# Crossover Calculator

Created by Steven Wooding
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Dec 21, 2022

This speaker crossover calculator will help you design a set of amazing sounding speakers. It'll tell you what capacitors and inductors you need to create a passive crossover design for either two speakers (a 2-way passive crossover) or three speakers (a 3-way passive crossover).

In the 2-way mode, the calculator uses the impedance of your tweeter and woofer to produce a 2-way speaker crossover design. By choosing three speakers, it becomes a 3-way crossover calculator, in case you also want to incorporate a midrange speaker into your design.

There are also a couple of additional circuits for a single speaker. One to help stabilize the speaker's impedance as frequency changes (Zobel) and another that attenuates the volume (L-pad).

In this article, you'll learn why, if you want to get the best sound, you need more than one speaker, and how, by using the right electronic components, you can send only the most suitable frequencies to each speaker. By the end, you'll know a low-pass crossover from a high-pass crossover.

## Why more speakers are better than one

If you are new to the field of hi-fi speaker design, you might be wondering, why we can't just use one speaker? After all, you will probably find devices around your home that only have a single speaker, such as a small portable radio or your mobile phone. But do they sound great at all frequencies?

A common complaint of single-speaker designs is the lack of bass response. That means low volume and sound distortions at low frequencies, such as the bass instrument in a music track. To fix this issue, you could make the speaker bigger, but then high frequencies would be low in volume. For a hi-fi speaker design, we are looking for the same sound volume output across as wide a range of frequencies as possible.

The solution is to have two or three (maybe more, but these are less common) specialist speakers inside each speaker unit. A speaker that outputs high frequencies is called a tweeter, and one that produces low frequencies is called a woofer.

For a three-speaker setup, you would also have a midrange speaker to cover a range of frequencies between higher quality tweeter and woofer speakers.

However, there is a problem when it comes to connecting our multiple speaker solution to an amplifier. The speaker cable contains all frequencies (as electronic signals), so the woofer will still get the high frequencies, and the tweeter the low frequencies. This frequency mismatch will produce sound distortion, and could even damage a speaker if it gets a loud enough signal at the wrong frequency.

## Passive crossover design

One solution to this problem is to split up the signal coming from the amplifier according to the signal frequency. Then, for example, low-frequency signals will go to the woofer and high-frequency signals to the tweeter. A combination of the right capacitors and inductors creates filters that only allow the right range of frequencies to go to the correct speaker (or driver).

When two speakers are involved, this is known as a 2-way passive crossover design. For three drivers, it's known as a 3-way passive crossover. It is called "passive" as there is no additional power source required by the speaker.

Another solution you may come across is an active crossover design, which involves splitting up the signal before amplification, with each specialist speaker having an amplifier, requiring the speakers to be powered. Note that this calculator is only applicable to passive crossover designs.

For a 2-way crossover design, you have a low-pass crossover filter and a high-pass crossover filter. A low-pass filter lets through frequencies less than a certain amount, while a high-pass filter only lets higher frequencies through. The crossover frequency is where the low-pass filter starts to fade, and the high-pass filter starts to increase the amplitude of the signal. A typical value for a 2-way crossover frequency is 2000-3000 Hz.

A 3-way crossover design adds a band-pass filter that selects midrange frequencies for the midrange speaker. Now when music plays through the speaker, each range of frequencies has the same sound level, with minimal distortion. The total harmonic distortion calculator can tell you more about how this phenomenon can affect sound accuracy.

## Order and filter type

This calculator allows you to select the order of the crossover and the filter characteristic. The simplest is a 1st-order crossover design, which uses only one capacitor and one inductor. It has a 6 dB/octave slope, which is the lowest slope possible. The value of the slope tells us how much attention the filter is applying as the frequency changes. This simple design minimizes power loss.

However, it still allows signals to go to the wrong speaker (due to the low filter slope value), so the damage could yet be done to the tweeter if it receives a significant signal with a lower frequency than it can handle.

Let's summarize the features of the higher-order designs. The second-order crossover design:

• Has a 12 dB/octave slope, allowing more attenuation of unwanted signals.
• Is commonly used as it still uses relatively few components.
• Provides adequate protection for the high-frequency tweeter driver.
• Has a wide choice of filter characteristics, including Butterwork, Bessel, Linkwitz, and Chebyshev.

A third-order crossover design:

• Has an 18 dB/octave slope, offering even more attenuation of out-of-band frequencies.
• Is still not too complex to introduce significant power loss.
• Is available with Butterworth or Bessel filter characteristics.

Finally, for a fourth-order crossover design:

• Has a very steep slope of 24 dB/octave.
• Is a complex design with many more components.
• Has components that may start to interact with each other, affecting sound quality.
• Could have noticeable power loss that reduces the sound level of the speaker.

## How to use the speaker crossover calculator

1. Choose the number of speakers in your design, which you'll find at the top of the crossover calculator. For crossover designs, choose either two (tweeter and woofer) or three (tweeter, midrange speaker and woofer) speakers.

2. Choose the desired order and filter characteristics. Recall that a 2nd-order crossover filter offers a good compromise between complexity and quality.

4. Enter the crossover frequency(s). For a two-speaker setup, look up the frequency response ranges of the speakers and choose a frequency that is covered by both speakers.

When designing for three speakers, you'll need to set a low and a high crossover frequency using the same method. Note that you can only choose a spread between these frequencies of either 3 or 3.4 octaves.

5. You will now see the capacitor and inductor component values you will need for your passive crossover design in the results section. You also get a circuit diagram, so you know how to wire up the components to build your crossover filter.

## Example of calculating a 2-way passive crossover design

Now let's go through how to calculate a relatively simple 2-way, 2nd order crossover with Butterworth characteristics, consisting of two capacitors and two inductors. The equations for the four components are as follows:

\small \begin{aligned} \text{capacitor}_1 &= \frac{0.1125}{\substack{\text{tweeter} \\ \text{impedance}} \times \substack{\text{crossover} \\ \text{frequency}}} \\ \text{capacitor}_2 &= \frac{0.1125}{\substack{\text{woofer} \\ \text{impedance}} \times \substack{\text{crossover} \\ \text{frequency}}} \\ \text{inductor}_1 &= \frac{0.2251 \times \substack{\text{tweeter} \\ \text{impedance}}}{\text{crossover frequency}} \\ \text{inductor}_1 &= \frac{0.2251 \times \substack{\text{woofer} \\ \text{impedance}}}{\text{crossover frequency}} \\ \end{aligned}

The equations for other orders and filter types are similar to those above, but with varying constants. You can find all of these in the book by Vance Dickason called The Loudspeaker Design Cookbook, 7th edition (2006), pages 163-169.

Let's say we have a tweeter impedance of 6 Ohms, a woofer impedance of 4 Ohms, and a crossover frequency between the two of 3000 Hz. You would then calculate each component as:

$\text{capacitor}_1 = \frac{0.1125}{6 \times 3000} = 6.25 \times 10^{-6} \ \text{F} = 6.25 \ \text{μF}$
$\text{capacitor}_2 = \frac{0.1125}{4 \times 3000} = 9.375 \times 10^{-6} \ \text{F} = 9.375 \ \text{μF}$
$\text{inductor}_1 = \frac{0.2251 \times 6}{3000} = 0.0004502 \ \text{H} = 0.4502 \ \text{mH}$
$\text{inductor}_2 = \frac{0.2251 \times 4}{3000} = 0.0003001 \ \text{H}= 0.3001 \ \text{mH}$

This example was relatively simple, but for higher-order crossovers, this crossover calculator makes it a breeze to work out which components you need to build your custom speaker design. Then, you can use the speaker box calculator to aid in the creation of the housing of your components.

If you set the number of speakers in the calculator to one, you'll be able to choose from two additional circuits that involve a single speaker - Zobel and L-pad. Let's briefly explore these circuits.

#### Zobel circuit

A speaker contains a coil of wire, which acts as an inductor. This behavior then causes the speaker's impedance to change with the frequency of the sound. However, the calculations for the crossover circuit assumes a constant speaker impedance.

The solution is to place a Zobel circuit between the crossover circuit and the speaker, which stabilises the speaker's impedance as seen from the crossover circuit.

The Zobel circuit is quite simple, consisting of a resistor and capacitor wired in parallel to the speaker (as shown in the circuit diagram).

Enter the speaker's inductance and resistance (these values should be on the speaker's specification sheet), and the calculator will give capacitor and resistor values for this circuit.

The equations for the values of the capacitor and resistor in the Zobel circuit are as follows:

\small \begin{aligned} R_z &= 1.25 R_s \\ C_z &= \frac{L_s}{R_z^2} \end{aligned}

where:

• $R_z$ is the value of the resistor in the Zobel circuit;
• $R_s$ is the resistance of the speaker;
• $C_z$ is the value of the capacitor in the Zobel circuit; and
• $L_s$ is the inductance of the speaker.

For example, if a speaker has a resistance of 6 Ohms and an inductance of 1.3 mH, the calculations would be as follows:

\small \begin{aligned} R_z &= 1.25 \times 6 = 7.5 \ \Omega \\ C_z &= \frac{0.0013}{7.5^2} = 0.000023 = 23 \ \text{μF}. \end{aligned}

This circuit is used to attenuate the signal to a speaker and consists of two resistors in an arrangement that resembles the letter "L" (as shown in the circuit diagram). Enter the speaker's impedance and the amount of attenuation required in decibels (dB) to calculate the values of the two resistors.

The formulas for the two resistors are:

\small \begin{aligned} R_1 &= Z_s \frac{10^{\frac{Loss}{20}} - 1}{10^{\frac{Loss}{20}}} \\ R_2 &= \frac{Z_s}{10^{\frac{Loss}{20}} - 1} \end{aligned}

where:

• $R_1$ is the series resistor (Resistor 1 in the circuit diagram);
• $Z_s$ is the impedance of the speaker;
• $\text{Loss}$ is the attenuation of the signal in dB; and
• $R_2$ is the parallel resistor (Resistor 2 in the circuit diagram).

As an example, say we wanted to attenuate a speaker with an impedance of 8 Ohms by 5 dB. The calculations for the two resistors are:

\small \begin{aligned} R_1 &= 8 \frac{10^{\frac{5}{20}} - 1}{10^{\frac{5}{20}}} = 3.5 \ \Omega \\ R_2 &= \frac{8}{10^{\frac{5}{20}} - 1} = 10.28 \ \Omega. \end{aligned}
Steven Wooding
Number of speakers
2
Filter order & characteristic
1st Order Butterworth
Woofer impedance
Ω
Tweeter impedance
Ω
Crossover frequency
Hz
Capacitor & Inductor Values
Capacitor 1
μF
Inductor 1
mH
Circuit Diagram
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