Welcome to stream PCB Academy.
In this video we are going to discuss about transmission lines and their properties.
Plus we'll see a couple of demos on cadence or cadence Sigrity simulation tools.
So let's get started.
We'll start with what is transmission line?
A transmission line is composed of any two conductors that have lengths.
Transmission line used to send a signal from point A to point B, as you can see on the screen.
The conductor I talked about during the definition of transmission lines are signal path and its return
path.
Further on transmission line, we can define an ideal transmission line using some circuit elements,
for example R, L, and C plus.
Apart from these resistive inductive and capacitive properties, we have two more very important parameters
that we should consider for an ideal transmission line are its characteristic impedance and time delay.
You can ask why characteristic impedance and propagation delay is so important, and the answer is if
impedance and propagation delay is uniform throughout the transmission line, there will be no signal
integrity problem.
Let's discuss what is interconnects.
So as I told you on my previous video about signal integrity, I told you between transmitter and receiver
signal travels through different packages vias, boards, stubs.
Then it reaches to receiver.
So these are all the things which comes between transmitter and receivers are interconnects.
Now here it comes the very important principle.
As per doctor Bogatin SciPy simplified book.
That is all the interconnects are transmission line.
So that means during designing we have to keep this thing in our mind that route all the interconnects
accordingly and make sure all the interconnects should follow the same design rules.
For example, characteristic impedance should be uniform throughout the line between TX and RX.
Further on this, let's discuss what is uniform transmission line.
So as its name suggests, uniform means throughout the transmission line.
Few things or few properties will not change.
So what are those few properties that makes a transmission line uniform?
First property which makes a transmission line uniform is its cross section down the line.
And the second property is how identical signal and its return path is.
Now here we are going to introduce another principle from CIP simplified book.
We can say all uniform transmission lines are controlled impedance lines.
Let's see few examples of uniform transmission line.
First is twisted pair, second one is coaxial cable, third one is coplanar then microstrip.
And maybe you have also seen the embedded microstrip.
And then the sixth one is stripline.
Now let's see some examples of transmission line models using Cadence Topology Explorer.
It helps you to you to create topology of your circuit using models.
Now let's open Cayden's Topology Explorer.
And here I'm going to place interconnects.
And let's see what our ideal transmission line looks like.
So I have placed that okay.
And if you see the property of the first transmission line as we already discussed.
So what are the two properties of a transmission line.
One is its characteristic impedance and another one is its length or delay.
So if you wanted to switch between length and propagation delay you have to just click over here.
And from there you can switch.
So now it will start showing the length of a transmission line.
All right.
Now I'm going to give you one example of a lossy transmission line.
So again we'll click over this one and we'll select microstrip one.
Okay.
Right click and.
Okay.
So this is our lossy transmission line.
And as you can see we have discussed a couple of types of losses that is possible in a transmission
line.
So we have to put all these values here right.
So it has trace conductivity thickness dielectric losses dielectric thickness.
What is the thickness of dielectric above the signal line.
What is the below the signal line.
Right.
Similarly you can see one more example of strip line.
All right.
So as you can see here we'll see couple of more extra parameters that will be trace width trace thickness.
And yeah and all few things are similar to the the microstrip transmission line.
So yeah these are the few things.
And we'll we'll see these things in more details during the simulation part.
If you want a free trial of cadence tools, you can go to the link given in the description and fill
the form.
Now let's talk about LC model to represent a transmission line.
So as you can see on the screen we call it first order model of a transmission line.
Like we discussed a transmission line consists of signal and its return path.
And if we represent that into its LC model.
So here L will be the loop inductance of every circuit return current.
And C will be the coupling capacitor between signal and its return path.
So we can represent a transmission line with this model as well.
Now we'll see how to estimate the capacitance and inductance per unit length for a transmission line.
So we use a very simple equation for that for capacitance per unit length.
It is 83 divided by its characteristic impedance multiplied by square root of dielectric constant.
And similarly for inductor it will be 0.083 multiplied by the characteristic impedance of a transmission
line multiplied by square root of dielectric constant, and its unit will be nano Henry per inch.
Let's take a very quick example.
Let's suppose we have a transmission line of 50 ohm characteristic impedance.
And the dielectric constant we are using is four.
Then the capacitance per unit length and inductance per unit length of that transmission line will be
3.3 picofarad per inch and 8.3 nano Henry per inch.
So I got this value from the formulas we discussed earlier.
Before going for the derivation of this formula, maybe you can have this question in your mind that
why we should know about these capacitor and inductor per unit length.
And the reason is very simple.
We can model any transmission line on spy simulator.
So as you can see on the spies I am recording a step response of a two inch transmission line which
has 50 ohm impedance, and the dielectric constant is four, which has a 200 ohm source resistance and
50 ohm termination resistor.
So let's see the step response.
As you can see, we are getting different transient response of different nodes from the circuit.
We can know okay these are the nodes that we are probing and we are getting different response.
We'll go into much detail because I have already planned.
So right now as you can see on the circuit we are using a 50 ohm termination.
Similarly there will be different response if we do like open transmission line.
And in case if it is shorted then there will be different response.
Right now this termination is equal to the the impedance of transmission line.
If it is less than the impedance of a transmission line, what will happen if it is greater than the
transmission line Impedance.
Then what will be the response?
Similarly, if I put a capacitive load and inductive load.
So it is a very huge topic and I have already planned a video on that.
So for now I just wanted to show you okay, why we needed those two equations to model a transmission
line on a space.
Now in the next step, I am going to derive the equations that we have discussed earlier for capacitance
per unit length of a transmission line and inductance per unit length.
Why I am going to do this derivation.
Because through this derivation, we are going to learn a couple of more equations which are very useful
for a design engineer.
So the first condition for this derivation is.
So we have to consider that we have in finite number of.
LC elements.
On a transmission line.
Okay.
So this is the first condition that will make sure this is the case only then.
Then this derivation or these equations will be so much effective.
All right.
So for this case what will be the total capacitance.
So C total will be.
Capacitance per unit length multiplied by the total length of a transmission line.
Right.
Let's name it equation one.
Similarly what will be the total inductance.
So L total will be the inductor per unit length multiplied by the total length of a transmission line.
This will be our second equation.
Now.
On the given LC model, if you recall the LC model that we have discussed earlier.
It will apply network theory and solve.
The differential Equation.
We'll get two equations out of it.
So the first equation will be.
Characteristic impedance will be square root of inductance per unit length divided by.
Capacitance per unit length.
That will be our third equation.
What else we got to know from that.
Another is its time delay.
So the time delay will be.
Square root of C total multiplied by L total.
Okay.
Let's make it equation four.
Okay.
And similarly if on this equation if we put the equation one and equation two from above uh discussion
we'll get a formula of time delay which will be length square root of c l multiplied by l.
All right.
So this will be also equation for.
All right because we derived it from this one only.
Now what else we use for time delay.
So for time delay on a transmission line is equal to length divided by the velocity of signal.
Right.
Now what is the velocity of the signal.
Velocity of a signal is.
So you can just send this here right.
And this will be here.
So velocity of a signal will be length divided by time delay.
All right.
Now we're going to put a value of length from here.
So if we put that equation for will get velocity will be is equal to one upon under root of kl multiplied
by wl.
All right.
So this will be our equation for right.
And you can also use these equations to get the estimate velocity of a signal at all.
All right now.
What is the relation between speed and dielectric constant?
If you recall from our discussion what is the relation between speed and dielectric constant.
So from that we got to know velocity of a signal will be speed of light divided by square root of dielectric
constant.
Right.
And we always this is very known equation that we use to get the velocity of a signal right on a particular
dielectric material.
And here c will be equal to 12 inch per nanosecond okay.
So this is the light speed that we are considering here okay.
Now put these values on our equations that we have discussed earlier.
So we have a constant here.
All right.
And we'll put that value on our equations, which is velocity is equal to one upon under root of CL
into LX.
So after putting this velocity is equal to light speed divided by square root of dielectric constant,
we will put that value we will get to know from equation five.
CL will be is equal to seven multiplied by dielectric constant divided by inductance per unit length.
Right.
And similarly if you send this here this here it will be the equation for inductance.
All right.
Now just recall the equations that we have discussed earlier.
One is z naught is equal to lx upon CL.
All right.
And if will and velocity is equal to this is equation number five.
One upon CL multiplied by LX.
Now from these equations, if we put the value of either CL or LX on this.
All right we'll get a relation of CL is equal to one upon z naught into velocity.
And similarly so this is very important equation.
Let's write it down on next page.
Similarly LX will be is equal to z naught upon v right.
And we know the formula for v right.
It is c upon square root of epsilon r right.
And if we put that value and the constant will get the our equation for calculating the capacitance
per unit length of a transmission line and inductance per unit length.
So we will get this formula CL is equal to 83 upon z naught Multiplied by square root of epsilon r and
L is equal to 0.083 multiplied by.
Characteristic impedance multiplied by square root of epsilon r nano Henry per inch.
And this will be picofarad per inch.
Right.
So these are the equations that we got.
From this derivation.
All right.
Plus we got to know a couple of more equations that we can use to estimate the signal speed and estimate
the characteristic impedance.
We know the capacitance and inductance right.
Next from a types of transmission line discussion we have already covered ideal uniform or lossless
transmission line.
And we have discussed it in very detail.
We have discussed how to estimate the properties of a lossless transmission line.
Now another part is lossy transmission line.
Where we consider different parameters to estimate the losses of a signal throughout the line between
transmitter and receiver.
So as per doctor Bogatin s book, we have divided losses into five different categories.
First category of loss is radiative loss.
Second is coupling to adjacent layer or trace.
Third one is return current loss.
Fourth is skin effect losses.
And fifth one is thermal losses.
We will discuss these losses, their sources and how to overcome these during lossy transmission line
in future video.
So in conclusion with what I covered in this video, I hope you have a better understanding of what
a transmission line is.
The equation you can use to estimate the capacitance and inductance per unit length.
And finally, how cadence modeling and simulation tools help you to get a better understanding of signal
topology and behavior.
See you in the next video.