Impedance calculation formula, polar si9000 (tutorial)

For beginners.
A lot of people have been asking me how impedance is calculated. People ask more, I want to make a material for everyone, in their own is a convenient. If you have any questions or documentation errors, welcome to discuss and advise!
Before calculating the impedance, I think it is necessary to understand the meaning of the impedance here.

The origin and significance of transmission line impedance
Transmission line impedance is derived from the Telegraph equation (specifically, the microwave theory can be queried)
For example, it is a parallel two-wire distribution parameter equivalent circuit:

From this graph, we can derive the Telegraph equation.

The sinusoidal form of the voltage and current on the transmission line

Have

Introduction of general Solution


Defining the characteristic impedance

R=0 under no-cost line, g=0

Note that the conceptual difference between this characteristic impedance and the wave impedance (see plane wave definition of the wave impedance specifically)
The relationship between the characteristic impedance and the wave impedance can be introduced from this relational formula.
Ok, understand the characteristics of the impedance theory is how to look at the actual meaning, when the voltage and current in the transmission line propagation, if the characteristic impedance is inconsistent, the solution of the Telegraph equation is not consistent, resulting in the so-called reflection phenomenon and so on. In the field of signal integrity, such as reflection, Crosstalk, Problems such as power plane cutting can be categorized as impedance discontinuities, so the importance of matching is shown here.

Definition of laminated (stackup)
We look at one of the following stackup, motherboard commonly used 8-layer Board (4-layer Power/ground and 4-layer route layer, SGGSSGGS, respectively defined as L1, L2 ... L8) so the impedance to be calculated is L1,l4,l5,l8

Below are familiar with the underlying concepts in the stack, and manufacturers often use the deal
The concept of Oz
Oz would have been the weight of the Unit OZ (ounce) =28.3 g (g)
As defined in the stack, the thickness of an ounce of copper on a square foot is 1Oz, and the corresponding units are as follows

The concept of dielectric constant (DK)
The electrical capacity of CX with the presence of a dielectric between the capacitor plates is the permittivity of the same shape and size of the vacuum capacitance co:
ε= cx/co =ε '-ε '

The concept of Prepreg/core
PP is a medium material, composed of glass fiber and epoxy resin, core is actually the type of PP media, but he is covered with copper foil on both sides, and PP did not.

calculation of characteristic impedance of transmission line
First, let's look at the basic types of transmission lines, when calculating the impedance there are usually the following types: Microstrip lines and strip lines, for their distinction, the simplest understanding is that the Microstrip line only 1 reference, and the Ribbon line has 2 reference, as shown in

Compared to the above-mentioned 8-layer motherboard, only the top and bottom line layer is the Microstrip line type, the other line layer is the Ribbon line type
In the calculation of transmission line characteristic impedance, the motherboard impedance requirements are basically: single-line impedance requirements of 55 or 60OHM, the difference is 70~110ohm, the thickness of the requirements is generally 1~2mm, according to the thickness of the requirements to layered to obtain the height of each layer.
This assumes that the plate thickness of 1.6mm, that is, about 63mil, the single-ended impedance requirements of 60OHM, the differential impedance of 100OHM, we assume the following stack to follow the line

First to calculate the characteristic impedance of the Microstrip line, because the top layer and the bottom layer symmetry, only need to calculate the top layer impedance is good, using polar si6000, the corresponding calculation graph is as follows:

In the calculation of the attention is:
1, all you need to do is to calculate the line width W (target) by the impedance requirement of the wire.
2, the manufacturers of the process capacity is inconsistent, so the calculation method is not the same, need and manufacturers to confirm
3, the surface uses coated Microstrip calculates the reason is, the factory will have the green paint, therefore does not use surface microstrip computation, but also has the factory uses surface microstrip to calculate, it is calibrated
4,W1 and W2 are not the same because the PCB board manufacturing process is from top to bottom corrosion, so corrosion out of the sense of trapezoid (of course, not exactly)
5, this does not calculate the exact 60Ohm impedance, the reason is the actual process when the manufacturers will slightly change the parameters, no need to be so accurate, within the 1,2ohm range I feel no problem
6,h/t parameter corresponding you can refer to the Stack view
And then calculate the characteristic impedance of the L5 as

Remember the original version for Stripline and symmetrical stripline calculation diagram, the actual difference from the literal understanding is symmetrical stripline is actually the special case of offset stripline H1=H2
In the calculation of the differential impedance and similar to the above calculation, in addition to the required through the line impedance requirements to calculate the line width of the target in addition to the wire width is also the cable distance, not listed here
The chosen figure is


In the calculation of differential impedance note is:
1, in satisfying the DDR2 clock 85ohm~1394 110Ohm differential impedance while satisfying its single-ended impedance, so I usually choose to meet the differential impedance (many of the current mode to take the voltage) and then consider the single-ended impedance (usually the plate factory is not considered, actually do a lot of boards, the problem is not really big, It seems that the difference line or the line of the same layer with via the same distance requirements must be met.

----------would like to miss the hard years of the beginner Si

Characteristic impedance formula (with Microstrip line, strip line calculation formula)

A. Microstrip line (microstrip)
Z={87/[sqrt (er+1.41)]}ln[5.98h/(0.8w+t)] wherein, W is the line width, T is the copper thickness of the trace, H is the distance of the trace to the reference plane, Er is the dielectric constant of the PCB plate (dielectric constant). This formula must be applied in the case of 0.1< (w/h) <2.0 and 1< (Er) <15.

B. strip Line (Stripline)
Z=[60/sqrt (Er)]ln{4h/[0.67π (0.8w+t)]} where h is the distance between the two reference planes, and the route is in the middle of the two reference planes. This formula must be applied in the case of w/h<0.35 and t/h<0.25

Calculation method and formula of differential impedance

The differential impedance Calculator is provided free to registered users. Register here

Instructions:
1. Select the number of substrate layers required.
2. You'll then being presented with a table representing the suggested stack-up for that type of substrate.
3. Modify the variables to examine the effects on the trace characteristic and differential impedance.

Number of physical board layers
4	6	8	10	12

Important : The trace separation should not being adjusted to alter the differential impedance-trace separation should a Lways is kept to the minimum clearance specified by the PCB vendor.

Note:

1. All dimensions is in MIL (thousands of an inch).

2. The dielectric Constant of FR4 material may vary by as much as 20% (4.2 to 5.2).

3. The overall dielectric Thickness (Cu to Cu) should total and MIL nominally.

4. Variables unavailable for modification has no significant effect on the impedance of the traces.

5. The default multilayer board Stack-ups is taken from Advance Design for SMT, Barry OLNEY/AMC.

6. The impedance Calculator uses formulae derived from:

· Ipc-d-317-design standard for Electronic packaging utilizing high speed techniques.

· EMC & the printed circuit board-montrose.

7. Only Edge coupled differential Pairs is considered. No allowance have been made for Broad Side coupling from adjacent layers. It is the good practice to route adjacent layers orthogonal to all other in order to reduce any coupling that may occur.

8. To reduce EMI, high frequency, fast rise time signals should be routed between the reference planes.

All care had been taken to ensure that the results was correct but no responsibility was taken for any errors.

If you prefer to does the calculations Yourself-please use the formulae below.

Microstrip Differential Impedance (For traces routed in an outer layer)	Unbalanced stripline differential impedance (for traces embedded between planes)
Zo = [87/sqrt (er+1.41)]* ln (5.98h/(0.8w+t)) Zdiff = 2*zo (1–0.48 e-0.96d/h)	Zo = [80/sqrt er]* ln (1.9 (2H+T)/(0.8w+t)) * (1-(H/4 (H + C + T))) Zdiff = 2*zo (1–0.347 e-2.9d/b)

where

W = trace Width

T = trace Thickness

H = distance to nearest reference plane

Er = Dielectric constant

D = Trace edge to edge spacing

C = Signal layer Separation

B = Reference plane separation

Material	Dielectric Constant
FR4 Fiberglass Epoxy	4.7
Teflon	2.2
Teflon Glass	2.5
Polyimide	3.5
Polyimide Glass	4.2

Relative dielectric Constants of substrate materials

PCB Impedance Design Detailed
1. Preface

With the development of science and technology, especially in the accumulation of materials in the circuit of the progress of the operation speed has been significantly improved, to facilitate the accumulation of the circuit to high-density ﹑ small volume, a single 10 pieces, which led to today and the future of the printed circuit board to high-frequency response, high-speed digital circuit application, that is, must control the Low noise and low crosstalk and EMI suppression. Impedance design becomes more and more important in PCB design. As the front part of PCB manufacturing, it is responsible for the analog calculation of impedance and the design of impedance bar. Customers to the impedance control more stringent requirements, and the number of impedance controls are also the original, how to quickly and accurately design impedance, is the pre-system personnel are very concerned about a problem.

2. Main types of impedance and influencing factors

Impedance (Zo) Definition: The total resistance generated by alternating currents flowing through the known frequencies is called impedance (Zo). For a printed circuit board, it is the impedance of a circuit layer (signal layer) that is the sum of its closest related layer (reference plane) under a high-frequency signal.

2.1 Impedance Type:

(1) Characteristic impedance in the electronic information products such as computer ﹑ wireless communication, the transmission energy in the circuit of the PCB is a square wave signal which is composed of voltage and time (square wave signal, called Impulse Pulse), and the resistance it encounters is called characteristic impedance.

(2) The differential impedance driver side of the input polarity opposite the two same signal waveform, divided by two differential line transmission, at the receiving end of the two differential signal phase minus. The differential impedance is the impedance zdiff between two lines.

(3) The impedance of two lines in the odd-mode impedance zoo, the two-line impedance is the same.

(4) Two identical signal waveforms with the same polarity as the input polarities of the coupled-mode impedance drive, the impedance zcom when the two wires are connected together.

(5) Impedance of the first line to ground in two lines of common-mode impedance Zoe, the two-wire impedance is the same, usually greater than the odd-mode impedance.

The characteristic and differential are the common impedance, and common mode and odd mode are rare.

2.2 Factors affecting the impedance:

W-----Line width/Line spacing increases the impedance decreases, the distance increases the impedance increases;
H----the thickness of insulating thickness increases the impedance;
T------Copper thick copper thickness increases the impedance becomes smaller;
H1---Green oil thick thickness increase the impedance becomes smaller;
Er-----Dielectric constant Reference Layer DK value increases, the impedance is reduced;
Undercut----w1-w undercut increase, the impedance becomes larger.

　　3. Automatic impedance Calculation

Today, the most commonly used impedance computing tool in our industry is Polar's Si8000 Field solver,si8000, the new boundary element Fachang Solver calculator software built on the easy-to-use user interface of our familiar early polar impedance design system. This software contains a variety of impedance modules, the person by selecting a specific module, input line width, line spacing, dielectric thickness, copper thickness, er value and other related data, can calculate the impedance results. A PCB impedance control number is 4, 5 groups, more than dozens of groups, each group of control line width, the thickness of the medium layer, copper thickness and so on are different, if one by one to check the data, and then manually enter the relevant parameters calculation, very time-consuming and error prone.

Below, we will show you how to use the industry-leading design engineering software solution supplier Inplan software, automatic impedance design, greatly improve pre-production efficiency.

AO Bao Technology Inplan system, can be connected with Si8000, on the basis of the following database establishment, automatically calculate the impedance: First, in the Inplan to establish a complete material library, according to different manufacturers, model classification. Built according to the actual process parameters of the plant to obtain the thickness of the pressure, copper thickness of the substrate, pp, such as the amount of plastic content data.

Then, in the Inplan to establish the rules of the calculation of the impedance rule, such as the green oil thickness, undercut value can also be based on different copper thickness, impedance module or internal and external layers of the different set rules. The dielectric constant is mainly based on the types of materials, impedance modules are written in different formulas. Impedance, the impedance line width tolerance is also written to the rule by Inplan rule. When calculating the impedance, the Inplan automatically brings out the relevant impedance influence parameter values according to the rules, and calculates the optimal impedance result. And no matter how many sets of impedance, just click a button, a few seconds to get all the results.

　4. Automatic generation of impedance strips

If the customer does not have their own design impedance bar, we need to design the impedance bar on the edge of the board or break (in general, the impedance bar on the broken edge requires the customer's consent). circuit board manufacturers in the circuit board design to meet the customer impedance control of all characteristics and parameters of the impedance bar, by testing the impedance bar impedance value, reflecting the circuit board to meet customer impedance control requirements. To correctly test the resistance value of the plate, the key is the design of the impedance bar.

General PCB Factory Impedance Bar Design method is: MI engineer according to the calculated impedance results fill in the impedance attachment table, such as impedance value, reference layer, control line width, test hole, reference layer properties (plus and minus) and so on.

The CAM engineer then uses the impedance table provided by the MI to manually make the impedance bar, or through script, input the relevant impedance data, and use the program to run the impedance bar. In general, an impedance value we design an impedance bar, make an impedance bar, generally takes 10 minutes, repetitive manual data filling, very time-consuming, and error prone.

We can use the Incoupon function of the Ao Bao, the relevant rules of the impedance bar into the system, can automatically produce high-quality impedance bar, directly into the Genesis system. Incoupon using embedded development architecture, at the semi-finished level can detect the most ideal drilling position between the layers, so that the existing layer of drilling operations can be fully consistent with the Coupon line layer, integrated with the complete CAM and engineering technology, resulting in impedance measurement of the Coupon line, The development of architectures and semi-finished tables, and the ability to find the most ideal connectivity to the coupon hierarchy, replacing complex, manual calculations with intelligent operators, and automatically calculating reliable measurement line coupon in seconds, makes coupon's design a simple and standard job.

　5. Summary

PCB competition is more and more intense, sample delivery is getting shorter, impedance design in the pre-system work accounted for a large proportion, how to shorten the impedance production time, to meet customer requirements of the impedance matching, is the front of the system must consider a problem. The appearance of Inplan and Incoupon provides a good help for impedance design. Of course, the PCB factory own impedance calculation rules, layout and size will not be the same, Inplan system needs special personnel for development, maintenance, in order to truly realize its function. However, it is believed that the automation of impedance design will become more and more popular in the front of PCB system.

Impedance calculation formula, polar si9000 (tutorial)