Characteristic impedance problem of PCB technology in high-speed design
In high-speed design, the characteristic impedance problem of controlled impedance boards and lines troubles many Chinese engineers. This article introduces the basic properties, calculation and measurement methods of characteristic impedance in a simple and intuitive way.
In high-speed design, the characteristic impedance of controlled impedance boards and lines is one of the most important and common problems.
First, let’s understand the definition of transmission line: a transmission line consists of two conductors of a certain length, one conductor is used to send signals and the other is used to receive signals (remember that “loop” replaces the concept of “ground”). In a multilayer board, each line is a part of the transmission line, and the adjacent reference plane can be used as a second line or loop. The key to a line becoming a “good performance” transmission line is to keep its characteristic impedance constant throughout the line.
The key to a circuit board becoming a “controlled impedance board” is to make the characteristic impedance of all lines meet a specified value, usually between 25 ohms and 70 ohms. In a multilayer circuit board, the key to good transmission line performance is to keep its characteristic impedance constant throughout the line.
But what exactly is characteristic impedance?
The easiest way to understand characteristic impedance is to look at what the signal encounters during transmission. When moving along a transmission line with the same cross-section, this is similar to the microwave transmission shown in Figure 1. Assume that a 1-volt voltage step wave is added to this transmission line, such as connecting a 1-volt battery to the front end of the transmission line (which is located between the transmission line and the return line). Once connected, this voltage wave signal propagates along the line at the speed of light, and its speed is usually about 6 inches/nanosecond. Of course, this signal is indeed the voltage difference between the transmission line and the return line, which can be measured from any point on the transmission line and the adjacent point on the return line. Figure 2 is a schematic diagram of the transmission of this voltage signal.
Zen’s method is to “generate a signal” first, and then propagate it along this transmission line at a speed of 6 inches/nanosecond.
The first 0.01 nanosecond advances 0.06 inches. At this time, the transmission line has excess positive charge, and the return line has excess negative charge. It is these two charge differences that maintain the 1-volt voltage difference between the two conductors, and the two conductors form a capacitor.
In the next 0.01 nanosecond, the voltage of a 0.06-inch transmission line must be adjusted from 0 to 1 volt.
This requires adding some positive charge to the sending line and some negative charge to the receiving line. For every 0.06 inches of movement, more positive charge must be added to the sending line and more negative charge to the loop. Every 0.01 nanosecond, another section of the transmission line must be charged, and then the signal begins to propagate along this section. The charge comes from the battery at the front end of the transmission line. When moving along this line, it charges the continuous part of the transmission line, thus forming a voltage difference of 1 volt between the sending line and the loop. Every 0.01 nanosecond forward, some charge (±Q) is obtained from the battery, and the constant amount of electricity (±Q) flowing out of the battery within a constant time interval (±t) is a constant current. The negative current flowing into the loop is actually equal to the positive current flowing out, and just at the front end of the signal wave, the AC current passes through the capacitor composed of the upper and lower lines, ending the entire cycle. The process is shown in Figure 3.
Impedance of the line
From the battery’s perspective, as the signal propagates along the transmission line, it charges the continuous 0.06-inch transmission line segment every 0.01 nanoseconds. When a constant current is drawn from the power source, the transmission line looks like an impedance and its impedance value is constant, which can be called the “surge” impedance of the transmission line.
Similarly, as the signal propagates along the line, what current can raise the voltage of this step to 1 volt within 0.01 nanoseconds before the next step? This involves the concept of instantaneous impedance.
From the battery’s perspective, if the signal propagates along the transmission line at a steady speed and the transmission line has the same cross-section, then each step forward in 0.01 nanoseconds requires the same amount of charge to produce the same signal voltage. When moving along this line, the same instantaneous impedance is generated, which is considered a characteristic of the transmission line and is called characteristic impedance. If the characteristic impedance of the signal is the same at each step in the transmission process, then the transmission line can be considered a controlled impedance transmission line.
Instantaneous impedance, or characteristic impedance, is very important for the quality of signal transmission.
During the transmission process, if the impedance of the next step is equal to the impedance of the previous step, the work can proceed smoothly, but if the impedance changes, there will be some problems.
In order to achieve the best signal quality, the design goal of the internal connection is to keep the impedance as stable as possible during the signal transmission process. First of all, the characteristic impedance of the transmission line must be kept stable. Therefore, the production of controllable impedance boards has become increasingly important. In addition, other methods such as minimizing the length of the excess line, removing the end, and using the whole line are also used to keep the instantaneous impedance stable during signal transmission.
Calculation of characteristic impedance
Simple characteristic impedance model: Z=V/I, Z represents the impedance of each step in the signal transmission process, V represents the voltage when the signal enters the transmission line, and I represents the current. I=±Q/±t, Q represents the amount of electricity, and t represents the time of each step.
Electricity (from the battery): ±Q=±C×V, C represents capacitance, and V represents voltage. The capacitance can be derived using the transmission line unit length capacity CL and the signal transmission speed v. The length of the unit pin is regarded as the speed, and then multiplied by the time t required for each step, and the formula is obtained: ±C=CL×v×（±）t. Combining the above items, we can derive the characteristic impedance: Z=V/I=V/（±Q/±t）=V/（±C×V/±t）=V/（CL×v×（±）t×V/±t）=1/（CL×v）
It can be seen that the characteristic impedance is related to the transmission line unit length capacity and signal transmission speed. In order to distinguish the characteristic impedance from the actual impedance Z, we add 0 after Z. The transmission line characteristic impedance is: Z0=1/（CL×v）
If the transmission line unit length capacity and signal transmission speed remain unchanged, then the transmission line characteristic impedance remains unchanged. This simple explanation can link the common sense of capacitance with the newly discovered characteristic impedance theory. If the transmission line unit length capacity is increased, such as thickening the transmission line, the transmission line characteristic impedance can be reduced.
Characteristic Impedance Measurement
How do you measure the infinite impedance when you connect an ohmmeter to a 3-foot RG58 cable while the battery is connected to the transmission line (assuming the impedance is 50 ohms at that time)? The impedance of any transmission line is time dependent. If you measure the impedance of the cable in a shorter time than the cable reflects, you measure the “surge” impedance, or characteristic impedance. But if you wait long enough for the energy to reflect back and be received, you will see a change in impedance. Generally, the impedance bounces up and down before reaching a stable limit.
For a 3-foot cable, the impedance measurement must be completed within 3 nanoseconds. TDR (Time Domain Reflectometry) can do this, and it measures the dynamic impedance of the transmission line. If you measure the impedance of a 3-foot cable in 1 second, the signal will reflect back and forth millions of times, so you will get different “surge” impedances.
Eric Bogatin received his BS in Physics from MIT and his MS and PhD in Physics from Arizona State University. He has worked for AT&T, Bell Labs, and Sun Microsystems. He is currently an independent consultant for Bogatin Corporation, specializing in signal integrity and interconnect design training.
