Interconnect for impedance circuit board design

One of the more and more important and concerned topics in the field of high-speed PCB design is the circuit board design of controlled impedance and the characteristic impedance of interconnection lines on the circuit board. However, for non electronic design engineers, this is also a very confusing and not intuitive problem. Even many electronic design engineers are also confused about this. This document will give a brief and intuitive introduction to the characteristic impedance, hoping to help you understand the fairly basic quality of transmission lines.

What is a PCB transmission line?

What is a transmission line? Two conductors of a certain length constitute a transmission line. One of the conductors becomes the channel for signal transmission, while the other conductor forms the return path of the signal (here we refer to the return path of the signal, which is actually what we usually understand, but for the convenience of description, let's forget the concept of "ground".). In a multi-layer circuit board design, each PCB interconnection line constitutes a conductor in the transmission line, which uses the adjacent reference plane as the second conductor of the transmission line or the return path of the signal. What kind of PCB interconnection line is a good transmission line? Generally, if the characteristic impedance on the same PCB interconnection line is consistent everywhere, such transmission line will become a high-quality transmission line. What kind of circuit board is called a circuit board with controlled impedance? The circuit board with controlled impedance means that the characteristic impedance of all transmission lines on the PCB conforms to the unified target specification. Generally, it means that the value of the characteristic impedance of all transmission lines is between 25 Ω and 70 Ω.

From the perspective of signal

An effective way to consider the characteristic PCB impedance is to examine what the signal itself sees when it travels along the transmission line. To simplify the discussion of the problem, it is assumed that the transmission line is of the type of microwave transmission belt, and the cross section of the transmission line is consistent when the signal travels along the transmission line.

Add a step signal of 1V amplitude to the transmission line. The step signal is a 1V battery, which is connected by the front end and is respectively connected between the signal line and the return path. At the moment of switching on the battery, the signal voltage waveform will travel in the dielectric at the speed of light, and the speed is usually about 6 inches/ns (why the signal travels so fast, rather than approaching the speed of electron propagation, which is about 1cm/s, which is another topic, and will not be further introduced here). Of course, here the signal still has a conventional definition. The signal is defined as the voltage difference between the signal line and the return path, which is always obtained by measuring the voltage difference between any point on the transmission line and the adjacent signal return path.

The signal is transmitted forward at a speed of 6 inches/ns along the transmission line. What happens to the signal during transmission? During the first 10ps interval, the signal traveled 0.06 inches along the transmission line. Assuming that the locking time is at this moment, consider what happens to the transmission line. During the traveling distance, the signal transmission establishes a constant signal with a stable amplitude of 1V between this transmission line and the corresponding adjacent signal return channel. This means that additional positive charges and additional negative charges have accumulated on the traveling transmission line and the corresponding return path to establish this stable voltage. It is the difference of these charges that establishes and maintains a stable 1V voltage signal between the two conductors, and the stable voltage signal between the conductors establishes a capacitance between the two conductors.

The transmission line segment behind the signal wavefront at this moment is not clear that there will be signals to be transmitted, so the voltage between the signal line and the return path is still maintained at zero. In the next 10ps time interval, the signal will travel a certain distance along the transmission line, and the result of the signal continuing to propagate is that a 1V signal voltage will be established between another 0.06 inch long transmission line segment and the corresponding signal return path. In order to achieve this, a certain amount of positive charge must be injected into the signal line, and the same amount of negative charge must be injected into the return path of the signal. Every 0.06 inch length of the signal along the transmission line, more positive charges will be injected into the signal line, and more negative charges will be injected into the signal return path.

Where do these charges come from? The answer is from the signal source, that is, the battery we use to provide the step signal and connect to the front of the transmission line. As the signal propagates on the transmission line, the signal continuously charges the transmission line segment it passes through to ensure that a voltage of 1V is established and maintained between the signal line and the return path wherever it goes during signal transmission. Every 10ps interval, the signal will travel a certain distance on the transmission line and draw a certain amount of charge from the power system δ Q。 Battery at a time interval δ The inside of t provides a certain amount of charge to the outside δ Q. A constant signal current is formed. A positive current flows from the battery into the signal line, while a negative current of the same magnitude flows through the return path of the signal.

The negative current flowing through the signal return path is exactly the same as the positive current flowing into the signal line. Moreover, at the position of the signal wave front, the AC current flows through the capacitor consisting of the signal line and the signal return path to complete the signal loop.

Characteristic impedance of transmission line

From the perspective of the battery, once the design engineer connects the lead of the battery to the front end of the transmission line, there will always be a constant current flowing out of the battery, and the voltage signal will remain stable. Some people may ask, what kind of electronic components have such behavior? When adding a constant voltage signal, it will maintain a constant current value, which is of course a resistance.

For the battery, when the signal propagates forward along the transmission line, 0.06 inches of transmission line will be added every 10ps interval and charged to 1V. The newly added charge obtained from the battery ensures that a stable current is maintained from the battery. When a constant current is absorbed from the battery, the transmission line is equivalent to a resistance, and the resistance value is constant. We call it the surge impedance of the transmission line.

Similarly, when the signal travels forward along the transmission line, the signal will continuously probe the electrical environment of the signal line every certain distance, and try to determine the impedance when the signal travels further forward. Once the signal has been added to the transmission line and propagated along the transmission line, the signal itself is always checking how much current is required to charge the length of the transmission line propagated within a 10ps time interval, and keep charging this part of the transmission line segment to 1V. This is exactly the instantaneous impedance value we want to analyze.

From the perspective of the battery itself, if the signal travels along the transmission line at a constant speed, and the transmission line is assumed to have a consistent cross section, then every time the signal travels a fixed length (such as the distance of signal propagation in a 10ps time interval), it is necessary to obtain the same amount of charge from the battery to ensure that this transmission line is charged to the same signal voltage. Every time the signal travels a fixed distance, it will get the same current from the battery, and keep the signal voltage consistent. In the process of signal transmission, the instantaneous impedance of all parts of the transmission line is consistent.

In the process of signal propagation along the transmission line, if there is a consistent signal propagation speed everywhere on the transmission line, and the capacitance per unit length is also the same, then the signal will always see a completely consistent instantaneous impedance in the process of propagation. Since the impedance of the whole transmission line remains constant, we give a specific name to represent this feature or characteristic of a specific transmission line, which is called the characteristic impedance of the transmission line. Characteristic impedance refers to the value of the instantaneous impedance seen by the signal when it travels along the transmission line. If the characteristic impedance seen by the signal is consistent at any time during the transmission of the signal along the transmission line, such transmission line is called the transmission line with controlled impedance.

Characteristic impedance of transmission line is a very important factor in design

The transient impedance or characteristic impedance of the transmission line is a very important factor affecting the signal quality. If the impedance between adjacent signal propagation intervals is consistent during signal propagation, the signal can propagate forward very smoothly, so the situation becomes very simple.

In order to ensure better signal quality, the goal of signal interconnection design is to ensure that the impedance seen in the signal transmission process remains as constant as possible. This mainly refers to keeping the characteristic impedance of the transmission line constant. Therefore, PCB design, production and manufacturing of PCB with controlled impedance become more and more important. As for any other design know-how, such as rather small golden finger length, terminal matching, daisy chain connection or branch connection, etc., it is to ensure that the signal can see consistent transient impedance.

Calculation of characteristic impedance

From the above simple model, we can deduce the value of the characteristic impedance, that is, the value of the instantaneous impedance seen during the transmission of the signal. The impedance Z seen by the signal at each propagation interval is consistent with the basic definition of impedance

Z=V/I

The voltage V here refers to the signal voltage applied to the transmission line, while the current I refers to the signal voltage applied to the transmission line at each time interval δ Total charge obtained from the battery in t δ Q. So

I= δ Q/ δ t

The charges flowing into the transmission line (these charges finally come from the signal source) are used to form the capacitance between the newly added signal line and the return path during signal transmission δ C is charged to voltage V, so

δ Q=V δ C

We can relate the capacitance value CL of the unit length of the capacitance simultaneous interpreting transmission line caused by the signal traveling a certain distance in the transmission process and the speed U of the signal propagation on the transmission line. At the same time, the distance of signal propagation is the speed U multiplied by the time interval δ t。 therefore

δ C=CLU δ t

Combining all the above equations, we can deduce that the instantaneous impedance is:

Z=V/I=V/（ δ Q/ δ t）=V/（V δ C/ δ t）=V/（VCLU δ t/ δ t）=1/（CLU）

It can be seen that the instantaneous impedance is related to the capacitance value of unit transmission line length and the speed of signal transmission. It can also be assumed that this is the definition of the characteristic impedance of the transmission line. In order to distinguish the characteristic impedance from the actual impedance Z, a subscript 0 is specially added to the characteristic impedance. From the above derivation, the characteristic impedance of the signal transmission line has been obtained:

Ｚ０＝１／（CLU）

If the capacitance value per unit length of the transmission line and the speed of signal propagation on the transmission line remain constant, the transmission line will have a constant characteristic impedance within its length range, and such transmission line is called the transmission line with controlled impedance.

It can be seen from the above brief description that some intuitive understanding of capacitance can be linked with the intuitive understanding of the newly discovered characteristic impedance. In other words, if the signal wiring in the PCB is widened, the capacitance value per unit length of the transmission line will increase, and the characteristic impedance of the transmission line can be reduced.

A thought-provoking topic

You can often hear some confusing statements about the characteristic impedance of PCB transmission lines. It is known from the above analysis that after the signal source is connected to the transmission line, the characteristic impedance of the transmission line with a certain value should be visible, for example, 50 Ω. However, if an ohmmeter is connected to a 3-foot RG58 cable, the measured impedance is infinite. The answer to the question is that the impedance value seen from the front end of any transmission line changes with time. If the time for measuring the cable impedance is short enough to be comparable to the time for the signal to go back and forth in the cable, you can measure the surge impedance of the cable or the characteristic impedance of the cable. However, if you wait for enough time, part of the energy will be reflected back and detected by the measuring instrument. At this time, you can detect the change of impedance. Generally, in this process, the impedance will change back and forth until the impedance value reaches a stable state: if the end of the cable is open circuit, the final impedance value is infinite; if the end of the cable is short circuit, the final PCB impedance value is zero.