Controlling the impedance of your PCB traces is so important for maintaining signal integrity.
So today I will talk about trace impedance.
Why the impedance of a PCB trace is so important, and how to bridge ideal and real world devices.
Along with demo on cadence orcad and piece for lossless transmission lines.
So let's get started.
What is impedance of a PCB trace?
Electrically impedance is relation between current through a device and voltage across it.
As you can see on a given diagram, its impedance will be voltage divided by current through this device.
There are two types of devices.
Ideal devices and real devices.
Ideal devices are those on which we can perform simulation, mathematical modeling, circuit theory,
applications, etc. and real devices can be interconnects, traces on the board, leads in a package,
and decoupling capacitors, etc..
Now here we can recall two very popular statements about real and ideal devices.
Maybe you have heard these before.
First one is we can't measure impedance of an ideal device, but we can calculate.
And second one is we can't calculate the impedance of real device but we can measure it.
Then what is the solution for this ideal and real world crisis.
Our goal is to model real devices using ideal circuit elements, so its simulated impedance can be approximately
equal to actual measured impedance values.
I will show you how.
As you can see on the left side of your screen, we have a physical or real world ceramic capacitor.
And at the right side of the screen we have ideal capacitor.
And in both cases the value is one nanofarad.
What do you think?
Which one is correct?
Obviously in ideal world we will get exact value, but in real world we will get few parasitics along
with capacitance.
As you can see for this case we will have capacitor which will be 0.67 Nanofarad.
Measured resistance will be 0.5Ω and inductance will be 1.78 nano.
Henry.
Now, if we move this information to ideal world, we'll get a equivalent circuit of a capacitor.
And if we'll simulate this, we'll get impedance versus frequency response, which will be equal to
the measured value of impedance at particular frequency.
Now I'll show you how we can model a physical ceramic capacitor in ideal world.
For that I'm going to open capture sis.
And here you can see I've made a very simple circuit which has voltage source, source resistor and
equivalent circuit of ceramic capacitor with its parasitics.
Now if we run this simulation, we'll get these kind of waveforms.
One is the voltage across the equivalent capacitor which will be voltage between this point and ground
and current through the equivalent capacitor.
Now just recall the very first formula we have discussed at the beginning of this video, which was
impedance is equal to voltage upon current.
I did the same thing here.
So this is the plot of impedance versus frequency response.
So on this x axis we have frequency.
And on the y axis we have impedance.
So as you can see on this impedance versus frequency response at the very lowest point of this plot
this capacitor will act like a resistor.
And at the left side of your screen it will act like a capacitor.
Why?
Because when we are increasing the frequency, its impedance is going low.
And similarly, at the right side of the plot, it will act like a inductor.
Because when we increase the frequency, its impedance will increase.
I also plot for log of impedance.
So maybe you are familiar with these kind of plot on the data sheet of ceramic capacitors.
So now these values will be very much similar to the actual measured values, because we have imported
the physical capacitor on ideal world.
Now I will show you the plot of which is recorded on VNA which is impedance versus frequency response.
And you will find it very similar with the simulated plot for a ceramic capacitor.
So till now we have discussed very general properties of impedance and how we can bridge ideal and real
world.
From now on we will talk about impedance of a PCB trace and transmission lines.
Another topic is concept of instantaneous and characteristic impedance.
We will start with drawing a first order model of a transmission line.
And if you do not know about the transmission line, you can simply click over the I button.
I have already made a made a detailed video on this topic on this first order model.
As signal travels through the transmission line, it will see some impedance depends on the value of
loop inductance and its coupling capacitor between signal and its return path.
That impedance is instantaneous impedance of a transmission line, and we represent it with z naught.
Z naught is equal to square root of inductance per unit length, divided by capacitance per unit length.
On the same first order model, if impedance is same at every instance means z naught, one should be
equal to z naught two and z naught three.
We call it uniform transmission line.
On this given transmission line model, its instantaneous impedance characterizes the line.
That's why we call it characteristic impedance means.
For a uniform transmission line, instantaneous impedance will be equal to characteristic impedance.
Now I have a question for you.
If line is non-uniform what will be its characteristic impedance type?
Your answer in comment section below.
Low till now.
After these many discussions, we got to know the importance of uniform transmission line and why impedance
should be same throughout the interconnects.
Now I will show you a quick demo.
What will happen if impedance is not same throughout the transmission line or track?
For that, let's open capture Rs.
And here I have made a very simple Spice model.
As you can see, I have added a voltage source for step response.
Then it has a source resistor of 200 ohm, and I have added three transmission line of 50 ohm, 80 ohm
and 50 ohm again.
So that means there is a impedance discontinuity.
And I have terminated those transmission line with a 50 ohm resistor.
Time delay for each transmission line is same.
Now before going for the simulation, I want you to expect what will be the results of simulation.
So we will start with this point here.
Signal is travelling and it will see a first transmission line of 50 ohm.
Then there will simply apply a voltage divider which will be 50 divided by 200 plus 50.
So if you calculate that, you will get 0.2V because the step response is for one volt.
Now again if will if signal move further after 170 picosecond it will see another transmission line
which has 80 ohm.
Then again will put voltage divider and will get 80 divided by 200 plus 80 which will be 0.285V.
So that means after 170 picosecond it will move to 0.285V.
Then again it will see a 50 ohm.
That means it will return back to 0.2 volt.
And after that we have a termination resistor.
Then it will be remain constant on 0.2V.
So this is what we are expecting.
Let's see the waveform.
So after running the simulation as expected for 170 picosecond, it is there at 200 Millivolt.
Right after that it is going to 0.28V or 280 millivolt because we have a 80 ohm transmission line.
Then again it's come back to 50 ohm.
And here we are getting some glitch or some further reflection which is because of termination resistor.
All right.
And then it is stabilized continuously.
Now here I am just sending a single step response.
Let's suppose we are sending continuous pulse here.
Then this kind of reflection will be happening on each step.
All right so I'm going to attach this project.
You can download it from description I want you to just spend some time with it and, you know change
values and play with the reflection concept.
So from here you got to know how these impedance continuity is so important.
Let's move to four factors that affects the impedance of a PCB trace.
First one is trace width.
Second is copper thickness.
Third one is dielectric thickness.
And last is dielectric constant.
Trace width is width of a copper foil.
And as we increase the trace width, its capacitance per unit length will increase and its inductance
per unit length will decrease.
And overall, its characteristic impedance will decrease.
Because characteristic impedance is square root of inductance per unit length divided by capacitance
final length.
As you can see on table 1.1, I have increased the trace width from 5 to 10 mil and its characteristic
impedance reduced from 81 to 63, and inductance per unit length decreased from 11.6 to 9.038.
And similarly, capacitance unit length increased from 1.7 to 2.26.
But there will be no change on propagation delay.
You can ask why there is no change in propagation delay because it is a function of length of a transmission
line and speed of signal, it is independent of other physical properties or parameters.
Copper thickness is thickness of a PCB trace.
We can also say it will increase plating thickness or copper weight.
The copper thickness will increase of a PCB trace.
Let's see how it is related to the characteristic impedance z naught.
If will increase the copper weight, plating thickness or copper thickness, capacitance per unit length
will increase and inductance per unit length will decrease and overall you will see the impedance characteristic
impedance will decrease.
Let's see from table 1.2.
I have increased the copper plating thickness from 1oz to 2 ounce and its characteristic impedance reduced,
inductance reduced and its capacitance increased.
There will be no change on propagation delay and similar results are found on table number 1.3.
When I have changed the copper weight from 0.5oz to 1.5oz.
Dielectric thickness is the thickness of insulating material between signal and its return path.
If we increase the dielectric thickness, capacitance per unit length will decrease and inductance per
unit length will increase.
But you will see the overall characteristic impedance of a signal line.
It will increase.
As you can see on table 1.4, I have increased dielectric thickness from 10 to 20mm and its characteristic
impedance increased from 54 to 79.
Its inductance per unit length increased.
Capacitance per unit length decreased.
But there will be no change on propagation delay.
Dielectric constant is.
Ratio of electric permittivity of material and electric permittivity of vacuum for a fixed frequency.
If we increase the value of dielectric constant, its capacitance per unit length will increase, but
there will be no change on inductance per unit length, and overall characteristic impedance will decrease.
Now here you can ask why I haven't included any table here.
Because for variable frequency we can't predict the impedance behavior for any dielectric value.
It can increase the impedance for a particular frequency.
And similarly the same dielectric material can decrease the impedance for different frequencies.
So these are the four factors to look at to ensure signal integrity in your designs.
I hope you found this video useful and now have a better understanding of what impedance is in terms
of PCB trace, and why it is important to maintain good signal integrity.
Make sure to check out links provided in the description below.
If you would like to learn more about impedance and in an upcoming video, I will talk about single
ended and differential impedance.