DIY SYNTH VCF Part 1: Analog Filtering Basics

if you look at a bunch of schematics for voltage controlled filters floating around the internet you'll quickly notice that they are quite convoluted and hard to figure out not only do they often use obscure and unusual components they also arrange them in strange ways this might lead you to believe that filtering is inherently tricky and complex but that's actually not at all true if you strip away all the control amplification and resonance circuitry and just focus on the actual filtering going on you'll find that most filters share the same very simple core concept to understand that core concept we'll first have to talk about what filters do exactly let's start out by looking at a low-pass filter the simplified gist of it is that low-pass filters take in an audio signal remove a set amount of high frequencies and then send out a filtered signal that's mostly just base and low mids in other words they pass low frequencies your flat's walls basically act just like that if someone is talking in the next room that person's voice will sound muffled and distant because a lot of the high frequencies are filtered out the music your neighbors are listening to will be filtered even more since it has to pass through a bunch of additional walls okay but how does this translate to the world of electronics it's actually really straightforward to visualize because we're able to look at different kinds of sounds with an oscilloscope to make our lives a little simpler we'll check out sound waves coming from an oscillator these are way less complex and way more repetitive than most sound waves you'll encounter in the real world which makes them easy to analyze over here we have what's called a square wave square waves have lots of overtones and are therefore rich in high frequency content in contrast this sine wave over here is tonally pure which means that it has no overtones and no frequency content above its base pitch let's now imagine that both are oscillating at the exact same frequency this means that while their base pitch is identical the square wave will have all these high frequencies that make it sound really harsh while the sine wave will sound mellow and rounded here's a quick example as you can hear both are tuned to the same pitch but there's an extreme difference in tone color and that is solely due to the overtones and difference in high frequency content coincidentally if we send our square wave through a low pass filter the result will actually look and sound a lot like our sine wave here if that's the case and you'll need to take my word for it for now then we can make a rough assumption about which trait gives a waveform its high frequency content because if we overlay our square and our sine wave we can clearly identify what sets them apart while the sine wave gently slopes upward and downward without any sudden change in direction the square wave does exactly the opposite it only deals in sharp immediate 90 degree turns and it's exactly those sharp turns that create a whole load of overtones so as a rule of thumb you could say that the pointier the waveform the harsher it will sound and this leads us to a very basic definition of what filtering is in a visual sense it's all about changing the shape of a given waveform so while low pass filters kinda sand down the edges and round them out high pass filters will make them more pointy and sharp if possible there there's more filter types out there by the way but for now we'll focus on these two now you might ask how that definition helps us in any way since we are basically talking geometry here and electrons don't actually take 90 degree turns to answer that we'll first have to think about what an electrical oscillation actually is when we look at an oscilloscope and see a waveform what's it drawing there exactly well in most if not all cases an oscilloscope will show you the voltage applied to its input terminals over time think of its display as a system of coordinates with the x-axis showing time while the y-axis is showing voltage waves like these are then by definition recurring characteristically shaped voltage swings if that doesn't mean anything to you let's take a step back and recap the absolute basics there's three main properties we're interested in when talking about electronic circuits resistance voltage and current to make these less abstract we can use a common beginner's metaphor and compare the flow of electrons to the flow of water through a pipe in that metaphor resistance would be the width of a pipe the wider it is the more water can travel through it at once and the easier it is to push a set amount from one end to the other current would then describe the flow while voltage would describe the pressure pushing the water through the pipe you can probably see how all three properties are interlinked more voltage increases the current while more resistance to that voltage in turn decreases the current looking at our waveforms we can forget about current and resistance for now because essentially those waveforms are just the visualization of a rising and falling pressure level that we measure somewhere so that means that our square waves sharp turns represent a very abrupt rise or fall in pressure while the sine waves soft slopes represent a way more gradual shift so in order to create a low-pass filter we will need to find a way to slow these abrupt pressure changes down because remember those pointy edges are what create all of the square waves overtones how do we do that it's actually really simple all we need is two components a resistor and a capacitor set them up like this and you get a basic low-pass filter now any signal that we send in here will have some of its overtones removed the result can then be picked up from here in case you're confused about how this works let's dissect this little circuit first of all we'll take a look at what a resistor does in this scenario resistors if you don't know basically act like narrow pipes that you can use to connect two points in your circuit we measure their width or in actual terms resistance value in ohms the more ohms the more resistance and the tighter the pipe so by using a resistor to connect these two points we are restricting the flow of electricity from here to here now this by itself without the capacitor would not achieve anything in regards to our waveform as long as no water is actually flowing out of our output here no water is passing through a narrow pipe and this means that the pushing force coming from here just gets transmitted as is so the pressure level here will always be exactly the same as the pressure level here even if that pipe is really really narrow but as soon as we introduce that capacitor our circuit suddenly behaves very differently and that's because capacitors basically act like balloons that you can attach to the open end of a pipe these balloons come in different sizes ranging from very tiny to very huge we measure that in a unit called ferret as these balloons are filled with water they begin to expand and just like with a real balloon it will get harder and harder to push more water in as the balloon starts pushing back increasingly once the force coming from here exactly matches the balloon's responding force no water will flow anymore the balloon is full but note that full in this context simply means as full as the given pressure can force it to be if we were now to increase the pressure the balloon will fill up even more until the forces are balanced again of course we can't do this indefinitely at some point the balloon will pop just like a capacitor can explode if you push it too far but let's assume that we're staying well within specifications then once the pressure at this point drops the filled balloon will push its contents back into the pipe as more and more water leaves the pressure within the balloon will drop until the two forces are once again balanced going back to our filter circuit let's try and apply that model we'll keep track of the voltage levels here and here in these two graphs we now know that the resistor acts like a flow restricting narrow pipe while the capacitor acts like a water storing balloon so let's say that we suddenly apply a pressure of 5 volts to this point unlike before that pressure will now cause water to flow through the resistor and into the balloon inflating it this means that pressure is no longer instantly transmitted from here to here because filling the balloon up takes some time only once the balloon is full we read five volts on this side but of course the rate at which it fills up depends on two key factors the size of the balloon and the width of the pipe the bigger the balloon the longer it takes to fill it up the wider the pipe the more water can flow and the quicker the balloon is filled up next we'll imagine that the voltage on this side suddenly drops to zero volts this means that the balloon will start pushing its content back into the pipe and through the resistor since there is no opposing force anymore while the balloon is emptying the pressure here is slowly declining until it finally hits zero volts and again the duration of that process depends on the balloon size and the pipe width you'll notice that i've drawn a slight quirk into the way the voltage ramps up here and declines there and that's because pushing water into the balloon gets harder as we approach the maximum pressure level and the pressure inside the balloon gets weaker as it empties out the end result is a waveform that is decidedly less angular than the square wave we send in even though it's of course still quite far away from being a pure sine wave but nevertheless we can expect it to sound a lot less harsh to try this out we'll first have to decide on specific values for the resistor and capacitor since i largely tried to stay away from formulas i simply tested a few value combinations and found that a 470 kilo ohm resistor and a 10 nano farad capacitor work best for our purposes here if you want to build along make sure that you use either a foil or ceramic capacitor anything that isn't polarized and that's because unlike with our example audio signals mostly swing across not strictly above the zero volts line while this has no general impact on our filter's functionality it would pose a problem if the capacitor was polarized because polarized capacitors really don't like negative voltages setting the circuit up is really simple on this cable i have a square wave signal coming from my synthesizers vco using a jack socket i'll connect the signal wire to my breadboard also we have to plug this ground wire into our breadboard's ground rail that's because whenever you couple devices and circuits together you need to connect the ground levels as well from here i'll then use the resistor to route the signal to this point where it will connect to one of the capacitors terminals the other terminal connects straight to ground this is because the capacitor needs space to expand into so to speak then i'll plug my oscilloscope and my amp in here so we can check on the raw square wave first and here's how that looks and sounds like note how sharp the edges are and how harsh the sound is now if i switch to the filter's output we should see a rather drastic change and there it is as expected the waveform looks smoother and the sound is definitely more mellow but what if we want to adjust the amount of filtering we apply to our square wave it's actually quite simple the longer it takes for our capacitor to charge and discharge the more overtones will be removed in synth terms we often talk about this as the filter's cutoff point this describes the frequency at which a filter will begin filtering for our low pass filter that means we have two options if we want to move its cutoff point we can change the value of either the capacitor or the resistor but because swapping them out for parts with different values is rather impractical we should think about more elegant alternatives since there are no viable options for varying a capacitors value on the fly we can narrow our focus on variable resistors there's a bunch of options here but the classic choice is using a potentiometer this is essentially a resistor whose value you can control by turning a knob for our purposes we can ignore the fact that it has three connectors for now we'll only be using these two so i'll replace the resistor with a one mega ohm potentiometer this means that we can now vary the resistance here from 0 to 1 mega ohms and here's how that looks like on the oscilloscope right now the potentiometer is set to 0 ohms so our filter is completely open the capacitor fills up almost instantly and so the signal is not really affected much but watch what happens as i slowly increase the resistance value the waveform gets filtered more and more and slowly morphs into a triangular shape but what if we want to filter out low frequencies instead doing that is really straightforward we just need to switch the resistor and capacitors positions like this going back to our water analogy here's how that works in detail you can imagine the balloon now being used like an elastic membrane between two adjacent pipes it prevents any water from flowing between these two pipes but it will allow pressure to be transmitted via displacement the resistor on the other hand now acts like a kind of equalizing valve it allows water to slowly drain out of this area when the pressure is high or to be slowly sucked up when the pressure is low that's because a ground connection is not a one-way street think of it more like a path to a near infinite low pressure reservoir of water let's walk through the filtering process step by step like before we'll keep track of the pressure levels down here we're using the same square wave signal as an input so the pressure on this side will very suddenly jump to 5 volts because the water here can simply push through the balloon those 5 volts will be instantly transmitted to the other side but while the pressure stays high here it will start falling over here since the excess water begins draining out through the resistor the speed of that draining process will again depend on two factors the capacitor size and the resistance value the bigger the balloon the more water it can displace keeping the pressure here high for longer and the wider the pipe the faster the displaced water can leave allowing the pressure to decline quicker at some point we'll enter a state of balance where we've got 5 volts on this side and near zero volts on this side but since this balance depends on the fact that the balloon is squeezed into this space here something odd happens once the square wave swings to its low state the pressure on this side will shoot into the negatives an absence of pressure here causes a vacuum over here because we have that resistor as our equalizing valve that vacuum is only short-lived water from ground will slowly flow up here raising the pressure to near zero volts again this behavior centering the output signal around 0 volts is circumstantial for the filtering process but in other contexts it can be quite useful if you've seen my diy vco series you might recognize this as an ac coupling circuit the only difference being larger and fixed values for the components but back to our filter the end result is a wave that's decidedly more spiky than the square we send in which like i said before means that we've effectively killed a lot of the low end audibly we should get a more nasal sound to see if that's indeed the case let's rework our low pass into a high pass filter all we have to do is swap the capacitor and potentiometer's positions around right now the filter is completely open the wave just goes through largely unchanged but as i dial down the resistance value you can clearly see the wave getting spikier and the sound getting somewhat sharper now you might have noticed that both our filters do a pretty bad job at really eliminating the high or the low end you could in both cases hear a lot of unwanted frequencies bleed through this is because both of them are simple first order filters which means that there's just one single filtering stage an ideal filter would be able to completely eliminate all frequencies beyond its set cutoff point a first order filter on the other hand is really not live up to that standard instead it gradually reduces the volume after the cutoff point by 6 decibels per octave to be precise in many applications this is just two week a performance so what can we do to give our filters more byte it's quite simple we just chain multiple filtering stages together two will make a second order filter three a third order and four a fourth order and so on for every filtering stage we add we will get a steeper roll-off and that kind of makes sense because we are basically just applying the same filtering process to an already filtered signal think of it as if you're screening sand and then you're screening the screened sand again there's just one catch if we want to try this out on the breadboard for a second order filter to work properly these two resistance values need to be equal now if we use standard non-variable resistors that wouldn't be a problem but since we'd like to change the cutoff point on the fly we're running into a bit of an issue here we could of course use two same value potentiometers and then try to turn them at the same time but since this is impractical and imprecise that wouldn't really be fun luckily there's a ready-made solution for this kind of problem stereo potentiometers you can think of these as two separate potentiometers controlled by the same knob so whatever resistance value we dial in will be what both potentiometers are set to with this putting together a second order low pass filter is really straightforward you just route the first filter's output to the second filter's input so we get our final filtered signal right here and this is what it looks and sounds like unlike before the result is much closer to being a sine wave and so the high end is nearly inaudible i'd say this is a big improvement over the first order filter and should be perfectly usable as the basis for rvcf because of course simple passive filters like these have a bunch of major shortcomings first of all as they remove part of the input signal they also reduce the overall volume level since they are passive they by definition can't apply any kind of amplification so as we close the filter the sound gets more and more quiet second and very much related to that a passive filter can't produce any resonance because resonance is created by amplifying some select few frequencies and finally our design only allows for the cutoff point to be controlled manually in a proper vcf that should be doable with a control voltage so in the next video we'll tackle the amplification issue and turn our passive filters into active ones once we've done that we'll be able to add some nice screaming resonance until then feel free to check out my patreon if these videos are helpful and you'd like to see more of them in the future consider supporting me on there anyways thanks for watching and until next time

Channel: Moritz Klein

Views: 67,215

Rating: 4.9754958 out of 5

Keywords: DIY, VCF, Filter, Synth

Id: 3tMGNI--ofU

Length: 21min 46sec (1306 seconds)

Published: Tue Dec 15 2020

Reddit Comments

[u/dangerous_dickhead]

hi all,

here's the first part in my new DIY VCF series. we're tackling the absolute basics first: passive low- and high pass filters and how to chain them in order to improve performance.

next episode, we'll add amplification and resonance.

thanks for watching!

[u/Lil_chrissie]

At first I read this as “video game series” and I was like “hell yeah!!”

Can someone pls make this happen?

[u/Lizard_repositioner]

I actually just subbed to your patreon, Mr. Dickhead! Great, great content.

[u/[deleted]]

Thank you!

[u/Instatetragrammaton]

Weird question: how did they come up with the circuitry for this in the first place? To me, most circuits seem like snippets of code - you kind of throw them together and then hope it works, but I’ve always had a hard time figuring out the absolute fundamentals of it.

[u/Tek_Flash]

Insanely useful video. After 10 minutes I understood capacitance better than a month of lessons in school.

[u/NeedsSomeSnare]

Great stuff!

[u/myweirdotheraccount]

Oh I'm definitely returning to this. Thanks!

[u/AlphaRecoveryGroup]

Not sure if I want to take electronics advice from a dangerous dickhead haha