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Impedance matching is a suitable way of matching between a signal source or a transmission line and a load. Impedance matching is divided into low frequency and high frequency two cases discussed.
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Impedance matching is a suitable way of matching between a signal source or a transmission line and a load. Impedance matching is divided into low frequency and high frequency two cases discussed.

We start by driving a load from a DC voltage source. Because of the actual voltage source, there is always an internal resistance (see the output impedance for a question), we can put an actual voltage source, equivalent to an ideal voltage source with a resistor in series. Assuming that the load resistance is R, the supply electromotive force is U and the internal resistance is r, then we can calculate the current flowing through the resistor R: I = U / (R + r), we can see that the smaller the load resistance R The greater 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. And then calculate the resistance R consumption of power:

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

= U2 × R / [(R-r) 2 + 4 × R × r]

= U2 / {[(R-r) 2 / R] + 4 × r}

For a given signal source, its internal resistance r is fixed, and the load resistance R is chosen by us. (Rr) 2 / R], the maximum output power can be obtained on the load resistance R when R = r). That is, when the load resistance is equal to the impedance of the signal source, the load can get the maximum output power, which is one of the impedance matching we often say. For pure resistance 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 need for signal source and load impedance of the real part of the same, the imaginary part of the opposite number, which is called conjugate matching. In the low-frequency circuit, we generally do not consider the transmission line matching problem, only consider the signal source and load between the situation, because the low-frequency signal wavelength relative to the transmission line is very long, the transmission line can be seen as "short", the reflection can not Consider (it can be understood: because the line is short, even if the reflection back, with the original signal or the same). From the above analysis we can conclude that if we need a large output current, choose a small load R; if we need the output voltage is large, then select the large load R; if we need the maximum output power, then select the source resistance Matching resistance R. Sometimes the impedance does not match there is another layer of meaning, for example, some of the instrument output is designed under specific load conditions, if the load conditions change, it may not achieve the original performance, then we will be called impedance mismatch The

In the high-frequency circuit, we must also consider the reflection of the problem. When the frequency of the signal is high, the wavelength of the signal is very short, when the wavelength is short with the transmission line length can be compared, the reflected signal superimposed on the original signal will change the original signal shape. If the characteristic impedance of the transmission line is not equal to the load impedance (ie, does not match), reflection is generated at the load side. Why the impedance does not match the reflection and the characteristic impedance of the solution method, involving the second-order partial differential equation solution, here we do not elaborate, and can be interested in electromagnetic fields and microwave books in the transmission line theory. The characteristic impedance of the transmission line (also called the characteristic impedance) is determined by the structure and material of the transmission line, regardless of the length of the transmission line and the amplitude, frequency and so on of the signal.

For example, the commonly used closed-circuit television coaxial cable characteristic impedance of 75Ω, and some RF equipment is commonly used on the impedance of 50Ω coaxial cable. There is also a common transmission line is the characteristic impedance of 300Ω flat parallel line, which is used in rural TV antenna frame is more common, used to do Yagi antenna feeder. Because the input impedance of the RF input of the TV is 75Ω, the 300Ω feeder will not match it. In fact, how to solve this problem? Do not know if you have not noticed, the TV attachment, there is a 300Ω to 75Ω impedance converter (a plastic package, one end of a circular plug that stuff , There are about two big thumbs). It is actually a transmission line inside the transformer, the 300Ω impedance, into 75Ω, so you can match up. It is important to emphasize that the characteristic impedance is not a concept with what we usually understand. It is independent of the length of the transmission line and can not be measured by using an ohmmeter. In order not to produce reflections, the load impedance should be equal to the characteristic impedance of the transmission line, which is the impedance matching of the transmission line. If the impedance does not match what adverse consequences? If they do not match, it will form a reflection, energy transfer is not past, reduce efficiency; will form a standing wave in the transmission line (simple understanding, that is, some local signal is strong, some local signal weak ), Resulting in reduced power capacity of the transmission line; power transmission does not go out, and even damage the launch device. If the circuit board on the high-speed signal lines and load impedance does not match, will produce shock, radiation interference.

When the impedance does not match, what methods to match it? First, you can consider the use of transformers to do impedance conversion, as mentioned above, the TV as an example. Second, consider using a series / shunt capacitor or inductor, which is often used in debugging RF circuits. Third, you can consider the use of series / parallel resistance approach. Some of the drivers have a low impedance and can be connected in series with a suitable resistor to match the transmission line, such as a high-speed signal line, sometimes in series with a few tens of ohms. And some of the receiver input impedance is relatively high, you can use the parallel resistance method to match the transmission line, for example, 485 bus receiver, often in the data line terminal in parallel with 120 ohm matching resistor.

In order to help you understand the impedance problem when the impedance does not match, let me give two examples: Suppose you are practicing boxing - playing sandbags. If it is a suitable weight, the hardness of the appropriate sandbags, you will feel very comfortable to play up. But if one day I made the sandbag, for example, inside the iron sand, you still use the previous force to fight up, your hand may not stand - this is the heavy load situation, will Produce a lot of resilience. On the contrary, if I put the inside into a very light and light things, you punch, you may be empty, the hand may not stand - this is the situation is too light. Another example, do not know if you have had this experience: that is, when you can not see the stairs when the stairs, when you think there are stairs, there will be "load does not match" this feeling. Of course, perhaps this example is not appropriate, but we can take it to understand the load does not match the reflection of the situation.

We start by driving a load from a DC voltage source. Because of the actual voltage source, there is always an internal resistance (see the output impedance for a question), we can put an actual voltage source, equivalent to an ideal voltage source with a resistor in series. Assuming that the load resistance is R, the supply electromotive force is U and the internal resistance is r, then we can calculate the current flowing through the resistor R: I = U / (R + r), we can see that the smaller the load resistance R The greater 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. And then calculate the resistance R consumption of power:

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

= U2 × R / [(R-r) 2 + 4 × R × r]

= U2 / {[(R-r) 2 / R] + 4 × r}

For a given signal source, its internal resistance r is fixed, and the load resistance R is chosen by us. (Rr) 2 / R], the maximum output power can be obtained on the load resistance R when R = r). That is, when the load resistance is equal to the impedance of the signal source, the load can get the maximum output power, which is one of the impedance matching we often say. For pure resistance 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 need for signal source and load impedance of the real part of the same, the imaginary part of the opposite number, which is called conjugate matching. In the low-frequency circuit, we generally do not consider the transmission line matching problem, only consider the signal source and load between the situation, because the low-frequency signal wavelength relative to the transmission line is very long, the transmission line can be seen as "short", the reflection can not Consider (it can be understood: because the line is short, even if the reflection back, with the original signal or the same). From the above analysis we can conclude that if we need a large output current, choose a small load R; if we need the output voltage is large, then select the large load R; if we need the maximum output power, then select the source resistance Matching resistance R. Sometimes the impedance does not match there is another layer of meaning, for example, some of the instrument output is designed under specific load conditions, if the load conditions change, it may not achieve the original performance, then we will be called impedance mismatch The

In the high-frequency circuit, we must also consider the reflection of the problem. When the frequency of the signal is high, the wavelength of the signal is very short, when the wavelength is short with the transmission line length can be compared, the reflected signal superimposed on the original signal will change the original signal shape. If the characteristic impedance of the transmission line is not equal to the load impedance (ie, does not match), reflection is generated at the load side. Why the impedance does not match the reflection and the characteristic impedance of the solution method, involving the second-order partial differential equation solution, here we do not elaborate, and can be interested in electromagnetic fields and microwave books in the transmission line theory. The characteristic impedance of the transmission line (also called the characteristic impedance) is determined by the structure and material of the transmission line, regardless of the length of the transmission line and the amplitude, frequency and so on of the signal.

For example, the commonly used closed-circuit television coaxial cable characteristic impedance of 75Ω, and some RF equipment is commonly used on the impedance of 50Ω coaxial cable. There is also a common transmission line is the characteristic impedance of 300Ω flat parallel line, which is used in rural TV antenna frame is more common, used to do Yagi antenna feeder. Because the input impedance of the RF input of the TV is 75Ω, the 300Ω feeder will not match it. In fact, how to solve this problem? Do not know if you have not noticed, the TV attachment, there is a 300Ω to 75Ω impedance converter (a plastic package, one end of a circular plug that stuff , There are about two big thumbs). It is actually a transmission line inside the transformer, the 300Ω impedance, into 75Ω, so you can match up. It is important to emphasize that the characteristic impedance is not a concept with what we usually understand. It is independent of the length of the transmission line and can not be measured by using an ohmmeter. In order not to produce reflections, the load impedance should be equal to the characteristic impedance of the transmission line, which is the impedance matching of the transmission line. If the impedance does not match what adverse consequences? If they do not match, it will form a reflection, energy transfer is not past, reduce efficiency; will form a standing wave in the transmission line (simple understanding, that is, some local signal is strong, some local signal weak ), Resulting in reduced power capacity of the transmission line; power transmission does not go out, and even damage the launch device. If the circuit board on the high-speed signal lines and load impedance does not match, will produce shock, radiation interference.

When the impedance does not match, what methods to match it? First, you can consider the use of transformers to do impedance conversion, as mentioned above, the TV as an example. Second, consider using a series / shunt capacitor or inductor, which is often used in debugging RF circuits. Third, you can consider the use of series / parallel resistance approach. Some of the drivers have a low impedance and can be connected in series with a suitable resistor to match the transmission line, such as a high-speed signal line, sometimes in series with a few tens of ohms. And some of the receiver input impedance is relatively high, you can use the parallel resistance method to match the transmission line, for example, 485 bus receiver, often in the data line terminal in parallel with 120 ohm matching resistor.

In order to help you understand the impedance problem when the impedance does not match, let me give two examples: Suppose you are practicing boxing - playing sandbags. If it is a suitable weight, the hardness of the appropriate sandbags, you will feel very comfortable to play up. But if one day I made the sandbag, for example, inside the iron sand, you still use the previous force to fight up, your hand may not stand - this is the heavy load situation, will Produce a lot of resilience. On the contrary, if I put the inside into a very light and light things, you punch, you may be empty, the hand may not stand - this is the situation is too light. Another example, do not know if you have had this experience: that is, when you can not see the stairs when the stairs, when you think there are stairs, there will be "load does not match" this feeling. Of course, perhaps this example is not appropriate, but we can take it to understand the load does not match the reflection of the situation.

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