# A Crossover

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Have you ever wondered how the tweeter and wooferhave their responses combined in a speaker system, or what the crossovernetwork is and how it works? If so, thisarticle will shed some light on the least seen and perhaps most undervaluedpart of the speaker system, the crossover network. Unlike the electronic world where the filtershave gone from using tubes, to analog computers to digital signal processors,modern day passive crossovers, a pair offrequency selective filters designed to work together as a single network, arebasically the same as they were about 100 years ago when the speaker businesswas in its infancy. While crossovercomponents and materials and construction have changed, the underlying theoryand practice has not.

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**What does the Crossover Do?**

Like yourown brain, the crossover network is a director.In addition to its primary function, the passive crossover in practiceis expected to do more than simply split the frequency band in two.

1) The crossover allows you to placetwo 8 ohm speakers in parallel, one for the highs and one for the lows, andstill present an 8 ohm, not a 4 ohm load to the amplifier (which is what theamp would see without the network)

2) The crossover allows you to matchtwo drive units of different efficiencies so that the combination of the twodoes not result in a large shelf in the frequency response.

3) The crossover allows you to equalizethe frequency response of either the woofer or tweeter, making the compositeresponse smoother than the unfiltered curves of either driver (woofer ortweeter) would seem to indicate is possible.

Let’s getback to the basic job of the crossover, and see if we can understand how itaccomplishes this by learning a few new but simple concepts. The basic job is to send the high frequencyinformation to the tweeter, and eliminate this same band of high frequenciesfrom the woofer. Next, send the lowfrequency information to the woofer, and eliminate this same band of lowfrequencies from the tweeter. Acrossover is in essence two frequency filter sections working in parallel. A high pass section and a low passsection. These terms are selfexplanatory. The high pass passes highfrequencies, the low pass passes low frequencies. The high pass is placed in series with thetweeter, and the low pass is in series with the woofer. A normal two way crossover will have sixterminals. Two in, and four out. Usually the two sections (high-pass andlow-pass) are in parallel and both sections ONLY work properly when the wooferand tweeter are both attached and operational. To understand how the crossoverdoes its job, we must first understand the concept of impedance.

The threemain passive elements used in all crossovers are resistors, inductors, andcapacitors. Impedance is a measure ofhow much the resistor, capacitor or inductor impedes the flow of electrons atany given frequency. Resistors are thesimplest components, and the easiest to understand. The have a constant resistance to the flow ofelectrons which does not vary with the frequency of the signal. Resistors do not change the phase of the signal, the time relationshipbetween voltage (electrical pressure) and current (flow of electrons). Theyonly consume power and convert it to heat.That is all they do. In a perfectspeaker system there is no need for resistors at all. Of course, while there are no perfectspeakers, all the basic crossover theory's we use start with that premise.

The secondelement we shall consider is a capacitor.The capacitor impedes the flow of electrons through it in a waywhich is NOT independent of frequency. (It would not be technically correct touse the word resistance, but you can certainly think of it as such toconceptualize this). The capacitor has an impedance which is inverselyrelated to frequency. This is to saywhen you double the frequency of a signal applied to the capacitors terminals,its impedes that electrical flow by half as much as it did at the lower frequency. If you halve the frequency applied, thecapacitors impedance (How much it impedes the flow of electrons) isdoubled. This is a very usefulcharacteristic which we use to create networks which are frequency selective(like a crossover).

**The Maths**

Theimpedance of a capacitor is determined by the equation: Z = 1/j(2piF*C)

Where Z =Impedance magnitude,

J = thesquare root of (-1) ('Imaginary' component to describe the phase)

pi = 3.1414etc

C = Valueof Capacitance in Farads; 1 Farad = 1,000,000 ufd

I think thefirst time I read about the square root of (-1) I had an allergicreaction. So, for those of us who arefinding it difficult to comprehend phase for the first time, we can pretend itis not there, and to simplify the discussion we will admit to this equationbeing somewhat incomplete without the “j”, but for the determination of thesteady state and not transient value of the impedance, we are OK.

When acapacitor is put in series (shares one electrical terminal) with a resistor,the capacitor acts as a high pass filter. At some frequency it has the sameimpedance as the resistor, and at a much higher frequency it is like a short,just a piece of wire with little to no resistance (at least in a perfectcapacitor). At very low frequencies theimpedance of the capacitor becomes so high, that essentially nothing can passthrough it. It is this characteristicwhich is used in endless electronic circuits to allow AC signals to passthrough yet completely block DC voltages from one part of the circuit to another.

**Figure 1**

### A Crossover

Lets say wehave a 10 ufd capacitor and put in in series with an 8 ohm resistor. At some frequency, the capacitors impedancemagnitude will be equal to the 8 ohm impedance of the resistor. (Which ofcourse is still 8 ohms at any frequency from DC to daylight.)

Lets do the math.

Z = 8 =1/{(2)*(3.14)*(F)*(10)*(10^{-6})}

The capacitor is MICRO Farads, which is millionths of a Farad, so wemust multiply the 10 by 0.000001( 10^{-6}) to convert microfarads intoFarads, so we can solve for the frequency (F) in Hz. By cross multiplying (multiplying both sidesby F and dividing both sides by 8) we get:

F =1/(2*3.14*8*10*10^{-6)}) = 1990 Hz.

What thistells us is that at 1990 Hz (2 kHz if you are among friends) the impedance ofthe capacitor is equal to that of the resistor, so at this point the power intothe resistor is half what it would be without the capacitor. Put another way, at 1990 Hz, the power intothe resistor is 3 db less and this is your crossover point. Above this frequency the attenuation(reduction in power to the resistor) is less, and as we go lower in frequencythe capacitors impedance grows larger, while the resistor is unchanged, so theattenuation of signal to the resistor increases. At a frequency of 995 Hz, the attenuationwill be 6 db. At 498 Hz, it will be 12db. We call this a first order or 6 dbper octave crossover. That is, in anutshell, how this works. It grows incomplexity when more parts are used, but the basic function is the same. Now if your speaker is a perfectly resistiveload, your 10 ufd series capacitor will be a perfect passive 6 db per octaveHigh Pass (HP) filter. Don't worry,life is not that simple.

The otherimportant element used in a crossover network is the Inductor; sometimes calleda choke, and sometimes called a coil.They are all refer to the same thing.The Inductor is in many ways the inverse of the capacitor. It too changes impedance with frequency, butin a way entirely opposite to the capacitor.The inductors impedance grows LARGER with increasing frequency, notsmaller like the capacitor. Itsimpedance grows larger at the same rate as the capacitor grows smaller, and thesimilarity ends there. So if we replaceour capacitor with an inductor in the first case we have a first order low passfilter. (As shown in figure # 1)

Note thatin higher order networks, second order and above, both inductors and capacitorsare used in the same circuit to provide high-pass (HP) or low-pass (LP)filtering. In the HP filter, capacitorsare put in series with the load while inductors are put in parallel. (A resistor represents the load in figure 1,and the speakers represent the load in figure 2). In the LP filter the opposite is true, theinductors are in series and the capacitors in parallel with the load (orspeaker if you are making a crossover network).Hopefully this makes sense if you keep in mind the direction of theimpedance changes of the parts with increasing or decreasing frequency.

**Figure 2**

### A Crossover Cable

In thenetwork pictured in figure 2, the HP blocking capacitor, C1, increases inimpedance with decreasing frequency, while at the same time the shortinginductor L1, decreases in impedance with decreasing frequencies, hence shortingout the low frequencies while the capacitor is increasingly blocking them. The inverse is true of the LP filter. L2 is blocking highs and passes lows, whileC2 is shorting out the highs and passing the lows. This is how the LP filter blocks highs andpasses lows while the HP filter is performing the inverse function. It is this dual action that allows this kindof network to create twice the blocking action (12 db) per octave of frequencythan the simpler 6 db/octave network. Ifyou did not understand this on the first read, that is OK, you have a lot ofcompany. Think about how the capacitorand inductor change their impedance with frequency, and take another look atthis circuit diagram. If you try, youcan figure out what is going on as the frequencies change.

Back to thesimplest network, the 6 db per octave. If I have an 8 ohm resistor, and a 0.001Henry (1.0 millihenry inductor), at what frequency do I have a 3 db attenuationacross my resistor? Let's calculate thefrequency where the inductor equals 8 ohms.

The valueof the impedance of an inductor is determined by the formula

Z ={(2pi)*(J)*(F)*(L)} where F= Frequencyin Hz, L = Inductance in Henries Z= Impedance in Ohm

Like we didfor the capacitor, we shall ignore the imaginary 'J' term and pushahead.

8 =(2pi)(F)(0.001H) Therefore: F = 8/{(2pi)(0.001)= 1273 Hz

If we wantto set the Low Passfrequency equal to the HighPass frequency of 1990Hz, what inductor do we need? We set F =1990 and then we can solve for L.

L =8/{(2pi)(F)} = 6.4 + 10^{-4} Henries =0.64 millihenries

We have calculated the parts needed for our first crossover network for our 8ohm tweeter and 8 ohm woofer with a crossover frequency of 1990 Hz Network below:

**FIGURE 3**

The narrator of the novel (which is told in verse) is Josh Bell, an 8th-grade boy. He and his twin brother Jordan—or JB—are basketball stars and are best friends on and off the court. Basketball is extremely important to them, and they both want to play professionally someday. Their father, Chuck “Da Man” Bell, was a famous basketball player back in the day, but he no longer plays because, as the boys discover when snooping through his box of memorabilia, he has patellar tendonitis. Dad is always giving them his famous “Basketball Rules” and telling stories of when they were children and could shot free throws by age three. Their mother, Dr. Crystal Bell, is the assistant principal at their school.

When the novel begins, summer is over and the new season has started. The boys are working diligently to win the championship. They pull off some fantastic wins early on.

### A Crossover Car

Their parents are very supportive of the game, but Mom says Dad is *too *supportive because he gets too worked up. This is bad for his hypertension, and she encourages the family to eat healthily and for Dad to see a doctor. He laughs this off and claims he does not trust doctors because his father died after he went to the doctor.

There is a new girl at school with pink Reeboks who also plays basketball, and JB falls hard for her. Josh is a bit disconcerted at his brother’s lack of focus. It is clear JB wants Alexis—or “Miss Sweet Tea,” as Josh calls her because once, after a game, she offered JB some of that drink—to be his girlfriend.

Over time, Josh grows more frustrated with JB pulling away from him. At one game, this all comes to a head when Josh passes the ball extremely hard at JB’s face and almost breaks his nose. He is punished by being suspended from the team, but JB’s refusal to talk to him or accept his apology is almost worse.

### A Crossover Jeep

While Josh is off the team and trying to make amends with JB, Dad displays more evidence of being sick. He gets a nosebleed while yelling at the referee at one of the games, and he throws up at home. Mom insists he go to the doctor and he finally agrees. However, he also decides that he has to get back on the court, so he accepts a coaching position at a local college.

Josh makes small inroads with JB after writing him a letter and trying to be patient with him. He is still a little bummed about both JB and now their friend Vondie having girlfriends as well as his not being on the team. His hope is to get back on for the playoffs. Coach comes to him and tells him he has to make things right with JB and get on the court.

### A Crossover In Basketball

One day, while everyone is at the rec center playing hoops, Dad clutches his chest and falls to the floor. Alexis calls 911; JB runs to get water, but Dad is out cold.

Dad falls into a coma because of a myocardial infarction. He might be able to hear them and the doctor thinks he will be fine, but JB is sobbing and Mom is shocked. When Josh talks to his dad privately, he bitterly wonders why his Dad jumped ship; he had thought his dad was “Da Man.”

Dad finally wakes up; he and Josh are able to talk to each other honestly, but it is very hard for him. He still feels far away from JB and does not like that Dad is living in the hospital. However, he is able to play in the championship game.

Unfortunately, on the way to the game, Mom gets a call and exclaims that Dad had another heart attack and she needs to go to the hospital. JB and Josh are not sure what to do at first, but JB leaps on his bike to follow Mom to the hospital. Josh decides to go along with Vondie and his dad to the game; he feels his father telling him to do so.

### Toyota Crossover

At the same time as Josh leads his team to a glorious victory, Dad passes away. Josh does not know how to deal with this. There is a funeral and during the reception at the house; Alexis calls and Josh answers. She is very kind and says she is sorry for their loss. She invites him to go with her, JB, her dad, and her sister to see Duke play. He is happy and accepts.

Josh and JB finally reconcile while out shooting free throws.