RF Basics: How to Understand Impedance Matching

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RF Basics: How to Understand Impedance Matching [Copy link]

Impedance matching refers to a suitable matching method between a signal source or transmission line and a load. Impedance matching is discussed in two cases: low frequency and high frequency. Let's start with a DC voltage source driving a load. Since the actual voltage source always has internal resistance, we can make an actual voltage source equivalent to a model of an ideal voltage source connected in series with a resistor r. Assuming that the load resistance is R, the power supply electromotive force is U, and the internal resistance is r, then we can calculate the current flowing through the resistor R as: I=U/(R+r). It can be seen 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. Let's calculate the power consumed by resistor R: P=I*I*R=[U/(R+r)]*[U/(R+r)]*R=U*U*R/(R*R+2*R*r+r*r) =U*U*R/[(Rr)*(Rr)+4*R*r] =U*U/{[(Rr)*(Rr)/R]+4*r} For a given signal source, its internal resistance r is fixed, and the load resistance R is selected by us. Note that in the formula [(Rr)*(Rr)/R], when R=r, [(Rr)*(Rr)/R] can achieve the minimum value of 0, and the maximum output power Pmax=U*U/(4*r) can be obtained on 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 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 changes. That is, the real part of the signal source and load impedance must be equal, and the imaginary part must be opposite to each other. This is called common impedance matching. In low-frequency circuits, we generally do not consider the matching problem of transmission lines, but only consider the situation between the signal source and the load. Because the wavelength of the low-frequency signal is very long compared to the transmission line, the transmission line can be regarded as a "short line" and reflection can be ignored (it can be understood as follows: 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 conclude that 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 a resistor R that matches the internal resistance of the signal source. Sometimes impedance mismatch has another meaning. For example, the output end of some instruments is designed under specific load conditions. If the load conditions change, the original performance may not be achieved. At this time, we also call it 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 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 does not match (equal to) the load impedance, reflection will occur at the load end. Why reflection occurs when the impedance does not match and how to solve the characteristic impedance involve solving the second-order partial differential equation. We will not go into details here. Those who are interested can refer to the transmission line theory in books on electromagnetic fields and microwaves. The characteristic impedance of the transmission line (also called characteristic impedance) is determined by the structure and material of the transmission line, and has nothing to do with the length of the transmission line, the amplitude and frequency of the signal. For example, the characteristic impedance of the commonly used closed-circuit television coaxial cable is 75 ohms, while some RF equipment often uses coaxial cables with a characteristic impedance of 50 ohms. Another common transmission line is a flat parallel line with a characteristic impedance of 300 ohms, which is more common on TV antenna racks used in rural areas and is used as a feeder for Yagi antennas. Because the input impedance of the RF input end of the TV is 75 ohms, the 300 ohm feeder will not match it. How is this problem solved in practice? I wonder if you have noticed that there is a 300 ohm to 75 ohm impedance converter in the accessories of the TV (a plastic package with a round plug on one end, about the size of two thumbs)? It is actually a transmission line transformer that converts the 300 ohm impedance into 75 ohms, so that it can be matched. One thing that needs to be emphasized here is that characteristic impedance is not the same concept as the resistance we usually understand. It has nothing to do with the length of the transmission line and cannot be measured by using an ohmmeter. In order to avoid 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 consequences if the impedance does not match? If it does not match, reflection will be formed, energy cannot be transmitted, and efficiency will be reduced; standing waves will be formed on the transmission line (in simple terms, the signal is strong in some places and 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 produce 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 to do impedance conversion, just like the example in the TV mentioned above. Second, you can consider using the method of series/parallel capacitors or inductors, which is often used when debugging RF circuits. Third, you can consider using the method of series/parallel resistors. Some drivers have a relatively low impedance, and a suitable resistor can be connected in series to match the transmission line. For example, high-speed signal lines sometimes have a resistor of tens of ohms connected in series. Some receivers have a relatively high input impedance, and the method of parallel resistors can be used to match the transmission line. For example, the 485 bus receiver often connects a 120-ohm matching resistor in parallel at the data line terminal. To help everyone understand the reflection problem when the impedance does not match, let me give two examples: Suppose you are practicing boxing - hitting a sandbag. If it is a sandbag of appropriate weight and hardness, you will feel very comfortable when you hit it. However, if one day I tamper with the sandbag, for example, replace the inside with iron sand, and you still hit it with the same force as before, your hand may not be able to bear it - this is the case of overload, which will produce a large rebound force. On the contrary, if I replace the inside with something very light, you may miss when you punch, and your hand may not be able to bear it - this is the case of underload. Another example, I don’t know if you have ever had this experience: going up/down the stairs when you can’t see the stairs clearly, and when you think there are stairs, you will feel like "load mismatch". Of course, this example may not be appropriate, but we can use it to understand the reflection situation when the load is mismatched.