How to Understand impedance matching?

 

Impedance matching is a suitable combination between the signal source, transmission line, and load. Impedance Matching is divided into two types: low frequency and high frequency.

 

 

 

Let's start with a dc voltage source to drive a load. Because the actual voltage source always has internal resistance (see the output impedance), we can equivalent an actual voltage source to an ideal voltage source in series with a resistance r. Assuming that the load resistance is R, the power source EMR is U, and the internal resistance is r, we can calculate the current flowing through the resistance R: I = U/(R + r). We can see that, the smaller the load resistance 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. Calculate the power consumption of resistance R as follows:

P = I2 × R = [U/(R + r)] 2 × R = U2 × R/(R2 + 2 × R × r + r2) = U2 × R/[(R-r) 2 + 4 × R × r]= U2/{[(R-r) 2/R] + 4 × r}

For a given signal source, the internal resistance r is fixed, while the load resistance R is selected by us. Note: In the formula [(R-r) 2/R], when R = r, [(R-r) 2/R] can obtain the minimum value 0, in this case, the maximum output power Pmax = U2/(4 × R) can be obtained for the load resistance 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..This conclusion is also applicable to low frequency and high frequency circuits. When the AC circuit contains capacitive or inductive impedance, the conclusion is changed, that is, the signal source must be equal to the real part of the load impedance, and the virtual part is opposite to each other. In low-frequency circuits, we generally do not consider the transmission line matching problem, but only the signal source and the load, because the wavelength of the low-frequency signal is very long than that of the transmission line, the transmission line can be regarded as a "short line", and reflection can be ignored (it can be understood that, even if the line is short, the reflection is the same as the original signal ). From the above analysis, we can draw a conclusion: if we need to output a large current, select a small load R; if we need to output a large voltage, select a large load R; if we need the maximum output power, select the resistance R that matches the internal resistance of the signal source. Sometimes impedance mismatch has another meaning. For example, some output ends of the instrument are designed under specific load conditions. If the load conditions change, the original performance may not be achieved, this is also called impedance mismatch.

 

In high-frequency circuits, we must also consider the reflection problem. When the signal frequency is very high, the signal wavelength is very short. When the wavelength is shorter than the transmission line length, the reflection signal overlay the original signal and changes the shape of the original signal. If the characteristic impedance of the transmission line is not the same as the load impedance (that is, the load impedance does not match), reflection is generated at the load end. Why does the resolution of the reflection and feature impedance occur when the impedance does not match? The solution of the second-order partial differential equation is involved. Here we will not elaborate on it, if you are interested, please refer to the transmission line theory in the electromagnetic and microwave books. The Characteristic Impedance of a transmission line (also called the characteristic impedance) is determined by the structure and material of the transmission line, and is independent of the length of the transmission line, as well as the amplitude and frequency of the signal.

For example, the characteristic impedance of common closed-circuit television coaxial cables is 75Ω, while that of some RF equipment is commonly used. In addition, a common transmission line is a flat parallel line with a characteristic impedance of 300 Ω, which is common in television antenna frames used in rural areas and is used as a feeder for eight-wood antennas. Because the input impedance of the RF input of the TV is 75 Ω, the Feeder of the 300 Ω cannot match it. In reality, how does one solve this problem? I don't know if you have noticed that there is an impedance converter from 300 Ω to 75 Ω in the TV accessories (a plastic package with a circular plug at one end, it's about two thumbs up ). It is actually a transmission line Transformer, which converts the 300 Ω impedance into 75 Ω, so that it can be matched. It should be emphasized that the characteristic impedance is not a concept of resistance that we generally understand. It has nothing to do with the length of the transmission line and cannot be measured using an ohm table. In order not to produce reflection, the load impedance should be equal to the characteristic impedance of the transmission line, which is the impedance matching of the transmission line. What are the adverse effects of impedance mismatch? If the signal does not match, reflection will be formed, and the energy transmission will not pass over, reducing the efficiency. 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 ), as a result, the effective power capacity of the transmission line is reduced; power transmission fails, and may even damage the transmission device. If the High-speed signal line on the circuit board does not match the load impedance, it will produce shock and radiation interference.

 

When the impedance does not match, how can we make it match? First, you can consider using a transformer for impedance conversion, as in the example in the TV set above. Second, you can consider using a series/parallel capacitor or inductance method, which is often used in RF circuit debugging. Third, you can consider using the series/parallel resistance method. Some drivers have relatively low impedance and can be connected to a suitable resistance to match the transmission line. For example, high-speed signal lines may sometimes concatenate a resistance of dozens of euros. The input impedance of some receivers is relatively high, and the method of parallel resistance can be used to match with the transmission line. For example, the 485 bus receiver often matches the resistance of 120 euro in parallel with the data line terminal.

To help you understand the reflection problem when the impedance does not match, Let me give two examples: You are practicing boxing-sandbags. If it is a sandbag with proper weight and hardness, you will feel comfortable. However, if one day I made a sandbag, for example, if it was replaced by Isha, you would still use the previous force to fight it, your hand may be unable to handle it-this is the case of heavy load, which will produce a lot of elastic. On the contrary, if I replace it with something very light, you may leave it empty and your hands may not be able to stand it-this is the case where the load is too light. In another example, I don't know if you have ever had such an experience: when you can't see the stairs, you can go up/down the stairs. When you think there are still stairs, it will feel like "load mismatch. Of course, this example may not be appropriate, but we can use it to understand the reflection when the load does not match.