PCB Technical - Why shouldn't there be sharp and right angles when the printed circuit boards is routed

Radio frequency, high-speed printed circuit boards digital circuit: Prohibit acute angles, try to avoid right angles.
If it is a radio frequency line, if the corner is at a right angle, there will be discontinuities, and discontinuities will easily lead to the generation of high-order modes, which will affect the radiation and conduction performance. If the RF signal line runs at a right angle, the effective line width at the corner will increase, and the impedance will be discontinuous, causing signal reflection. In order to reduce the discontinuity, to deal with the corners, there are two methods: chamfering and rounding. The radius of the arc angle should be large enough, generally speaking, to ensure: R>3W.

Acute and right-angle routing
Acute-angle wiring is forbidden in general wiring. Right-angle wiring is generally a situation that needs to be avoided as much as possible in wiring. It has almost become one of the standards for measuring the quality of wiring. So how much influence will the right-angle wiring have on signal transmission? In principle, the sharp and right-angled wiring will change the line width of the transmission line and cause discontinuity in impedance. Line width changes cause impedance changes, and when the equivalent width of the trace changes, it will cause signal reflection. We can see that when we are routing, if the line width changes, the impedance of the trace will change.
Microstrip line, which consists of a ribbon wire and a ground plane, with a dielectric in the middle. If the dielectric constant of the dielectric, the width of the line, and the distance from the ground plane are controllable, then its characteristic impedance is also controllable, and its degree will be within ±5%.
A stripline is a copper tape placed in the middle of a dielectric between two conductive planes. If the thickness and width of the line, the dielectric constant of the medium, and the distance between the two ground planes are controllable, the characteristic impedance of the line is also controllable, and the accuracy is within 10%. Discontinuity in impedance will reflect the acute angle difference, right angles second, obtuse angles again, rounded corners again, straight lines. When the driver sends a signal into the transmission line, the amplitude of the signal depends on the voltage, the internal resistance of the buffer and the impedance of the transmission line. The initial voltage seen at the driver end is determined by the voltage division of the internal resistance and the line impedance.

Reflection coefficient, where -1≤ρ≤1
No reflection occurs when ρ=0
When ρ=1 (Z 2 =∞, open circuit), total regular reflection occurs
When ρ=-1 (Z 2 =0, short circuit), total negative reflection occurs
The initial voltage is the source voltage Vs (2V) divided by Zs (25 ohms) and the transmission line impedance (50 ohms). The subsequent reflectivity of Vinitial=1.33V is calculated according to the reflection coefficient formula. The reflectivity of the source end is calculated according to the source end impedance (25 ohms) and the transmission line impedance (50 ohms) according to the reflection coefficient formula. It is -0.33; the reflectivity of the terminal is According to the terminal impedance (infinity) and the transmission line impedance (50 ohms), it is calculated as 1 according to the reflection coefficient formula; we get this waveform by superimposing the initial pulse waveform according to the amplitude and delay of each reflection, which is why, Impedance mismatch is the cause of poor signal integrity. Due to the existence of connections, device pins, trace width changes, trace bends, and vias, the impedance has to be changed. So reflection is inevitable.

Is there any reason besides reflection? The influence of right-angle routing on the signal is mainly reflected in three aspects.
1. The corner can be equivalent to the capacitive load on the transmission line, which slows down the rise time;
2. Discontinuous impedance will cause signal reflection;
3. It is EMI generated at right angles.
4. There is another saying: acute angles will cause corrosion residues in the production process, which is not easy to process. It should not be difficult for the current processing technology and should not be used as a reason. The parasitic capacitance caused by the right angle of the transmission line can be calculated by the following empirical formula: C=61W(Er)1/2/Z0 In the above formula, C refers to the equivalent capacitance of the corner (unit: pF), and W refers to walking The width of the line (unit: inch), εr refers to the dielectric constant of the medium, and Z0 is the characteristic impedance of the transmission line. For example, for a 4Mils 50 ohm transmission line (εr is 4.3), the capacitance brought by a right angle is about 0.0101pF, and then the rise time change caused by this can be estimated: T10-90%=2.2* C*Z0/2 = 2.2*0.0101*50/2 = 0.556ps. It can be seen by calculation that the capacitance effect brought by the right-angle trace is extremely small. As the line width of the right-angle trace increases, the impedance there will decrease, so a certain signal reflection phenomenon will occur. We can calculate the equivalent impedance after the line width increases according to the impedance calculation formula mentioned in the transmission line chapter, and then Calculate the reflection coefficient according to the empirical formula: ρ=(Zs-Z0)/(Zs+Z0). Generally, the impedance change caused by right-angle wiring is between 7%-20%, so the reflection coefficient is about 0.1. Moreover, as can be seen from the figure below, the impedance of the transmission line changes within a long time of W/2, and then returns to the normal impedance after W/2. The entire impedance change is extremely short, often within 10pcs. Such fast and small changes are almost negligible for general signal transmission. Many people have this understanding of right-angle routing, and think that it is easy to transmit or receive electromagnetic waves and generate EMI. This has become one of the reasons why many people think that right-angle routing cannot be done. However, many actual test results show that right-angled traces will not produce obvious EMI than straight lines. Perhaps the current instrument performance and the test level restrict the testability, but at least it illustrates a problem. The radiation of the right-angle wiring is already smaller than the measurement error of the instrument itself. In general, the right-angle routing is not as terrible as imagined. At least in the application of non-RF and high-speed circuit board circuits, any effects such as capacitance, reflection, EMI, etc. produced by it are hardly reflected in the TDR test. High-speed circuit board circuit board design engineers should still focus on layout, Power/ground design, wiring design, vias and other aspects. Of course, although the impact of right-angle wiring is not very serious, it does not mean that we can use right-angle wiring in the future. Attention to detail is the basic quality that every engineer must have. Moreover, with the rapid development of digital circuits, PCB engineers The frequency of the processed signal will also continue to increase. In the field of RF design above 10GHz, these small right angles may become the focus of high-speed printed circuit boards problems