What is output impedance? What is impedance matching?

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What is output impedance? What is impedance matching? [Copy link]

1. Output Impedance

Before understanding the issue of "impedance matching", let us first learn what "output impedance" is?

In actual circuit design, whether it is a signal source, amplifier or power supply, there is the problem of output impedance.

Output impedance is actually the internal resistance of a signal source. Originally, for an ideal voltage source (including power supply), the internal resistance should be 0, and for an ideal current source, the impedance should be infinite. People tend to "forget" output impedance.

Next, we will use the voltage source as an example to explain this problem.

In reality, voltage sources basically cannot achieve zero internal resistance. We often use an ideal voltage source in series with a resistor r to equate an actual voltage source. The resistor r in series with the ideal voltage source is the internal resistance of the voltage source. When this voltage source supplies power to the load, a current I will flow through the load and produce a certain voltage drop on the resistor. This will cause the output voltage of the power supply to drop, thereby limiting the maximum output power (why the maximum output power is limited? This is also the "impedance matching" problem that we focus on in this article, please continue reading). Similarly, for an ideal current source, the output impedance should be infinite, but this is impossible to achieve in actual circuits.

Generally speaking, the smaller the output impedance of a voltage source, the better, while the larger the output impedance of a current source, the better (Note: this is only suitable for low-frequency circuits. In high-frequency circuits, impedance matching issues must also be considered. In addition, this does not apply to signal sources that require current limiting or voltage limiting protection).

2. How to understand impedance matching?

First, let's look at the definition of impedance matching: Impedance matching refers to a suitable match 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 actual voltage sources always have internal resistance (this is why we talk about "output impedance" first), we can equate an actual voltage source to a model of an ideal voltage source connected in series with a resistor r. Assuming the load resistance is R, the power supply electromotive force is U, and the internal resistance is r, we can calculate the current I=U/(R+r) flowing through the resistor 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 the resistor R:

For a given signal source, its internal resistance r is fixed, and the load resistance R is selected by us. Note that [(Rr)2/R] in the formula, when R=r, [(Rr)2/R] can reach the minimum value of 0, and the maximum output power Pmax=U2/4r 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, which is called conjugate 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 relative to the transmission line, the transmission line can be regarded as a "short line" and reflection can be ignored (it can be understood 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 conclude that if we need a large output current, we should choose a small load R; if we need a large output voltage, we should choose a large load R; if we need the maximum output power, we should 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, which is also called 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 is not equal to the load impedance (i.e., mismatched), reflection will occur at the load end. We will not go into details here as to why reflection occurs when the impedance is mismatched, and how to solve the characteristic impedance (involving the solution of the second-order partial differential equation). 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 of the signal, the frequency, etc.

For example, the characteristic impedance of the commonly used closed-circuit television coaxial cable is 75Ω, while some RF equipment often uses coaxial cables with a characteristic impedance of 50Ω. In addition, another 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 is used as a feeder for Yagi antennas. Because the input impedance of the RF input end of the TV is 75Ω, the 300Ω feeder will not match it. How is this problem solved 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, about the size of two thumbs) in the accessories of the TV. It is actually a transmission line transformer that transforms the 300Ω impedance into 75Ω, 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 of impedance mismatch? If it does not match, the signal energy transmission efficiency will be reduced at the least; at the worst, reflection will be formed, and the signal energy will be completely reflected back; at high power, it may even damage the previous circuit or signal source. If the high-speed signal line on the circuit board does not match the load impedance, oscillation, radiation interference, etc. will occur.

When the impedance does not match, what methods are there to make it match? First, you can consider using a transformer to do impedance conversion, just like the example of 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. The impedance of some drivers is relatively low, 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. The input impedance of some receivers is relatively high, and the parallel resistor method can be used to match the transmission line. For example, the 485 bus receiver often connects a 120Ω matching resistor in parallel at the data line terminal.

How to understand the reflection problem when impedance is not matched? Here is an example: suppose you are practicing boxing - hitting a sandbag. If the sandbag is of the right 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 excessive load, 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 too light load.