1. What is characteristic impedance

Characteristic impedance refers to the impedance per unit length of a transmission line (such as a cable, microstrip line, coaxial cable, etc.) that propagates electromagnetic signals. Characteristic impedance is commonly used to describe the characteristics of transmission lines, which is the sum of the resistance and reflection encountered by electromagnetic waves during propagation in the transmission line.

Characteristic impedance is the ratio of voltage to current at each point on a uniform transmission line. The characteristic impedance is related to the physical structure of the transmission line, mainly influenced by the dielectric constant, distance from the transmission line to the reference layer, line width, line thickness, and line spacing. For non-uniform transmission lines, it cannot be called characteristic impedance, which can only be considered as an instantaneous impedance. In engineering, most of the impedance we usually refer to is also this instantaneous impedance, because in PCB (printed circuit board) design, changes in the routing layer, routing topology, component locations, through holes, and uneven etching of the transmission line can all cause impedance changes in the transmission line.

The characteristic impedance is usually determined by factors such as the geometric shape of the transmission line, material characteristics, and electromagnetic environment. For an ideal transmission line, the characteristic impedance is a constant value that does not change with frequency. For common coaxial cables, such as 50 ohms or 75 ohms, they are typical values of their characteristic impedance.

Characteristic impedance is very important in electronic communication and circuit design, especially in the fields of high frequency and microwave. Matching the characteristic impedance of transmission lines and circuits can maximize signal transmission, reduce signal reflection and loss, and thus improve system performance.

The characteristic impedance of transmission lines, also known as characteristic impedance, is a concept that we often mention when designing high-speed circuits. However, many people do not understand this concept and sometimes misunderstand it as DC impedance. Understanding this concept is necessary for us to better design high-speed circuits. Many design rules for high-speed circuits are related to characteristic impedance.

In the high-frequency range, during signal transmission, a momentary current is generated between the signal line and the reference plane (power or ground plane) at the location where the signal reaches due to the establishment of an electric field. If the transmission line is isotropic, there will always be a current I as long as the signal is transmitted. If the output level of the signal is V, the transmission line will be equivalent to a resistance in V/I during signal transmission, which is called the characteristic impedance Z of the transmission line. During signal transmission, if the characteristic impedance on the transmission path changes, the signal will reflect at nodes with discontinuous impedance. Characteristic impedance refers to the resistance experienced by a high-frequency signal or electromagnetic wave in the transmission signal line (i.e. the copper wire of the circuit board we make) at a certain frequency, relative to a reference layer (commonly known as the shielding layer, projection layer, or reference layer), during the propagation process. It is actually a vector sum of impedance, inductance, capacitance, etc.

Phenomenon analogy: Poor road conditions on transportation lines (similar to characteristic impedance in transmission lines) can affect the speed of transportation fleets. The narrower the road, the greater the obstruction effect of the road (the higher the characteristic impedance, the smaller the energy of the radio waves passing through); The wider the road and the better the road conditions, the faster the passing convoy (with more radio wave energy). If one section of the road is in particularly good condition and another section of the road is in particularly poor condition, the convoy needs to slow down when entering the poor section from the good condition section. This indicates that the road conditions of the two sections do not match (impedance mismatch).

So for non-uniform transmission lines, it cannot be called characteristic impedance. This can only be called "instantaneous impedance" because it is impossible to maintain a certain impedance on the circuit board all the time. Due to changes in routing, layer switching, reference plane changes, routing topology, via, and other reasons, the impedance of the transmission line can change. Therefore, what we usually refer to is instantaneous impedance.

In summary,

1. The input impedance at the beginning of the transmission line is abbreviated as impedance

2. The real-time impedance that a signal encounters at any time is called instantaneous impedance

3. If the transmission line has a constant instantaneous impedance, it is called the characteristic impedance of the transmission line

Characteristic impedance describes the transient impedance that a signal experiences when propagating along a transmission line, which is a major factor affecting signal integrity in transmission line circuits. Unless otherwise specified, the characteristic impedance is generally referred to as the transmission line impedance

Simply put, the impedance of a transmission line can be explained by the above formula, but if we delve deeper, we need to analyze the behavior of the signal in the transmission line.

When the signal moves along a transmission line with the same cross-section, it is assumed that a 1V step wave (0V~1V jump) is added to the transmission line (such as connecting a 1V battery to the transmitting end of the transmission line, with the voltage spanning between the transmitting line and the loop).

Once connected, this voltage step wave propagates along the line at the speed of light, typically around 6 inches/ns. This signal is the voltage difference between the transmission line and the circuit, which can be measured from any point on the transmission line and adjacent points on the circuit.

That is, the signal and its nearest GND.

The signal energy advanced by 0.06 inches at 0.01ns, and at this point, the transmission line had excess positive charge (provided by the battery), while the circuit had excess negative charge. It was these two charge differences that maintained the 1V voltage difference between these two conductors, and a capacitor was formed between these two conductors.

In the next 0.01ns, the voltage of the next 0.06-inch transmission line needs to be adjusted from 0 to 1V, which requires adding some positive charges to the transmitting line and some negative charges to the receiving 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 0.01ns, 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 the signal moves along this line, it charges the continuous part of the transmission line, forming a 1V voltage difference between the transmission line and the circuit. For every 0.01ns advance, 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 alternating current, through the capacitance composed of the upper and lower lines, ends the entire cycle process.

When a signal is transmitted, an electric field is established within the transmission line, and the speed of signal transmission depends on the speed of charge charging, discharging, and magnetic field generation of the metal material around the signal and circuit.

For batteries, when the signal propagates along the transmission line and charges a continuous 0.06-inch transmission line every 0.01ns. When a constant current is obtained 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, the energy (current) required to increase the voltage of this step to 1V before the next step (within 0.01ns) involves the concept of instantaneous impedance.

If the signal propagates along the transmission line at a stable speed and the transmission line has the same cross-section, then the same amount of charge is required for each subsequent step in 0.01ns to generate the same signal voltage. At this point, when the signal advances along this line, it will encounter the same instantaneous impedance, 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 as a controlled impedance transmission line.

Instantaneous impedance is crucial 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. However, if the impedance changes (impedance mismatch), some problems may arise. In order to achieve signal quality, the design goal 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 length of the stub, removing the end, and using the entire line are also used to maintain the stability of the instantaneous impedance in signal transmission.

2. Why do we need the concept of characteristic impedance

To understand the concept of characteristic impedance, we first need to clarify what a transmission line is. Simply put, a transmission line is a connecting line that can transmit signals. Power cables, video cables, USB connection cables, and wiring on the PCB board can all be referred to as transmission cables. If the signal transmitted on the transmission line is a low-frequency signal, assuming it is 1KHz, then the wavelength of the signal is 300 kilometers (assuming the signal speed is the speed of light). Even if the length of the transmission line is 1 meter long, it is still very short compared to the signal. For the signal, the transmission line can be regarded as a short path, and its impact on the signal is very small. However, for high-speed signals, assuming the signal frequency increases to 300MHz, the signal wavelength decreases to 1 meter. At this point, the 1 meter transmission line and the signal wavelength can be completely compared, and there will be fluctuation effects on the transmission line, resulting in different voltage and current at different points on the transmission line. In this case, we cannot ignore the impact of transmission lines on the signal. A transmission line is a long line relative to a signal, and we need to use the theory of long line transmission to solve the problem.

Characteristic impedance is a concept in long-distance transmission. During the transmission of a signal on a transmission line, an electric field is formed between the transmission line and the reference plane at a point where the signal reaches. Due to the presence of the electric field, an instantaneous small current is generated, which exists at every point on the transmission line. At the same time, there is also a certain voltage in the signal, so during the signal transmission process, each point of the transmission line will be equivalent to a resistor, which is the characteristic impedance of the transmission line we mentioned. It is necessary to distinguish a concept here, which is that the characteristic impedance is for AC signals (or high-frequency signals), and for DC signals, the transmission line has a DC voltage divider, which may be much smaller than the characteristic impedance of the transmission line.

Characteristic impedance is a very important concept in electronic engineering:

Signal matching and transmission optimization: Feature impedance can help design engineers ensure signal matching between transmission lines and circuits to maximize signal transmission while reducing signal reflection and loss. Matching the characteristic impedance of transmission lines and circuits can improve system performance and ensure stable transmission of signals throughout the entire circuit.

Impedance conversion and adaptation: In electronic circuits, connections between different characteristic impedances are often involved, and impedance conversion or adaptation is required to ensure the normal transmission of signals. Understanding and using the concept of characteristic impedance can help engineers design suitable matching networks or transmission line connectors.

Transmission line design: When designing transmission lines, characteristic impedance is a key parameter. By selecting appropriate transmission line structures and materials, specific characteristic impedances can be achieved to meet the requirements of circuit design. The correct design of characteristic impedance can ensure the stability and performance of transmission lines.

EMI/EMC (Electromagnetic Interference/Compatibility): The characteristic impedance is also related to electromagnetic interference and compatibility. By designing the characteristic impedance of transmission lines correctly, the electromagnetic radiation and sensitivity to external electromagnetic interference during signal transmission can be reduced, and the electromagnetic compatibility of the system can be improved.

Network analysis and simulation: In the analysis and simulation of electronic circuits, characteristic impedance is an important parameter. By considering the characteristic impedance, it is possible to more accurately simulate and analyze the behavior of the circuit, predict the transmission of signals in the circuit, and optimize circuit performance.

3. What determines the value of "characteristic impedance"

Once the characteristics of the transmission line, such as line width and distance from the reference plane, are determined, the characteristic impedance of the transmission line is determined.

Several factors that affect the characteristic impedance of transmission lines:

a. The line width is inversely proportional to the characteristic impedance. Increasing linewidth is equivalent to increasing capacitance, which reduces characteristic impedance, and vice versa

b. The dielectric constant is inversely proportional to the characteristic impedance. Similarly, increasing the dielectric constant is equivalent to increasing the capacitance

c. The distance from the transmission line to the reference plane is proportional to the characteristic impedance. Increasing the distance between the transmission line and the reference plane is equivalent to reducing the capacitance, which in turn reduces the characteristic impedance, and vice versa.

d. The length of the transmission line is not related to the characteristic impedance. Through the formula, it can be seen that L and C are both parameters of a unit length transmission line, and are not related to the length of the transmission line.

e. The wire diameter is inversely proportional to the characteristic impedance. Due to the skin effect of high-frequency signals, the impact is smaller than other factors

The calculation formula for characteristic impedance depends on the type of transmission line used.

A typical transmission line on a PCB is a microstrip line that runs on the surface and has a reference plane below.

One is a strip line that runs through the inner layer and has reference planes on both sides.

A microstrip line is composed of a strip of wire connected to the ground plane, with a dielectric in the middle. If the dielectric constant of the dielectric, the width of the line, and its distance from the ground plane are controllable, then its characteristic impedance is also controllable, and its accuracy will be within ± 5%.

A strip line is a copper strip placed in the middle of a dielectric between two conductive planes. If the thickness and width of the line, the dielectric constant of the medium, and the distance between the two grounding planes are all controllable, then the characteristic impedance of the line is also controllable, and the accuracy is within 10%.

4. Why is characteristic impedance independent of frequency?

The reason why the characteristic impedance is independent of frequency is mainly due to the structure of the transmission line and the uniformity of the material. Specifically:

Uniform distribution: In ideal conditions, the electrical parameters (resistance, inductance, capacitance) on the transmission line are uniformly distributed along the unit length of the transmission line. This means that regardless of whether it is a high-frequency or low-frequency signal, the electrical parameters per unit length remain unchanged.

Fundamentals of Electromagnetic Theory: The characteristic impedance is derived from electromagnetic theory and does not depend on frequency. The propagation of electromagnetic waves in transmission lines is frequency independent. Therefore, characteristic impedance, as a fundamental parameter for describing the electromagnetic characteristics of transmission lines, is also frequency independent.

Material properties: The material properties of transmission lines are usually relatively constant within a specific frequency range. Although the characteristics of some special materials may change at extremely high frequencies (such as above the microwave frequency band), the material characteristics can be considered frequency independent within the frequency range commonly used in electronic circuit design.

In summary, the characteristic impedance is independent of frequency and is based on the uniform distribution of transmission lines, electromagnetic theory, and material property constancy. This allows the characteristic impedance to be considered as a frequency independent constant when designing and analyzing electronic circuits.

Characteristic impedance is the ratio of voltage and current at each point on a uniform transmission line. The characteristic impedance is affected by factors such as dielectric constant, dielectric thickness, and line width.

In actual transmission lines, there may be some non ideal factors, such as resistance, inductance, capacitance, and conductivity of conductors in the transmission line, which may slightly change with frequency variation, which may make the characteristic impedance exhibit frequency dependence to a certain extent. However, in most cases, the frequency dependence of characteristic impedance is very small and can be considered as a frequency independent constant in circuit design and analysis.

5. Why is the characteristic impedance usually set to 50 ohms and 75 ohms

Below is a brief introduction to the characteristic impedances of transmission lines that we often hear, which are 75 ohms and 50 ohms. Why are these two values, rather than other values? These two values are chosen by people in engineering practice. For coaxial cables, when the diameter ratio of the inner and outer conductors is 1.65, the wire has the maximum power transmission capacity, and the corresponding impedance is about 30 ohms. However, the signal attenuation caused by low impedance is relatively large. Considering the attenuation factor of the cable, the attenuation coefficient is the smallest when the impedance is 77 ohms. Therefore, for the convenience of calculation in engineering, the calculated value of the characteristic impedance is taken as 75 ohms, which can achieve a good attenuation coefficient to reduce signal attenuation. If we consider the power transmission capacity and attenuation coefficient as a compromise, we obtain 50 ohms, which is also a convenient value for engineering calculations. That is to say, whether it is 75 ohms or 50 ohms, it is a compromise choice that considers various factors and is artificially specified.

The reason for selecting characteristic impedances of 75 ohms and 50 ohms is mainly due to historical and practical considerations.

Standardization: In the telecommunications and electronics fields, standardized characteristic impedances are usually used to facilitate interconnection and compatibility between devices. 75 ohm and 50 ohm characteristic impedances are two widely used standard characteristic impedances, which have been widely accepted and incorporated into various standards, such as television, broadcasting, network communication, and other fields.

Historical reasons: The characteristic impedances of 50 ohms and 75 ohms were formed in different historical contexts. 50 ohms are commonly used in the fields of radio and communication, while 75 ohms are commonly used in the field of video signal transmission, such as television and video equipment.

Performance and loss: The selection of characteristic impedance is also related to the transmission linear energy and loss. Generally speaking, a 50 ohm transmission line has lower losses at high frequencies and is suitable for applications that require high-frequency signal transmission, while a 75 ohm transmission line has better performance in the video field.

Interconnection standards: In many interconnection standards, such as RS-232, RS-485, etc., a characteristic impedance of 50 ohms or 75 ohms is also used.