Quick review: a passive EQ uses resistors, capacitors and inductors to change the frequency response of a signal—a filter. However, doing this causes an overall loss of gain, so after that loss caused by the passive filter, there’s an amplifier to bring things back up in level.
What would be an Active EQ? Well, it would be a circuit that doesn’t require the boost of gain after the filter, and instead there's some sort of amplification built into the filter.
First, we need to know what an amplifier is.
An amplifier takes a small signal and makes it bigger. There’s a bunch of cars on the highway. You’re driving on another road. When you speed up or slow down or wiggle your car, ALL the cars on the highway do the same thing as your car. My one car isn’t powering the other cars, but it is controlling the other cars—modulating them. If I “connect” my car to a larger highway I can then control more cars.
How does my car control the other cars on the highway? The road my car is on changes the properties of the highway the other cars are on. If I drive fast, my road makes the highway faster, if I go right, my road bends right and makes the highway bend right.
Let’s call the road my car is on the Control Road. And let’s call the highway The Power Road. Control Road modulates and changes the Power Road.
If I route the car through an obstacle course and keep changing the way the car is facing and turning, speeding up and slowing down, etc, and I put that car on the Control Road, the cars on the Power Road will do the same things my car is doing.
That obstacle course is a filter. If I run a signal through a filter and change it, then put that on the Control Road, then the Power Road behaves in accordance with the physics of the filter.
The roads are paths for cars to follow. The cars are signals. So now we have a Signal coming out of the filter and going into the control, which varies the power.
So, the basic construction of an Amplifier is that there’s going to be a path that we can run a lot of cars down—energy. There’s got to be a way to get on that path—we’ll call it the input, and a way to get off of it—we’ll call that the output. And there’s a place to stick a control signal in.
The control signal modulates the output of the amplifier. The control signal doesn’t necessarily directly interact with the power, or the output; what it does is change the properties of the amplifier, which varies the output. Does that make sense to you?
All amplifiers are going to work this way: a smaller signal controls a larger one. What will be different about amplifiers is the technology used to get a bunch of power in a situation where it can be varied (modulated) by a control signal.
In audio, the two technologies most used are Vacuum Tubes and Transistors. They both do the same thing in terms of the end result, but they go about doing it a bit differently.
Vacuum Tubes
These are really easy to understand. Inside a tube is a Cathode and a Plate. These aren’t physically touching each other, but what happens is electrons form on the cathode and then jump across to the plate, forming an electric field and a magnetic field. Call it an EM field. In between the cathode and the plate, we stick something called a Grid. The grid interferes with the electric field. The control signal feeds to the grid; the grid interferes with the electric field such that that electric field now “looks” like the control signal, only it’s a lot more powerful.
How does the grid interfere?
Remember, when we have a current, we generate an electric field—wires transmit using an electric field. A grid is basically a bunch of wires, and when we put signal through it, we get an EM field. The EM fields passing from the cathode to the plate interacts with the EM fields around the grid. Depending on how things interact, the energy flowing from the cathode to the plate varies.
To get back to cars, imagine the grid is a network of stoplights and cops, all dictating the flow of traffic.
Tubes, however, don't really work well in active EQ situations. They're heavy, hot, unreliable, and require a lot of calibrating and tweaking, as well as being noisy. But understanding how tubes work will make understanding how transistors work easier when we get to that next week.
Plug-in Errata
Our Amplified Instrument Processor, the AIP, has a four-band parametric EQ in it. It's based on a Siemens tube equalizer from the 1950s, the RZ062.
Like virtually all tube equalizers, the RZ062 was passive, using inductors and capacitors to create filters and then boosting their outputs back up, similar to how a Pultec works. But the EQ on the AIP is fully parametric. What's going on there?
Dan figured out the math to make an RZ062, and then he experimented and rewrote the equations to make a digital version of what would be incredibly difficult to do: make a continuously adjustable parametric EQ out of capacitors and inductors. To give you an example of how difficult this would be: a two-band passive equalizer would require a specific inductor and capacitor set for each band. How many different inductor/capacitor sets would be needed to make an EQ sweeping from 20Hz to 20kHz? 19,980? Something insane like that?
The AIP's EQ has the frequency response curves of an RZ062, and the saturation characteristics of it, without requiring four air-conditioned barns each stuffed with thousands of components for each band.
The AIP EQ, by the way, is gorgeous. It has about the sweetest high-end band of any EQ we've worked with.
Quick question, and feel free to write me, would homework help you to better understand this stuff?
Cut-Off Frequencies
We can make a circuit that lets higher frequencies through using a capacitor. The result is a high-pass shelf—an EQ curve where the low end drops off and the highs stay level.
By adjusting the value of the capacitor and the other elements in the circuit, we can control the frequency where the low end begins to fall away. We call this the cut-off frequency—the point where the shelf starts dipping.
We can also make a circuit that lets lower frequencies through using an inductor. This produces a low-pass shelf, a mirror image of the capacitor version. The lows stay level, and the highs roll off.
And by adjusting the inductor and the components around it, we control the frequency where the high end begins to fall away. This is also called the cut-off frequency—the point where that upper shelf starts dipping.
If we combine those two circuits together, we get one that shelves away the lows and shelves away the highs, leaving only the frequencies in the middle. That is called a band-pass filter.
The distance between the high-pass cut-off frequency (where the lows get removed) and the low-pass cut-off frequency (where the highs get removed) is called the bandwidth. The wider the distance between those two cutoffs, the wider the band of frequencies that passes through. The closer they are, the narrower the band.
A band-pass filter doesn’t really have one cutoff frequency — it has two. There’s a cutoff at the low end, where the high-pass section starts allowing frequencies through, and a cutoff at the high end, where the low-pass section starts blocking them.
The frequency right in the middle of those two cutoffs is the center frequency—that’s the one the band-pass filter passes the strongest.
All of these circuits above work by getting rid of frequencies. No matter which one we use, the audio signal feeding in loses power. Using these circuits by themselves, we can cut the bass, cut the highs, or cut both the bass and the highs, leaving only the middle.
Boosting with a Passive EQ
Now… if we want to make the highs louder — like a high-shelf boost — we can’t do it directly with passive parts, because passive circuits can only cut. So what we do instead is:
Step 1: Use a high-pass shelf to cut the bass, leaving the highs less affected.
Step 2: Then amplify everything that comes out of that filter.
The result is that the highs appear boosted, even though all we did was cut the lows first and then re-amplify the entire signal. That’s how passive EQ “boost” works.
To make the lows louder — a low-shelf boost — we do the same thing but at the opposite end of the spectrum:
Step 1: Use a low-pass shelf to cut the highs, leaving the lows less affected.
Step 2: Then amplify everything that comes out of that filter.
To make an area in the midrange louder, we combine the two shelves:
Step 1: Use a high-pass shelf to cut the bass, leaving the highs less affected.
Step 2: Use a low-pass shelf to cut the highs, leaving the lows less affected.
Step 3: Then amplify everything that comes out of that filter.
What’s left — the band in the middle — ends up louder after the make-up gain. That’s a passive midrange boost, better known perhaps as a Peak Boost.
We’ve figured out how to make EQ circuits that reduce the power in areas of the frequency spectrum, and we’ve figured out how to make circuits that raise the power in areas of the frequency spectrum.
What if we want to cut some frequencies and boost others at the same time?
Easy: we just combine all of these individual circuits into one larger network.
Everything we want to cut gets its own part of the circuit.
Everything we want to boost gets its own part of the circuit.
In other words, cutting the low end and boosting the low end aren’t two aspects of one function — they’re two completely separate circuits, each designed to shape the signal in its own way. The EQ lets us use them together at the same time.
The reality of these different boosting and cutting circuits is that they aren’t precise opposites of each other. A passive low-shelf cut doesn’t perfectly mirror a passive low-shelf boost. The shapes of the curves depend on the actual circuit design, and they can be very different from one another.
The Pultec Low-End Trick
Most of you know the classic Pultec EQP-1. It’s a passive EQ, built on the principles we’ve been talking about — though in practice, the real circuit is a lot more intricate than our simplified explanations. It can boost and cut at various frequencies, but remember: boosting and cutting live in separate parts of the circuit, so their curves don’t line up like mirror images.
That’s the whole basis for the famous “Pultec Low-End Trick.”
An engineer dials in a low-frequency cut with one knob, and a low-frequency boost with another. Because the cut curve and the boost curve are shaped differently, they don’t just cancel each other out. They overlap and interact. The cut provides one shape, the boost a different shape. The resulting curve is a wide shelf boost with a dip above it. How this sounds is a huge amount of lows with a chunk taken out of the low mids — this is a very common sort of EQ move to make.
The Pultec has the sound it has not only because of the shapes of its EQ curves, but because there are amplifiers in there providing makeup gain. But it’s even crazier than that.
When we think about a circuit — whether it’s the circuit in a Pultec, a compressor, or an entire console — we tend to picture it like a flowchart:
Input → low-shelf section → high-shelf section → makeup gain amplifier → output
For a compressor we might picture:
Input → detector circuit → gain-reduction circuit → makeup gain amplifier.
This is a convenient way for us to understand signal flow. It’s how we visualize what goes where and in what order.
But that isn’t what’s actually happening physically.
Electricity in a circuit moves at just under the speed of light. Which means that, for all practical purposes, the signal is everywhere in the circuit at once. It’s arriving at the input, being cut, boosted, amplified, filtered, and showing up at the output simultaneously.
And because of this, every part of the circuit affects every other part of the circuit — all the time.
The boost affects the cut affects the makeup gain amplifier affects the input affects the output affects the boost ad infinitum.
Everything pushes and pulls on everything else, all at once.
And because impedance changes with frequency, this interaction is slightly different for every frequency that’s in the circuit.
The overall tone, personality or “sound” of a piece of gear is the total result of all of these interactions happening simultaneously. That’s why no two EQs sound the same, even if they technically perform the same EQ moves on paper, and why we like how some EQs sound for certain tasks in the studio, why one might sound warm, another might sound clinical.
People speak of analog gear as sounding “alive.” This is why. Because the entire thing is reacting to itself at just below the speed of light. If you add microphones in, or an amplifier and a speaker, they become part of the whole, interconnected at almost light speed, the whole thing “breathing."
But What About Plug-ins
Let’s take this into the digital realm. Let’s make an EQ plugin. There are two ways to do this. Simple way first:
We can have chunks of program — a little routine that does a shelving EQ, another that does a peaking boost, another that lowers gain, another that adds distortion, etc. Think of these as Lego blocks.
We build these Lego blocks into a structure that does equalization, compression, saturation, whatever we want. We can swap in different blocks with different characteristics, and we can even fine-tune those individual blocks. We can absolutely get something that sounds very good, and it might even get close to the sound of a particular analog unit.
But what it can’t do is interact with itself the way a real analog circuit does.
In our Lego-style plugin, audio flows through one block, then the next, then the next. The output of Block A feeds Block B, but Block B doesn’t naturally “push back” or interact with Block A. The output can’t affect the EQ curve, the distortion, or the dynamics unless we explicitly program that to happen.
In an analog piece of gear, that kind of interaction happens as a consequence of the circuit’s existence. Everything is talking to everything else all the time, because it’s all one continuous electrical system, not a row of separated Lego blocks.
Now, there’s the complex way to make a plugin.
Early on, we looked at some formulas for Current, Voltage, Resistance, and Impedance. We didn’t get heavily into the math of things, but every section of a circuit can be described by a math equation. Capacitors, inductors, resistors, amplifiers—they’re all describable by an equation. In fact, the entire piece of equipment is a bunch of equations which become part of a giant equation that is the math of the circuit and describes what the circuit is doing at any given moment.
To digitally model a piece of analog equipment, one has to figure out the math of all the different sections of the circuit and then combine them into one massive circuit/equation and then have the computer solve all those equations at the same time. If you do it this way, then one section of the equation can affect another section of the equation. Which means the digital circuit is responding to itself in the way an analog circuit responds to itself.
How often does the equation have to be solved? Well, at a sample rate of 48kHz, it has to be solved at 48,000 times a second. How accurate is the solution to the equation? Whatever the bit rate is — 24 bit, 32 bit float, whatever it might be.
Obviously, doing things this way, which is called Component Level Modeling, typically requires more out of the computer system than Lego style.
Which one, Lego Style or Component Level Modeling, sounds more alive and analog? Which one requires more work?
Here’s a surprise that shouldn’t be a surprise: Korneff Audio’s plugins are Component Level Modeled. Yes, Dan sits there, behind a computer, and figures out the math. These days he has a standing desk, so he also stands there and figures out the math.
Once we figure out the math, we get our hands on the actual hardware thing and compare it to the math. In the case of our Shure Level-Loc, first we did the math, then flew to Chicago to work with Shure and Tchad Blake to fine tune the math so it sounded even more like the actual hardware. In fact, we mathematically modeled three different hardware units, all of which are available on our Shure Level-Loc plugin.
Not every plug-in developer does the math. We do.
We’re actually working on a bunch of mathy stuff right now, and you’ll all get to see it as a new plug-in soon.
Last week, we ran into electric fields. When electrons "push" a lot into the plate of a capacitor, an electric field is formed to store that energy, and then when the capacitor drains, that energy feeds back through the electrons and into the circuit.
These "pushes" we've been talking about... we've been thinking of them as a unit of energy. We've developed a mental picture of electrons passing a "push" along from one electron to the next. What that push really is, is an electric field pushing its way through the material.
In fact, the push doesn’t travel down the wire as electrons moving. The push travels as a wave in the electric field. The electrons barely move. The field is what moves.
It gets more bizarre: when the push travels through a wire, the energy isn’t even inside the wire. It’s not in the copper. It’s actually in the electric field around the wire and its insulation. The wire just guides the field, the way a track guides a train, but the energy rides outside the metal.
SO... when we have a circuit, we're moving and manipulating electric fields that travel around the circuit but kind of outside of it. It's hard to fathom. You can think of it as a push, or a message being sent from electron to electron, or as an electric field. Whatever helps you to see it in your head.
Now, when the electrons move the field along, they physically move a tiny tiny bit. They do this comparatively slowly—much slower than the speed at which the electric field travels. So, the electrons themselves aren't racing through the circuit. They're shuffling a little bit as they pass the field along.
But, when they shuffle, they create a tiny magnetic field. In fact, whenever you have an electric field passing through, causing electron shuffle, a magnetic field is generated. It is typically very weak to the point it's inconsequential.
However, if you get a lot of electrons together, the magnetic field increases in power. How do you get a lot of electrons moving together? You use thicker materials—fatter wires—and then you wrap those wires into coils or shapes so that all those tiny magnetic fields add up. You cram as many electrons as possible into a given space and get them all wiggling in the same direction.
That's an inductor, isn't it? It's also, with some modifications, a transformer, or, with a lot of modifications, analog tape!
Inductors
We already know that an inductor is a coil of wire. And we already know that when we push on a bunch of electrons and keep switching the direction of the current — which is what alternating current does, and an audio signal is alternating current — the electrons find it difficult to switch from pushing in one direction to pushing in the other. That difficulty impedes the signal from passing through easily.
Let’s rephrase that.
When the electric field pushes into an inductor, it moves the electrons a tiny bit, and they generate a magnetic field. The stronger the electric field is — the bigger the push — the stronger the magnetic field becomes.
Now, electrons don’t have mass inertia in any meaningful way inside a conductor. They aren’t like cars trying to accelerate or slow down. Their actual drift speed, or physical movement, is incredibly slow. But the current — the organized movement of charge — has something very much like inertia. When you get a current going, it takes energy to change it. That “current inertia” lives in the magnetic field.
So when the electric field becomes less powerful, the electrons don’t instantly stop responding. The magnetic field collapses, and as it does, it pushes energy back into the electrons and keeps the current flowing a little longer. That’s why we say a magnetic field “stores energy.”
Now, when the electric field changes direction — because it's an alternating current — the electrons keep trying to push the way they were pushing, powered by the collapsing magnetic field. Only when that magnetic field is fully drained can they finally start pushing in the opposite direction. As they begin to move in the new direction, they generate a new magnetic field, opposite the old one. Every time the current tries to reverse direction, the magnetic field has to collapse first before the electrons can switch and build a new field.
All of this happens extremely fast — fast enough that you don’t see it happening — but it is still not as fast as the electric field itself travels. That lag has important consequences that we’ll cover later.
Back to our circuit with an inductor in it...
The faster the current tries to change direction, the less energy gets stored in the magnetic field. In other words:
High frequencies store less magnetic energy.
Low frequencies store more magnetic energy.
If there is a lot of magnetic energy stored up, that energy all has to drain before the electrons can push in a different direction. If less energy is stored, it's easier for the electrons to push in a different direction.
The result is that the inductor impedes low frequencies — it makes it harder for them to get around the circuit. Low frequencies spend too much time building big magnetic fields, and those magnetic fields push back hard.
At high frequencies, the inductor doesn't store much energy so it has less energy to push back, so high frequencies slip through the inductor and travel around the circuit more easily.
Do we need to recap all this?
Charge moves about a circuit as an electric field.
Capacitors store energy as an electric field, and they roll off the highs.
Inductors store energy as a magnetic field, and they roll off the lows.
Put them together and you get a bandpass filter.
Next week, we’ll talk about passive EQs.
The basis of an audio circuit is how difficult or how easy it is for a signal at a given frequency to travel around the circuit. If we make it easy for a frequency to get around the circuit, that frequency will have more power. If we make it more difficult for that frequency, it will have less power. It's all about how much we impede the signal.
Resistance always fights the flow of signal through the circuit, regardless of frequency, and it takes that energy and turns it into heat. But if we want to shape the frequency response of signals, we need to be able to impede the signal differently at different frequencies. We need devices that act like frequency-dependent resistors. Capacitors and inductors help us to do this, as well as some other components we'll discuss later.
Our current model/metaphor for things is electron guys giving each other a push. A bunch of electrons are lined up, passing that push from one to the other, and that is like a piece of wire — a conductor. How strong that push is, we call that Voltage. How many guys are pushing, we call that Current.
So, the “push” ...what is that exactly?
Gah! That requires quantum mechanics. Let's not go there today. Our brains will explode.
Let’s think of the push as a little unit of energy. The push is exactly what it sounds like: electrons naturally repel each other using that energy. Every electron wants other electrons to get out of its personal space. The strength of that repulsion is voltage. And that voltage travels down a wire as one electron pushes the next guy, who pushes the next guy, and so on.
In a capacitor, the plate is full of electrons — or, in our metaphor, a room full of electron guys — separated from another room (the other plate) by a wall (the dielectric). The electrons on one plate get pushed, and they try to shove that push straight into the next plate. But they can’t, because the dielectric blocks them. So instead, that push energy gets stored in the electric field between the plates.
Think of this field as an invisible closet where the electrons toss their leftover push. They can’t pass it through the wall, so they stash it in the space between the plates.
As more electrons shove on that plate, the electric field gets stronger. And the stronger the field gets, the more it resists being stuffed with more energy. It pushes back.
Now, if the electrons stop pushing into the capacitor, the field doesn’t just sit there. It starts returning the energy stored in the electric field back to the electrons on the plate — letting the push flow back out into the circuit.
There’s a kind of inertia to this give-and-take. Not literal mass inertia, but energy-storage inertia: the electric field resists changes in how much energy is in it. It resists being filled too quickly, and it resists being emptied too quickly.
The result is a natural “in-and-out” action, like pushing down and releasing a spring:
- when you push energy into a capacitor, it pushes back;
- when you stop pushing, it pushes energy out.
Because capacitors want a consistency to the amount of energy in their electric field, they tend to want the voltage to be consistent — they want a regularity to the pushes they store.
So, capacitors resist sudden changes in voltage, the same way a spring smushes and pushes.
Now, this isn’t resistance like we talked about with a resistor. A resistor simply dissipates energy into heat. A capacitor reacts to the energy it gets. It doesn’t waste the energy — it stores it in an electric field, or releases it from that field, in an effort to keep the voltage smooth and consistent.
We call this Capacitive Reactance.
A capacitor smushes to absorb the push, then it pushes back.
Now, if you push on a spring slowly, you can store a lot of energy in it. Storing a lot of energy means there is a lot of energy with which to react. Storing a lot of energy in a capacitor means it has high capacitive reactance.
But if you push and release a spring really quickly, more like wiggling it, you don’t have much time to store much energy. Likewise, with a capacitor, if the frequency is high, there isn’t enough time for the field to store much energy, so capacitive reactance goes down.
I'll repeat this differently in an effort to cement this into your brain because this is important.
As frequency goes down, capacitive reactance goes up — because the capacitor has more time to store more energy in the field and thus react with more energy — more forcefully, pushing back harder, storing more and releasing more. This is disruptive to the low frequencies. It gets in the way of low frequencies traveling around the circuit, so their energy goes down.
If the capacitor isn’t storing and releasing a lot of energy, the energy in the circuit flows more easily. The result is that as frequency goes up, the capacitor makes the circuit more efficient at passing the signal.
By carefully choosing capacitors, we can impede signals wherever we want in the frequency spectrum. Well, we need more than just capacitors, but I think you get the idea. We can have different impedances at different frequencies — remember at the beginning I wrote that we wanted a frequency-dependent resistor? We don't have that, but we come close: we have a frequency reactive capacitor, and for audio purposes, that works out really well.
Next week we have to dip more into Inductors.
Our current analogy for how things work is we have a bunch of guys running around in the circuit, electron guys. They can run down hallways—wires—we can narrow the hallway or put junk in it, which gets in the way and makes it harder for them to pass through a certain point in the circuit, and we call that a Resistor. We can add a Capacitor, which is like a room into which the guys run, get stuck, and then run out while the room on the other side of a partition fills up. We have an Inductor, which is a very crowded hallway that the electron guys have trouble getting through because it's full of other electron guys—kind of the opposite of a capacitor.
Do you notice that all of these components get in the way and impede the travel of the electron guys? Keep that in mind, and that word "impede."
We have to amend our analogy a bit. Guys running around makes it seem like the electrons are whipping up and down empty hallways. Not really. It's more like they're packed together shoulder-to-shoulder, and they give each other a push or a poke. They basically stay still, but they push each other. One guy pushes the next guy that pushes the next. That push travels through the electrons at just below the speed of light. That push is like a message or a signal. The electrons are all basically playing "telephone," transmitting a signal around the circuit.
The push they give each other can be weak, like a little love tap, or strong, like a punch in the head. We can think of this as voltage. The potential strength of the signal (push) is Voltage.
Picture that the power source sends out the initial push, and let's say it is strong. Now, it might go through the electrons and keep its strength, but things could also happen to weaken that push, or perhaps add power to that push. The power source might send a low voltage push, too. There are all sorts of potential voltages that affect the force of the electrons pushing each other.
But there is something else to consider. Voltage is how powerful a push could be, but it also affects the number of guys involved in the pushing. High voltage tends to get a lot of guys pushing. Lower voltages tend to get less guys pushing. But we can also have a lot of guys pushing, or very few.
The amount of guys pushing is called Current. Do you see how current and voltage are different things, but very related?
What electrical circuits basically do is dick around with the force of the push and the number of guys pushing... or, said more maturely, electric circuits manipulate the signal by changing voltage and current.
So, the next question is, how do they change voltage and current?
A big changer of current and voltage is resistance.
Resistance does two things: it limits how many guys can push, and it makes it harder for them to push. So when the signal runs into resistance, the push gets weaker and fewer guys are pushing.
Long wires, like long audio cables running from amplifiers to speakers, offer more and more resistance as the wire gets longer. The push loses energy. Where does that energy go? It turns into heat.
Some materials are better at passing the push along, and they might even have more electrons available to push. Copper is good at this, gold even better. Wood sucks. Things that transmit the push along well are good Conductors. Things that don't transmit the push at all are called Insulators.
Size also makes a difference. Thick, good conductors—like the cables you see on telephone poles—have lots of guys transmitting a strong push. But try to squeeze that strong push through something thin that adds a lot of resistance, and you'll turn that signal into heat—this is how a heater works. And lightbulbs.
So, now we have Voltage, Current, and Resistance. That's the big three. And they all affect each other according to a formula called Ohm's Law. Uh oh! MATH!!!
V means Voltage (the strength of the push). I means Current (the number of guys pushing). R means Resistance (what gets in the way of the guys pushing)
SO...
The push is equal to how many guys are pushing, times what gets in the way of the guys pushing.
V = I x R
And we can flip this formula around:
The number of guys pushing equals how strong the push is, divided by how hard it is to push.
I = V/R
How hard it is to push equals how strong the push is, divided by how many guys are pushing.
R = V/I
NOW... all of this works just fine if the pushes are happening in one direction—if all the electron guys are facing in the same direction. It's easy. You just tap or punch the guy in front of you on the back, and then he does that to the guy in front of him, etc. This works fine with Direct Current, or DC. DC is when the push goes in one direction.
But audio signals switch direction. They're AC, Alternating Current. Current is the amount of guys running around. Direct means they all go in one direction. Alternating means they switch direction.
So, now these guys basically have to stop pushing in one direction, turn and push in the other direction, and then turn and push in the opposite direction, and if we want to hear that, they have to do it between 20 and 20.000 times a second. It's like an insane dance that keeps varying in terms of strength (the push, or Voltage), the number of dancers (Current), how hard it is to push (Resistance) and now, dancers getting confused and mixed up, and not knowing which way to push.
Imagine what a mess this could be: you're dancing along and suddenly everyone in the room turns in a new direction and you do too, but some guys can't turn fast enough before they have to turn back, because as frequency goes up it makes the changes of direction happen faster, and you end up slamming into that guy and you're both pushing on each other's face AND... you're also dancing in something that doesn't conduct well, like peanut butter, so it is harder to move, and maybe there's less room for dancers and less dancers available, or more.
Do you see how that confusion caused by time, which is frequency, adds to the difficulty?
Remember the word "impede" we used at the start? Do you see how Resistance and these timing issues sort of blend together? That's called Impedance. It's resistance but it takes into account the issues caused by Alternating Current and Frequency.
Now we have a different formula, still Ohm's law.
V = I x Z
Z is impedance.
It's like resistance but it's affected by frequency.
That's more than enough for now. I hope you're seeing that this stuff isn't as hard to understand as you might have thought.
We're talking about EQ circuits for the next few weeks—call this audio tech talk for beginners.
We'll start with passive EQs and then we'll move to active and then digital emulations, but we need to start before all of that with an understanding of Capacitors and Inductors.
Let’s start with a circuit.
We have electrons flowing from a power source through a wire. We stick a resistor in the circuit.
Now, when the electrons come to it, it gets in their way a bit—picture a bunch of guys running down a hall who come to a doorway and have to squeeze through. The resistor is the doorway. It’s like the hallway gets narrower.
Now let’s stick a capacitor in the circuit.
A capacitor is like a room. The guys running down the hallway pile into the room—but there’s a wall across the middle with another door on the far side. They can’t cross that wall. They can only go back out the way they came.
Physically, a capacitor is two metal plates separated by a dielectric—an insulator. The “room” the electron guys get stuck in is one plate or the other, and the wall is the dielectric.
If the electrons in the circuit always move in one direction (DC, or Direct Current), they fill up one side of the “room” and have nowhere to go. The current stops—everything backs up. Electron constipation. That’s different from the resistor, which just makes the hallway narrower but still lets everyone through.
But audio signals are AC—Alternating Current. They flow one direction through the circuit and then the other. Because an audio waveform is a series of peaks and valleys—or as the English in the early 1960s might say, peaks and troughs—ups and downs.
How often does the current alternate? Well, at 60 Hz, it changes direction 60 times a second. Which means the electron guys run into one room, then leave and run into the other room 60 times in one second. At 2850 Hz, they’re in-out, in-out 2850 times per second.
So, a capacitor is a room with a divider, and a bunch of guys fill up one side of the room, leave, and then fill up the other side, each side entering and exiting through the only door they have access to. Electrically, the electrons accumulate on one plate, discharge, then fill up the other plate.
So, you’re wondering why this is important—or handy...
Back to our electron guys. We stuff them in the room, the room fills up, the flow of electron guys stops. Then we reverse the flow, the guys have to leave the room, and the other side fills up, which stops the flow of guys in the opposite direction. If the frequency is low, the guys have more time to stuff themselves into the room, the room gets more filled up. It’s like there’s a guard at the door saying, “Get in, plenty of room, keep coming, get in, get in…” And then when the flow reverses, the guard says, “Ok, get out, come on, keep moving, get out, get out…”
If we slow things down—fill up the room fully, empty it, then refill it fully from the other side—we gum up the works a bit. Things back up. There's electrons waiting around while the room fills up. The guys (electrons) can’t flow easily. So, there’s less movement, less “power” in the circuit.
But if the frequency is higher, the guard says, “Get in, get in—oh wait, we’re changing directions—get out, get out!” The room doesn’t fill up as much, which means it can empty faster. Not as many electrons collect on the plate, so there aren’t as many that have to leave the plate. The result is more movement in the circuit, which means more power.
So... as the frequency goes up, the capacitor makes it easier for electrons to flow through the circuit. As the frequency goes down, the capacitor makes it harder for electrons to move. When it’s harder for electrons to move, the power goes down—which means the low frequencies have less power. They roll off.
You’ve just made a high-pass filter.
Now we need a low-pass filter.
How do we do that?
Well, if a capacitor gives us a high-pass, then we need something like a backwards capacitor to make a low-pass. Makes sense, right?
What the hell is a backwards capacitor?
Well... if a capacitor is a room with a divider, and a bunch of guys fill up one side of the room, then the other, it seems to me that a backwards capacitor would be like a huge hallway that is always full of guys. No one leaving. No emptiness. Tons of guys.
So, if our electrons are running around the circuit and suddenly they get into a huge hallway packed with other electrons, that screws them up. How do they get through? “Excuse me, pardon me, pardon me, excuse me, sorry, I didn’t mean to touch your butt, pardon me…”
This gums up the works differently, doesn’t it? It’s kind of the same thing as a capacitor—we’re still messing with the flow of electrons—but in a different way.
Let’s bring frequency into this.
First of all, let’s give this hallway stuffed with extra guys a name. We’ll call it an inductor.
We have our running electron guys, and let’s say they’re changing directions at 100 Hz—one hundred times a second. That gives them 1/100 of a second to get through the inductor, which is a room packed with guys. So there’s time for them to go, “Excuse me, pardon me, pardon, whoops, sorry, pardon me…” But if we increase the frequency, we start giving them less time to get through the room, so it’s more like, “Pardon me, excuse—oh, I have to go the other way—excuse me, you again, pardon—oh! I have to go the other way, damn… me again, sorry, sorry…”
Do you see that as the frequency goes up, the electron guys kind of get caught in the inductor? At low frequencies, the electrons have time to get in and out, but as frequency goes up, they have less, and they get stuck in a swamp of other guys. When we gum up the works and inhibit movement, we decrease the power. Now we're gumming up the works at higher frequencies. The high frequencies have less power. We're rolling off the high frequencies. We have a low-pass filter.
Inductors pass the lows and roll off the highs.
What is an inductor physically like? Since we need space for lots of electrons, we need something big. Like a fatass chunk of wire. Like a coil of wire. And when we coil the wire, it’s sort of like taking the hallway and bending it a bunch, which makes it even harder for the electron guys to get through. Picture you’re at a long, bendy nightclub full of people and you’re trying to get through. The more time you have, the more able you are to make it to the other side. But at high frequencies, you come to the door of the club and think, “Screw this. I’m not even going in.”
We can control the frequency response of the inductor by making it from different types of materials, thicker wire, thinner wire, more coils, less coils, wrapping the wire around something, etc.
What if we stick a capacitor AND an inductor in the circuit at the same time?
Hmmm... so like this?
Well, if we stick this:
With this:
We get this:
And by adjusting capacitors and inductors, we can move the hump up and down the frequency spectrum, and make the hump narrower or wider. This is a bandpass filter.
The problem is that we're reducing gain only. We're rolling off the lows with the capacitor, and rolling off the highs with the inductor, so to make that hump louder compared to the highs and lows, so we have to amplify the signal after that. We need to add gain. So we stick an amplifier after, and now we have something like a Pultec, a passive EQ.
Why passive? Because the tone shaping uses passive components: resistors, capacitors, and inductors are passive: they work without additional electricity fed into them, and they can't amplify a signal.
A passive EQ means the signal is being reduced overall, because we're cutting things out of it, and then we amplify the whole thing, which brings the stuff we reduced back up to nominal and the things we passed get louder.
Kind of like what happens with a compressor, right? We selectively reduce the signal and then overall amplify it.
My circuit diagrams are ridiculously simplified—they don't have an input or an output—but the point is that you understand what's going on and start learning the symbols. It isn't hard to read a circuit diagram. You're already doing it. True, it's "Run, Spot! Run" for now, but eventually it will be, "The only completely stationary object in the room was an enormous couch, on which two young women were buoyed up as though upon an anchored balloon."
I also simplified a TON of electrical engineering stuff. Like electrons and what’s actually happening as things flow through wires and components. It’s not quite guys running around. And there are more words to learn, more jargon. But it’s a useful way to think of things at this stage. We’ll add some more ideas next week.
You don’t need to know this theory perfectly, but you’ll learn enough in the next few weeks that it will improve your engineering.