In high-speed design, the characteristic impedance problem of controllable impedance boards and circuits troubles many Chinese engineers. This article introduces the basic properties, calculation, and measurement methods of characteristic impedance through a simple and intuitive approach.

In high-speed design, the characteristic impedance of controllable impedance boards and circuits is one of the most important and common issues. Firstly, let's understand the definition of a transmission line: a transmission line consists of two conductors of a certain length, one conductor used to send signals and the other used to receive signals (remember to replace the concept of "ground" with "loop"). In a multi-layer board, each line is a component of a transmission line, and adjacent reference planes can serve as a second line or loop. The key to becoming a "high-performance" transmission line is to keep its characteristic impedance constant throughout the entire line.

The key to making a circuit board a "controllable impedance board" is to ensure that the characteristic impedance of all circuits meets a specified value, typically between 25 ohms and 70 ohms. The key to good transmission linearity in multi-layer circuit boards is to maintain a constant characteristic impedance throughout the entire circuit.

But what exactly is characteristic impedance? The simplest way to understand characteristic impedance is to observe 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. Assuming 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 (located between the transmission line and the circuit), once connected, this voltage wave signal propagates along the line at the speed of light, typically around 6 inches per nanosecond. Of course, this signal is indeed the voltage difference between the transmission line and the circuit, which can be measured from any point on the transmission line and the adjacent point on the circuit. Figure 2 is a schematic diagram of the transmission of the voltage signal.

Zen's method is to first "generate a signal" and then propagate along this transmission line at a speed of 6 inches per nanosecond. The first 0.01 nanosecond advances 0.06 inches, at which point there is excess positive charge on the transmission line and excess negative charge on the circuit. It is these two charge differences that maintain the 1-volt voltage difference between these two conductors, which in turn form a capacitor.

In the next 0.01 nanoseconds, the voltage of a 0.06 inch transmission line needs to be adjusted from 0 to 1 volt, which requires adding some positive charges to the transmission line and some negative charges to the reception line. For every 0.06 inches of movement, more positive charges must be added to the transmission line and more negative charges must be added to the circuit. Every 0.01 nanoseconds, 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, and when it moves along this line, it charges the continuous part of the transmission line, thus forming a voltage difference of 1 volt between the transmission line and the circuit. Every 0.01 nanoseconds, 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 circuit is actually equal to the positive current flowing out, and it happens to be 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 process.

Impedance of the circuit

For batteries, when the signal propagates along the transmission line and charges a continuous 0.06 inch transmission line segment every 0.01 nanoseconds. When obtaining a constant current from the power supply, the transmission line looks like an impedance device, and its impedance value is constant, which can be called the "surge impedance" of the transmission line.

Similarly, when the signal propagates along the line, which current can increase 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 perspective of the battery, if the signal propagates along the transmission line at a stable speed and the transmission line has the same cross-section, then in 0.01 nanoseconds, the same amount of charge is required for each preceding step to generate the same signal voltage. When traveling 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 of the transmission process, then the transmission line can be considered a controllable impedance transmission line.

Instantaneous impedance or characteristic impedance is crucial for the quality of signal transmission. During the transmission process, if the impedance of the next step is equal to that of the previous step, the work can proceed smoothly. However, if the impedance changes, some problems may arise.

In order to achieve optimal signal quality, the design goal of internal connections is to maintain impedance stability as much as possible during signal transmission. Firstly, it is necessary to maintain the stability of the characteristic impedance of the transmission line. Therefore, the production of controllable impedance boards has become increasingly important. In addition, other methods such as shortening the remaining wire length, removing the end, and using the entire wire are also used to maintain the stability of instantaneous impedance in signal transmission.

Calculation of characteristic impedance

A simple characteristic impedance model: Z=V/I, where Z represents the impedance at each step of the signal transmission process, V represents the voltage at which 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 for each step.

Electricity level (from battery): ± Q=± C × V, where C represents capacitance and V represents voltage. The capacitance can be derived from the unit length capacity CL of the transmission line and the signal transmission speed v. The length value of a unit pin is taken as the velocity, multiplied by the required time t for each step, to obtain the formula: ± C=CL × v × (±) t. Taking into account the above factors, we can obtain 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 unit length capacity and signal transmission speed of the transmission line. To distinguish between the characteristic impedance and the actual impedance Z, we add 0 after Z. The characteristic impedance of the transmission line is Z0=1/(CL × v)

If the unit length capacity and signal transmission speed of the transmission line remain unchanged, then the characteristic impedance of the transmission line also remains unchanged. This simple explanation can connect the common knowledge of capacitance with the newly discovered characteristic impedance theory. If the unit length capacity of the transmission line is increased, such as thickening the transmission line, the characteristic impedance of the transmission line can be reduced.

Measurement of characteristic impedance

When the battery is connected to the transmission line (assuming an impedance of 50 ohms at the time), how to measure infinite impedance by connecting an ohmmeter to a 3-foot RG58 fiber optic cable? The impedance of any transmission line is time-dependent. If you measure the impedance of a fiber optic cable in a shorter time than its reflection, what you measure is the "surge" impedance, or characteristic impedance. But if we wait long enough until the energy is reflected back and received, it can be measured that there is a change in impedance. Generally speaking, the impedance value will reach a stable limit after bouncing up and down.