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## PCB Materials

A PCB is made up of layers of different materials pressed together to create layers with different properties, see figure 1. These layers consist of conductive layers, conductive tracks laminated onto a non-conductive substance and dielectric layers. Some of the conductive layers are power planes and ground planes. The power planes contain one or more different voltage levels connected to different components by vias.

To dramatically reduce the electrical noise and crosstalk interference created from the circuit traces one or more levels of conductive material can be used as a ground plane [3]. A dielectric material is an electrical insulator that can be polarized by an applied electric field. The dielectric layers are usually made out of FR4 which is a heat resistant glass-reinforced epoxy laminated sheet [4]. In our tests we are calculating for ideal circumstances and therefor use the permittivity for vacuum, defined by equation (1) where c equals the speed of light in vacuum and µ0 is the vacuum permeability which is defined as 4π * 10-7 H m-1. In a vacuum the defined permittivity is 8.854 187 817… * 10−12 [F/m].

**Transmission line**

For the PCB to be able to reach different parts of the board some kind of connection to send the signal has to be made. Those lines are called etches and are usually made out of copper. These etches can go on top of a board and inside, though not move between different layers. The different kinds of etches will be talked about later in this chapter.

**Impedance**

The ratio of voltage and current wave traveling at any point of the transmission line is called the characteristic impedance. If the end of the transmission lines impedance does not exactly matches the characteristic impedance a portion of the signal will be terminated to ground and the rest of the signal will be sent back to the source through the transmission line. This adds to the transmitted wave and possibly generates another reflection off the source. This reflection continues until the line reaches a stable condition [6], see Figure 2.

In this thesis we calculated the impedance measured in ohm using a lossless line model using equation (2) where L is the inductance per unit length and C is the capacitance per unit length.

A microstrip transmission line is made up of a conductive line on top or on the bottom of the PCB, which is separated from the ground plane with an isolating substance. Because of the placement both air and the dielectric substance affect the impedance [9]. Too calculate the characteristic impedance of an single ended signal with a copper trace we used equation (3) where ϵr is the PCBs dielectric constant, H is the transmission lines distance to ground, W and T is the width and thickness of the transmission line [8]. The answer is commonly measured in mils, but can also be represented in the SI derived unit microns.

The capacitance can be calculated with equation (4) and measured in farad per meter.

If a differential signals is used (See figure 4) the difference in impedance is calculated with equation (5) where Z0 is the characteristic impedance of the traces and S is the space between the two transmission lines and H is the transmission lines distance to ground.

Fig. 4: A differential microstrip line over a dielectric layer spaced from a ground plane where hr is distance from ground or power, W and T is the width and the thickness of the microstrip line and S is the spacing between the two transmission lines [10].

### Stripline

Fig. 5: A symmetric transmission line between two layers of ground or power where W and T is the width and thickness of the etch, H is the distance from ground or power and B is the spacing between the two layers [8].

A stripline, unlike the microstrip cannot be placed on top or the bottom of a board, but has to be located between two ground planes which are connected. This means that the board has to consist of no less than three layers, this also leads to the isolation on the transmission lines becoming a lot better. Unlike the figure the transmission line does not have to be centered, but can be asymmetrically placed.

The asymmetric placed transmission lines impedance is given by equation (6) where ϵr is the PCBs dielectric constant, H is the smaller distance from trace in dielectric substance to the ground plane and H1 is the larger distance from trace in dielectric substance to the other ground plane. T and W are the thickness and width of the trace. The capacitance propagation delay and inductance per unit length of the asymmetric placed is defined in equation (7), (8) and (9) calculated in and [12].

If the traces on the board are symmetrically placed towards the ground/power plane it gives us equation (10) and (11) [11].

If the stripline is a differential (see figure 6) the difference between the two signals is calculated with equation (12) where Z0 is the characteristic impedance of the transmission lines, S is the spacing between the two traces and H is the distance from the trace to power/ground plane [13].

Fig. 6: A differential stripline symmetrically placed between two planes of ground or power where S is the spacing between the two transmission lines and b is the spacing between the two layers [10].

**Angle (Bend)**

When creating a connection between different components there are often a need for an angle. But a 90 degree angle in PCB will reflect a large amount of the signal back towards the source of the signal. That causes a lot of problems for high-speed signals, however according to page 305 in Johnson and Graham [3] right-angle bends can work for digital designs in speeds up to 2 Gbps . To prevent the extra capacitance the most common way is using “mitering”.

**Length matched**

For differential signals it is crucial that the logic goes to zero at the same time. That is a problem unless the transmission lines are length matched. If the differential signal is not length matched the logic that switches to zero will happen at different times and a noise pulse will occur on the receiver, see figure 8A and figure 8B [10].

**Single-ended**

A single-ended signal is a signal that uses one wire that has a shared reference and carries all voltages for one circuit to represent the signal. [3, p. 365] The main reasons for using it over differential signals is the lower cost and twice the number of inputs for the same size wiring connector. The disadvantages is that the input can suffer from noise picked up caused by the wire acting as an aerial [15].

#### Differential

A differential signal is a signal which sends current on two wires: the first wave carries the main signal and the second wave is provided for the flow of returning signal current. The voltages will not be opposite of each other but the current will be. This means that there is no need for a global reference voltage since the wires are references to each other. This also makes the system more reliant against disturbances provided the disturbance does not exceed the power-supply noise tolerance [3, p. 368-369].

**Via**

To connect one place on the PCB with another, going through the board is often required to do that. These plated holes are conductive and usually filled with copper-tungsten (CuW) for a low-resistance microwave grounding path, and offer high thermal conductivity [16]. A via consist of a barrel, a pad to connect the barrel with components or the trace and an antipad whose purpose it is to make sure that the via does not touch any unwanted connections [6, p. 102].

There are three different kinds of vias used in this thesis: Through hole via, blind via & buried via, see figure 9.

**Blind via**

A blind via is a via that does not go through the whole board. This creates more space inside the board for traces and can keep the bards dimensions smaller. The biggest downfall of a blind via and also the buried via is the cost and the time to make them [19].

**Buried via**

Buried vias is a hole that does not reach the top or the bottom board, which makes more space for components and traces.

**Through hole via**

The most common and least expensive is the through via. It goes as the name suggest through the whole board and can connect to any layer on the board. The simulations in this thesis have focused on filled plated-through vias since they are the most cost efficient and easiest to probe onto.

**Table of contents :**

Abstract

Sammanfattning

Acknowledgements

Terminology

Abbreviations and acronyms

List of figures

**1 Introduction **

1.1 Background and problem motivation

1.2 PCB background

1.3 Probe background

1.3.1 Flying probe background

1.4 Limitations

1.5 Problem definition

**2 Theory **

2.1 PCB Materials

2.2 Transmission line

2.2.1 Impedance

2.2.2 Stripline

2.2.3 Angle (Bend)

2.2.4 Length matched

2.2.5 Single-ended

2.2.6 Differential

2.3 Via

2.3.1 Blind via

2.3.2 Buried via

2.3.3 Through hole via

2.3.4 Stub

**3 Methodology **

3.1 Printed Circuit Board check

3.2 Oscilloscope measurements

3.3 Programming

3.3.1 Python

3.3.2 Matlab

3.4 Simulation

3.4.1 HFSS

3.4.2 ADS

**4 Results **

4.1 Simulation Results

4.2 PCB Measurement Results

**5 Discussion **

5.1 Simulations/Hardware

5.2 Conclusions

5.3 Future Work

**Reference List**