I think if I would have clicked on the video at 23:26 I would have immediately clicked it away and thought "woah that looks like way too much detail- I'm designing musical circuits, not building a rocket engine"- but fortunately I started at the beginning and understood very clearly the purpose of the equations. @22:00 you say "Now I'm going to do something fairly odd". That is not odd at all to a mathematician, it's the celebrated "telescope trick" used in many proofs (translating directly from German, not sure if it has the same name in English)- which should be in every mathematician's toolbox :).
Platinum-film resistive temperature detectors (RTD's) are a lot more tightly controlled than the old wire-wound tempcos. Since tempcos are always hard to find and expensive, a modern design should probably use a 4100-ppm/K Pt RTD in series with a fixed resistor. Now I need to go work out how to get a current that varies 5100 ppm/K for supplying the common emitter of a Gilbert waveshaper that needs 5100 ppm/K (1.5× the transistor tempco)
THANK YOU for these videos. something about your voice, or colloquial mannerisms, or maybe just the cadence even, something, whatever it is, im not sure, but you are so far the most understandable source ive found yet. so again, for your time, effort, and seemingly unending knowledge on all these videos, thank you, you are incredibly appreciated.
Thank you for your kind words! They are especially encouraging since I'm quite self-conscious about my voice; I don't have a "radio DJ voice," and although I'm pretty dynamic in live lectures, I find it challenging to inject energy into my delivery when I'm the only person in the room.
@@Lantertronics i get that. do it myself even. but your videos are almost like programming my brain, it feels like. your explanations actually sink and and anchor themselves in my brain as opposed to just kinda coming in and bumping around a bit and then getting shoved out later by whatever else. ive actually learned so much ive tried to for so long with so many other avenues. i cant express enough how awesome these videos are. again, i greatly appreciate these, and im sure im not alone and that there will be scores of others behind me.
I love the professor's lectures. However, I have a suggestion on how the temperature coefficient of R_F can be derivative much easier: Note that the thermal voltage V_T is proportional to the absolute temperature and thus we want R_F to also be proportional to the absolute temperature (assuming that R_0 is close to constant in temperature - an assumption the lecture makes without mentioning). The reference temperature of 25Celsius corresponds to 298.15K absolute temperature, let's make that 300 Kelvin for simplicity. The unit of the temperature coefficient is ppm/K, so dimensional analysis suggests that the temperature coefficient should be the inverse of the absolute temperature, i.e., 1/300K = 0.33%/K = 3300ppm/K. This can be justified as follows: when we start at the reference temperature of 300K and increase by 1K, the absolute temperature increases by 0.33%. We want R_F to increase by the same relative amount of 0.33%=3300ppm. But by definition, this is just the temperature coefficient.
This is very good explanation of one of the most complicated problems there is with analogue synths. This is the problem that many diy-s switch to digital domain. But if you love analogue electronics than you have to love this solution of the problem. It's at the same time messy and brilliant. But what is also important to know is that it is not the only solution there is
Ahhh beautiful, this part of VCO's has always been kind of a black box for me, but you explain it so clearly and it's really enticing to hear your enthusiasm :)
I just found out about you this weekend, and please do not stop what you are doing you are helping out a lot here not just me , I'm not a "real" engineer but have designed a few things like VCA, VCO (not completed well the design is complete but have not drawn it in DipTrace for fabrication) stuff like that and i find this very interesting. This is well worth a sub :).
Plodding thru. dude, you rock! Somehow my brain adapts to these formulae way better hearing it in diagram, then maybe one day, an actual breadboard, but this time I have a couple dozen xistors to run through for comparison when I get there. yay THANKS!
I can't thank you enough for these videos! I really get how these beasts work now, I took notes like crazy, and I'll soon be ready to build one for myself and bootstrap my first modular synth project. That's just awesome!
I think it would help to go into the limitations of these things a bit. When first working on this stuff it can be really frustrating to design an oscillator core and then a converter and hook them together to see that they don't really work together. I realize that that stuff might be a topic yall touch on in a different class or a different part of this class, but just realizing that the exponential converter doesn't really work like a perfect current source is one of those things that sounds obvious when you say it but a person hacking stuff together might not think of. An easy way to have that happen would be to use an op-amp schmitt trigger based design for your core, and set the schmitt triger thresholds at something like +-5v for the eurorack standard. Then you wire it all up with a simple resistor to -12v as your current sink and see it working. So you go back and make this exponential current sink only for it to just freeze, because the current sink can't go below 0v.
I found some other explanations of these themes, using more simnple analogies. But coming from a mathematical background, this appeals more to me. Now to the experimentation phase!
At around 1:30, shouldn't ic = Is [exp(vbe/VT) - 1]? It really doesn't change anything after the approximation so it is "good enough for rock & roll" ...
At 4:14 the isn't the -1 outside the argument of the exponential? Rene has it there and it makes more sense why ic >> Is would permit the simlification
@@PATRIK67KALLBACK They made a PCB layout (as did all the other students for their final projects). This semester I plan to sort through the various student PCB designs and see what ones are most ready to fab and test.
You have your parentheses in the wrong place: I_c=I_S [exp(V_be/V_T) - 1]. Given opposite temperature coefficients, you can always choose values to yield the resistance and temperature coefficient that you need.
Has Ian Fritz website been closed down? The domain shown in this video doesn't seem to work anymore... And really nice video! Thank you for that! As other people have already stated, this is really helpful to get into the details of synth-making.
UPDATE: 3300ppm Tempco PTCs are only available as new old stock by now. A big producer of these (Akaneohm) stopped producing the convenient axial leaded 1%3300ppm 1k/2k/10k Resistors in 2018. Their resistors can be found for ~2$ a piece in several diy synth shops. Is there a way to get around this shortage? Maybe mixing higher coefficients with regular resistors?
Great lecture! Could you explain where the ic2/ic1 comes from? (around 7:00). I assume this would be due to the differential pair but I honestly wouldn't be able to write this down on paper
Calculating ic2/ic1 is purely an intermediate step to be able to get ic2 in terms of a "constant" ic1 without any Is term. Since he later sets ic1 as iref with the feedback op amp to ensure a constant iref, ic1 no longer has an Is term either. Since the value of ic2 is dependent on ic1, it also has no Is term either. ic2/ic1 doesn't show up as any sort of output in the circuit itself.
I am not an engineer but I have been creating various oscillator for my music projects, for the past three years. As I learn more, through videos such as yours and more hands on building videos, I have had inconsistent results with implementing exponential VC circuits, integrators and bias. Through your videos/lectures I am starting to question my understanding of voltage control. It seems that current is what really controls the musical quality of a circuit ad voltage is more or less the plotting range for a waveform, is this thought going in the right direction? I must admit when it comes to voltage and current I don't really seem to consider current/amperage as significant but now I am wondering if it's voltage that is arbitrary. Your help is much appreciated, thank you for creating this channel.
Almost every component is current controlled, you have to read the papers carefully what the device respond to, but in general it is current. (BJT is current controlled i guess this is what you wanted to know, but IF you only use it as an switch you just have to put a V or three you know it opens hard). Only actual Voltage controlled are those mosfets that i know of and i never use them so i do not really know.
Thank you great lecture! I always wondered if there was an easier method to achieve this conversion. Matching a couple of transistors and then dealing with temperature it is a lot of work (still fun to me). But I always ask myself, In each op amp and ota there is a differential pair, but sometimes temperature compensates (If i'm understand correctly). Is there any method to empoy that? for example trying to take the output from an operational amplifier power line? totally noob question, sorry if I'm ignoring some basic rules.
What you can also do is stabilize temperature at some higher state like 40 celsius with a resistor so that there is no fluctuations in ambient temperature at the current mirror
You mean use a TL07x in place of a LM301? Yeah. I’d be careful about going the other direction though, depending on application. TL07x is such a useful general purpose op amp, it’s good to have a drawer full of them.
The Electronotes exponential converter has several mistakes so it is not a good starting point. It is a corruption of applications notes published by Analog Devices, National Semiconductor and Texas Instruments in the late 60s/early 70s and misunderstands the importance of an attenuator comprising a 15k resistor and a 1k Q81 TC resistor. To be fair, it was never explained that the 15k resistor corrects the TC to be more like the necessary 3354ppm. If you put the wirewound TC resistor in the feedback of an adder you only get its actual TC which has a +/-10% tolerance. (The 1% is the resistance tolerance not the TC's.) 3018 to 3689 ppm is NOT close enough for rock and roll! Wirewound TC resistors are manufactured from a reel of wire that is stretched during winding which alters the TC. The whole reel TC is carefully measured in an oil bath and the stretched TC is predicted and not measured after winding due to the difficulty and time to test individual components, hence the sloppy tolerance. TC resistors from the same batch will have the same error, but will not match another batch made from a different reel. If you build several VCOs from random TC parts they will diverge with temperature changes. Modern platinum film RTD resistors are more accurate and have a TC of 3850ppm, but need a different circuit: one stage that adjusts the TC to 3450ppm and then another that adjusts 1V/oct to that. Moral: don't believe everything you read in Electronotes, go back to the sources and then validate them. btw, please stop using Protective Earth symbols for 0V Common, it's really annoying reading schematics drawn by somebody who does not understand grounding. These symbols are international standards defined in IEC 60417 and not a matter of personal preference.
Something for your nightmares: I was in our senior design lab one evening, and I heard a *boom* from a table occupied by a team advised by another professor, so I went over and asked if I could help. Among other things, I discovered they had attempted to solve their grounding problems by strapping the ground to the neutral *near the bench outlet*. We had a *long* talk, and then I told them to not do *anything* else until they had spoken in detail with their advisor.
@@Lantertronics An inverted hollow triangle. The third ground symbol is Chassis Ground which has 45 degree lines. Each has a distinct meaning and although they get connected together they are not equivalent, the difference is where the currents flow. It is best to not call any of them "ground" as that creates confusion. Try to say "0V" or "Common" when describing circuits, unless you really mean "Chassis" or "PE". Look up the AES48 standard and the AES reprint on Shields and Grounds, available from their website, to understand why this is especially important for audio equipment. There are also some good videos here by Bill Whitlock on the subject.
A nitpick: Kelvin scale is NOT a "degrees" scale. A "degree" in temperature is defined as a set change in temperature measurement against an arbitrary (and relative) scale, while Kelvin temperature is defined as a set change in thermal energy defined by Boltzmann constant.
Hi Mr. Lanterman. I've been testing the Rene Schmitz VCO, and I have the same problem always. I let the temperature to set down, tunning to 32.7Hz. Next I put a random CV in, making the VCO play at high frequencies. Then I turn off the CV, and I see that the basic tunning isn't there anymore, because the transistor os hotter due to the high corrent of the high frequencies. And the tempco is not able to compensate for this, because the transistor is getting hotter from the inside. If tou have sugestion on how to deal with that I would be grateful.
Your tempco isn't aware that the transistor is heating up. Try better thermal coupling between the transistor and the tempco. Like thermal paste and clamp the two components together, maybe with a wire twisted around them.
If the transistor is getting that hot, maybe use a small heat sink, and attach the tempco to it also, with sufficient thermal paste between components & heatsink.
Anyone got any tips on making this circuit get more than one or so mA? Lowering the reference current resistor increases the slope, but doesn't change the max current -- high reference current with no other changes results in a sort of sigmoid shape. The actual max current seems to be controlled by the feedback resistor, but with the high voltage drop across it, lowering the resistance/increasing the current too much gets to unacceptably high wattage very quickly. Then again, maybe I just need to change the control range for the filter this leads to. Current control is weird, and I'm not really sure what values are best for avoiding noise while keeping power consumption low.
In most situations you probably don't *want* more than a mA -- if your filter is OTA based more than that may damage your OTA. If you want to change the total range you can try different values for the filter capacitors.
@@rolab280 Nah, I hate to nitpick the lecture with this stuff, but technically the unit is just “Kelvin”, not “degrees Kelvin” Honestly, in practice no one should care, but if you put it in a paper, it’s just 273K rather than 273°K. Makes typesetting easier anyway 😁
I think if I would have clicked on the video at 23:26 I would have immediately clicked it away and thought "woah that looks like way too much detail- I'm designing musical circuits, not building a rocket engine"- but fortunately I started at the beginning and understood very clearly the purpose of the equations. @22:00 you say "Now I'm going to do something fairly odd". That is not odd at all to a mathematician, it's the celebrated "telescope trick" used in many proofs (translating directly from German, not sure if it has the same name in English)- which should be in every mathematician's toolbox :).
The single most useful video I’ve seen for my designs. Fantastic resources in here and great basic understanding of design fundamentals.
Platinum-film resistive temperature detectors (RTD's) are a lot more tightly controlled than the old wire-wound tempcos. Since tempcos are always hard to find and expensive, a modern design should probably use a 4100-ppm/K Pt RTD in series with a fixed resistor.
Now I need to go work out how to get a current that varies 5100 ppm/K for supplying the common emitter of a Gilbert waveshaper that needs 5100 ppm/K (1.5× the transistor tempco)
THANK YOU for these videos. something about your voice, or colloquial mannerisms, or maybe just the cadence even, something, whatever it is, im not sure, but you are so far the most understandable source ive found yet. so again, for your time, effort, and seemingly unending knowledge on all these videos, thank you, you are incredibly appreciated.
Thank you for your kind words! They are especially encouraging since I'm quite self-conscious about my voice; I don't have a "radio DJ voice," and although I'm pretty dynamic in live lectures, I find it challenging to inject energy into my delivery when I'm the only person in the room.
@@Lantertronics i get that. do it myself even. but your videos are almost like programming my brain, it feels like. your explanations actually sink and and anchor themselves in my brain as opposed to just kinda coming in and bumping around a bit and then getting shoved out later by whatever else. ive actually learned so much ive tried to for so long with so many other avenues. i cant express enough how awesome these videos are. again, i greatly appreciate these, and im sure im not alone and that there will be scores of others behind me.
I love the professor's lectures. However, I have a suggestion on how the temperature coefficient of R_F can be derivative much easier:
Note that the thermal voltage V_T is proportional to the absolute temperature and thus we want R_F to also be proportional to the absolute temperature (assuming that R_0 is close to constant in temperature - an assumption the lecture makes without mentioning).
The reference temperature of 25Celsius corresponds to 298.15K absolute temperature, let's make that 300 Kelvin for simplicity. The unit of the temperature coefficient is ppm/K, so dimensional analysis suggests that the temperature coefficient should be the inverse of the absolute temperature, i.e., 1/300K = 0.33%/K = 3300ppm/K.
This can be justified as follows: when we start at the reference temperature of 300K and increase by 1K, the absolute temperature increases by 0.33%. We want R_F to increase by the same relative amount of 0.33%=3300ppm. But by definition, this is just the temperature coefficient.
This is very good explanation of one of the most complicated problems there is with analogue synths. This is the problem that many diy-s switch to digital domain. But if you love analogue electronics than you have to love this solution of the problem. It's at the same time messy and brilliant. But what is also important to know is that it is not the only solution there is
Ahhh beautiful, this part of VCO's has always been kind of a black box for me, but you explain it so clearly and it's really enticing to hear your enthusiasm :)
I just found out about you this weekend, and please do not stop what you are doing you are helping out a lot here not just me , I'm not a "real" engineer but have designed a few things like VCA, VCO (not completed well the design is complete but have not drawn it in DipTrace for fabrication) stuff like that and i find this very interesting.
This is well worth a sub :).
Thank you for your kind words!
Plodding thru. dude, you rock! Somehow my brain adapts to these formulae way better hearing it in diagram, then maybe one day, an actual breadboard, but this time I have a couple dozen xistors to run through for comparison when I get there. yay THANKS!
Hats off for different angles, beautiful👒
Thanks!
I can't thank you enough for these videos! I really get how these beasts work now, I took notes like crazy, and I'll soon be ready to build one for myself and bootstrap my first modular synth project. That's just awesome!
I think it would help to go into the limitations of these things a bit. When first working on this stuff it can be really frustrating to design an oscillator core and then a converter and hook them together to see that they don't really work together. I realize that that stuff might be a topic yall touch on in a different class or a different part of this class, but just realizing that the exponential converter doesn't really work like a perfect current source is one of those things that sounds obvious when you say it but a person hacking stuff together might not think of.
An easy way to have that happen would be to use an op-amp schmitt trigger based design for your core, and set the schmitt triger thresholds at something like +-5v for the eurorack standard. Then you wire it all up with a simple resistor to -12v as your current sink and see it working. So you go back and make this exponential current sink only for it to just freeze, because the current sink can't go below 0v.
I found some other explanations of these themes, using more simnple analogies. But coming from a mathematical background, this appeals more to me. Now to the experimentation phase!
Fantastic video.
Thank you so much! :)
At around 1:30, shouldn't ic = Is [exp(vbe/VT) - 1]? It really doesn't change anything after the approximation so it is "good enough for rock & roll" ...
Ah yeah, that's a typo.
Outstanding job. 🙂
At 4:14 the isn't the -1 outside the argument of the exponential? Rene has it there and it makes more sense why ic >> Is would permit the simlification
Great video!
Thanks!
@@Lantertronics I'm just curious... Did you and any of your students made a Prophet5 module?
@@PATRIK67KALLBACK They made a PCB layout (as did all the other students for their final projects). This semester I plan to sort through the various student PCB designs and see what ones are most ready to fab and test.
hi , if i have 1k 3000 ppm tempco what values have to change on schem to match everithing????
You have your parentheses in the wrong place: I_c=I_S [exp(V_be/V_T) - 1]. Given opposite temperature coefficients, you can always choose values to yield the resistance and temperature coefficient that you need.
Has Ian Fritz website been closed down? The domain shown in this video doesn't seem to work anymore...
And really nice video! Thank you for that! As other people have already stated, this is really helpful to get into the details of synth-making.
UPDATE: 3300ppm Tempco PTCs are only available as new old stock by now. A big producer of these (Akaneohm) stopped producing the convenient axial leaded 1%3300ppm 1k/2k/10k Resistors in 2018. Their resistors can be found for ~2$ a piece in several diy synth shops.
Is there a way to get around this shortage? Maybe mixing higher coefficients with regular resistors?
Pinning this. Thanks!
thnx, it's pretty confusing having a "negative" voltage from an op-amp heading in to the base a transistor.
Dear, Aaron, I want to notice that the OBMx has direct right base voltage for ladder - as you said is possible. The left base going to the ground.
Great lecture! Could you explain where the ic2/ic1 comes from? (around 7:00). I assume this would be due to the differential pair but I honestly wouldn't be able to write this down on paper
Calculating ic2/ic1 is purely an intermediate step to be able to get ic2 in terms of a "constant" ic1 without any Is term. Since he later sets ic1 as iref with the feedback op amp to ensure a constant iref, ic1 no longer has an Is term either. Since the value of ic2 is dependent on ic1, it also has no Is term either. ic2/ic1 doesn't show up as any sort of output in the circuit itself.
I am not an engineer but I have been creating various oscillator for my music projects, for the past three years. As I learn more, through videos such as yours and more hands on building videos, I have had inconsistent results with implementing exponential VC circuits, integrators and bias. Through your videos/lectures I am starting to question my understanding of voltage control. It seems that current is what really controls the musical quality of a circuit ad voltage is more or less the plotting range for a waveform, is this thought going in the right direction? I must admit when it comes to voltage and current I don't really seem to consider current/amperage as significant but now I am wondering if it's voltage that is arbitrary. Your help is much appreciated, thank you for creating this channel.
Almost every component is current controlled, you have to read the papers carefully what the device respond to, but in general it is current. (BJT is current controlled i guess this is what you wanted to know, but IF you only use it as an switch you just have to put a V or three you know it opens hard).
Only actual Voltage controlled are those mosfets that i know of and i never use them so i do not really know.
Thank you great lecture! I always wondered if there was an easier method to achieve this conversion. Matching a couple of transistors and then dealing with temperature it is a lot of work (still fun to me). But I always ask myself, In each op amp and ota there is a differential pair, but sometimes temperature compensates (If i'm understand correctly). Is there any method to empoy that? for example trying to take the output from an operational amplifier power line? totally noob question, sorry if I'm ignoring some basic rules.
What you can also do is stabilize temperature at some higher state like 40 celsius with a resistor so that there is no fluctuations in ambient temperature at the current mirror
@@krolu aaah, that's why moog do it! Never understood why, thank you very much.
Can i substitute the lm301 for a TL07x?
You mean use a TL07x in place of a LM301? Yeah. I’d be careful about going the other direction though, depending on application. TL07x is such a useful general purpose op amp, it’s good to have a drawer full of them.
@@Lantertronics Thank you!! 😄
The Electronotes exponential converter has several mistakes so it is not a good starting point. It is a corruption of applications notes published by Analog Devices, National Semiconductor and Texas Instruments in the late 60s/early 70s and misunderstands the importance of an attenuator comprising a 15k resistor and a 1k Q81 TC resistor. To be fair, it was never explained that the 15k resistor corrects the TC to be more like the necessary 3354ppm. If you put the wirewound TC resistor in the feedback of an adder you only get its actual TC which has a +/-10% tolerance. (The 1% is the resistance tolerance not the TC's.) 3018 to 3689 ppm is NOT close enough for rock and roll!
Wirewound TC resistors are manufactured from a reel of wire that is stretched during winding which alters the TC. The whole reel TC is carefully measured in an oil bath and the stretched TC is predicted and not measured after winding due to the difficulty and time to test individual components, hence the sloppy tolerance. TC resistors from the same batch will have the same error, but will not match another batch made from a different reel. If you build several VCOs from random TC parts they will diverge with temperature changes.
Modern platinum film RTD resistors are more accurate and have a TC of 3850ppm, but need a different circuit: one stage that adjusts the TC to 3450ppm and then another that adjusts 1V/oct to that.
Moral: don't believe everything you read in Electronotes, go back to the sources and then validate them.
btw, please stop using Protective Earth symbols for 0V Common, it's really annoying reading schematics drawn by somebody who does not understand grounding. These symbols are international standards defined in IEC 60417 and not a matter of personal preference.
I'm pinning this post.
What would the symbol for 0V common be?
Something for your nightmares: I was in our senior design lab one evening, and I heard a *boom* from a table occupied by a team advised by another professor, so I went over and asked if I could help. Among other things, I discovered they had attempted to solve their grounding problems by strapping the ground to the neutral *near the bench outlet*.
We had a *long* talk, and then I told them to not do *anything* else until they had spoken in detail with their advisor.
@@Lantertronics An inverted hollow triangle. The third ground symbol is Chassis Ground which has 45 degree lines. Each has a distinct meaning and although they get connected together they are not equivalent, the difference is where the currents flow. It is best to not call any of them "ground" as that creates confusion. Try to say "0V" or "Common" when describing circuits, unless you really mean "Chassis" or "PE". Look up the AES48 standard and the AES reprint on Shields and Grounds, available from their website, to understand why this is especially important for audio equipment. There are also some good videos here by Bill Whitlock on the subject.
hello the 18mv has to be + or -??
A nitpick: Kelvin scale is NOT a "degrees" scale. A "degree" in temperature is defined as a set change in temperature measurement against an arbitrary (and relative) scale, while Kelvin temperature is defined as a set change in thermal energy defined by Boltzmann constant.
Think bucla keeps Vlr at .7v because of some sort of capacitor threshold level?
Hi Mr. Lanterman. I've been testing the Rene Schmitz VCO, and I have the same problem always. I let the temperature to set down, tunning to 32.7Hz. Next I put a random CV in, making the VCO play at high frequencies. Then I turn off the CV, and I see that the basic tunning isn't there anymore, because the transistor os hotter due to the high corrent of the high frequencies. And the tempco is not able to compensate for this, because the transistor is getting hotter from the inside. If tou have sugestion on how to deal with that I would be grateful.
Not sure -- I'd recommend sending Rene an e-mail.
Your tempco isn't aware that the transistor is heating up.
Try better thermal coupling between the transistor and the tempco.
Like thermal paste and clamp the two components together, maybe with a wire twisted around them.
If the transistor is getting that hot, maybe use a small heat sink, and attach the tempco to it also, with sufficient thermal paste between components & heatsink.
Anyone got any tips on making this circuit get more than one or so mA? Lowering the reference current resistor increases the slope, but doesn't change the max current -- high reference current with no other changes results in a sort of sigmoid shape. The actual max current seems to be controlled by the feedback resistor, but with the high voltage drop across it, lowering the resistance/increasing the current too much gets to unacceptably high wattage very quickly.
Then again, maybe I just need to change the control range for the filter this leads to. Current control is weird, and I'm not really sure what values are best for avoiding noise while keeping power consumption low.
In most situations you probably don't *want* more than a mA -- if your filter is OTA based more than that may damage your OTA. If you want to change the total range you can try different values for the filter capacitors.
@@Lantertronics Mm, that makes sense! Thanks!
Guess which vid is going in my citations? ;3
BTW, isn't there a way to extract Vt out of a matched transistor junction?
History of these circuits would suggest not, but all the math is here, you should try!
Doubles every 10K* --- Kelvin aren't measured in degrees
Ofcourse it is. Kelvin, Celcius and Farenheit are all measured in degrees. What else would it be measured in?
@@rolab280 Nah, I hate to nitpick the lecture with this stuff, but technically the unit is just “Kelvin”, not “degrees Kelvin”
Honestly, in practice no one should care, but if you put it in a paper, it’s just 273K rather than 273°K. Makes typesetting easier anyway 😁
@@enginerdy i never realized that.
@@Mogwai06 Yeah I learned it here too. ;)
man, i better start studying more math
More math is always good! :)
gyrators (current voltage) 2 ports are fun