Understanding Impedance and Impedance Matching

1. The concept of impedance

In a circuit with resistance, inductance and capacitance, the resistance to alternating current is called impedance. It is usually represented by Z, and its value is determined by the interaction of the frequency of the alternating current, resistance R, inductance L, and capacitance C. It can be seen that the impedance of a specific circuit changes at any time, and it will change with the change of the current frequency.

2. The concept of impedance matching

Impedance matching is a part of microwave electronics. It is mainly used on transmission lines to ensure that all high-frequency microwave signals can be transmitted to the load without any signal reflection back to the source, thereby improving energy efficiency. What are the consequences of mismatch? If it does not match, reflection will be formed, the energy cannot be transmitted, and the efficiency will be reduced. Standing waves will be formed on the transmission line, 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, oscillation and radiation interference will occur. Its impact on the entire system is very serious. 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 (because the line is short, even if it is reflected back, it is still the same as the original signal).

When the impedance does not match, what methods can be used to match it? First, you can consider using a transformer to convert the impedance. Second, you can consider using series/parallel capacitors or inductors, which are often used when debugging RF circuits, but are rarely used in general circuit design. Third, you can consider using series/parallel resistors, which are series terminal matching and parallel terminal matching.

The following is a brief introduction to the third matching method .

1) Series terminal matching

The theoretical starting point of series terminal matching is to connect a resistor R in series between the signal end and the transmission line under the condition that the impedance of the signal source end is lower than the characteristic impedance of the transmission line, so that the output impedance of the source end matches the characteristic impedance of the transmission line, and suppresses the re-reflection of the signal reflected from the load end. Series matching does not require the signal driver to have a large current driving capability.

The signal transmission after series terminal matching has the following characteristics:

A Due to the effect of the series matching resistor, the driving signal propagates to the load end with 50% of its amplitude;

The reflection coefficient of signal B at the load end is close to +1, so the amplitude of the reflected signal is close to 50% of the original signal amplitude.

C The reflected signal is superimposed on the signal transmitted from the source end, so that the amplitude of the signal received by the load end is approximately the same as that of the original signal;

The reflected signal at the load end D propagates toward the source end and is absorbed by the matching resistor after reaching the source end;

After the reflected signal E reaches the source, the source drive current drops to 0 until the next signal transmission.

The principle of selecting the series terminal matching resistance value is very simple, that is, the sum of the matching resistance value and the output impedance of the driver is required to be equal to the characteristic impedance of the transmission line. The 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 amplitude and frequency of the signal, etc. The 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 it cannot be measured by using an ohmmeter. It can be measured by special instruments. For example, there is information on the Internet that a vector network analyzer can be used to accurately measure the characteristic impedance of a balanced twisted pair transmission line. The output impedance of TTL and CMOS will change with the change of the level. Therefore, in TTL or CMOS circuits, it is impossible to achieve complete impedance matching very accurately, and only a compromise can be considered.

Series matching is the most commonly used terminal matching method. Its advantages are low power consumption, no additional DC load on the driver, no additional impedance between the signal and the ground; and only one resistor element is required.

2) Parallel terminal matching

The theoretical starting point of parallel terminal matching is to add parallel resistance to match the input impedance of the load end with the characteristic impedance of the transmission line when the impedance of the signal source end is very small, so as to eliminate the reflection at the load end. There are two forms of implementation: single resistance and double resistance.

The signal transmission after parallel terminal matching has the following characteristics:

① The driving signal propagates along the transmission line at approximately full amplitude;

② All reflections are absorbed by the matching resistors;

③ The signal amplitude received by the load end is approximately the same as the signal amplitude sent by the source end.

In actual circuit systems, the input impedance of the chip is very high, so for a single resistor, the parallel resistance value at the load end must be close to or equal to the characteristic impedance of the transmission line. Since the driving capability of typical TTL or CMOS circuits is very small, this single resistor parallel matching method rarely appears in these circuits.

The parallel matching of the dual resistor form, also known as the Thevenin terminal matching, requires less current driving capability than the single resistor form. This is because the parallel value of the two resistors matches the characteristic impedance of the transmission line, and each resistor is larger than the characteristic impedance of the transmission line. Considering the driving capability of the chip, the selection of the two resistor values ​​must follow three principles:

① The parallel value of the two resistors is equal to the characteristic impedance of the transmission line;

② The resistance value connected to the power supply cannot be too small, so as to avoid excessive driving current when the signal is at a low level;

③ The resistance value connected to the ground cannot be too small to avoid excessive driving current when the signal is at a high level.

The advantage of parallel terminal matching is that it is simple and easy to implement; the obvious disadvantage is that it will bring DC power consumption: the DC power consumption of the single resistor method is closely related to the duty cycle of the signal; the dual resistor method has DC power consumption regardless of whether the signal is high or low. Therefore, it is not suitable for systems with high power consumption requirements such as battery-powered systems. In addition, the single resistor method is not used in general TTL and CMOS systems due to driving capability issues, while the dual resistor method requires two components, which puts forward requirements on the board area of ​​the PCB, so it is not suitable for high-density printed circuit boards.