Impedance matching principle

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Impedance matching is a part of microwave electronics. It is mainly used on transmission lines to ensure that all high-frequency microwave signals can be transmitted to the load point without any signal reflection back to the source point, thereby improving energy efficiency.

Generally speaking, there are two types of impedance matching: one is by changing the impedance (lumped-circuit matching), and the other is by adjusting the wavelength of the transmission line (transmission line matching).

To match a set of lines, first normalize the impedance value of the load point by dividing it by the characteristic impedance value of the transmission line, and then plot the value on the Smith chart.

Changing the impedance

By connecting a capacitor or inductor in series with a load, the impedance value of the load can be increased or decreased, and the points on the graph will move along the circle representing the real resistance. If the capacitor or inductor is grounded, the points on the graph will first rotate 180 degrees from the center of the graph, then move along the resistance circle, and then rotate 180 degrees along the center. Repeat the above method until the resistance value becomes 1, and the impedance can be directly changed to zero to complete the matching.

Adjusting the transmission line

By lengthening the transmission line from the load point to the source point, the dots on the graph will move counterclockwise along the center of the graph until they reach the circle with a resistance value of 1. Then, capacitors or inductors can be added to adjust the impedance to zero, thus completing the matching.

Impedance matching means high transmission power. For a power supply, when its internal resistance is equal to the load, the output power is the largest, and the impedance is matched at this time. The maximum power transmission theorem, if it is high frequency, is no reflected wave. For ordinary broadband amplifiers, the output impedance is 50Ω, and impedance matching needs to be considered in the power transmission circuit. However, if the signal wavelength is much larger than the cable length, that is, the cable length can be ignored, there is no need to consider impedance matching. Impedance matching means that when energy is transmitted, the load impedance must be equal to the characteristic impedance of the transmission line. At this time, the transmission will not generate reflection, which indicates that all energy is absorbed by the load. Otherwise, there is energy loss in the transmission. When high-speed PCB wiring, in order to prevent signal reflection, the line impedance is required to be 50 ohms. This is an approximate number. It is generally stipulated that the baseband of coaxial cable is 50 ohms, the frequency band is 75 ohms, and the twisted pair is 100 ohms. It is just rounded up for the convenience of matching.

Impedance is literally different from resistance. Only one of them is the same, what about the other one? Simply put, impedance is resistance plus reactance, so it is called impedance; to be more comprehensive, impedance is the sum of resistance, capacitive reactance and inductive reactance in vector. In the world of direct current, the effect of an object on the current is called resistance. All substances in the world have resistance, but the resistance value is different. Substances with low resistance are called good conductors, substances with large resistance are called non-conductors, and superconductors, which are called superconductors in the high-tech field recently, are things with a resistance value close to zero. However, in the field of alternating current, in addition to resistance, capacitance and inductance will also hinder the flow of current. This effect is called reactance, which means the effect of resisting current. The reactance of capacitance and inductance is called capacitive reactance and inductive reactance, respectively, or capacitive reactance and inductive reactance for short. Their measurement units are ohms, the same as resistance, and their values are related to the frequency of alternating current. The higher the frequency, the smaller the capacitive reactance and the larger the inductive reactance. The lower the frequency, the larger the capacitive reactance and the smaller the inductive reactance. In addition, capacitive reactance and inductive reactance also have phase angle issues and have a vector relationship, so it is said that impedance is the vector sum of resistance and reactance.

Impedance matching refers to a working state in which the load impedance and the internal impedance of the excitation source are adapted to each other to obtain the maximum power output. For circuits with different characteristics, the matching conditions are different.

In a purely resistive circuit, when the load resistance is equal to the internal resistance of the excitation source, the output power is maximum. This working state is called matching, otherwise it is called mismatch.

When the internal impedance of the excitation source and the load impedance contain reactance components, in order to obtain the maximum power for the load, the load impedance and the internal resistance must satisfy a conjugate relationship, that is, the resistance components are equal, and the reactance components are only equal in value but opposite in sign. This matching condition is called conjugate matching.

Research on Impedance Matching

In high-speed design, impedance matching is related to the quality of the signal. Impedance matching technology can be said to be rich and varied, but how to reasonably apply it in a specific system requires weighing multiple factors. For example, in our system design, many of them use series matching of the source segment. Under what circumstances is matching required, what matching method is used, and why this method is used.　

For example: differential matching mostly uses terminal matching; clock uses source segment matching;

a. Series terminal matching

The theoretical starting point of series terminal matching is to connect a resistor R in series between the source end of the signal and the transmission line under the condition that the impedance of the signal source end is lower than the characteristic impedance of the transmission line, so that the output impedance of the source end matches the characteristic impedance of the transmission line, and suppresses the re-reflection of the signal reflected from the load end.

The signal transmission after series terminal matching has the following characteristics: due to the effect of the series matching resistor, the driving signal propagates to the load end with 50% of its amplitude; the reflection coefficient of the signal at the load end is close to +1, so the amplitude of the reflected signal is close to 50% of the original signal amplitude; the reflected signal is superimposed on the signal propagated from the source end, so that the amplitude of the signal received by the load end is approximately the same as the original signal; the reflected signal at the load end propagates to the source end, and is absorbed by the matching resistor after reaching the source end; after the reflected signal reaches the source end, the source end driving current drops to 0 until the next signal transmission.

Compared with parallel matching, series matching does not require the signal driver to have a large current driving capability.

The principle of selecting the series terminal matching resistor value is very simple, that is, the sum of the matching resistor value and the output impedance of the driver is required to be equal to the characteristic impedance of the transmission line. The output impedance of an ideal signal driver is zero. The actual driver always has a relatively small output impedance, and the output impedance may be different when the signal level changes. For example, a CMOS driver with a power supply voltage of +4.5V has a typical output impedance of 37Ω at a low level and a typical output impedance of 45Ω at a high level [4]. Like CMOS drivers, TTL drivers have output impedance that changes with the signal level. Therefore, for TTL or CMOS circuits, it is impossible to have a completely correct matching resistor, and only a compromise can be considered. The
signal network with a chain topology is not suitable for series terminal matching. All loads must be connected to the end of the transmission line. Otherwise, the waveform received by the load connected to the middle of the transmission line will be the same as the voltage waveform at point C in Figure 3.2.5. It can be seen that for a period of time, the signal amplitude at the load end is half of the original signal amplitude. Obviously, the signal is in an indeterminate logic state at this time, and the signal noise tolerance is very low.

Series matching is the most commonly used terminal matching method. Its advantages are low power consumption, no additional DC load on the driver, no additional impedance between the signal and the ground, and only one resistor element is required.

b. Parallel terminal matching

The theoretical starting point of parallel terminal matching is to add parallel resistance to match the input impedance of the load end with the characteristic impedance of the transmission line when the impedance of the signal source end is very small, so as to eliminate the reflection at the load end. There are two forms of implementation: single resistance and double resistance.

The signal transmission after parallel terminal matching has the following characteristics: the driving signal propagates along the transmission line at approximately full amplitude; all reflections are absorbed by the matching resistor; the signal amplitude received by the load end is approximately the same as the signal amplitude sent by the source end.

In actual circuit systems, the input impedance of the chip is very high, so for a single resistor, the parallel resistance value at the load end must be close to or equal to the characteristic impedance of the transmission line. Assuming that the characteristic impedance of the transmission line is 50Ω, the R value is 50Ω. If the high level of the signal is 5V, the static current of the signal will reach 100mA. Since the driving capability of typical TTL or CMOS circuits is very small, this single resistor parallel matching method rarely appears in these circuits.

The parallel matching of the dual resistor form, also known as the Thevenin terminal matching, requires a smaller current driving capability than the single resistor form. This is because the parallel value of the two resistors matches the characteristic impedance of the transmission line, and each resistor is larger than the characteristic impedance of the transmission line. Considering the driving capability of the chip, the selection of the two resistor values must follow three principles: the parallel value of the two resistors is equal to the characteristic impedance of the transmission line; the resistance value connected to the power supply cannot be too small to avoid excessive driving current when the signal is at a low level; the resistance value connected to the ground cannot be too small to avoid excessive driving current when the signal is at a high level.

The advantage of parallel terminal matching is that it is simple and easy to implement; the obvious disadvantage is that it will bring DC power consumption: the DC power consumption of the single resistor method is closely related to the duty cycle of the signal?; the dual resistor method has DC power consumption regardless of whether the signal is high or low. Therefore, it is not suitable for systems with high power consumption requirements such as battery-powered systems. In addition, the single resistor method is not used in general TTL and CMOS systems due to the problem of driving capability, while the dual resistor method requires two components, which puts forward requirements on the board area of PCB, so it is not suitable for high-density printed circuit boards.

Of course, there are also: AC terminal matching; diode-based voltage clamping and other matching methods.

Think of the signal transmission as a hose delivering water to the flowers

a. In the signal line of the multilayer board of the digital system, when the square wave signal is transmitted, it can be imagined as a hose that delivers water to the flowers. One end is pressurized at the grip to make it shoot out a water column, and the other end is connected to the faucet. When the pressure applied at the grip is just right and the water column falls on the target area correctly, both the giver and the receiver are happy and the mission is successfully completed. Isn't this a small achievement that comes easily?

b. However, if you use too much force and the water injection distance is too long, not only will it fly over the target and waste water resources, but the strong water pressure may have nowhere to vent, so it will rebound to the source and cause the hose to break free from the faucet! Not only will the mission fail and there will be setbacks, but you will also make a big mistake and be embarrassed!

c. On the contrary, if the grip is not squeezed enough to make the shot too close, the desired result will not be achieved. Too much is as bad as too little, and only the right amount can hit the mark and make everyone happy.

d. The simple details of daily life mentioned above can be used to illustrate the rapid transmission of square wave signals in multilayer board transmission lines (which are composed of signal lines, dielectric layers, and ground layers). At this time, the transmission line (common ones include coaxial cables, microstrip lines, or strip lines, etc.) can be regarded as a hose, and the pressure applied at the grip of the hose is like the resistor connected in parallel to the Gnd of the "receiver" component on the board, which can be used to adjust the characteristic impedance of its end point to match the internal requirements of the receiving end component.

Transmission line terminal control technology (Termination)

a. From the above, we can know that when the "signal" travels through the transmission line and reaches the end point, and wants to enter the receiving component (such as a CPU or a Meomery or other IC of different sizes) to work, the "characteristic impedance" of the signal line itself must match the electronic impedance inside the terminal component, so as not to fail in the mission. In technical terms, it means to execute instructions correctly, reduce noise interference, and avoid wrong actions. Once they fail to match each other, a small amount of energy will bounce back to the "sending end", thus forming the trouble of reflected noise.

b. When the characteristic impedance (Z0) of the transmission line itself is set by the designer to 28ohm, the grounding resistor (Zt) of the terminal control must also be 28ohm, so as to help the transmission line maintain Z0 and stabilize the overall design value of 28 ohm. Only in this matching situation of Z0=Zt can the signal transmission be most efficient and its "Signal Integrity" (a special term for signal quality) be the best.

Characteristic Impedance

a. When a signal square wave advances forward with a high-level positive voltage signal in the signal line of the transmission line assembly, then in the reference layer (such as the ground layer) closest to it, in theory, there must be a negative voltage signal induced by the electric field to accompany it (equivalent to the return path of the positive voltage signal in the opposite direction), so that the overall loop system can be completed. If the flight time of the "signal" is temporarily frozen during its forward movement, it can be imagined that it is subject to the instantaneous impedance value (Instantanious Impedance) presented by the signal line, dielectric layer and reference layer, which is the so-called "characteristic impedance". Therefore, the "characteristic impedance" should be related to the line width (w), line thickness (t), dielectric thickness (h) and dielectric constant (Dk) of the signal line.

b. Consequences of poor impedance matching

Since the original word of "characteristic impedance" (Z0) of high-frequency signals is very long, it is generally referred to as "impedance". Readers must be careful, this is not exactly the same as the impedance value (Z) that appears in the wires (not transmission lines) of low-frequency AC alternating current (60Hz). In digital systems, when the Z0 of the entire transmission line can be properly managed and controlled within a certain range (±10﹪ or ±5﹪), this good quality transmission line will reduce noise and avoid malfunctions. However, when any of the four variables (w, t, h, r) of Z0 in the above microstrip line is abnormal, such as when a gap appears in the signal line, the original Z0 will suddenly rise (see the fact that Z0 is inversely proportional to W in the above formula), and it will be unable to continue to maintain the proper stability and uniformity (Continuous), then the energy of the signal will inevitably be partially forward, while partially rebound and reflect. In this way, noise and malfunctions cannot be avoided. For example, if a hose for watering flowers is suddenly stepped on, causing abnormalities at both ends of the hose, this is a good example of the poor characteristic impedance matching problem mentioned above.

c. Poor impedance matching causes noise

The rebound of the above signal energy will cause the original good quality square wave signal to be abnormally deformed immediately (i.e., overshoot of the high level upwards, undershoot of the low level downwards, and subsequent ringing of the two). Such high-frequency noise will cause malfunctions when it is serious, and the faster the clock speed, the more noise there is and the easier it is to make mistakes.

呜呼哀哉

The moderator is very professional, the article is well written, and I have learned a lot.

btty038

Alas, published on 2022-6-28 08:57 The moderator is very professional and writes very well. I have learned a lot.

I didn't write it. I just forwarded it. It's worth learning. It involves learning these fields. Professional vocabulary explanations and door-breaking sections are also worth learning and discussing. We all stand on the shoulders of our predecessors to learn, understand, and discover the beauty of work.