What Is Inductor Impedance?

In a circuit with resistance, inductance, and capacitance, the blocking effect on the current in the circuit is called impedance. Impedance is commonly represented by Z, which is a complex number. The real part is called resistance, and the imaginary part is called reactance. The resistance of a capacitor to AC in a circuit is called capacitive reactance. For inductive reactance, the blocking effect of capacitors and inductors on alternating current in a circuit is collectively called reactance. The unit of impedance is ohms. The concept of impedance exists not only in circuits, but also in mechanical vibration systems. ^[1]
Right!

Z = R + i ( L 1 / ( C ) )

Note: The load is resistance,

in

Impedance input impedance

Input impedance is the equivalent impedance at the input of a circuit. Add a voltage source U to the input and measure the current I at the input. The input impedance R is U / I. You can think of the input as two ends of a resistor. The resistance of this resistor is the input impedance.

Motor rotor AC impedance tester

The input impedance is no different from an ordinary reactance element, it reflects the magnitude of the current blocking effect. For voltage-driven circuits, the larger the input impedance, the lighter the load on the voltage source, and therefore the easier it is to drive without affecting the signal source. For current-driven circuits, the smaller the input impedance, the The lighter the load on the current source. Therefore, we can think that if it is driven by a voltage source, the larger the input impedance is, the better; if it is driven by a current source, the smaller the impedance is, the better (note: only suitable for low frequency circuits, at high frequencies In the circuit, we also need to consider the impedance matching problem.) In addition, if we want to obtain the maximum output power, we must also consider the impedance matching problem.

Impedance Output Impedance

Regardless of the signal source, amplifier, or power supply, there are problems with output impedance. The output impedance is the internal resistance of a signal source. Originally, for an ideal voltage source (including power supply), the internal resistance should be 0, or the impedance of an ideal current source should be infinite. The output impedance needs special attention in circuit design.

But the voltage source in reality cannot do this. We usually use an ideal voltage source in series with a resistor r to be equivalent to an actual voltage source. This resistor r in series with the ideal voltage source is the internal resistance of (signal source / amplifier output / power supply). When the voltage source supplies power to the load, a current I flows through the load, and a voltage drop of I × r occurs on the resistor. This will cause the output voltage of the power supply to drop, thereby limiting the maximum output power (for why the maximum output power is limited, please see "Impedance Matching" later). Similarly, for an ideal current source, the output impedance should be infinite, but the actual circuit is impossible.

The concept of impedance matching

Impedance matching refers to a suitable matching mode between a signal source or transmission line and a load. Impedance matching is divided into two cases of low frequency and high frequency. We start by driving a load from a DC voltage source. Since the actual voltage source always has internal resistance, we can equate an actual voltage source with a model of an ideal voltage source in series with a resistor r. Assuming the load resistance is R, the power electromotive force is U, and the internal resistance is r, then we can calculate the current flowing through the resistance R as: I = U / (R + r). The larger the output current. The voltage on the load R is: Uo = IR = U / [1+ (r / R)]. It can be seen that the larger the load resistance R, the higher the output voltage Uo. Let's calculate the power consumed by the resistor R as:

P = I2 × R = [U / (R + r)] 2 × R = U2 × R / (R2 + 2 × R × r + r2)

= U2 × R / [(Rr) 2 + 4 × R × r]

= U2 / {[(Rr) 2 / R] + 4 × r}

For a given signal source, its internal resistance r is fixed, and the load resistance R is chosen by us. Note that [(Rr) 2 / R] in the formula, when R = r, [(Rr) 2 / R] can obtain the minimum value of 0, then the maximum output power Pmax = U2 / (4 × can be obtained on the load resistance R r). That is, when the load resistance is equal to the internal resistance of the signal source, the load can obtain the maximum output power, which is one of the impedance matching we often say. For purely resistive circuits, this conclusion also applies to low-frequency circuits and high-frequency circuits.

When the AC circuit contains capacitive or inductive impedance, the conclusion is changed, that is, the real part of the signal source and the load impedance must be equal, and the imaginary part is opposite to each other. This is called conjugate matching. In low-frequency circuits, we generally do not consider the matching of transmission lines, but only consider the situation between the signal source and the load, because the wavelength of low-frequency signals is very long compared to the transmission line, the transmission line can be regarded as "short lines", and reflection can be Consider (can be understood as such: because the line is short, even if it is reflected back, it is still the same as the original signal). From the above analysis, we can draw a conclusion: if we need a large output current, choose a small load R; if we need a large output voltage, choose a large load R; if we need the maximum output power, choose the internal resistance of the signal source Matched resistor R. Sometimes impedance mismatch has another meaning. For example, some instrument output terminals are designed under specific load conditions. If the load conditions are changed, the original performance may not be achieved. At this time, we also call impedance mismatch. .

In high frequency circuits, we must also consider the issue of reflection. When the frequency of the signal is high, the wavelength of the signal is very short. When the wavelength is short enough to be comparable to the length of the transmission line, the reflected signal superimposed on the original signal will change the shape of the original signal. If the characteristic impedance of the transmission line and the load impedance are not equal (that is, they do not match), reflections will occur at the load end. The reason why reflection and characteristic impedance are generated when impedances do not match involves the solution of second-order partial differential equations. We won't go into details here. If you are interested, you can refer to the theory of transmission lines in books on electromagnetic fields and microwave. The characteristic impedance (also called characteristic impedance) of a transmission line is determined by the structure and material of the transmission line, and has nothing to do with the length of the transmission line, and the amplitude and frequency of the signal.

For example, the characteristic impedance of a commonly used CCTV coaxial cable is 75, while some RF devices use a coaxial cable with a characteristic impedance of 50. Another common transmission line is a flat parallel line with a characteristic impedance of 300, which is more common on TV antenna frames used in rural areas and is used as a feeder for Yagi antennas. Because the TV's RF input has an input impedance of 75, a 300 feeder will not match it. How to solve this problem in practice? I do nt know if you have noticed that there is a 300 to 75 impedance converter in the TV accessories (the one with a plastic package and a round plug at one end is about the size of two thumbs) . It is actually a transmission line transformer, which converts the impedance of 300 to 75 so that it can be matched. What needs to be emphasized here is that the characteristic impedance is not a concept that is commonly understood as resistance. It has nothing to do with the length of the transmission line and cannot be measured by using an ohmmeter. In order not to cause reflection, the load impedance should be equal to the characteristic impedance of the transmission line. This is the impedance matching of the transmission line. If the impedance does not match, what are the adverse consequences? If they do not match, reflection will occur, energy transmission will not pass, and efficiency will be reduced; a standing wave will be formed on the transmission line (a simple understanding is that the signal is strong in some places and the signal is weak in some places), resulting in a reduction in the effective power capacity of the transmission line; Failure to launch can even damage launch equipment. If the high-speed signal line on the circuit board does not match the load impedance, it will cause vibration, radiation interference, etc.

When the impedance does not match, what are the ways to make it match? First, consider using a transformer for impedance conversion, as in the TV set example above. Second, you can consider using series / parallel capacitors or inductors, which is often used when debugging RF circuits. Third, consider using a series / parallel resistor. Some drivers have relatively low impedance, and a suitable resistor can be connected in series to match the transmission line. For example, a high-speed signal line sometimes has a resistor in the tens of ohms in series. Some receivers have a relatively high input impedance. You can use a parallel resistor to match the transmission line. For example, a 485 bus receiver often connects a 120 ohm matching resistor in parallel with the data line terminal.

How the impedance matches

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

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

Change impedance

By connecting a capacitor or inductor in series with the load, you can increase or decrease the impedance value of the load. 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 chart will first rotate 180 degrees around the center of the chart, then walk around the resistance circle, and then rotate 180 degrees along the center. Repeat the above method until the resistance value becomes 1, then you can directly change the impedance to zero to complete the matching.

Adjust the transmission line

Lengthen 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. You can add capacitance or inductance to adjust the impedance to zero. Complete the match.

Impedance matching has a large transmission power. For a power supply, when its internal resistance is equal to the load, the output power is the largest. At this time, the impedance is matched. The maximum power transmission theorem, if it is high frequency, is no reflected wave. For an ordinary wideband amplifier, the output impedance is 50, and impedance matching needs to be considered in the power transmission circuit. However, if the signal wavelength is much longer than the cable length, that is, the cable length is negligible, 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 reflect, which indicates that all energy is absorbed by the load. Conversely, there is energy loss during transmission. For high-speed PCB wiring, in order to prevent signal reflection, the impedance of the line must be 50 ohms. This is an approximate number. Generally, the coaxial cable base band is 50 ohms, the frequency band is 75 ohms, and the twisted pair is 100 ohms. It is only rounded, for convenience of matching.

Impedance is literally different from resistance. Only one of them is the same, and the other is the impedance? To put it simply, impedance is resistance plus reactance, so it is called impedance; to put it a little bit, impedance is the sum of resistance, capacitive reactance and inductive reactance on a vector. In the world of direct current, the effect of an object on current obstruction is called resistance. All substances in the world have resistance, just the difference in resistance value. A substance with a low resistance is called a good conductor, a substance with a high resistance is called a non-conductor, and a superconductor called in the high-tech field is a thing with a resistance value close to zero. However, in the field of alternating current, in addition to resistance, which obstructs current, capacitance and inductance also hinder the flow of current. This effect is called reactance, which means the effect of resisting current. The reactance of a capacitor and an inductor is called a capacitive reactance and an inductive reactance, respectively, referred to as capacitive reactance and inductive reactance. Their unit of measurement is the same as the resistance, and the value is related to the frequency of the alternating current. The higher the frequency, the smaller the capacitive reactance and the larger the inductive reactance. In addition, the capacitive reactance and the inductive reactance also have the problem of the phase angle, which has the relationship on the vector, so it will be said that the impedance is the sum of the resistance and the reactance on the vector.

Impedance matching refers to a working state where the load impedance and the internal impedance of the excitation source mutually adapt to obtain the maximum power output. For circuits with different characteristics, the matching conditions are different.

In a 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 of the excitation source and the load impedance contain reactance components, in order to obtain the maximum power from the load, the load impedance and the internal resistance must meet a conjugate relationship, that is, the resistance components are equal, and the reactance components have only equal values and opposite signs. This matching condition is called conjugate matching.

Impedance- related research

In high-speed designs, the impedance is related to the quality of the signal. Impedance matching technology can be said to be rich and diverse, but how to apply it reasonably in a specific system requires measuring various factors. For example, in the design of our system, many of them use series matching of source segments. For what situations need to match, what kind of matching, and why.

For example: most of the differential matching uses terminal matching; the clock uses source segment matching.

1. Tandem Termination

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

The signal transmission after series terminal matching has the following characteristics:

A Due to the role of series matching resistor, the driving signal is propagated to the load terminal at 50% of its amplitude when propagating

The reflection coefficient of the 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 propagated at the source, so that the amplitude of the signal received at the load end is approximately the same as the original signal

D The reflected signal at the load end travels to the source end and is absorbed by the matching resistor after reaching the source end.

E After the reflected signal reaches the source, the source drive 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 termination matching resistance value is simple. It is required that 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 an ideal signal driver is zero, the actual driver always has a relatively small output impedance, and when the signal level changes, the output impedance may be different. For example, a CMOS driver with a power supply voltage of + 4.5V has a typical output impedance of 37 at a low level and a typical output impedance of 45 at a high level [4]; the TTL driver has the same output impedance as the CMOS driver The level changes. Therefore, for a TTL or CMOS circuit, it is impossible to have a very correct matching resistor, only a compromise can be considered.

Signal networks with a chain topology are not suitable for series termination. 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 some time the amplitude of the signal at the load end is half the amplitude of the original signal. Obviously, the signal is in an indefinite logic state at this time, and the noise margin of the signal is very low.

Tandem matching is the most commonly used terminal matching method. Its advantages are low power consumption, no additional DC load to the driver, and no additional impedance between the signal and ground; and only a resistive element is required.

2. Termination in parallel

The theoretical starting point of parallel terminal matching is to increase the 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 large, so as to eliminate the load end reflection. Implementation forms are divided into two forms of single resistance and double resistance.

The signal transmission after parallel terminal matching has the following characteristics:

A drive signal propagates along the transmission line at approximately full amplitude

B All reflections are absorbed by the matching resistor

The amplitude of the signal received by the C load is approximately the same as the amplitude of the signal sent by the source.

In the actual circuit system, the input impedance of the chip is very high, so for the single resistance form, 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 50, the R value is 50. If the high level of the signal is 5V, the quiescent current of the signal will reach 100mA. Because the driving capability of typical TTL or CMOS circuits is very small, this single-resistor parallel matching method rarely appears in these circuits.

Double-resistor parallel matching, also known as Thevenin termination, requires less current drive capability than single-resistance. This is because the parallel value of the two resistors matches the characteristic impedance of the transmission line, and each resistance is greater than the characteristic impedance of the transmission line. Considering the driving ability of the chip, the selection of 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 should not be too small, so as not to drive the current too high when the signal is low

. The resistance value connected to the ground cannot be too small, so as not to drive the current too high when the signal is high.

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

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

Watering flowers

2.1 In the multi-layer signal line of the digital system (Signal Line), when a square wave signal is transmitted, it can be assumed to be a hose for watering and watering. One end is pressurized at the grip to make it shoot out of the water column, and the other end is connected to the faucet. When the pressure exerted by the grip tube is just right, and the range of the water column is properly sprinkled on the target area, it is not a trivial achievement to give and accept both to successfully complete the mission.

2.2 However, once the water injection process is too far, it will not only evacuate over the target to waste water resources, but may even be released due to strong water pressure, causing the source to rebound and cause the hose to break free from the faucet! Not only did the mission fail, but also setbacks, but it also leaked a lot of peas!

2.3 Conversely, when the squeeze at the grip is not enough to make the range too close, the desired result is still not obtained. After all, you can't do more than you want. Only when you are right can you rejoice.

2.4 The above simple life details can be used to explain that the Square Wave signal (Signal) is in a multi-layer transmission line (Transmission Line, which is a combination of the signal line, dielectric layer, and ground layer) Fast transfers made. At this time, the transmission line (common cable includes Coaxial Cable, Microstrip Line or Strip Line, etc.) can be regarded as a hose, and the pressure applied by the grip tube is like the "receiving end" on the board (Receiver) The resistor to which the element is connected in parallel to the Gnd is generally used to adjust the characteristic impedance of its end point (Characteristic Impedance) to match the internal requirements of the receiving end element.

Third, control technology

3.1 From the above, it can be known that when the "signal" travels quickly in the transmission line and reaches the end point, and wants to enter the receiving component (such as a different size IC such as CPU or Meomery) to work, the "characteristic impedance" of the signal line It must be matched with the internal electronic impedance of the terminal element, so as not to fail the task in vain. In terms, it means executing instructions correctly, reducing noise interference, and avoiding wrong actions. "Once they do not match each other, there will be a small amount of energy to bounce back towards the" transmitting end ", and then form the trouble of reflecting noise .

3.2 When the characteristic impedance (Z0) of the transmission line itself is set to 28ohm by the designer, the grounding resistor (Zt) of the terminal control tube must also be 28ohm, so as to assist the maintenance of the transmission line to Z0 and make the whole Stable at a design value of 28 ohm. Only under such a matching situation of Z0 = Zt can the signal be transmitted most efficiently, and its "Signal Integrity" (a term for signal quality) is also the best.

Fourth, characteristic impedance

4.1 When a square wave of a signal advances in the signal line of the transmission line assembly with a positive signal at a high level (High Level), the closest reference layer (such as the ground layer) is theoretically There must be a negative pressure signal induced by the electric field to accompany the forward movement (equal to the return path of the positive pressure signal in the reverse direction), so that the overall loop system can be completed. If the flight time of the "signal" is frozen for a short time, it can be imagined that it suffers from the instantaneous impedance value (Instantanious Impedance) presented by the signal line, dielectric layer and reference layer, etc. "Characteristic Impedance". Therefore, the "characteristic impedance" should be related to the signal line width (w), line thickness (t), dielectric thickness (h) and dielectric constant (Dk).

4.2 Consequences of poor impedance matching Because the original word "characteristic impedance" (Z0) of high-frequency signals is very long, they are generally referred to as "impedance". The reader must be careful. This is not the same impedance value (Z) that appears in low-frequency AC alternating current (60Hz) wires (not transmission lines). For digital systems, when Z0 of the entire transmission line can be properly managed, and if it is controlled within a certain range (± 10 or ± 5 ), a good quality transmission line will reduce noise and prevent malfunction. . However, when any of the four variables (w, t, h, r) of Z0 in the microstrip line is abnormal, such as a gap in the signal line, the original Z0 will rise suddenly (see Z0 and The fact that W is inversely proportional), and cannot continue to maintain its due stability (Continuous), the energy of its signal will inevitably partially advance, and some of the lack of rebound reflection. This will inevitably prevent noise and malfunction. For example, the watering hose is suddenly stepped on, causing abnormalities at both ends of the hose, which can precisely explain the problem of poor impedance matching.

4.3 Noise caused by poor impedance matching. The rebound of the above part of the signal energy will cause the original good quality square wave signal to appear abnormal deformation immediately (that is, Overshoot with a high level upward, Undershoot with a low level downward, and subsequent Ringing of the two). These high-frequency noises also cause malfunctions when they are severe, and the faster the clock speed, the more noise and the more prone to errors.

So when should I consider impedance matching?

In an ordinary wideband amplifier, because the output impedance is 50, it is necessary to consider impedance matching in a power transmission circuit. However, in fact, when the length of the cable is negligible for the wavelength of the signal, impedance matching is not required.

Consider the signal frequency is 1MHz, its wavelength is 300m in air, and about 200m in coaxial cable. Coaxial cables with a length of about 1 m are usually in a completely negligible range.