Optimized PCB Design Approach Through Network Theory Application
In the realm of electronic circuits, network theory plays a pivotal role in mastering network analysis, a crucial skill for designing efficient and reliable power distribution networks (PDNs) on Printed Circuit Boards (PCBs).
Network theory provides the fundamental principles and mathematical models to analyse, simplify, and design electrical circuits. It deals with how voltages, currents, impedances, and signals behave and interact within interconnected components.
PCB design applies these network theory principles to physically arrange and route electronic components on a printed circuit board. PCB designers use network theory to manage signal paths, control impedances, and ensure connectivity while minimising noise, interference, and signal reflections. High-speed PCB routing relies heavily on understanding the electrical network behaviour to maintain signal integrity and electromagnetic compatibility (EMC).
The power distribution network (PDN) on a PCB is a specialized subset of the network that ensures stable and clean distribution of power to all components. PDNs are modeled and optimised using network theory concepts, such as treating the PDN as a multi-stage low-pass filter, to manage voltage noise, current fluctuations, and stability for integrated circuits (like SoCs).
Current is the time rate of charge flow, measured in Amperes, while voltage is the electromotive force that results in charge flow, measured in Volts. Unilateral elements allow unidirectional current flow, while bilateral elements allow current flow in both directions.
In a parallel circuit, the reciprocal of the resultant equivalent resistor is equal to the sum of the reciprocals of resistances connected in parallel. In a series circuit, the aggregate resistance/impedance is the sum of resistances or impedances. Reactance, a combination of capacitance and inductance in an AC circuit, is denoted by X.
Network theory is essential for network analysis, which is crucial for the design of PCB transmission lines and power distribution networks. A network graph includes a group of nodes connected through branches, where a node is an intersection point for two or more branches, and a branch is a line segment that connects two separate nodes.
Mesh analysis is a method used in network analysis to calculate currents in planar circuits, where a mesh or loop current is assigned to every closed loop in the network. Nodal analysis is a method to analyse circuits using Kirchhoff's first law, where node voltages are defined as the variables to find solutions.
Ohm's Law states that the current through a conductor between two points is proportional to the voltage across the two points. Kirchhoff's circuit laws are a set of rules that govern the relation between current and voltage in electrical circuits. Kirchhoff's second law states that the sum total of voltages around a loop equals zero, while Kirchhoff's first law, also known as Kirchhoff's current law, states that the sum total of currents at a circuit node is equal to zero.
Thevenin's theorem states that any set of network elements can be replaced by a single voltage source and series resistor connected to a load, while Norton's theorem states that any set of network elements can be represented by an individual current source and parallel resistor. Tellegen's theorem states that the sum total of power in all branches of a network equals zero, provided the network also conforms to Kirchoff's Laws.
Impedance is the combined result of inductance and capacitance in an AC, denoted by Z. Active elements require power to function, while passive components cannot be controlled by other signals. An electrical network includes interconnected electric circuit elements such as capacitors, resistors, inductors, and switches.
Knowledge of network theory is also critical for streamlined PCB manufacturing processes. Network analysis is a structured method to mathematically analyse a network, useful for engineers in solving circuits with multiple component configurations and sources of power and voltage.
In summary, network theory underpins the electrical understanding needed to design efficient and stable power distribution networks as part of the overall PCB design. PCB designers leverage network theory insights to route signals and power effectively, achieve signal integrity, and ensure device functionality and reliability.
Technology based on controlled impedance is crucial in PCB design for managing signal paths and maintaining signal integrity.
Network theory, a technology, is essential for designing power distribution networks on Printed Circuit Boards (PDNs) to ensure stable and clean power distribution.
