¿Qué es la frecuencia de cruce Fc, las pendientes de cruce y por qué son importantes?

Los cruces son extremadamente importante para los sistemas de altavoces y un gran razón por la que podemos obtener la calidad de sonido que amamos.

Por otro lado, cosas como la frecuencia de cruce (Fc), las pendientes (db por octava y cómo funciona todo) pueden ser un poco complicados si no entiendes cómo funciona todo. ¡Me encantaría ayudar!

En este artículo explicaré:

Qué es la frecuencia de cruce Fc y por qué es importante
Qué es una pendiente cruzada y la más común con la que te encontrarás
Cómo calcular la caída de cruce de dB para frecuencias que incluyen Fc
El papel de los inductores y condensadores (y "reactancia" para Fc)

Frecuencia de cruce Fc y pendientes de cruce explicadas

Este diagrama muestra ejemplos de los 3 tipos de filtros principales que se utilizan en los cruces. También se muestran las pendientes cruzadas más comunes que es la "inclinación" del filtro (la eficacia con la que bloquean las frecuencias más allá de la frecuencia de cruce).

Una frecuencia de cruce, comúnmente escrita como Fc , es el punto de frecuencia de audio en hercios (Hz) en el que el cruce entrega una potencia de salida de -3dB (1/2) al altavoz. Fc es el punto de marcado después del cual las frecuencias de sonido se reducirán considerablemente para evitar que lleguen a un altavoz.

Más allá del punto de frecuencia de cruce (Fc), la potencia de salida del cruce caerá cada vez más, y se enviará cada vez menos potencia al altavoz. Da la casualidad de que en Fc, el voltaje de salida a la carga (altavoz) es 0,707 x el voltaje de entrada, lo que significa que puede calcular la caída de decibelios en función del voltaje de salida frente al voltaje de entrada.

Por qué las frecuencias de cruce son importantes

Al diseñar cruces de altavoces, la frecuencia de cruce (fc ) se utiliza como una especie de línea que marca dónde queremos empezar a bloquear las frecuencias de sonido enviadas a un altavoz. Por lo general, se basa en las especificaciones proporcionadas por un fabricante de altavoces que enumera las frecuencias de sonido que un altavoz puede producir con una buena respuesta de sonido y sin distorsión.

Por ejemplo, los tweeters no pueden reproducir notas graves de la música e incluso pueden dañarse. Sabiendo eso, nos gustaría elegir una frecuencia de cruce lo suficientemente alta como para bloquear las notas graves enviadas a los tweeters para evitar distorsiones o daños. (Por lo general, los tweeters tienen una frecuencia de cruce de miles de Hertz [escrito como KiloHertz o kHz para abreviar] como 3,5 kHz, 5 kHz, etc., bueno por encima del rango de sonidos graves y medios en la música).

Una frecuencia de cruce también se denomina a veces frecuencia de esquina o frecuencia de corte ya que pensamos en términos de cómo se “cortan” los sonidos después de ese punto.

La frecuencia de cruce Fc es muy importante para el diseño cruzado

Los cruces de parlantes (también llamados "pasivos" ya que no usan energía eléctrica para funcionar) usan capacitores e inductores que se seleccionan según los valores de las piezas disponibles y su costo. Un cruce se diseña en función de una frecuencia Fc inicial y se ajusta según sea necesario para los objetivos del diseño.

El uso de la frecuencia de cruce Fc como punto de partida permite a los diseñadores de sistemas de altavoces calcular los valores de las piezas necesarias (condensadores e inductores) en función de la impedancia del altavoz. Dado que no puede comprar piezas de cualquier valor, el Fc que obtenemos en función de lo que queremos es un buen punto de partida con el que podemos trabajar y ajustar según sea necesario para trabajar con piezas en función de la disponibilidad, el precio y otros factores.

Los amplificadores operacionales, también llamados amplificadores operacionales, son el bloque de construcción más importante para los cruces electrónicos. Electronic crossovers perform exactly the same job (and have the same basic behavior) as passive (speaker) crossovers. The difference is that they work on low-level signals before they’re amplified while passive crossovers work with amplified signals after the amp output.

NOTE: In this article while I describe how passive (non-electronic, non-powered) crossovers and Fc work, the principles are exactly the same for electronic filters.

Just like their larger passive capacitor or inductor-based counterparts, operational amplifier based crossovers have the same slopes and crossover frequency behavior. They simply do it with the signal before it’s amplified instead of after it.

How to calculate decibels (dB) for the crossover frequency Fc

All sound frequencies after the crossover frequency are cut more and more past it with an increasingly steep reduction – to the point where they’re almost completely blocked.

In other words, a crossover filters out a range of sounds you’d like to prevent reaching speakers, starting at the crossover frequency.

In the electrical engineering world, we traditionally use decibels (dB) when we talk about power measurements since they’re often non-linear. This just means that mathematically, power is often measured, charted, and tracked using exponential math such as logarithms (“10 to the power of x”, for example).

How crossover frequencies (Fc) and dB are related

Because crossovers reduce power at their output, it’s pretty common to measure the output reduction in decibels. One reason for this is that they have a gentle “slope” (downward curve) rather than a straight line if you were to see them graphed across the full range of audio frequencies.

For that and other reasons, we can measure the power output reduction in dB. To do so, you’ll need to know either (1) the power before and after the speaker/from the amp, or (2) the voltage at the speaker and from the amp.

Knowing those, you can easily calculate the dB output of a crossover with a scientific calculator on your computer or smartphone.

You can calculate dB for a crossover using these formulas:

For voltage: 20 x log(Vout / Vin ) =x dB
For power: 10 x log (Power_out / Power_in) =x dB

Understanding crossover signal level in vs out and “negative gain”

Crossover voltage out (called here “Vout”, the voltage to a speaker delivered from a crossover) can never be higher than the input – that’s not possible. Crossovers can only reduce the input directed to a speaker – they can’t amplify it. Some electronic crossovers do, but those intentionally have a gain on purpose and that’s not common in most cases.

For that reason, you’ll always get a negative dB answer if you do the math for the output of a crossover.

For the record, a negative dB value is used to show a reduction in engineering math while positive usually means a gain or increase in a signal. Amplifiers have a positive dB output (gain) while crossovers and some other components like resistors have a negative gain (a negative dB effect on a signal).

Attenuation is another way of describing a negative gain.

Nota: the gain control of an amplifier is there to compensate for a high or low input signal level and is a separate section from the crossover circuitry.

How a crossover frequency Fc works:example diagram

An example of a very common and simple high-pass crossover. A capacitor in series with a speaker will allow higher frequencies (above Fc) to pass with almost no volume or power drop to the speaker. It acts as a zero Ohm resistor (a short circuit wire) in series with it . However, for audio frequencies below Fc, the “resistance” (impedance, called capacitive reactance) of the capacitor will increase, allowing less and less voltage &power to reach the speaker. It will act like a very high-value resistor in series and therefore will block most of the signal from an amp sent to the speaker. In other words, a high-pass filter!

One of the problems I’ve found when we’re talking about this topic is picturing it in your mind. For example, it can be hard to understand what actually happens in real life when actually playing music in the real world vs just some explanation you’ve found on the internet.

All crossovers work the same – understand one, you understand them all (well, mostly!)

One important note I need to make is that the principles are the same regardless of the number of “orders”, or stages, a crossover has. For example, a simple 1st order crossover with a capacitor connected inline with a tweeter works on exactly the same principle as a fancier 2nd order 2-way crossover.

It’s just that the details are a little bit more complicated – not how it works. That part never changes.

There are some crossovers with more sophisticated features &designs I won’t get into here, but for the most part, the majority are all the same and do the same thing to varying degrees. The great thing is that once you understand the basics very well, you’ve got it figured out for the most part!

The fundamentals of how crossovers work with Fc

The most important thing to know is that crossovers work by “absorbing”, or preventing, voltage and power from going to the speakers they’re connected to for the sound frequencies we don’t want them to play.

In the example from my diagram further above, you can see that:

Above the cutoff frequency Fc, a capacitor acts like an almost zero resistance connection – nothing is blocked and it acts almost like a straight section of wire.
When audio frequencies begin to reach Fc, the impedance of the crossover goes up, acting like a high-value resistor in series with the speaker. At Fc, the speaker receives only 1/2 the power it would otherwise (which also happens to be .707 times the input voltage from the amp or stereo).
The farther we go past the Fc limit, the crossover’s impedance is much bigger in Ohms; in fact, past a certain point, it will be several hundred Ohms typically. When that happens the speaker has about 0v and no power to it.

As you can see elsewhere in my article, the “steepness” of the drop in the power &signal level to the speaker depends on the crossover slope. A crossover’s slope is basically just a result of how many “stages”, or crossover sections, are used as needed for the particular speaker system or speakers we’re working with.

Crossovers like you see here and are always in increments of 6 decibels (dB) Per Octave:

1st order crossover: a single capacitor or inductor is used, -6dB per octave reduction (not very steep).
2nd order crossover: Two components sections are used:one capacitor, one inductor. –12dB/octave reduction (steeper, more effective, very popular).
3rd order: two capacitors + 1 inductor or 2 inductors + 1 capacitor are used:–18dB/octave cutoff.

..and so on, with -12db being one of the most common crossover slopes you’ll find for both car audio crossovers and home audio speakers too.

An octave is just a half or double of an audio frequency. For example, 200Hz is an octave of 100Hz, 400Hz is one octave of 200Hz, then 800Hz, and so on. Equalizers and other audio electronics may use other variations with finer numbers like 1/3 octave, for example.

Crossover frequency formula math:inductive and capacitive reactance explained

Shown here are the basic formulas for simple 1st order crossovers using capacitors and inductors. Capacitors have an impedance (Ohms) value that depends on the frequency just like inductors do.

Capacitors and inductors have a “resistance” called reactance (in Ohms just like resistance) that depends on the frequency. Here are a few basic things to understand:

Capacitive reactance increases as the frequency DECREASES. It’s normally written as “Xc.” Capacitance is marked in units of Farads, with most capacitors being values in the microFarad (uF) range, nanoFarad (nF), or even picoFarad (pF).
Inductive reactance INCREASES as the frequency increases. It’s normally written as “Xl.” Inductance is marked in units of Henries and typically found in units of microHenries (uH) or milliHenries (mH).

Note:“ Micro” units are 1 x 10E-6 decimal places (ex. .000 001) while “nano” represents 1 x 10E-9 decimal places (ex. .000 000 001).

Again, it both cases, it’s just a form of impedance much like how a speaker voice coil that has a certain amount of inductance due to the coil of wire inside does. Both are measured in Ohms (Ω).

However, they complement each other and behave pretty much like the opposite of each other. For example:

Capacitors act like high-pass filters when connected in series and low pass filters in parallel.
Inductors act like low-pass filters when connected in series and high-pass-filters in parallel.

This graph shows an example of a simple high pass capacitor using a 3.98 microFarad capacitor with an 8Ω speaker with a crossover frequency (Fc) of 5kHz. At the Fc value, the impedance is the same as the speaker load (8Ω) which means the speaker power has dropped to 1/2. Further below Fc the impedance grows higher and higher, blocking bass frequencies more and more.

Need help? Don’t be shy! :)

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Thanks!

>Cómo conectar tweeters con un divisor de frecuencias integrado a un amplificador

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