I can't seem to get my head wrapped around as to why You subtracted Mutual inductance from L0... I thought you were going add it.... I can understand why 2Cm was added with C0, but Numerator part is bit confusing for me... Would love to hear your explanation Zach... As always, wonderful to learn from the master like you... Keep these videos coming and don't hesitate to lean on the difficult topics... ☺️
It's because we've defined the two signals to have opposite polarity and the impedance is defined in terms of the difference between these two signals. The Telegrapher's equations are being used to determine the propagation of opposite polarity signals down a transmission line, which requires taking a difference and produces the negative sign next to the mutual inductance. If we were looking at even-mode impedance (or common-mode impedance for the pair), we would have a positive in the numerator. If you write out a 1st order differential operator for the Telegrapher's equations (which will include mutual inductance) and then apply the operator to the pair of signals propagating on the coupled structure, the negative sign comes out naturally. If you like I can put together a video on this
Hi Zack, when talking about calculating the propagation constant. Just to clarify, you are talking about the rise/fall time frequency right, not a clock or signal frequency? The frequency would be about 0.35/Tr?
The propagation constant is used with the angular frequency to tell you the velocity of the signal, it is not a rise time or fall time. The signal will move a certain distance during its rise time, and that distance is the propagation velocity multiplied by the rise time. Also the equation you mention about "frequency = 0.35/Tr" has nothing to do with signal velocity, and it is probably the least understood equation in all of PCB design. Here is a video that tells you where that equation comes from and why it only applies in a specific situation that is not relevant to real high-speed designs: ruclips.net/video/eVV42ahG0as/видео.html
@@Zachariah-Peterson To be clear, as digital signals are a combination of infinite sinusoidal waves at different frequencies. The frequency used with the conversion factor 2pi, is the fundamental frequency, so the frequency at which the (square) wave repeats its pattern.
I would like to know whats the effect of differential impedance mismatch? In regular single tracks, impedance mismatch causes reflections. Is it the same for differential tracks, but what its reflected is a differential voltage?
All differential voltages are defined by the difference between signal levels on two traces. So if you have a differential impedance mismatch, you need to define what happens to each of the signals individually. To have a differential impedance mismatch, then there must be a mismatch on each individual trace. If that occurs on one of the traces, then that signal will reflect from the impedance mismatch or discontinuity, so if only one trace has a discontinuity then only that signal on that trace will reflect. If it happens on both traces, then both the opposite polarity signals reflect, so in this case you would think of it as a reflection of a differential voltage wave. No matter what happens on the two traces, the receiver will always be sensing a differential signal, which is just the difference between the two opposite polarity signals.
Excellent explanation. First of all, thank you very much for educating us. ha! Now, I have a question. Like all equations seen, they depend on the frequency of the signal (Lo, Co, Lm, Cm). How does Altium calculate impedances (single-ended or differential)?? considering that it does not allow us to enter a specific frequency. thank.!
TBH I don't know all of the details used in that calculation. Altium's impedance solver uses a 2D method of moments or boundary element method calculation with a wideband Debye model for the dielectric constant, just like other commercial solvers. I do not know if it applies the wideband optimization calculation I talk about in some of my research (See my channel for more on this). It is only returning the characteristic or differential impedance based on the stackup dimensions and materials, it is NOT the input impedance or anything else; this is standard for commercial stackup calculators. Some CAD packages with built-in interconnect analyzers will give you the impedance of each trace section with a similar algorithm based on the presence of nearby conductors, so they give you another level of accuracy. With Altium, you can export your data for use in other field solver applications.
Hello! I would like to ask how to handle rigid flex designs where a diff pair starts somewhere on the rigid part, say on a top layer with a 4 layer stackup, and then eventually is routed over to the flex part, going through the inner layers. Im not sure what kind of answer I'm looking for to be honnest, but just a general overview with an application example I find is really helpful. Thanks !
Great video!! Explains a lot. I just have one question. Recently I was watching one of Rick Hartley's videos on diff pairs in which he said that he once routed a diff pair in a way that one leg was on one end of the board and the other was on the other end just to show that the spacing does not matter. Could you please confirm if this is really the case?
The (combined) signal from a differential pair is the signal of one minus the signal of the other. So sure, you could even send them an hour apart on different types of paths (at the cost of a lot of latency and buffering). But why bother? The reason to use a differential pair in the first place is to better overcome noise, and if the two half-signals aren't facing similar conditions (similar effective length in similar location with similar interference), then you're really just sending two unrelated but redundant signals.
@@jimjjewett Sure, but what if I just length match the two signals? I am not really trying to route them apart just making sure that slight difference in coupling wont get the signal to fail, right? So, in theory if I route them a hundred mils apart and length match them, the signal should not fail?
@@waleedarshad8160 Length matching (ideally, with length weighted by impedance) means they arrive at the same time, which simplifies decoding them. But why are you even using a differential trace instead of just a single trace? Presumably, because you're worried about crosstalk or other interference corrupting your signal. With two traces that are very close, this can mostly cancel out. 1 - (-1) == 2, but so does ((1-3) - (-1-3)), even though noise of 3 would greatly overwhelm a single-trace signal. If they're too far apart, you're likely to instead get (1-3) - (-1), and ... the differential pair didn't really protect you from the noise.
I'm not Zach but I agree totally with you. And I believe this is just what it is explained in this video : there are only two 50 ohms traces that when you bring them close enough, well this mutual Cm&Lm start to affect your diff impedance which is no more 2*Zo. The reason to have differential pairs is to remove common mode noise (conducted). For cross talk forget it, twisted differential wires can cancel crosstalk radiated from around, but differential pairs are just routed on the same plan : they will never (ever) have the same crosstalk, unless a boldy guy decides to route a trace along this diff pair or on the layer above...
@@jimjjewett Your explanation is correct to an extent, but the common mode noise is most commonly due to ground offsets (if I am not wrong) and on a PC Boards with a uniform ground plane, I don't think this should be an issue. One common reason to use differential signaling instead of single ended signals is that the differential signals allow for greater data rates, which I think are not possible with single-ended transmission. Correct me if I am wrong, there is just too much information on the internet related to this topic and I am just trying to figure things out myself.
This is amazing sir keep up these lessons
Thank you ❤
What's your favourite exercise for triceps?
Pushups with a weight vest
I can't seem to get my head wrapped around as to why You subtracted Mutual inductance from L0... I thought you were going add it.... I can understand why 2Cm was added with C0, but Numerator part is bit confusing for me... Would love to hear your explanation Zach...
As always, wonderful to learn from the master like you... Keep these videos coming and don't hesitate to lean on the difficult topics... ☺️
It's because we've defined the two signals to have opposite polarity and the impedance is defined in terms of the difference between these two signals. The Telegrapher's equations are being used to determine the propagation of opposite polarity signals down a transmission line, which requires taking a difference and produces the negative sign next to the mutual inductance. If we were looking at even-mode impedance (or common-mode impedance for the pair), we would have a positive in the numerator.
If you write out a 1st order differential operator for the Telegrapher's equations (which will include mutual inductance) and then apply the operator to the pair of signals propagating on the coupled structure, the negative sign comes out naturally.
If you like I can put together a video on this
Great content and highly recommend!!
Excellent explanation thanks please keep going on, have you given any lecture on common mode impedance
Thank you, I have not created a video on that topic yet but it is something I have been meaning to do. Maybe we can get to it this week!
Perfectly clear and excellent expression! Thanks a lot!
Can we cover BGA via breakouts? Maybe something covering a SoC or DDR breakout example and tie in the recent length matching topic to it.
Thanks but what about common mode impedance? What is these two (differential and common mode) kind of impedances are?
Hi Zack, when talking about calculating the propagation constant. Just to clarify, you are talking about the rise/fall time frequency right, not a clock or signal frequency?
The frequency would be about 0.35/Tr?
The propagation constant is used with the angular frequency to tell you the velocity of the signal, it is not a rise time or fall time. The signal will move a certain distance during its rise time, and that distance is the propagation velocity multiplied by the rise time. Also the equation you mention about "frequency = 0.35/Tr" has nothing to do with signal velocity, and it is probably the least understood equation in all of PCB design. Here is a video that tells you where that equation comes from and why it only applies in a specific situation that is not relevant to real high-speed designs: ruclips.net/video/eVV42ahG0as/видео.html
@@Zachariah-Peterson To be clear, as digital signals are a combination of infinite sinusoidal waves at different frequencies. The frequency used with the conversion factor 2pi, is the fundamental frequency, so the frequency at which the (square) wave repeats its pattern.
I would like to know whats the effect of differential impedance mismatch? In regular single tracks, impedance mismatch causes reflections. Is it the same for differential tracks, but what its reflected is a differential voltage?
All differential voltages are defined by the difference between signal levels on two traces. So if you have a differential impedance mismatch, you need to define what happens to each of the signals individually. To have a differential impedance mismatch, then there must be a mismatch on each individual trace. If that occurs on one of the traces, then that signal will reflect from the impedance mismatch or discontinuity, so if only one trace has a discontinuity then only that signal on that trace will reflect. If it happens on both traces, then both the opposite polarity signals reflect, so in this case you would think of it as a reflection of a differential voltage wave. No matter what happens on the two traces, the receiver will always be sensing a differential signal, which is just the difference between the two opposite polarity signals.
also, there are different layered diff. pair (_P on L1, _N on L2), and there are NO GND diff pairs like RS-485 or ethernet.
Thanks
Excellent explanation. First of all, thank you very much for educating us. ha! Now, I have a question. Like all equations seen, they depend on the frequency of the signal (Lo, Co, Lm, Cm). How does Altium calculate impedances (single-ended or differential)?? considering that it does not allow us to enter a specific frequency. thank.!
TBH I don't know all of the details used in that calculation. Altium's impedance solver uses a 2D method of moments or boundary element method calculation with a wideband Debye model for the dielectric constant, just like other commercial solvers. I do not know if it applies the wideband optimization calculation I talk about in some of my research (See my channel for more on this). It is only returning the characteristic or differential impedance based on the stackup dimensions and materials, it is NOT the input impedance or anything else; this is standard for commercial stackup calculators. Some CAD packages with built-in interconnect analyzers will give you the impedance of each trace section with a similar algorithm based on the presence of nearby conductors, so they give you another level of accuracy. With Altium, you can export your data for use in other field solver applications.
Hello! I would like to ask how to handle rigid flex designs where a diff pair starts somewhere on the rigid part, say on a top layer with a 4 layer stackup, and then eventually is routed over to the flex part, going through the inner layers. Im not sure what kind of answer I'm looking for to be honnest, but just a general overview with an application example I find is really helpful. Thanks !
Please refer some electronics books for hardware engineer to learn basics of electronics.
I wish I could get private tutoring from you sir 😘
I'm preparing courses on all of this stuff, will eventually be offered through FEDEVEL
Great video!! Explains a lot. I just have one question. Recently I was watching one of Rick Hartley's videos on diff pairs in which he said that he once routed a diff pair in a way that one leg was on one end of the board and the other was on the other end just to show that the spacing does not matter. Could you please confirm if this is really the case?
The (combined) signal from a differential pair is the signal of one minus the signal of the other. So sure, you could even send them an hour apart on different types of paths (at the cost of a lot of latency and buffering). But why bother? The reason to use a differential pair in the first place is to better overcome noise, and if the two half-signals aren't facing similar conditions (similar effective length in similar location with similar interference), then you're really just sending two unrelated but redundant signals.
@@jimjjewett Sure, but what if I just length match the two signals? I am not really trying to route them apart just making sure that slight difference in coupling wont get the signal to fail, right? So, in theory if I route them a hundred mils apart and length match them, the signal should not fail?
@@waleedarshad8160 Length matching (ideally, with length weighted by impedance) means they arrive at the same time, which simplifies decoding them. But why are you even using a differential trace instead of just a single trace? Presumably, because you're worried about crosstalk or other interference corrupting your signal. With two traces that are very close, this can mostly cancel out.
1 - (-1) == 2, but so does ((1-3) - (-1-3)), even though noise of 3 would greatly overwhelm a single-trace signal. If they're too far apart, you're likely to instead get (1-3) - (-1), and ... the differential pair didn't really protect you from the noise.
I'm not Zach but I agree totally with you. And I believe this is just what it is explained in this video : there are only two 50 ohms traces that when you bring them close enough, well this mutual Cm&Lm start to affect your diff impedance which is no more 2*Zo. The reason to have differential pairs is to remove common mode noise (conducted). For cross talk forget it, twisted differential wires can cancel crosstalk radiated from around, but differential pairs are just routed on the same plan : they will never (ever) have the same crosstalk, unless a boldy guy decides to route a trace along this diff pair or on the layer above...
@@jimjjewett Your explanation is correct to an extent, but the common mode noise is most commonly due to ground offsets (if I am not wrong) and on a PC Boards with a uniform ground plane, I don't think this should be an issue. One common reason to use differential signaling instead of single ended signals is that the differential signals allow for greater data rates, which I think are not possible with single-ended transmission. Correct me if I am wrong, there is just too much information on the internet related to this topic and I am just trying to figure things out myself.
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