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Theoretical Analysis of Signal Integrity in Embedded Systems
In recent years, advances in semiconductor technology have significantly increased the level of chip integration, with clock frequencies rising to higher levels. This has resulted in shorter signal rise and fall times. When the clock frequency exceeds 50 MHz, it becomes essential to consider the PCB trace as a transmission line, as signal integrity issues can arise if not properly managed.
Signal integrity refers to the ability of a signal to maintain its correct timing and voltage level throughout the circuit. If a signal fails to meet these expectations, it indicates the presence of signal integrity problems. Among the most common causes are signal reflection and crosstalk [1].
Reflection occurs when there is an impedance mismatch along the transmission line, causing part of the signal to be reflected back. The magnitude of this reflection depends on the reflection coefficient, which is calculated using the following equation:
$$ \Gamma = \frac{Z_T - Z_0}{Z_T + Z_0} $$
Here, $ Z_0 $ represents the characteristic impedance of the transmission line, while $ Z_T $ is the impedance that causes the discontinuity.
The characteristic impedance $ Z_0 $ is defined as the ratio of voltage to current at any point along the transmission line. In PCB design, microstrip lines and striplines are commonly used. Therefore, the characteristic impedance should be approximated based on the specific type of transmission line [3]. For a microstrip line, the characteristic impedance can be calculated using the formula:
$$ Z_0 = \frac{87}{\sqrt{\varepsilon_r + 1.41}} \cdot \ln\left( \frac{5.98H}{0.8W + T} \right) $$
Where:
- $ W $ is the conductor width (in mm),
- $ T $ is the conductor thickness (in mm),
- $ H $ is the dielectric thickness (in mm),
- $ \varepsilon_r $ is the dielectric constant of the board material.
Crosstalk occurs when electromagnetic coupling between adjacent signal lines causes unwanted noise or interference. It is essentially the result of mutual capacitance and mutual inductance between transmission lines. As shown in Figure 1, crosstalk can be classified into two types: near-end crosstalk (NEXT), which occurs at the end of the driver, and far-end crosstalk (FEXT), which occurs at the opposite end.
Inductive coupling, or mutual inductance $ L_m $, happens when a changing current in one transmission line induces a voltage in another. The magnitude of mutual inductance can be calculated using the following equation:
$$ L_m = \frac{\mu_0 \mu_r}{2\pi} \cdot \ln\left( \frac{d}{w} \right) $$
Where:
- $ \mu_0 $ is the permeability of free space,
- $ \mu_r $ is the relative permeability of the medium,
- $ d $ is the distance between the lines,
- $ w $ is the width of the conductor.
To address signal integrity issues, several strategies can be implemented. For reflections, the most effective method is to terminate the transmission line and match its characteristic impedance. There are two main approaches: load-end termination (parallel termination) and source-end termination (series termination). Load-end termination is generally preferred from a system design perspective because it eliminates reflections before they return to the source, reducing noise and electromagnetic interference (EMI).
For crosstalk, although it cannot be completely eliminated, it can be minimized through proper PCB layout techniques. These include increasing the spacing between signal lines, minimizing parallel lengths between adjacent nets, using vertical routing between layers, and inserting ground lines or shielding for critical signals [8, 9]. By implementing these measures, crosstalk can be kept within acceptable limits, ensuring reliable signal performance in high-speed digital systems.