Hi everyone, welcome to PCB Academy.
My name is Avril.
Today I am going to talk about what is reflection in a transmission line and how voltage level fluctuates
when there is impedance discontinuity.
Then I will talk about some intentional and unintentional causes of reflections in a design, along
with couple of simulations in security Aurora 17.4 and Topology Explorer.
So let's get started.
We will start with very first question what is reflection in a transmission line.
So reflection is distortion on signal line due to impedance discontinuity.
And it may look like ringing but it is completely different from that.
We will understand that throughout the video.
Now due to reflections AC problem voltage can go low or high at any instances and cause false degree.
Now let's talk about what I mean by impedance discontinuity.
duty.
So impedance discontinuity means the change in instantaneous impedance signals is down the line.
Now it can be intentional or unintentional.
For example added corner on the transmission line, added vias, branches or stubs, connectors or packages,
etc. as you can see on the diagram.
Now let's try to understand reflection in terms of magnitude of signals sent and reflected.
So till now we got the idea of reflection.
And as a signal propagate down the transmission line it sees instantaneous impedance.
And if instantaneous impedance is uniform that means impedance one is equal to impedance two.
Equal to impedance three.
Then we call it characteristic impedance.
But if instantaneous impedance ever change for whatever reasons, some of the signals will reflect back
in opposite direction and some part of the signal will continue, but with different amplitude.
So here all the instances where impedance change we call them impedance discontinuity.
Continuity.
In the next step, I am going to talk about how to estimate reflection voltage.
So imagine on a PCB we have impedance discontinuity at one instant and their impedances are z one and
z two.
Now we are sending a signal on this transmission line of voltage V incident.
But due to impedance discontinuity some signal voltage will reflect.
We call it v reflected and some signal will continue to transmit.
We call it V transmitted.
As you can see on your screen.
So the relationship between the magnitude of incident and reflected signal will be v reflected divided
by v incident is equal to z two minus z one upon z two plus z one.
We also represent it with row and we call this ratio reflection coefficient.
So from this equation we got to know the amount of reflection is directly proportional to delta z or
change in impedance.
Now let's see let's see a quick example of how to apply this equation.
To calculate we reflected and we transmitted.
So as you can see in this example Z1 is equal to 50 ohm, z2 is equal to 75 ohm and v incident is one
volt.
Now we'll apply the formula v reflected divided by v incident.
It will be 75 -50 divided by 75 plus 50 which will be 0.2.
So if we multiply it by 100 we'll get reflection coefficient is 20%.
That means the amount of reflected voltage is 20% of V incident which is one volt.
And if we do that we'll get 0.2V is v reflected.
Similarly v transmitted will be v incident minus v reflected.
So it will be 0.8V.
So this is how you can apply this equation to calculate reflection voltage.
Now as we discussed reflection coefficient.
Similarly we have a term transmission coefficient which is t is equal to v transmitted divided by v
incident is equal to two times z to upon z one plus z two.
Now how we got the equations of transmission coefficient and reflection coefficient.
We have applied Ohm's law on these two equations.
First one is I incident minus I reflected is equal to I transmitted v incident minus v reflected is
equal to v transmitted.
And here we have to apply v is equal to I into z.
For z one and z two and we will get transmission coefficient and reflection coefficient equation from
there.
Now we can go ahead and see the simulation on Aurora 17.4.
So in Aurora 17.4 I have simulated statics two development board.
And this is the reflection post layout analysis.
And here you can see in the simulation table I have simulated for all the data buses which has 64 bits.
And from focus data you can select for which parameter you wanted to see the results.
So I have selected propagation delay here.
And by double clicking over propagation delay you can sort this table.
So as you can see parallel data bus 56 has maximum propagation delay.
So what I have done I have just selected that.
So as you can see this highlighted part of the track has maximum propagation delay and impedance discontinuity
due to these change in impedances inside the simulation plot.
You can see what you are sending from U7 which is our FPGA controller.
And what you are receiving at XU2 which is a Dimm module connector.
So if you select this waveform you can see this waveform has lot of false triggering.
It is not even crossing vine for few nanoseconds.
So this is happening due to reflection or impedance discontinuity on the line.
And similarly you can check for parallel data 57 5859.
All this set of propagation delays and it will highlight all the tracks which has impedance discontinuity.
So you can go back to layout, process and change all these layouts.
So if you want me to create a separate video on how I have done that post layout, reflection analysis,
step by step process, just let me know in the comment section.
Now we are good to go for bounce diagram.
So bounce diagram is representing the whole chain of reflection on a transmission line due to impedance
discontinuities even because of source resistors.
So for predicting reflection on any transmission line we need to know following parameters.
First is time delay of transmission line or length.
Second is impedance of each region of signal propagation.
And third one is V incident.
If we know these three parameters we can easily predict reflection through bounce diagram.
Now I'm just going to give you a quick demo of bounce diagram.
So let's see that.
So let's consider an example where source driving an open termination transmission line and we have
v source is equal to one volt.
Source impedance is equal to ten ohm which will be impedance discontinuity for 50 ohm transmission line.
And time delay is given one nanoseconds.
So in case time delay is not given you have to find out what is the length of the transmission line,
and you can calculate the time delay from that.
So in the very first step we are going to calculate v incident.
So we have v source which is connected to ten ohm source resistance.
And we have a 50 ohm transmission line.
Now we have to find the voltage between 10 ohm and 50 ohm.
And that will be V incident of 50 ohm transmission line.
So we'll apply simple voltage divider V incident is equal to V's multiplied by 50 divided by 50 plus
ten.
And when you will calculate it you will get 0.84 V.
four volt.
Now we are good to go to create a bounce diagram.
So in a bounce diagram we'll have source 50 ohm transmission line and resistor.
But remember that this source has ten ohm source resistors.
That means we incident is not one volt.
It is 0.84V that we have calculated in step one.
Now step two is what will receive at the receiver side.
So incident voltage 0.84V will reflect back because it is a open termination at the receiver end.
And when you probe it you will find at the receiver side will get 0.84V plus 0.84V, which will be 1.68V
at the receiver side.
So it will put that in a waveform you will get after two nanoseconds.
So one nanoseconds it will be zero because at that time signal will be travelling from transmitter to
receiver.
After one nanosecond it will reach there and will get the voltage of .68 volt.
Now let's talk about step three.
So because of open termination at the receiver end .84 volt will reflect.
And now this will be the incident voltage.
We'll apply the simple formula of V reflected upon V incident.
So that will be reflection coefficient is equal to z two minus z one upon z one plus z two.
So ten -50 divided by ten plus 50.
And we'll get -0.67V.
So this will be reflection coefficient.
And from that we have to find out reflected voltage.
So we'll get it by multiplying it by v incident which will be 0.84in this case.
So we'll get v reflected is equal to -0.56V.
Now this v reflected will be again reflected back to receiver side where at the other end we have 1.68V.
So again it is a open termination resistor when it will reach at the receiver side will get 1.68, -0.56,
-0.56.
If will summarise, it will get 1.68, minus two times 0.56 and will get 0.56V.
And if you see that in the waveform for one nanosecond, 1.68V will maintain because at that time signal
will be travelling to the transmitter side.
All right.
And then it will be reflected back.
And this time we'll get 0.56V at the receiver when we'll measure it.
So the receiver voltage will back to 0.56V.
Now let's move to step five.
So at step four we have seen that -0.56V will incident and -0.56V will reflect from receiver end.
All right.
It will take one nanosecond further to reach at step five.
So again due to open Point.
Termination.
-0.56V will reflect.
And again we'll going to calculate reflection coefficient.
We'll use the same formula where we'll have v reflected upon v incident minus ten -50 upon ten plus
50.
So it will be -0.67.
Now we have to multiply it with v incident to get the v reflected.
So v incident is -0.56.
So we'll get v reflected 0.37.
So now incident voltage for step six will be 0.37.
And we have open termination at the other side.
So it will multiply by two and add it to whatever the voltage there at step four.
So it will be 0.56 plus two times 0.37 which will be 1.3V.
So that means now the waveform voltage will go to 1.3V.
So after n number of reflection like we have discussed from point one to step five, our waveform will
be will be stable at one volt because one volt was the exact incident voltage.
All right, so I hope you got the idea of bounce diagram.
Let me know in the comment section in case of any doubt.
So at last I am going to summarize this video with list of discontinuities that can cause reflection
problem.
And the first one will be end of transmission line should be terminated.
So if you are not using proper termination there will be reflection on the line and which will cause
AC problems.
Second is a package lead.
Third one is an input capacitors pad.
So if you are using any capacitors on the line make sure they are paired.
Should be very small or you should use a small package of capacitor.
Fourth is vase on the signal line.
Fifth one is a connector stub.
Branches and test pads can cause reflection issues.
And last but not the least, crossover another transmission line.
So that's it from reflection side.
See you in the next video.