WEBVTT 00:00.520 --> 00:02.280 Welcome to stream PCB Academy. 00:02.440 --> 00:06.560 In this video we are going to discuss about transmission lines and their properties. 00:06.920 --> 00:11.160 Plus we'll see a couple of demos on cadence or cadence Sigrity simulation tools. 00:11.320 --> 00:12.480 So let's get started. 00:12.720 --> 00:14.720 We'll start with what is transmission line? 00:14.920 --> 00:19.680 A transmission line is composed of any two conductors that have lengths. 00:19.720 --> 00:25.040 Transmission line used to send a signal from point A to point B, as you can see on the screen. 00:25.360 --> 00:31.640 The conductor I talked about during the definition of transmission lines are signal path and its return 00:31.640 --> 00:32.000 path. 00:32.520 --> 00:37.600 Further on transmission line, we can define an ideal transmission line using some circuit elements, 00:37.600 --> 00:40.880 for example R, L, and C plus. 00:40.880 --> 00:46.760 Apart from these resistive inductive and capacitive properties, we have two more very important parameters 00:46.760 --> 00:53.120 that we should consider for an ideal transmission line are its characteristic impedance and time delay. 00:54.240 --> 00:59.720 You can ask why characteristic impedance and propagation delay is so important, and the answer is if 00:59.760 --> 01:04.970 impedance and propagation delay is uniform throughout the transmission line, there will be no signal 01:04.970 --> 01:05.970 integrity problem. 01:06.850 --> 01:08.770 Let's discuss what is interconnects. 01:09.050 --> 01:16.290 So as I told you on my previous video about signal integrity, I told you between transmitter and receiver 01:16.930 --> 01:21.970 signal travels through different packages vias, boards, stubs. 01:22.290 --> 01:24.890 Then it reaches to receiver. 01:25.970 --> 01:31.890 So these are all the things which comes between transmitter and receivers are interconnects. 01:31.930 --> 01:34.290 Now here it comes the very important principle. 01:34.410 --> 01:37.730 As per doctor Bogatin SciPy simplified book. 01:38.450 --> 01:41.570 That is all the interconnects are transmission line. 01:41.730 --> 01:48.490 So that means during designing we have to keep this thing in our mind that route all the interconnects 01:48.490 --> 01:54.170 accordingly and make sure all the interconnects should follow the same design rules. 01:54.170 --> 01:59.250 For example, characteristic impedance should be uniform throughout the line between TX and RX. 02:00.010 --> 02:03.470 Further on this, let's discuss what is uniform transmission line. 02:03.670 --> 02:07.870 So as its name suggests, uniform means throughout the transmission line. 02:07.910 --> 02:10.670 Few things or few properties will not change. 02:11.230 --> 02:15.270 So what are those few properties that makes a transmission line uniform? 02:16.270 --> 02:21.350 First property which makes a transmission line uniform is its cross section down the line. 02:21.790 --> 02:26.350 And the second property is how identical signal and its return path is. 02:27.070 --> 02:31.750 Now here we are going to introduce another principle from CIP simplified book. 02:32.870 --> 02:38.990 We can say all uniform transmission lines are controlled impedance lines. 02:39.030 --> 02:41.550 Let's see few examples of uniform transmission line. 02:41.590 --> 02:48.470 First is twisted pair, second one is coaxial cable, third one is coplanar then microstrip. 02:49.150 --> 02:52.110 And maybe you have also seen the embedded microstrip. 02:52.430 --> 02:54.750 And then the sixth one is stripline. 02:56.870 --> 03:01.350 Now let's see some examples of transmission line models using Cadence Topology Explorer. 03:01.710 --> 03:05.000 It helps you to you to create topology of your circuit using models. 03:05.840 --> 03:08.200 Now let's open Cayden's Topology Explorer. 03:09.080 --> 03:13.240 And here I'm going to place interconnects. 03:14.360 --> 03:18.560 And let's see what our ideal transmission line looks like. 03:19.200 --> 03:21.360 So I have placed that okay. 03:22.320 --> 03:28.720 And if you see the property of the first transmission line as we already discussed. 03:28.840 --> 03:31.240 So what are the two properties of a transmission line. 03:31.520 --> 03:37.520 One is its characteristic impedance and another one is its length or delay. 03:37.600 --> 03:42.520 So if you wanted to switch between length and propagation delay you have to just click over here. 03:42.520 --> 03:43.880 And from there you can switch. 03:45.400 --> 03:48.240 So now it will start showing the length of a transmission line. 03:49.440 --> 03:50.080 All right. 03:52.080 --> 03:54.880 Now I'm going to give you one example of a lossy transmission line. 03:54.880 --> 03:59.880 So again we'll click over this one and we'll select microstrip one. 04:01.240 --> 04:01.640 Okay. 04:02.930 --> 04:04.290 Right click and. 04:04.610 --> 04:04.970 Okay. 04:05.250 --> 04:08.130 So this is our lossy transmission line. 04:08.490 --> 04:14.290 And as you can see we have discussed a couple of types of losses that is possible in a transmission 04:14.290 --> 04:14.650 line. 04:14.810 --> 04:18.170 So we have to put all these values here right. 04:18.210 --> 04:24.650 So it has trace conductivity thickness dielectric losses dielectric thickness. 04:25.090 --> 04:30.010 What is the thickness of dielectric above the signal line. 04:30.130 --> 04:32.170 What is the below the signal line. 04:32.210 --> 04:32.690 Right. 04:32.970 --> 04:38.530 Similarly you can see one more example of strip line. 04:42.290 --> 04:42.890 All right. 04:43.130 --> 04:50.410 So as you can see here we'll see couple of more extra parameters that will be trace width trace thickness. 04:51.490 --> 04:59.850 And yeah and all few things are similar to the the microstrip transmission line. 05:01.130 --> 05:02.450 So yeah these are the few things. 05:02.450 --> 05:07.100 And we'll we'll see these things in more details during the simulation part. 05:07.860 --> 05:12.380 If you want a free trial of cadence tools, you can go to the link given in the description and fill 05:12.380 --> 05:12.900 the form. 05:13.180 --> 05:16.740 Now let's talk about LC model to represent a transmission line. 05:17.140 --> 05:21.980 So as you can see on the screen we call it first order model of a transmission line. 05:23.540 --> 05:27.740 Like we discussed a transmission line consists of signal and its return path. 05:28.020 --> 05:31.100 And if we represent that into its LC model. 05:31.100 --> 05:35.620 So here L will be the loop inductance of every circuit return current. 05:36.220 --> 05:41.540 And C will be the coupling capacitor between signal and its return path. 05:42.220 --> 05:45.860 So we can represent a transmission line with this model as well. 05:47.340 --> 05:53.300 Now we'll see how to estimate the capacitance and inductance per unit length for a transmission line. 05:54.300 --> 05:58.780 So we use a very simple equation for that for capacitance per unit length. 05:59.060 --> 06:05.600 It is 83 divided by its characteristic impedance multiplied by square root of dielectric constant. 06:06.080 --> 06:12.800 And similarly for inductor it will be 0.083 multiplied by the characteristic impedance of a transmission 06:12.800 --> 06:21.440 line multiplied by square root of dielectric constant, and its unit will be nano Henry per inch. 06:21.480 --> 06:23.080 Let's take a very quick example. 06:23.480 --> 06:27.880 Let's suppose we have a transmission line of 50 ohm characteristic impedance. 06:27.880 --> 06:30.400 And the dielectric constant we are using is four. 06:31.120 --> 06:36.720 Then the capacitance per unit length and inductance per unit length of that transmission line will be 06:36.720 --> 06:40.680 3.3 picofarad per inch and 8.3 nano Henry per inch. 06:40.840 --> 06:44.360 So I got this value from the formulas we discussed earlier. 06:45.040 --> 06:50.520 Before going for the derivation of this formula, maybe you can have this question in your mind that 06:50.560 --> 06:54.720 why we should know about these capacitor and inductor per unit length. 06:55.480 --> 06:57.080 And the reason is very simple. 06:57.320 --> 07:01.600 We can model any transmission line on spy simulator. 07:01.840 --> 07:08.970 So as you can see on the spies I am recording a step response of a two inch transmission line which 07:08.970 --> 07:15.650 has 50 ohm impedance, and the dielectric constant is four, which has a 200 ohm source resistance and 07:15.650 --> 07:17.890 50 ohm termination resistor. 07:19.010 --> 07:20.610 So let's see the step response. 07:20.810 --> 07:28.210 As you can see, we are getting different transient response of different nodes from the circuit. 07:28.210 --> 07:33.770 We can know okay these are the nodes that we are probing and we are getting different response. 07:33.890 --> 07:38.090 We'll go into much detail because I have already planned. 07:38.210 --> 07:42.490 So right now as you can see on the circuit we are using a 50 ohm termination. 07:42.490 --> 07:49.010 Similarly there will be different response if we do like open transmission line. 07:49.010 --> 07:52.650 And in case if it is shorted then there will be different response. 07:52.850 --> 07:57.970 Right now this termination is equal to the the impedance of transmission line. 07:57.970 --> 08:02.890 If it is less than the impedance of a transmission line, what will happen if it is greater than the 08:02.930 --> 08:04.660 transmission line Impedance. 08:04.940 --> 08:06.380 Then what will be the response? 08:06.620 --> 08:09.420 Similarly, if I put a capacitive load and inductive load. 08:09.420 --> 08:13.540 So it is a very huge topic and I have already planned a video on that. 08:13.700 --> 08:19.940 So for now I just wanted to show you okay, why we needed those two equations to model a transmission 08:19.940 --> 08:21.020 line on a space. 08:22.140 --> 08:29.020 Now in the next step, I am going to derive the equations that we have discussed earlier for capacitance 08:29.020 --> 08:32.940 per unit length of a transmission line and inductance per unit length. 08:33.500 --> 08:35.740 Why I am going to do this derivation. 08:35.740 --> 08:41.500 Because through this derivation, we are going to learn a couple of more equations which are very useful 08:41.500 --> 08:42.740 for a design engineer. 08:44.340 --> 08:49.300 So the first condition for this derivation is. 08:49.300 --> 08:57.140 So we have to consider that we have in finite number of. 08:59.380 --> 09:00.420 LC elements. 09:04.800 --> 09:06.760 On a transmission line. 09:10.720 --> 09:11.080 Okay. 09:11.200 --> 09:17.240 So this is the first condition that will make sure this is the case only then. 09:17.280 --> 09:20.800 Then this derivation or these equations will be so much effective. 09:21.280 --> 09:21.880 All right. 09:22.280 --> 09:26.400 So for this case what will be the total capacitance. 09:26.680 --> 09:28.400 So C total will be. 09:29.840 --> 09:34.840 Capacitance per unit length multiplied by the total length of a transmission line. 09:34.840 --> 09:35.320 Right. 09:35.520 --> 09:37.560 Let's name it equation one. 09:38.440 --> 09:40.880 Similarly what will be the total inductance. 09:41.440 --> 09:48.800 So L total will be the inductor per unit length multiplied by the total length of a transmission line. 09:49.240 --> 09:50.920 This will be our second equation. 09:52.240 --> 09:52.520 Now. 09:54.800 --> 09:59.320 On the given LC model, if you recall the LC model that we have discussed earlier. 10:01.600 --> 10:03.920 It will apply network theory and solve. 10:03.920 --> 10:05.370 The differential Equation. 10:05.650 --> 10:07.650 We'll get two equations out of it. 10:07.930 --> 10:09.450 So the first equation will be. 10:09.930 --> 10:16.890 Characteristic impedance will be square root of inductance per unit length divided by. 10:16.930 --> 10:18.370 Capacitance per unit length. 10:18.770 --> 10:20.490 That will be our third equation. 10:22.330 --> 10:24.290 What else we got to know from that. 10:25.050 --> 10:26.850 Another is its time delay. 10:28.330 --> 10:29.730 So the time delay will be. 10:34.570 --> 10:40.490 Square root of C total multiplied by L total. 10:42.210 --> 10:42.410 Okay. 10:42.410 --> 10:44.810 Let's make it equation four. 10:45.690 --> 10:46.010 Okay. 10:46.050 --> 10:53.330 And similarly if on this equation if we put the equation one and equation two from above uh discussion 10:54.210 --> 11:03.690 we'll get a formula of time delay which will be length square root of c l multiplied by l. 11:03.730 --> 11:04.330 All right. 11:04.530 --> 11:06.540 So this will be also equation for. 11:06.660 --> 11:08.700 All right because we derived it from this one only. 11:10.380 --> 11:13.620 Now what else we use for time delay. 11:15.460 --> 11:22.820 So for time delay on a transmission line is equal to length divided by the velocity of signal. 11:23.180 --> 11:23.620 Right. 11:24.100 --> 11:25.980 Now what is the velocity of the signal. 11:26.780 --> 11:28.220 Velocity of a signal is. 11:29.460 --> 11:32.460 So you can just send this here right. 11:32.460 --> 11:33.500 And this will be here. 11:33.860 --> 11:39.620 So velocity of a signal will be length divided by time delay. 11:39.620 --> 11:40.300 All right. 11:40.340 --> 11:43.180 Now we're going to put a value of length from here. 11:45.100 --> 11:53.100 So if we put that equation for will get velocity will be is equal to one upon under root of kl multiplied 11:53.100 --> 11:54.140 by wl. 11:54.700 --> 11:55.260 All right. 11:55.260 --> 12:00.220 So this will be our equation for right. 12:00.260 --> 12:06.300 And you can also use these equations to get the estimate velocity of a signal at all. 12:06.360 --> 12:08.480 All right now. 12:10.560 --> 12:14.240 What is the relation between speed and dielectric constant? 12:17.360 --> 12:23.400 If you recall from our discussion what is the relation between speed and dielectric constant. 12:23.760 --> 12:32.120 So from that we got to know velocity of a signal will be speed of light divided by square root of dielectric 12:32.120 --> 12:32.800 constant. 12:33.000 --> 12:33.360 Right. 12:33.400 --> 12:40.480 And we always this is very known equation that we use to get the velocity of a signal right on a particular 12:40.480 --> 12:41.640 dielectric material. 12:42.520 --> 12:51.880 And here c will be equal to 12 inch per nanosecond okay. 12:52.200 --> 12:57.240 So this is the light speed that we are considering here okay. 12:57.280 --> 13:01.120 Now put these values on our equations that we have discussed earlier. 13:02.160 --> 13:04.920 So we have a constant here. 13:05.360 --> 13:05.960 All right. 13:06.360 --> 13:14.010 And we'll put that value on our equations, which is velocity is equal to one upon under root of CL 13:14.050 --> 13:14.810 into LX. 13:17.450 --> 13:24.690 So after putting this velocity is equal to light speed divided by square root of dielectric constant, 13:25.090 --> 13:30.130 we will put that value we will get to know from equation five. 13:31.530 --> 13:40.290 CL will be is equal to seven multiplied by dielectric constant divided by inductance per unit length. 13:40.330 --> 13:40.490 Right. 13:40.530 --> 13:44.690 And similarly if you send this here this here it will be the equation for inductance. 13:45.530 --> 13:46.130 All right. 13:47.010 --> 13:51.610 Now just recall the equations that we have discussed earlier. 13:51.810 --> 13:58.010 One is z naught is equal to lx upon CL. 13:58.490 --> 13:59.130 All right. 14:00.050 --> 14:04.250 And if will and velocity is equal to this is equation number five. 14:05.250 --> 14:09.580 One upon CL multiplied by LX. 14:10.540 --> 14:18.660 Now from these equations, if we put the value of either CL or LX on this. 14:19.780 --> 14:28.900 All right we'll get a relation of CL is equal to one upon z naught into velocity. 14:30.300 --> 14:33.100 And similarly so this is very important equation. 14:33.140 --> 14:34.860 Let's write it down on next page. 14:37.300 --> 14:42.980 Similarly LX will be is equal to z naught upon v right. 14:43.020 --> 14:45.140 And we know the formula for v right. 14:45.380 --> 14:50.300 It is c upon square root of epsilon r right. 14:50.340 --> 14:57.540 And if we put that value and the constant will get the our equation for calculating the capacitance 14:57.540 --> 15:01.540 per unit length of a transmission line and inductance per unit length. 15:01.580 --> 15:11.590 So we will get this formula CL is equal to 83 upon z naught Multiplied by square root of epsilon r and 15:11.590 --> 15:17.030 L is equal to 0.083 multiplied by. 15:17.550 --> 15:24.110 Characteristic impedance multiplied by square root of epsilon r nano Henry per inch. 15:24.790 --> 15:27.950 And this will be picofarad per inch. 15:28.150 --> 15:28.630 Right. 15:28.870 --> 15:31.030 So these are the equations that we got. 15:31.270 --> 15:32.750 From this derivation. 15:33.350 --> 15:33.910 All right. 15:33.950 --> 15:40.510 Plus we got to know a couple of more equations that we can use to estimate the signal speed and estimate 15:40.510 --> 15:41.830 the characteristic impedance. 15:41.870 --> 15:46.310 We know the capacitance and inductance right. 15:49.710 --> 15:57.350 Next from a types of transmission line discussion we have already covered ideal uniform or lossless 15:57.350 --> 15:58.630 transmission line. 15:58.630 --> 16:00.790 And we have discussed it in very detail. 16:00.870 --> 16:06.550 We have discussed how to estimate the properties of a lossless transmission line. 16:07.910 --> 16:10.650 Now another part is lossy transmission line. 16:12.730 --> 16:19.530 Where we consider different parameters to estimate the losses of a signal throughout the line between 16:19.890 --> 16:21.410 transmitter and receiver. 16:22.210 --> 16:30.290 So as per doctor Bogatin s book, we have divided losses into five different categories. 16:31.210 --> 16:33.610 First category of loss is radiative loss. 16:33.850 --> 16:36.250 Second is coupling to adjacent layer or trace. 16:36.650 --> 16:38.290 Third one is return current loss. 16:38.490 --> 16:40.050 Fourth is skin effect losses. 16:40.410 --> 16:42.130 And fifth one is thermal losses. 16:42.770 --> 16:48.130 We will discuss these losses, their sources and how to overcome these during lossy transmission line 16:48.170 --> 16:49.210 in future video. 16:49.970 --> 16:54.770 So in conclusion with what I covered in this video, I hope you have a better understanding of what 16:54.810 --> 16:56.250 a transmission line is. 16:56.250 --> 17:00.250 The equation you can use to estimate the capacitance and inductance per unit length. 17:00.250 --> 17:07.010 And finally, how cadence modeling and simulation tools help you to get a better understanding of signal 17:07.050 --> 17:08.170 topology and behavior. 17:08.530 --> 17:09.610 See you in the next video.