Impedance matching refers to an appropriate matching method between the signal source or transmission line and the load. Impedance matching is divided into low frequency and high frequency discussion.
Let's start with a DC voltage source driving a load. Since the actual voltage source always has an internal resistance (please refer to the output impedance question), we can take an actual voltage source equivalent to a model in which an ideal voltage source is connected in series with a resistor r. Assuming that the load resistance is R, the electromotive force of the power supply is U, and the internal resistance is r, then we can calculate the current flowing through the resistance R as: I=U/(R+r). It can be seen that the smaller the load resistance R, then 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. 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/[(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. Note that in the formula [(Rr)2/R], when R=r, [(Rr)2/R] can obtain the minimum value of 0, then the maximum output power Pmax=U2/(4× 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 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 real part of the signal source and the load impedance are required to 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 problem of the transmission line, but only consider the situation between the signal source and the load. Because the wavelength of the low-frequency signal is very long relative to the transmission line, the transmission line can be regarded as a "short line", and reflection is not necessary. Consider (this can be understood: 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 the conclusion: if we need a large output current, we choose a small load R; if we need a large output voltage, we choose a large load R; if we need the maximum output power, we choose the internal resistance of the signal source Matched resistance R. Sometimes impedance mismatch has another meaning. For example, the output of some instruments is designed under specific load conditions. If the load conditions are changed, the original performance may not be achieved. At this time, we will also call impedance mismatch. .
In high-frequency circuits, we must also consider the problem of reflection. When the frequency of the signal is very high, the wavelength of the signal is very short. When the wavelength is as short as 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 is not equal to the load impedance (that is, does not match), reflections will occur at the load end. Why does the impedance mismatch produce reflection and the solution method of characteristic impedance involve the solution of second-order partial differential equations. We will not go into details here. If you are interested, please refer to the transmission line theory in the books on electromagnetic fields and microwaves. The characteristic impedance (also called characteristic impedance) of the 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 commonly used CCTV coaxial cable has a characteristic impedance of 75Ω, while some radio frequency equipment commonly uses a coaxial cable with a characteristic impedance of 50Ω. In addition, a common transmission line is a flat parallel line with a characteristic impedance of 300Ω, which is more common on TV antenna racks used in rural areas and used as a feeder for Yagi antennas. Because the input impedance of the TV's RF input end is 75Ω, the 300Ω feeder will not match it. How to solve this problem in practice? I don’t know if you have noticed that there is a 300Ω to 75Ω impedance converter (a plastic package with a round plug at one end) in the accessory of the TV. , About the size of two thumbs). Inside it is actually a transmission line transformer, which transforms the 300Ω impedance into 75Ω, so that it can be matched. What needs to be emphasized here is that the characteristic impedance is not a concept with the resistance we usually understand, it has nothing to do with the length of the transmission line, and it cannot 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. What are the bad consequences if the impedance is not matched? If it is not matched, reflection will be formed, energy cannot be transmitted, 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; the power cannot be transmitted, and even the transmitting equipment will be damaged. If the high-speed signal line on the circuit board does not match the load impedance, it will cause oscillation, radiation interference, etc.
When the impedance does not match, what are the ways to make it match? First, you can consider using a transformer for impedance conversion, just like the example in the TV set mentioned above. Second, consider the use of series/parallel capacitors or inductors, which are often used when debugging RF circuits. Third, consider the use of series/parallel resistors. 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 of several tens of ohms in series. The input impedance of some receivers is relatively high. Parallel resistors can be used to match the transmission line. For example, 485 bus receivers often connect a 120 ohm matching resistor in parallel at the data line terminal.
In order to help you understand the reflection problem when impedance does not match, let me give two examples: Suppose you are practicing boxing-punching sandbags. If it is a sandbag with the right weight and the right hardness, you will feel very comfortable when you hit it. However, if one day I make a sandbag with hands and feet, for example, the inside is replaced with iron sand, and you still use the previous force to hit it, your hands may not be able to bear it-this is the situation of excessive load. Produce a great rebound force. On the contrary, if I replace the inside with something very light and light, you may lose your hand when you punch it, and you may not be able to bear it-this is the case of too light load. Another example, I don’t know if you have ever experienced this: you just go up/down the stairs when you can’t see the stairs clearly. When you think there are stairs, there will be a feeling of "load mismatch". Of course, perhaps this example is not appropriate, but we can use it to understand the reflection when the load does not match.
