Impedance matching is a part of microwave electronics. It is mainly used in transmission lines to achieve the purpose that all high-frequency microwave signals can be transmitted to the load point, and no signal will be reflected back to the source point, so as to improve energy efficiency. In general, there are two kinds of impedance matching: one is by changing the impedance force, and the other is by adjusting the impedance matching. Impedance matching is a part of microwave electronics. It is mainly used on the transmission line to achieve the purpose that all high-frequency microwave signals can be transmitted to the load point without any signal reflecting back to the source point, so as to improve energy efficiency.
In general, there are two kinds of impedance matching, one is by changing the impedance force (lumped circuit matching), and the other is by adjusting the wavelength of the transmission line (transmission line matching).
To match a group 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 draw the value on the Smith chart.
Change impedance force
Connecting the capacitance or inductance with the load in series can increase or decrease the impedance value of the load. The points on the chart will walk along the circle representing the real resistance. If the capacitance or inductance is grounded, first the point on the chart will rotate 180 degrees from the center of the chart, then walk 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 force can be directly changed to zero to complete the matching.
Lengthen the transmission line from the load point to the source point. The dot on the chart will move counterclockwise along the center of the chart until it reaches the circle with resistance value of 1. Then add capacitance or inductance to adjust the resistance to zero. If matching impedance matching is completed, the transmission power is large. 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 50 Ω, and impedance matching needs to be considered in the power transmission circuit. However, if the signal wavelength is far greater than the cable length, that is, the cable length can be ignored, impedance matching does not need to be considered. Impedance matching means that when energy is transmitted, the load impedance is required to be equal to the characteristic impedance of the transmission line. At this time, the transmission will not produce reflection, which indicates that all energy is absorbed by the load On the contrary, there is energy loss in transmission. When high-speed PCB wiring, in order to prevent signal reflection, the impedance of the line 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 an integer for convenience of matching Impedance is literally different from resistance. Only one resistance word is the same, and the other resistance word? Simply put, impedance is resistance plus reactance, so it is called impedance; Circumferentially speaking, impedance is the sum of resistance, capacitive reactance and inductive reactance on the vector. In the world of direct current, the effect of objects on the obstruction of current is called resistance. All substances in the world have resistance, but the difference in resistance value. A substance with low resistance is called a good conductor, and a substance with high resistance is called a non conductor. Recently, in the field of high technology, it is called a superconductor, which has 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, that is, the effect of resisting current. The reactance of capacitance and inductance are called capacitance reactance and inductance reactance respectively, which are called capacitive reactance and inductive reactance for short. Their unit of measurement is the same as the resistance, and its value is related to the frequency of AC. the higher the frequency, the smaller the capacitive reactance, the greater the inductive reactance, and the lower the frequency, the larger the capacitive reactance and the smaller the inductive reactance. In addition, capacitive reactance and inductive reactance also have the problem of phase angle, which has the relationship on the vector. Therefore, it can be said that impedance is the sum of resistance and reactance on the vector.
Impedance matching refers to a working state in which the load impedance and the internal impedance of the excitation source adapt to each other to obtain the maximum power output. For circuits with different characteristics, the matching conditions are different.
In the pure resistance circuit, when the load resistance is equal to the internal resistance of the excitation source, the output power is the maximum. This working state is called matching, otherwise it is called mismatch.
When the internal impedance and load impedance of the excitation source contain reactance components, in order to obtain the maximum power of the load, the load impedance and internal resistance must meet the conjugate relationship, that is, the resistance components are equal, and the reactance components are only equal in value and opposite in sign. This matching condition is called conjugate matching.
I Research on impedance matching
In high-speed design, the matching of impedance is related to the quality of signal. Impedance matching technology can be said to be rich and diverse, but how to reasonably apply in a specific system needs to measure many factors. For example, in our system design, many use the serial matching of source segments. Under what circumstances, in what way, and why.
For example, most of the differential matching uses terminal matching; The clock adopts source segment matching;
1. Series terminal matching
The theoretical starting point of series terminal matching is to connect a resistance R between the source end of the signal and the transmission line in series under the condition that the impedance of the signal source end is lower than the characteristic impedance of the transmission line, so as to match the output impedance of the source end with the characteristic impedance of the transmission line and inhibit the re reflection of the signal reflected from the load end
The signal transmission after series terminal matching has the following characteristics:
A due to the effect of series matching resistance, the driving signal propagates to the load end with 50% of its amplitude;
The reflection coefficient of B 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.
C. the reflected signal is superimposed with the signal transmitted by the source end, so that the amplitude of the signal received by the load end is approximately the same as that of the original signal;
The reflected signal of D load end propagates to the source end and is absorbed by the matching resistance after reaching the source end;
E after the reflected signal reaches the source end, the driving current at the source end drops to 0 until the next signal transmission.
Compared with parallel matching, series matching does not require the signal driver to have great current driving ability.
The principle of selecting the matching resistance value of series terminal is very simple, that is, the sum of the matching resistance value and the output impedance of the driver is equal to the characteristic impedance of the transmission line. The output impedance of the 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, the typical output impedance of CMOS driver with power supply voltage of + 4.5V is 37 Ω at low level and 45 Ω at high level ; Like CMOS driver, TTL driver’s output impedance will change with the level of signal. Therefore, for TTL or CMOS circuits, it is impossible to have a very correct matching resistance, which can only be considered in a compromise.
The signal network with 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 the signal amplitude at the load end is half of the original signal amplitude for a period of time. Obviously, at this time, the signal is in an indefinite logic state, and the noise tolerance of the signal is very low.
Series matching is the most commonly used terminal matching method. It has the advantages of low power consumption, no additional DC load to the driver, and no additional impedance between the signal and the ground; And only one resistive element is required.
2. Parallel terminal matching
The theoretical starting point of parallel terminal matching is to match the input impedance of the load end with the characteristic impedance of the transmission line by increasing the parallel resistance when the impedance of the signal source end is very small, so as to eliminate the reflection of the load end. The realization forms are divided into single resistance and double resistance.
The signal transmission after parallel terminal matching has the following characteristics:
A. the driving signal propagates along the transmission line approximately at full amplitude;
B all reflections are absorbed by the matching resistance;
The signal amplitude received by the C load end is approximately the same as that sent by the source end.
In the actual circuit system, the input impedance of the chip is very high, so for the single resistance form, the parallel resistance value of 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 50 Ω, the R value is 50 Ω. If the high level of the signal is 5V, the quiescent current of the signal will reach 100mA. Because the driving ability of typical TTL or CMOS circuits is very small, this single resistance parallel matching mode rarely appears in these circuits.
Parallel matching in the form of double resistance, also known as Thevenin terminal matching, requires less current driving capacity than that in the form of single resistance. 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 ability of the chip, the selection of two resistance values must follow three principles:
(1) the parallel value of the two resistors is equal to the characteristic impedance of the transmission line;
(2) the resistance value connected with the power supply shall not be too small to avoid excessive driving current when the signal is low;
(3) the resistance value connected with the ground shall not be too small to avoid excessive driving current when the signal is high.
The advantage of parallel terminal matching is simple and easy; The obvious disadvantage is that it will bring DC power consumption: the DC power consumption of single resistance mode is closely related to the duty cycle of the signal?; Dual resistance mode has DC power consumption regardless of whether the signal is high level or low level. Therefore, it is not suitable for systems with high power consumption requirements such as battery power supply system. In addition, due to the problem of driving ability, the single resistance mode is not applied in general TTL and CMOS systems, while the double resistance mode requires two components, which is very important for PCB
Area requirements, so it is not suitable for high-density printed circuit boards.
Of course, there are: AC terminal matching; Voltage clamping and other matching methods based on diode.
II Think of the signal transmission as a hose to send water and water the flowers
2.1 in the signal line of the multi-layer board of the digital system, when the square wave signal is transmitted, it can be imagined as a hose to send water and water flowers. One end is pressurized at the hand to make it shoot out of the water column, and the other end is connected to the faucet.
When the pressure at the grip is just right, and the range of the water column is right in the target area, it is a small achievement to give and receive both happily and successfully complete the mission?
2.2 however, once the force is excessive and the water injection process is too far, it will not only fly over the target and waste water resources, but also may rebound to the source due to the lack of vent of the strong water pressure, resulting in the breakaway of the hose from the faucet! Not only did the mission fail, causing setbacks, but also made mistakes, full of beans and flowers!
2.3 on the contrary, if the grip is not squeezed enough so that the range is too close, the desired result will still not be obtained. It’s not what you want to go too far but not too far. Only when it’s right can you get it right and everyone is happy.
2.4 the above simple life details can be used to illustrate the rapid transmission of square wave signal in multilayer board transmission line (which is composed of signal line, dielectric layer and grounding layer). At this time, the transmission line (common coaxial cable, micro strip line or strip line, etc.) can be regarded as a hose, and the pressure applied at the grip is just like the resistor connected in parallel to GND by the “receiver” element on the board, which can be used to adjust the characteristic impedance at its end point to match the internal requirements of the receiver element.
III Terminal control technology of transmission line
3.1 it can be seen from the above that when the “signal” travels rapidly in the transmission line and reaches the destination, and wants to enter the receiving element (such as IC of different sizes such as CPU or meomery), the “characteristic impedance” of the signal line itself must match with the electronic impedance inside the terminal element, so as not to fail the task. In terms, it means to execute instructions correctly, reduce noise interference and avoid wrong actions “. Once they fail to match each other, a little energy will bounce back towards the “sending end” and form the trouble of reflected noise.
3.2 when the characteristic impedance (Z0) of the transmission line itself is set as 28ohm by the designer, the grounding resistor (ZT) of the terminal control tube must also be 28ohm, so as to help the transmission line maintain Z0 and stabilize the whole at the design value of 28 ohm. Only in this matching case of Z0 = ZT can the signal transmission be the most efficient, and its “signal integrity” (a special term for signal quality) is the best.
IV Characteristic impedance
4.1 when a signal square wave moves forward with the positive pressure signal of high level in the signal line of the transmission line assembly, there must be a negative pressure signal induced by the electric field in the nearest reference layer (such as grounding layer) (equal to the return path of the negative pressure signal in the reverse direction), so as to complete the integrated loop system. If the flight time of the “signal” is frozen for a short time, you can imagine what it will suffer
It comes from the instantaneous impedance jointly 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.
4.2 consequences of poor impedance matching because the original word of “characteristic impedance” (Z0) of high-frequency signal is very long, it is generally referred to as “impedance”. Readers should be careful that this is not exactly the same as the impedance value (z) in the wire (not the transmission line) of low-frequency AC (60Hz). Digital system when the Z0 of the whole transmission line can be managed properly and controlled within a certain range (± 10% or ± 5%), this transmission line with good quality will reduce noise and avoid misoperation. However, when any of the four variables (W, t, h, R) of Z0 in the above microstrip line is abnormal, for example, when there is a gap in the signal line, the original Z0 will rise suddenly (see the fact that Z0 is inversely proportional to w in the above formula) and cannot be used