteristics (Butterworth or Chebishev). Then, enter the Cutoff Frequency (F₀), select the Gain (2 or 10), and enter the initial Capacitance (C). At the bottom of the selection panel, the Resistor Tolerance (Exact, 1%, 2%, 5%, or 10%) and whether to use a Standard Value Capacitor ( SVC ) can be selected. The Exact setting will show the exact calculated values for the componenets.

On the right side of the calculator is the schematic and a table. The schematic will match the Filter Type (Low-Pass or High-Pass) and Configuration (MFB or VCVS) selected, and the component values will be listed. The default resistor tolerance is 5% but that can be changed at any time. The table below the schematic will show the two entries for each component. The first entry is the calculation used for that component. The second entry is the result of the calculation, adjusted according to the resistor tolerance selected.

Its common practice to unclutter a schematic by showing the design (analog or digital) and power connections, on a separate sheets. On small designs, power connections are often show at the bottom of a drawing away from the main design. Further, in many cases, especially where a package may contain multiple devices, only one of the devices may show power connections. But the power connections are equally as important as the main design. The same approach is used here, with the calculators shown above having references to +V , -V , and Ground , but not containing any description of the references.

The specific connections that you use, depends on the your power supply arrangement and the device you have selected. Most garden variety Op-Amps are designed to work with Dual Power Supplies . Dual Power Supplies are simply two equal voltage power supplies, with the negative (-V) of one supply connected to the positive (+V) of the other. This effectively forms a three wire connection between the power supplies and the Op-Amp circuit. These power supplies can be +9V/-9V , +15V/-15V , +18V/-18V , or anything in between. The intent is to provide the output of the Op-Amp with an equal voltage swing above and below zero.

The diagram on the left shows how you might connect a dual (+12V/-12V) power supply. The 0.1 uF capacitors are used to decouple the Op-Amp from any noise spikes that might be on the power lines. These capacitors are connected to the power and ground pins of the Op-Amp and must be located as close to the Op-Amp as possible.

But suppose you only had a Single Voltage Power Supply . This can certainly be used, but there will be some small changes to the filter drawings and possibly some limitations. The diagram on the right shows how it can be done. First a reference voltage ( V-Ref ) is created with a voltage divider using R1, R2, and C3. Because there is very little current required by the Op-Amp, the resistors can be almost any value. But a good choice is shown. The capacitor C3 is used as a filter to stabilize V-Ref , and not reflect changes in the Op-Amps current draw.

For example, the MFB Low-Pass filter show the «+» input of the Op-Amp, and the input capacitor «C» connected to ground. For use with a Single Voltage Power Supply , both of those connections need to be disconnected from ground and connected to V-Ref . This biases the Op-Amp at +V/2 . But this also means that the filter input and output connections will no longer be referenced to zero voltage (Ground). To fix this issue, the input and output of the filter can be coupled with series capacitors. The input capacitor and output capacitor will serve as DC isolators for the filter. Along with the input/output impedances, the capacitors will form a low frequency High-Pass filter. With the components specified (1 uF), the the low frequency response will start rolling off at around 16 Hz. The exact value depends on the frequency you are using. If you are working a low frequencies, you might want to increase the series capacitors.

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Crossover Calculator:
LR2, Bessel, Butterworth & Cheybyscheff

It is very helpfull if you are able to measure the frequency response of the drivers to choose the best crossover frequency.

If you choose a crossover point in a range where the driver’s frequency response is changing rapidly off-axis, the off-axis response will have large response anomalies.
Large variations in the off-axis response degrade the power response the listener perceives. Reflected and reverberant response will be significantly different from the on-axis response, and generally devalue the overall quality.

Selecting the best slope is important, both to protect the tweeter (in particular), and to ensure that the drivers are all operated within their optimum frequency and power handling ranges.

A 6dB/octave (first-order) filter has the most predictable response, and is affected less by impedance variations than higher orders. On the negative side, the loudspeaker drivers will be producing sound at frequencies that are very likely outside their upper or lower limits.

12dB/octave (second-order) filters are better at keeping unwanted frequencies out of the individual speakers, but are more complex, and are affected by impedance variations to a much greater degree. The tolerance of the components used will also have a greater effect. The capacitance used must remain predictable and constant over time and power, which specifically excludes the use of bipolar electrolytics.

A 18dB/octave (third-order) filter requires closer tolerances than a second order, and is again even more susceptible to any impedance variations than the 12dB filter.

24dB/octave (fourth-order) filters increases the complexity and tolerance requirements even further — a point must be reached where the requirements versus the complexity and sensitivity will balance out.

How does it work?

For this example i use a second order (12dB) Highpass crossover network for 1 kHz.

Crossover frequency: 1 kHz ( Linkwitz-Riley Crossover )
Driver impedance: 10 ohm
Inductor: 3.18 mH
Capacitor: 8 uF

Now, the capacitor is in series with the driver and the inductor is parallel with the driver.

The capacitor and the inductor together with driver are a voltage divider.

Calculation of this divider:
6.66 ohm / (6.66 ohm + 20 ohm) = 0.25

That means a input-voltage of 1 volt will be a output-voltage of 1 * 0.25 = 0.25 volt

And how much dB is that?
20 * log(0.25) = -12dB

Brief explanation

Second order Linkwitz-Riley ( LR2 )

(The Linkwitz-Riley filter has a crossover frequency where the output of each filter is 6dB down, and this has the advantage of a zero rise in output at the crossover frequency.)
Second-order Linkwitz-Riley crossovers (LR2) have a 12 dB/octave (40 dB/decade) slope. They can be realized by cascading two one-pole filters, or using a Sallen Key filter topology with a Q value of 0.5. There is a 180° phase difference between the lowpass and highpass output of the filter, which can be corrected by inverting one signal. In loudspeakers this is usually done by reversing the polarity of one driver if the crossover is passive.

Bessel filter

( Maximally flat phase, Fastest settling time, Q: 0.5 to 0.7 (typ) )
A Bessel filter is a type of linear filter with a maximally flat group delay (maximally linear phase response). Bessel filters are often used in audio crossover systems. Analog Bessel filters are characterized by almost constant group delay across the entire passband, thus preserving the wave shape of filtered signals in the passband.

Butterworth filter

( Maximally flat amplitude, Q: 0.707 )
The Butterworth filter is a type of signal processing filter designed to have as flat a frequency response as possible in the passband. It is also referred to as a maximally flat magnitude filter.

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