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# PCB Tech

## PCB Tech

Understanding of input impedance and output impedance
2021-08-25
View：47
Author：IPCB

1. Input impedance

Input impedance refers to the equivalent impedance of the input terminal of a circuit. Add a voltage source U to the input terminal and measure the current I at the input terminal, then the input impedance Rin is U/I. You can think of the input terminal as both ends of a resistor , The resistance of this resistor is the input impedance.

The input impedance is no different from an ordinary reactance element. It reflects the magnitude of the current hindrance. For voltage-driven circuits, the greater the input impedance, the lighter the load on the voltage source, and the easier it is to drive. It will have an impact on 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 input impedance is The larger the better; if it is driven by a current source, the smaller the impedance, the better. Consider impedance matching

2. Output impedance

Regardless of the signal source or amplifier and power supply, there is a problem of output impedance. The 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 ideal current source The impedance should be infinite. The output impedance is the most important thing to pay attention to in circuit design, but the actual voltage source cannot do this. We often use an ideal voltage source in series with a resistor r to be equivalent to an actual voltage source. This The resistance r in series with the ideal voltage source is the internal resistance of (signal source/amplifier output/power supply). When this voltage source supplies power to the load, a current I will flow through the load and be generated on this resistance The voltage drop of I×r. 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 "impedance matching" question below). Similarly, an ideal current Source, the output impedance should be infinite, but the actual circuit is impossible

Three, 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 two cases of low frequency and high frequency.

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 turn an actual voltage source into an ideal voltage source and an A model of resistance r in series. 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 load The smaller the 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 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, the 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 can be obtained from the load resistance R 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. This is one of the impedance matching we often say. For pure resistance circuits, this conclusion is also applicable to low-frequency circuits and high-frequency circuits. When the AC circuit contains capacitive or inductive impedance, the conclusion changes, that is, the signal source and The real part of the load impedance is 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 low-frequency signal The wavelength is very long compared to the transmission line. The transmission line can be regarded as a "short line", and reflection can be ignored (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 get 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 maximum output power, choose a resistor R that matches the internal resistance of the signal source. Sometimes impedance Mismatch also 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 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 (that is, it does not match), reflection will occur at the load end. Why does reflection occur when the impedance does not match and the method of solving the characteristic impedance involves second-order bias The solution of the differential equation, we will not go into details here. If you are interested, please refer to the transmission line theory in the electromagnetic field and microwave. The characteristic impedance of the transmission line (also called the characteristic impedance) is determined by the structure and material of the transmission line, and The length of the transmission line, and the amplitude and frequency of the signal are irrelevant.

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 in rural areas. The TV antenna rack used is more common and used to make the feeder of the Yagi antenna. 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. Have you noticed that there is a 300Ω to 75Ω impedance converter in the accessory of the TV (a plastic package with a round plug at one end, about the size of two thumbs). Inside is actually a transmission line transformer, which transforms the impedance of 300Ω into 75Ω, so that it can be matched. It should be emphasized here 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. 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. This is the impedance matching of the transmission line. What will be the bad consequences if the impedance is not matched? If it is not matched, reflection will be formed , The energy cannot be transmitted and the efficiency is 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 it may even damage the transmission Equipment. If the high-speed signal line on the circuit board does not match the load impedance, it will produce oscillations, 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 above. Second, you can consider using series/parallel capacitors Or inductance, which is often used when debugging RF circuits. Third, you can 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, such as high-speed signal lines, sometimes A resistor of tens of ohms will be connected 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 matching resistor of 120 ohms 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 hardness, you will feel comfortable playing it. But. , If one day I make a sandbag with hands and feet, for example, if the inside is replaced with iron sand, 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, which will produce A lot of rebound force. On the contrary, if I replace the inside with something very light and light, you may be empty when you punch, and your hand may not be able to bear it-this is the situation of too light load. For example, I don’t know if you have ever experienced this: when you can’t see the stairs clearly, go up/down the stairs, and when you think there are stairs, there will be a feeling of "load mismatch". Of course, maybe such an example Not very appropriate, but we can use it to understand the reflection when the load does not match.

Why is the input stage impedance of the preamplifier high? What are the ways to increase the impedance

The high input impedance means that the power absorbed by the circuit (or the output of the previous circuit) is small, and the power supply or the previous stage can drive more loads. For measurement circuits, such as electronic voltmeters, oscilloscopes, etc., a very high input impedance is required so that the impact on the circuit under test is as small as possible after being connected to the instrument.

How to improve: (1) Field effect tube, the input impedance is naturally high. (2) Use bootstrap connection to increase input impedance. (3) Adopt a common-collection amplifier circuit, and the input stage of the triode amplifier circuit is generally connected in a common-collection mode.

In an ideal state, a voltage-driven back-stage circuit only draws voltage from the previous stage, and no current, so it does not draw power. For the previous stage, it is almost no-load, so the larger the impedance, the easier it is to drive. In fact, the input impedance of the rear stage can only be close to infinity. The input of a vacuum tube or CMOS device can reach the GΩ level, and the current drawn from the front stage is extremely small.

For example, the field effect tube belongs to the voltage-driven type, and the circuit formed by it is a voltage-driven circuit. Because its input impedance is so large that its input current can be ignored, the power consumption is also ignored;

The triode belongs to the current-driven type, and the circuit formed by it is a current-driven circuit, because it needs to inject current to work, although its input impedance is relatively small, it still generates a certain amount of power consumption.

Personal understanding:

The so-called input impedance mainly considers the power consumed by the circuit itself (it can be understood as meaningless loss). For voltage drive circuits, the greater the impedance, the smaller the current, P=I*I*R, the smaller the current In terms of the driving circuit, the smaller the impedance, P=I*I*R, the smaller the power consumption, so that the latter circuit can output more power.