Impedance matching refers to the specific cooperative relationship between the load impedance and the internal impedance of the signal source during signal transmission. A certain relationship that should be satisfied between the output impedance of a device and the connected load impedance, so as to avoid the obvious influence on the operation of the device itself after the load is connected. Regarding low frequency circuits and high frequency circuits, impedance matching is very different.

Before understanding impedance matching, it is necessary to understand input impedance and output impedance.

1. Input impedance

Input impedance is the equivalent impedance at the input of a circuit. Add a voltage source U on the input end, measure the current I at the input end, then the input impedance Rin is U/I. You can think of the input as the two ends of a resistor, and the resistance of this resistor is the input impedance.

The input impedance is no different from a general reactive element, which reflects the size of the blocking effect on the current. For voltage-driven circuits, the larger the input impedance, the lighter the load on the voltage source, so it is easier to drive and will not affect the signal source; for current-driven circuits, the smaller the input impedance, 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, the better; if it is driven by a current source, the smaller the impedance, the better (Note: only suitable for low-frequency circuits, in high-frequency circuits, the impedance matching problem must also be considered). In addition, if you want to obtain the maximum output power, you must also consider the impedance matching problem.

2. Output impedance

Regardless of the signal source or amplifier and power supply, there is a problem of output impedance. 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. But real voltage sources cannot do this. We often use an ideal voltage source in series with a resistor r to be equivalent to an actual voltage source. The resistor r connected 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 will flow through the load, and a voltage drop of I×r will occur across the resistance. This will lead to a drop in the output voltage of the power supply, thereby limiting the maximum output power (for why the maximum output power is limited, please see the question "Impedance Matching" later). Similarly, an ideal current source, the output impedance should be infinite, but the actual circuit is impossible.

3. Impedance matching

Impedance matching refers to a suitable matching method between the signal source or transmission line and the load. Impedance matching is divided into low-frequency and high-frequency discussions. Let's start with a DC voltage source driving a load. Since the actual voltage source always has internal resistance, we can equate an actual voltage source 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 power supply 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), 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. Then 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 [(R-r)2/R] in the formula, when R=r, [(R-r)2/R] can obtain the minimum value of 0, then the maximum output power Pmax=U2/(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. This conclusion is equally applicable to low-frequency circuits and high-frequency circuits. When the AC circuit contains capacitive or rational 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, which is called conjugate matching. In low-frequency circuits, we generally do not consider the matching 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 relatively long compared to the transmission line, the transmission line can be regarded as a "short line", and the reflection can be ignored (you can understand it this way: 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 highest 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 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 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, it does not match), reflection will occur at the load end.

Why reflection occurs when the impedance does not match and the solution to the characteristic impedance involves the solution of 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 (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, the fluctuation 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. Another common transmission line is a flat parallel line with a characteristic impedance of 300Ω, which is more common on TV antenna stands used in rural areas, and is used as a feeder for Yagi antennas. Because the input impedance of the RF input terminal of the TV is 75Ω, the 300Ω feeder will not match it. How is this problem dealt with in practice? I don’t know if we have noticed that in the accessories of the TV, there is a 300Ω to 75Ω impedance converter (a plastic package with a round plug at one end, about the size of two thumbs).

It is actually a transmission line transformer inside, which transforms the impedance of 300Ω 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 cause reflections, 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 will be the adverse consequences? If it does not match, it will cause reflection, the energy will not be transmitted, and the power will be reduced; it will form a standing wave on the transmission line (simple understanding, that is, some local signals are strong, and some local signals are weak), resulting in a decrease in the effective power capacity of the transmission line; the power cannot be transmitted, and even damage the transmitting equipment. If the high-speed signal line on the circuit board does not match the load impedance, vibration, radiation interference, etc. will occur.

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, you can consider the method of using series/parallel capacitors or inductors, which is often used when debugging RF circuits. Third, the method of using series/parallel resistors can be considered. The impedance of some drivers is relatively low, and a suitable resistor can be connected in series to match the transmission line. For example, a high-speed signal line, sometimes a resistor of tens of ohms is connected in series. The input impedance of some receivers is relatively high, and the method of connecting resistors in parallel can be used to match the transmission line. For example, 485 bus receivers often connect a matching resistor of 120 ohms in parallel at the end of the data line. (serial matching at the beginning end, parallel matching at the end)

In order to help us understand the reflection problem when the impedance is not matched, let me give two examples: Suppose you are practicing boxing - punching sandbags. If it is a sandbag with the right weight and hardness, you will feel very comfortable when you hit it. However, if one day I make sandbags into limbs, for example, the inside is replaced with iron sand, and you hit it with the same force as before, your hands may not be able to bear it-this is the case of overloading, which will produce a lot of rebound force. On the contrary, if I replace the inside with something very light and light, when you punch, you may miss the air, and your hand may not be able to bear it-this is the case of the load being too light.