 Welcome to the talk, Manipulating Signals, Designing Filters for Signals and Voltages Yourself by Jakob Lerch. This talk is being translated into English for you by Kalluera and Isegrim. Any feedback is appreciated. Please use the hashtag C3Lingo on Twitter or mustered on We hope you enjoyed the talk. Welcome to this topic will be a little more unusual. We are looking into the analog circuit technology. We are looking to annoy a neighbor away from the night neighbor to a filter which reduces these bass signal noises. So there will be a Q&A in the end and if you have questions please ask them at the end and on Twitter or mustered on under the hashtag Rc3Fem or in the IRC or on the rocket chain. Please use the translated audio stream in the web player. Hello, my name is Jakob and now have fun with the talk. Hello, my name is Jakob. I am studying engineer computer science at the Uni Ilmenau and I want to talk about how signals are manipulated and at first what are signals and what is manipulating them. So let's start. Imagine you are having a party and your neighbor is really annoyed because it is at loud and complains and you should turn off the music because otherwise you will call the police and you don't want that but you also don't really want to stop completely. And what would be nice if these deep frequencies which you may be hearing when your neighbors are having a party that is what you can hear especially. So an idea would be if the low frequencies would be filtered out then the neighbors would be less annoyed. It might not be that nice but it's better than turning the music off. So what do we do? We have to put something between the microphone and the speaker so it's a signal. So when we are doing that the neighbor is happy and we are also happy and we can continue our party. That's the aim of this talk that we want to know how the signal looks and how can we manipulate it. So at first I will talk about what is a signal and special audio signal, where the audio signal is a motivation then I will talk about how you manipulate signals and then I will show some circuits which you can use, which you can use in different dimensions with different behaviors or filters and you can set them up and use them. So a small repetition, what is a voltage? It's work that has to be done to move charges from one point to another in our circuit. So I don't want to talk about the physics deeply but we have to know we get a voltage from this voltage source and then it will go down over the rest of the circuit. And some notation, this and you see sometimes this ground symbol on circuits and that is a reference point where the voltage is always zero. If you measure the point from there to there, from that point to that point then it's always zero and the other voltages are also referenced to that point and that's helped with the analogization. If you say the voltage at that point has that and that voltage and then you have it for the difference between these two points and sometimes if it gets more complicated you can leave the blue line out and then everywhere where you have this ground symbol always painted in but there are two different symbols, two different points in the drawing but they are the same point so we can measure the voltage over a component or between a point to ground. And another thing, so you have seen I used before the left one with the line in the middle which goes through, that symbol, I will use the right one here, then the voltage doesn't change but that's easy and I will use the right one and in this talk it's a signal source so the voltage changes often and the voltage of our time is something we can show in a diagram and that's our signal and that's then what we use to transmit information. So a very easy signal is the sign. If you measure the voltage there then it would be changed like this, it would start at zero, go up to one, fall back down to minus one, go back up to one and that's periodical and I prepared something which would look like this. You would have a circuit like this and we see the voltage here in the colors which changes and in the diagram you also see the value from up there to ground. The sinus frequencies have very different rates and it can have a different frequency or it can have a high or low amplitude and you can do some nice things with it and another signal here, it's a square wave so it's like technical informatics so it's for viewers and ones to code them and I don't really mean that here, we don't interpret the signal, we don't interpret the signal and we are just looking how it looks and the other part we are not doing in this context and I could have a triangle wave or I just chose a rectangular wave. So I also drawn this in the simulation here so we see that the voltage changes immediately and so we get the square wave here. Now it's getting interesting, every signal we encounter here typically can be shown as the sum of different sinus waves in technically as a sum of infinite number of sinus waves. I've plotted this here so the blue signal is the, it's stopped after two iterations, two summations, the yellow one after six and the green one after 34 addons and the red one very close to the actual rectangular wave, this is after 258 sine waves, summing up 58 sine waves. So we can basically do this for any kind of wave, sort of waves for triangle waves and so if we look at that we see that we do the plot versus the frequency here which sine waves can be found at which frequency and with this simple example of a sine wave we know that it only consists of one sine wave here so here with 200 hertz and the amplitude of one world. So with a square wave we can create this by summing up lots of different sine waves and this is plotted here. So here we see that we see a very low frequency sine wave with an amplitude of a bit more than 1.2 volts and that's what you see here and you see that the total amplitude is a bit more than 1.2 volts and we can do cool things with that because we can now construct filters that attenuate certain sine waves and amplify other sine waves here. So this diagram here is what we call the spectrum of a signal, this is a different way of showing the same signal but it contains the same information as looking at the time at the time axis here. So that's the basics. So how do we manipulate signals and what do I mean with that? So what we've learned that a signal consists of all these different sine waves here and then I'll play some music that's lots of sine waves being added up and there are low ones among them and especially the low ones are those that travel through walls and so the low ones are the. So in our case we want to filter out the low frequency sine waves from that one. So how do we do this? So as I said we put something in between here but before we want to have a look at how this signal could look like. So I've put a very simple version of that, technically this microphone cable is a lot more complicated. So basically we have a signal source here and some signal receiver and between that we have a simple cable, simple tap wires. And so here in this case we have one wire that's the ground and another wire that contains the signal. So if you measure the voltage between the red one and the blue one you get a voltage signal that contains information for example the sound. So this can have multiple that are shown wet. So for example if you have two you could get a stereo signal through that but right now we are only looking at the simple source. So between so we cut this open and between that we put some electric circuit. So this circuit is what we call an LTE filter. So what's that? An LTE filter is something much more general. It's some electrical circuit taking an input signal here as you in. That's a voltage. We see at these two connections here and outputs a manipulated value out. So I'm just you out here. LTE meaning linear time invariant. I'm going to show what linear means later on but let's show later how this works here. So we putting one signal in and another signal gets out here. So in this case it's an attenuated and you could get other signals that just passes through so factor of one or you could get signals in and which gets amplified here. So for example you could put time waves in that gets amplified here. So which one are and which are not depends on the frequency. So it could be that well it also depends on the system. So there could be systems that so some things we have a high frequency, some have a low frequency. We have high passes which do not filter out the high pass that has low passes. So there are two more words here. So two more ways. This is the homogeneity and the additivity. So the homogeneity meaning if I scale up the input signal then the output signal gets amplified by the same factor. So we have the input signal has the same frequency as on the bottom then above but just a higher amplitude then the output signal is also as the same frequency but different amplitude. The other interesting thing is the sum. So if I add two input signals or I show this here then the output is also the sum of the answers of these two systems. So we can't even just put a sinus waves in but we can also put square waves in or anything else. That's just that you can create by summing up sinus waves. So what we also want to describe how these this kind of LTE systems behave. So there are some low so we know that there are low passes and high passes but there are quite a couple of others that I want to show here. So we can describe this by the transfer function. This is the amplification factor depending on the frequency. And omega is the circular frequency here which is the frequency of the sine wave multiplied by 2 pi. And if the input is a sine wave with one frequency it gets a different amplification than the one as from another frequency. So we can plot this function over the frequency and what we see here is that low frequency gets suppressed and with higher frequency gets amplified or we just push through. So we have one problem. We want for a high pass or low pass filter we want to have to say exactly up until that frequency it let's pass or it amplifies or it attenuates. So this graph doesn't have corners so we don't really have can see a critical frequency here. So what we are doing here we are drawing the asymptotes the straight lines which go closely to the function in the infinity which I show here and where they overlap and then we are drawing a line down where that's our critical frequency which is one for us which I made it easy for myself and our transmission function comes here without a derivation. And it's j omega over 1 over omega j omega plus 1 and we are not going to derivate it here. It's important that it looks like this and later we can vary omega g with in our circuits and later we are just having simple equations where we put our values in and then we get our transmission function and we don't have to think about a transmission function but I want to show you so you know where it comes from. And there are also different filters which have different transmission functions. Here it's a high pass and there are also a band pass which attenuates high and low frequency and just lets the frequency in between pass or amplifies it. And this filters can also be implemented in electric circuits and in the following I want to show you the low pass and the band pass and the very easy filter the amplifier and here you see a low pass filter and it lets low frequencies pass and low frequencies get attenuated. Here you see the asymptones again and here is again the critical frequency and the transmission function is similar as before. It's 1 over 1 over omega g j omega plus 1 and here is the band pass filter. It attenuates low frequencies and attenuates high frequencies and in between it lets the frequencies pass and we are drawing the asymptotes here and then we are seeing the critical frequencies here and we have 2 critical frequencies omega 1 and omega 2 and in reality if we are working with actual audio signals they are actually higher than here but here it's only about the concept and our transmission function is j omega over 1 over omega 1 j omega plus 1 times 1 over omega 2 j omega plus 1 and you can imagine that you put a high pass and a low pass filter just you put them after each other and the high pass attenuates the low frequencies and the low pass attenuates the low frequencies and everything in between gets passed and the amplifier is a really easy filter and it amplifies all the amplitudes independent of the frequency so there is no critical frequency and it has an amplifying factor of k in this time. Here it was 10 and so what did we learn? Well we know we have different ways how to look at voltages which is especially important when I show the images of the circuits where you will use this ground symbol and we have signals and we can show our signals as a sum of assigned frequencies which have a different amplitude for each frequency and then if you add them out if you get that signal and with LTE I filters you can amplify or attenuate these frequencies and the temp depends on the frequency of these so our old goal was to filter a signal and our new goal is to build a circuit which follows this transmission function so we are designing filters and at first I want to show you two components we know the resistance the resistance follows the equation u equals r times i so the voltage over the resistor is the value which is written on it and so if you have a capacity then it's like an ideal capacity and then at first we add a capacity and then we don't just write uc equals c times ic but we write run over j omega c times ic and raise the s dot because we're calculating with imaginary complex numbers and I don't have the time to go into that and that's where the j omega comes from and we will see it later in the transmission function and that's where we get the transmission function from so after the r we have here 1 over omega c and when we have a resistor and a capacity serially we don't have r plus c but r plus 1 over j omega c and another thing is the operational amplifier where we have two inputs one inverting and one non-inverting input which are quite like that we have also a voltage plus it's an example with plus v and minus plus v the minus plus and once we are also connecting it with ground and that's where our signal comes out and then after it depends a little bit how you're doing it and it works a little bit differently but we are just using it once and then it works like we wanted and it helps us filtering signals and I will show it to you in the circuits I'm going to show all the parts which are crossed out here will not be shown but in practice they are there so this makes it a lot easier to actually draw this one here so in reality if you use such an operational amplifier you are going to need these connections so this means that you have a look at a certain number of things but I will mention this later on so in a typical OP that you can order your electronic parts would be an LM358 so if you find this any others have a look at the datasheet and see whether they fit your needs so what we need here to design a filter is the inverting OP circuit which looks at fault so we have the OP here we have the signal source here this signal is delivering the input voltage going into this resistor here in the first branch here which is connected to the inverting input of the OP the non-inverting input is connected to the ground here and the output is connected to R2 with the second resistor which is also connected to the inverting input here so we are picking up the output voltage here which is our output signal here so if we want to actually wire this one so we are putting a wire here one wire here and to ground we put this into our cable and that's our filter this filter here as shown here is just an amplifier so it doesn't filter anything yet but later we are going to show filter circuits that do filter because we place this resistor here with either serial or parallel connections of capacitors so for each of the circuits by now I'll derive the transfer function also I'll derive the amplification factor in the non-anerated area and the cut-off frequency so in depend of what the factor is so the amplifier looks like that so the transfer function is minus R2 divided by R1 which this is because if you analyze this one but I'm not going to do that but let me just sketch this here so you write a minus you write a fraction and on the top you get the resistor coming from the output and on the denominator you get the resistor from the input so let me show this here so this one here is an amplifier we see a 3 kilo ohm here and 1 kilo ohm here so the amplification factor is minus 3 here we see this here, 5 volts input and the output is 50 volts output here so it works so let's have a look at our high pass here so high pass has in the first branch here a serial circuit from a capacitor and a resistor and in this branch here it's just a resistor so this is the transfer function the amplification factor is again R2 divided by R1 and the kind of frequency see the formula here so I will look at this one here so this is at 16 hertz so let me turn up the frequency so we see the input signal is 5 volts and there's almost no attenuation here so almost 5 volts here but this is a high pass so high frequencies are not being attenuated but low frequencies will be attenuated so let's turn down the frequency here we see that the amplitude gets smaller so the amplitude is just about a little less than 1 volt here or even though the input is 1 volt here and that's our high pass here so if you want to build if you want to design a high pass you just take this circuit here you have to commit to one of these components so for example if you have a 1 kilo ohm resistor you set R1 to 1 kilo ohm and then you design which amplification factor you want to have so let's say it's supposed to be 1 so R2 needs to be 1 kilo ohm as well then you write this down and then you do some simple math there and you might be getting some so if you have a capacitor like that you can start with that if you don't and have some others then you maybe have to tweak the other elements as well to get to the same one so how do we get this formula here for the strands of function this one here so with the inverting amplifier we have the feedback branch divided by input branch so the feedback branch here is R2 and the first branch the input branch is a series of goods from R1 plus the 1 divided by j omega c1 so now we do some magic math here multiplying by a 1 so we can move things around here so that's the formula that we get here so we are doing something similar with the low pass as well so we see that we remember up to the kind of frequency we let everything through and above that it's just a tenuous and that's how this looks like here so the feedback branch we have a parallel circuit from a capacitor and a resistor and the input branch we have just a resistor and that's the formula we get from that same amplification factor same again here and that's the formula we get from that same amplification factor same again here and kind of frequency as well so let's have a look at the simulation here so again that's a low pass meaning low frequencies are not getting attenuated so the input signal 5 volt, output signal 4.8 and now we turn up the frequency so if we increase the frequency the amplitude should get smaller and we see that this happens actually happens so our low pass also works so again depending on which frequency you have to modify these three components here so the amplification function can again derive like that so this is the feedback branch and this is the input branch same formula here so the parallel circuit looks like that and then again lots of math a little bit of math and we're getting to the same formula here and that's the transfer function that we get here so now we are having the band pass but we're just a bit lazy we have a low pass and we have a high pass so we plug a band pass, a high pass and a low pass and then we have here these critical frequencies 10 to the power of 0 and 10 to the power of 2 then we are taking a high pass filter with the critical frequency of 10 to the power of 0 and we have lower frequencies stamped and our high pass, our low pass dumps everything above that critical frequency so we just plug our two circuits we had before together we have our amplification factor which is just the both of these amplification factors multiplied for each other and the critical frequencies are those of these thermal circuits and when we're looking at it here we have a very low frequency here and then we're seeing it's 4 hertz and then we have now we are making the frequency a bit higher that was too much so now we make it higher the signal isn't as damped as before and we are in the area where the signal gets passed through and when we increase the frequency again we are seeing again that the amplitude of the signal is damped and that's exactly what we want and that's what succeeded with plugging two different circuits after each other and let's think what was the most important we have a signal which consists of a sum of multiple sinus waves depending on their frequencies they have different amplitudes then we can design circuits which work like LTI systems and which amplify certain frequencies or damp on others and then we have a body diagram which shows that behavior and this filtering behavior we can do in a circuit and there are really many different ones with different critical behaviors it's a really easy design which we have here but I think it's for trying around it's really nice and there are some things we shouldn't not talk about a real operational amplifier it's not ideal we have two things which might be a bit annoying so it starts to damp at a certain frequency and you can see it in its data sheet and it's damps and everything and the voltage which goes out and you see it needs a voltage to work and the output voltage can't be higher than that voltage so if you have an input signal of five volts we want to amplify it by the factor of 10 so we should get 50 volts but if we have a real one which has five volts supply voltage and then our signal doesn't get higher than five volts and we get rectangular waves that might be nice for some overdrive effects but if you want to send some signals it's not really nice that was everything about the op amp and if you want to talk directly to a speaker you probably doesn't work with that one and there are other amplifiers which you can use for that with power amplifiers which you put after the op amp and then the power is amplified and then you can hear it through a speaker and in the last slides I put some interesting links in there and there's also a YouTube video linked of someone who did that and if you're thinking about the health of your signal source because it might break then you should put a non inverted amplifier in there and you can look it up on the internet it's not more complicated than what we've done here and there is some current flowing back if you have something non inverting amplifier then there won't be any current flowing but the voltage is still transmitted and the signal source is protected the images of the circuits were generated with false.com that's nice for small projects and how it looks and there are other tools and if you want to do it more professional there is LT Spice which is an analysis tool which does something similar as false. but it's more efficient and it's not a program on the web and it works really well and the Python library is also with Python control you can plot plots and there are also other libraries but it doesn't really restrict you on your transmission functions and false.com I already said and paySDR is something more about signal manipulation how does it look, how can you control it LearnElectronics is something on YouTube for trying around with this and there are some really nice videos and this video is something how you do it and here is some more literature some more links, some hard tools some calculating helps for high and low pass and I just have to say to you very much fun there will be a round of questions later and you can ask questions and have fun thank you very much Jakob for this really interesting talk so I never learned something learned that much about analog technique so thank you I could learn a lot now we are going to the questions and answers and for those of you who have questions and hadn't posted them somewhere please write them into the IRC hack-end into the kanal AC3-FAM into the AC3 rocket-chip into the channel FAM or on Twitter or in the FIDI-verse the hashtag AC3FAM without the dash let's start with the questions we have a question which was supposed to be what does a Wiener filter has to do with a filter? okay so look at Wikipedia before that one there is a Wiener bridge it's a certain kind of electrical circuit and it can do something with electrical filters there but I don't really know in my university courses it was always in the context of we would like to know something and we use these kind of bridges but you can certainly use this for filters as well is it like a bridge or circuit? is it something for my... I use something for my study IR bridges and then you have for resistors yes exactly that's what this is and you can use this with filters as well or I don't know any examples but we can probably do that well next question the... about the slide 56 what do you recommend against Lippic? so I hope you know the amplitude that's coming from the source so for example you know that's about 10 volts or whatever you have here there and then you need to make sure that the supply voltage for the OOP is... well choose that so you know the input might be 5 volts and we say that we supply it with plus minus 5 volts or maybe a bit more so to have some buffer there some reserve there next question looks... that's not a question that's just a comment here was the wish that you would explain the bandwidth for the bandpass so bandwidth is so the bandpass has two critical frequencies and the upper frequency f2 minus the lower frequency f1 and this is the band with then so the difference between the two critical frequencies so that could be the definition so next question how much would it... how useful would it be to decouple the low noises from the walls and the ground and maybe let it hang from the... from the... I don't know much about that that's not my expertise here so the thing with the microphone and karaoke this is more like motivation for this talk here so we have an audio signal we want to filter that and that's where I jumped right into the discussion but if there's more about... about PA technique then you would have to look into that then there's a question about the images of the circuits and why you have another dot on one of the ground I think it was the slide where there was additional ground in there which just went to a dot which didn't go on further I think you meant the slide where there were several ground cymbals and as I said in the talk so if you have some standard circuit diagram like you know from school without these cymbals here so you could consider one point there to be your reference and that's where you draw the ground cymbal there and you can also draw this on other points as well and if you do that you say that these points are connected meaning the same point there and this makes the circuit... this symbolifies the circuit this representation of the circuit yeah there's another question why don't you do it directly in software why would you do it as a physical circuit? yeah cause it's fun well I thought this talk would make a lot of sense for people who sold a lot who would like to create physical things and that's why I started this with analog filters so if you want to do this with digital filters go ahead can you do that? yeah another question from locally about the high pass filter there we had directly after the input signal there was a capacity and a resistor and the resistor which was in the feedback branch it has the same value as the first one which would lead to an amplification of one can you not just leave the op amp away that doesn't the capacity do everything here now? it can be that you still want to amplify it so for example you could put a variable resistor there which you can then use to increase or lower the amplification factor turn the volume to 11 and there could be some other effects in there but I would have to check here so there are passive high passes or passive low passes which is just combining a capacitor and a resistor but they have a couple of downsides so we would have to check the literature for that there is a really new question now here and do you do it just for fun or was a part of your studies? okay so this was part of my university courses I thought this is a topic that's cool and that's easy to create some slides here but there's not that much media for that so basically the knowledge I presented here is coming from several different courses there and I just wanted to give you the some way for building photos here so it's from my university courses so we have a small comment here in this list somebody wants to recommend the YouTube channel sound file about acoustics in rooms and there was something on the ERC which frequencies do you want to attenuate there was a discussion about that and there was a comment that it depends how the room actually looked like yeah then at last another question in this list two questions what would be necessary to choose the frequency when the filter attenuates a lot you have some knob you can turn around where you can choose so what I meant was so you have the OP filter and the critical frequency of that one this only depends on the actual component if you want to have a higher critical frequency of the OP you need a different one higher cutoff frequency so it means you can't put it very wait let me check the question I got the question wrong it's about critical frequency not cutoff frequency so you have a look at the formula FP is this by that so you take one of these two components either the C or the R and it makes it a variable so for example there are variable resistors but there are also variable capacitors so we can change the capacity there and if you take one of those two as the variable variant then you can change them but you have to be careful of course that you don't change the application factor at the same time so you have to this can become compensated another question which I also asked myself why do I use the inverting input and not the non-inverting input why do we have to invert the signal so two basic circuits on how you can use the OPV maybe a bit more but two are very important so there's the inverting circuit and the non-inverting one the non-inverting looks a bit different so the feedback also goes to the negative one the voltage source is different so the reason why we're using this one here is that the transfer function the formula for that one gets relatively simple so we can realize this function in a rather simple way because you just basically you just divide the feedback loop by the input loop the feedback branch by the input branch for the other so it's just to don't have too hard calculation so with this simple filters it's just three components two resistors, one capacitor and that's it with one of these basic circuits and that's he yeah there is one question do you there are some thoughts about analog computers do we have some? okay so I've heard about analog computers only from some fellow students of mine so they I have never worked with those I haven't done with anything but I know that with OP you can't implement mathematical operations so there's the non-inverting and the inverting circuit but there are addition or subtraction circuits with those so you take the so you have two inputs and you either subtract or add these two and you can use this I think you can use this for analog computers as well I have never really thought about those in detail okay yeah otherwise I see no more questions in the list and the IRC there's also nothing more then I want to say thank you very much for this for the answering the questions and for this really interesting talk yeah and that was it for today that was generally the last talk on the FAM channel thank you all those thanks to all the listeners to the whole audience who are looking and watching so there's only the C3 news show at midnight so we will see tomorrow the other news shows and until then thank you very much for watching thank you for your attention also from the translation booth you have just heard the talk designing filters for voltage signals and it was translated by Isogrim and Kahluera if you have feedback for us please use the hashtag C3lingo on Twitter or on Mastodon