Kaj je frekvenca križanja Fc, nakloni križanja in zakaj so pomembni?

Crossoverji so izredno pomembno za sisteme zvočnikov in veliko razlog, da lahko dobimo kakovost zvoka, ki nam je všeč.

Po drugi strani pa so lahko stvari, kot so križna frekvenca (Fc), strmine (db na oktavo in kako vse to deluje), nekoliko zapletene, če ne razumete, kako vse deluje. Rad bi pomagal!

V tem članku bom pojasnil:

Kaj je križna frekvenca Fc in zakaj je pomembna
Kaj je križni naklon in na katerega boste najpogostejši naleteli
Kako izračunati dB crossover padec za frekvence, vključno s Fc
Vloga induktorjev in kondenzatorjev (in "reaktanca" za Fc)

Razložena frekvenca kretnice Fc in naklon kretnice

Ta diagram prikazuje primere 3 glavnih vrst filtrov, ki se uporabljajo v kretnicah. Prikazani so tudi najpogostejši križni nakloni kar je "strmost" filtra (kako učinkovito blokirajo frekvence, ki presegajo križno frekvenco).

Križna frekvenca, običajno zapisana kot Fc , je zvočna frekvenčna točka v Hertzih (Hz), pri kateri kretnica oddaja -3dB (1/2) izhodne moči zvočniku. Fc je označevalna točka, po kateri se zvočne frekvence močno zmanjšajo, da preprečijo, da bi dosegle zvočnik.

Čez točko kretniške frekvence (Fc) bo izhodna moč kretnice vedno bolj padala, z vse manjšo močjo, poslano zvočniku. Kot se zgodi, je pri Fc izhodna napetost za obremenitev (zvočnik) 0,707 x vhodna napetost, kar pomeni, da lahko izračunate padec decibelov glede na izhodno napetost v primerjavi z vhodno napetostjo.

Zakaj so križne frekvence pomembne

Pri načrtovanju kretnic za zvočnike frekvenca kretnic (fc ) se uporablja kot nekakšna črta, ki označuje, kje želimo začeti blokirati zvočne frekvence, poslane zvočniku. Običajno temelji na specifikacijah proizvajalca zvočnikov, ki navajajo zvočne frekvence, ki jih zvočnik lahko proizvede z dobrim odzivom zvoka in brez popačenj.

Na primer, visokotonci ne morejo predvajati nizkih tonov iz glasbe in jih lahko celo poškodujejo. Ker to vemo, želimo izbrati dovolj visoko frekvenco križanja, da blokiramo nizke tone, poslane visokotoncem, da preprečimo popačenje ali poškodbe. (Običajno imajo visokotonci prehodno frekvenco v tisočih Hertzih [napisano kot KiloHertz ali na kratko kHz], na primer 3,5 kHz, 5 kHz in tako naprej – no nad obsegom nizkih in srednjih zvokov v glasbi).

Križna frekvenca se včasih imenuje tudi kotna frekvenca ali mejna frekvenca saj razmišljamo v smislu, kako so zvoki po tej točki »odrezani«.

Križna frekvenca Fc je zelo pomembno za oblikovanje križancev

Križnice za zvočnike (imenovane tudi »pasivne«, ker za delovanje ne uporabljajo električne energije) uporabljajo kondenzatorje in induktorje, ki so izbrani glede na razpoložljive vrednosti delov in njihovo ceno. Križanje je zasnovano na podlagi začetne frekvence Fc in po potrebi prilagojeno za cilje načrtovanja.

Uporaba križne frekvence Fc kot izhodiščne točke omogoča načrtovalcem zvočniškega sistema, da izračunajo potrebne vrednosti delov (kondenzatorjev in induktorjev) glede na impedanco zvočnikov. Ker ne morete kupiti delov v poljubni vrednosti, je Fc, ki ga dobimo na podlagi tega, kar želimo, dobro izhodišče, s katerim lahko delamo in se po potrebi prilagodimo za delo z deli glede na razpoložljivost, ceno in druge dejavnike.

Operacijski ojačevalniki, imenovani tudi operacijski ojačevalniki, so najpomembnejši gradnik elektronskih kretnic. Elektronske kretnice opravljajo popolnoma enako nalogo (in imajo enako osnovno obnašanje) kot pasivne kretnice (zvočniki). Razlika je v tem, da delujejo na signalih nizke ravni pred so ojačeni, medtem ko pasivne kretnice delujejo z ojačenimi signali po izhod ojačevalnika.

OPOMBA: Medtem ko v tem članku opisujem, kako delujejo pasivne (neelektronske, nenapajane) kretnice in Fc, so načela popolnoma enaka za elektronske filtre.

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.

Opomba: 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. Na primer:

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.