Before the explanation of impedance calculation, let us first understand the origin and meaning of impedance:
The transmission line impedance is derived from the telegraph equation (for details, please refer to microwave theory)
is as shown in the figure below, which is the equivalent circuit of the distributed parameter of parallel double wires:
From this figure, the telegraph equation can be derived
Take the sinusoidal form of the voltage and current on the transmission line
have to
General solution Define characteristic impedance Under the lossless line, r=0, g=0 get Note the conceptual difference between this characteristic impedance and wave impedance (see the definition of wave impedance of plane waves for details)
The relationship between characteristic impedance and wave impedance can be derived from this relationship.
Ok, understand what the characteristic impedance is in theory, and look at the actual meaning. When the voltage and current propagate on the transmission line, if the characteristic impedance is inconsistent, the solution of the telegraph equation obtained is inconsistent, causing the so-called reflection phenomenon, etc. In the field of signal integrity, problems such as reflection, crosstalk, and power plane cutting can all be classified as impedance discontinuities, so the importance of matching is shown here.
Definition of stackup
Let's look at the following kind of stackup, the 8-layer board commonly used on the motherboard (4-layer power/ground and 4-layer wiring layer, sggssggs, respectively defined as L1, L2...L8), so the impedance to be calculated is L1, L4, L5, L8
Be familiar with some of the basic concepts in the stack, which are often used when dealing with manufacturers
The concept of Oz
Oz is originally a unit of weight Oz (ounce) = 28.3 g (gram)
is defined in the laminate. The thickness of one ounce of copper spread on a square foot area is 1Oz, and the corresponding unit is as follows
The concept of dielectric constant (DK) The ratio of the capacitance Cx when there is a dielectric between the capacitor plates and the vacuum capacitance Co of the same shape and size is the dielectric constant: Ε = Cx/Co = ε'-ε"
The concept of Prepreg/Core Pp is a kind of dielectric material, composed of glass fiber and epoxy resin, core is actually a pp type medium, but it is covered with copper foil on both sides, and pp does not.
Calculation of characteristic impedance of transmission line
First of all, let's look at the basic types of transmission lines. When calculating impedance, there are usually the following types: microstrip line and strip line. The stripline has 2 reference grounds, as shown in the figure below
Compared with the commonly used 8-layer motherboards above, only the top and bottom wiring layers are microstrip line types, and the other wiring layers are stripline types.
When calculating the characteristic impedance of the transmission line, the main board impedance requirements are basically: single-line impedance requirements are 55 or 60 Ohm, differential line impedance requirements are 70 ~ 110 Ohm, thickness requirements are generally 1 ~ 2 mm, and each thickness is obtained by layering according to the thickness requirements. .
Here we assume that the board thickness is 1.6mm, which is about 63mil. The single-ended impedance requires 60 Ohm, and the differential impedance requires 100 Ohm. We assume that the wiring is routed in the following stack.
First, calculate the characteristic impedance of the microstrip line. Since the top layer and the bottom layer are symmetrical, only the top layer impedance needs to be calculated. Polar si6000 is used, and the corresponding calculation graphics are as follows:
When calculating, pay attention to:
1, what you need is to calculate the line width W (target) through the trace impedance requirements
2, the process capabilities of each manufacturer are inconsistent, so the calculation method is different, and you need to confirm with the manufacturer
3, the reason why the surface layer is calculated with coated microstrip is that the manufacturer will cover the green paint, so the surface microstrip calculation is not used, but some manufacturers use the surface microstrip to calculate, it is calibrated
4, the reason why w1 and w2 are different is that the PCB board is corroded from top to bottom during the manufacturing process, so the corrosion has a trapezoidal feeling (of course not exactly)
5, the accurate 60 Ohm impedance is not calculated here, because the manufacturer will slightly change the parameters during the actual manufacturing process, and there is no need to be so precise. I don't think it is a problem within the range of 1,2 ohm
6, the h/t parameter corresponds to you can refer to the stack to see
Then calculate the characteristic impedance of L5 as shown in the figure below
Remember that there were calculation diagrams for stripline and symmetrical stripline in various versions. The actual difference is that symmetrical stripline is literally understood. In fact, it is a special case of offset stripline H1=H2
When calculating the differential impedance, it is similar to the above calculation, except that the target of the line width is calculated by the trace impedance requirement, in addition to the line width and the line distance, which are not listed here
The selected picture is
When calculating the differential impedance, pay attention to:
It satisfies the DDR2 clock 85Ohm~1394 110Ohm differential impedance while also meeting its single-ended impedance. Therefore, I usually choose to meet the differential impedance first (many of the current mode takes the voltage) and then consider the single-ended impedance (usually the board manufacturer does not consider it. Yes, I actually do a lot of boards, the problem is really not too big, it seems that the differential line or the same layer and the same via and the same spacing must meet the requirements)
Characteristic impedance formula (including microstrip line, strip line calculation formula)
A. Microstrip
Z={87/[sqrt(Er+1.41)]}ln[5.98H/(0.8W+T)] where W is the line width, T is the copper thickness of the trace, and H is the trace to the reference plane Distance, Er is the dielectric constant of the PCB material. This formula must be applied when 0.1<(W/H)<2.0 and 1<(Er)<15.
B. stripline Z=[60/sqrt(Er)]ln{4H/[0.67π(0.8W+T)]} where H is the distance between the two reference planes, and the trace is located in the middle of the two reference planes. This formula must be applied when W/H<0.35 and T/H<0.25
Tracy
Tracy