# Crossover Calculator

Created by Davide Borchia
Last updated: Sep 09, 2022

With our speaker crossover calculator, you won't need annoying math to find out the best passive crossover design for your sound system: find out how to plan the circuits that will crank your sound experience up to eleven.

• What a crossover is, and why you need one;
• The types of crossovers and how to calculate them: the 2-way crossover and the 3-way crossover;
• Examples of calculations of a 1st order crossover and a 2nd order crossover in a two-driver speaker;
• A few words on single-driver speakers.

## Inside your speaker: how to optimize the sound of your setup

The bigger a body, the louder the sounds it can emit: it's no coincidence that small birds sing silvery melody while an elephant's trumpeting call makes your body vibrate. This general rule applies also to speakers: bigger speakers excel in reproducing basses (low frequencies), while small speakers reproduce most faithfully higher frequencies.

If the sound you are interested in has a broad spectrum (and music often covers frequencies from a few dozens Hz to a few kHz), a single speaker won't make it: the resulting sound would be distorted and lacking depth. Basses are often left out due to the size requirement of the appropriate sound system.

To reproduce a complex sound appropriately, we need multiple specialized speakers. In the most basic configuration, a loudspeaker with multiple elements has:

• A tweeter, a small speaker specialized in higher frequencies; and
• A woofer, a larger speaker which reproduces the bass.

It is possible to add more speakers; however, three is usually the limit. In a three speakers configuration, we can find a midrange speaker that improves the quality of the frequencies between the tweeter's and woofer's ranges.

While we can, theoretically, feed the whole signal to both units, this wouldn't be a wise choice. We risk damages to the equipment. The best practice is to split the signal, feeding to each speaker only the relevant portion of the waveform.

How do we perform this split? First, we choose a frequency above which we reroute the signal to the tweeter and below which we turn to the woofer. Then we ask our electric engineer friend, or CalcTool's crossover calculator, to design the best crossover for our speakers.

## What is a speaker crossover?

Crossovers are electronic circuits that splits a signal into appropriate frequency ranges. In our crossover calculator, we will deal only with passive crossover designs, circuits that use only passive components. Active crossovers require individual power sources for each speaker, making them more complex albeit better performing.

Long story short, a crossover is a well-designed set of filterscreated by joining inductors and capacitors (something similar to an RC circuit). Each filter operates at a specific frequency, allowing only higher (or lower) frequencies to pass. We can identify two basics type of filters:

• The high-pass filter, which cuts the lower frequencies; and
• The low-pass filter, which allows the lower frequencies through.

In the case of a midrange speaker, we need a filter that operates between two specified values. We call such a filter band-pass filter.

The number of speakers (drivers) in the system controls the first classification of our crossover: we identify 2-way crossovers and 3-way crossovers. The calculations differ slightly.

Once you decide which general type of crossover, you need to make other choices accordingly to the desired performance of the system. Let's check them out.

## 2-way crossover calculator: simple speaker crossover design

2-way crossovers split the signal at a single cut-off frequency. In the simplest design, a 2-way crossover has a single pair inductor-capacitor: we are dealing with first-order crossovers. A first-order crossover has the lowest power dissipation (thanks to the low number of components); however, on the downside, it has the lowest possible slope for a filter, clocking at $6\ \text{dB}/\text{octave}$. The filtering is not perfect, and some of the frequencies would still be directed to the wrong speaker.

Increasing the number of pairs of components, we improve the slope of the filter, passing from $6\ \text{dB}/\text{octave}$ for the first-order filter to the $12\ \text{dB}/\text{octave}$ of the second-order crossover, the $18\ \text{dB}/\text{octave}$ of the third-order crossover, and so on.

🙋 The higher the number of components, the higher the power dissipation: the power of the signal in input to the speakers decreases with the order of the crossover, the filtering would be good, but does it matter if you can't hear the music?

The values of the inductors and capacitors in each crossover design depend:

• On the impedance of each speaker;
• On the desired cut-off frequency; and
• On the type of crossover.

For each order, you can select various types of crossover. The most common one is the Butterworth, but you can find many other types, with variety increasing with the order of the crossover.

## An example of speaker crossover design: calculate a 1st order crossover for a two drivers speaker

Take a speaker with two drivers: a tweeter and a woofer:

• Our tweeter has a rated impedance of $8\ \Omega$; and
• The woofer has slightly better quality, with an impedance of $6\ \Omega$.

The suggested crossover frequency is $5\ \text{kHz}$. Choose now the desired type of crossover. We will go for a 1st order Solen Split.

To find the values of the capacitor and the inductor, we use the following equations:

\begin{align*} C_1&= \frac{0.1125}{Z_{\text{t}}\cdot f_{\text{c}}}\\ \\ L_1 &= \frac{0.2251 \cdot Z_{\text{w}}}{ f_{\text{c}}} \end{align*}

Where:

• $Z_{\text{w}}$ and $Z_{\text{t}}$ are, respectively, the impedances of woofer and tweeter;
• $f_{\text{c}}$ is the crossover frequency; and
• $C_1$ and $L_1$ are the crossover capacitance and inductance.

The calculations for a 2nd order crossover are not dissimilar and involve only a different choice of the multiplicative constant in the formulas above. Try to change the circuit to a 2nd order crossover in the calculator: we will readily output the new set of values.

## 3-way crossover calculator

If you add a midrange driver to your speaker, the complexity of the math required to calculate the best crossover design increases accordingly. To calculate a 3-way crossover, you need to know:

• The impedances of all speakers (tweeter, woofer, and midrange);
• The low crossover frequency (separating midrange and woofer);
• The high crossover frequency (separating midrange and tweeter); or

Low crossover frequency, high crossover frequency, and spread are related: the frequency range covered by the midrange driver is either $3$ or $3.4$ octaves, effectively linking one of the two frequencies to the other.

🙋 To choose the two crossover frequencies, refer to your drivers' datasheets, or decide the value you deem fit for your sound system.

As for the 2-way crossover calculator, you can choose the order of your 3-way crossover. Our tool offers calculations from the 1st order crossover to the 4th order one. Remember that the higher the number of components, the higher the complexity, power dissipation, and likelihood of mishaps!

For the 3-way crossover calculator, you can choose the following designs:

• 1st order, normal polarity;
• 2st order, reversed midrange polarity;
• 3st order, normal polarity;
• 3st order, reversed midrange polarity; and
• 4st order normal polarity.

## More than crossovers: single speakers circuits

Between a crossover and a speaker, there still is space. There, you can fit circuits designed to tweak the performances of a single speaker at a time. Our speaker crossover calculator allows you to calculate the design of two of them:

• The Zobel circuit; and

#### The Zobel circuit

Every speaker has an impedance, and the impedance increases with the frequency of the signal. This would affect the result of the calculations of a speaker crossover since we assumed a constant speaker's impedance. A Zobel circuit flattens the impedance curve of a speaker by adding a resistor and capacitor in parallel, right before the driver.

\begin{align*} R_{\text{Z}}& = 1.25\cdot R_{\text{S}}\\ \\ C_{\text{Z}} &= \frac{L_{\text{S}}}{R_{\text{Z}}^2} \end{align*}

Where:

• $R_{\text{Z}}$ and $C_{\text{Z}}$ are, respectively, the Zobel circuit's resistance and capacitance; and
• $R_{\text{S}}$ and $L_{\text{S}}$ are the speaker's resistance and inductance.

If you need to attenuate the signal before it reaches the speaker (preventing damages, for example), you can use an L-pad circuit. In this design, two resistors are connected to the speaker, one in parallel and one in series (in an... L-shape!). We can calculate the values of those two components required to attain the desired attenuation:

\begin{align*} R_1 &= Z_{\text{S}}\cdot \frac{10^{\frac{\text{loss}}{20}}-1}{10^{\frac{\text{loss}}{20}}}\\ \\ R_2&= Z_{\text{S}}\cdot \left(10^{\frac{\text{loss}}{20}}-1\right) \end{align*}

Where:

• $\text{loss}$ is the desired attenuation in decibel;
• $R_1$ and $R_2$ the values of the L-pad circuit's resistors; and
• $Z_{\text{S}}$ the speaker's impedance.
Davide Borchia
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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