What is a Linear Bilateral Network and What are its Characteristics?

March 16, 2020 Cadence PCB Solutions

Transparent components overtop an electrical schematic

 

If you are like most people, myself included, you prefer things to be linear or constant. Though I do realize that not everything should or can be consistent, it does not hurt to want things to be a certain way. However, as a general rule of thumb, consistency is usually better. Overall, linearity is the foundation for organization, fairness, and equality. Furthermore, it promotes the underlying basis for any civilized society. Moreso, it creates an environment in which a society's "laws of the land" promote proper enforcement.

So, as an example of this correlation between linearity and its effects on societal functionality, I will use a daily commute to work. Furthermore, we will narrow our focus to speed limit signs you encounter during your commute to and from work. Now, during your commute to work, the speed limit is always 55 MPH, i.e., linear. However, on the return trip on Monday, the speed limit is 50 MPH, and on the return trip on Tuesday, it is 52 MPH.

The return trip speed limits are, of course, non-linear, and to make matters worse, there is also strict enforcement. Also, the fluctuations of the speed limits do not follow any patterns, and they are entirely random. As you might imagine, this is a legal nightmare for anyone traveling those roads. Furthermore, this brings me to another characteristic descriptive, Bilateral. Which, in this case, the return trip speed limits should be the same as they were during your trip to work, i.e., Bilateral.

Linear Characteristics in Electronics

In the field of electronics, one of the first things I familiarized myself with is a network. Over time and as I branched out into computer technology, I could see how the principles that govern a network remain constant. Although the components that make up each individual network may differ, the requirements of connectivity, component placement, and interdependence for proper functionality are consistent. However, there are still some differences in the types of networks, characteristically speaking.

Moreover, one such characteristically different type of network is called a linear network. As I am sure you know, we define linear as something arranged in or extending along a straight or nearly straight line. Furthermore, we define linear as the progression from one stage to another in a single series of steps or sequential.

So, what does this mean in terms of a network? In summary, a linear network is a network that exhibits constant parameters, i.e., resistance and inductance. In other words, these parameters do not change with the changes in voltage or current.

Graphic of electrical routing across a blue screen

Working through a linear network is simpler than one might think due to its consistency of characteristics.

 

Bilateral Characteristics in Electronics

If you recall, I briefly referred to the characteristics of being Bilateral. In terms of a definition, bilateral is the having, pertaining to, or affecting two sides; typically, this also means equally. So, what does this mean within the field of electronics?

Well, bilateral is another one of those characteristically different types of networks. Moreso, a bilateral circuit is a circuit that exhibits its properties equally in either direction. Furthermore, a bilateral network is one in which the relation between current and voltage do not change in either direction in the network.

Also, a bilateral network consists of a circuit whose behavior or characteristics remain the same regardless of the direction of current through its various components. For example, a transmission line is a bilateral circuit because if you can supply power from any direction, the circuit's properties will remain constant. Thus, in a bilateral circuit, the circuit properties do not change, even when there is a change in the direction of the voltage or current source. In summary, a bilateral circuit permits the current to flow in both directions.

What is a Linear Bilateral Network?

We now know that a linear network is a network where the parameters of capacitance, inductance, and resistance remain constant with regard to voltage or current. Moreover, the current or voltage of its sources is directly proportional to or independent of the other currents and voltages, or their derivatives, within the network. Furthermore, we also know that a bilateral network is a circuit or network in which the magnitude of the current remains the same, even in the presence of a reversed voltage polarity.

However, it is also possible to achieve both of these characteristic states within a single network. This culmination of these two characteristic states is called a Linear Bilateral Network. So, what is a linear bilateral network, and what constitutes this particular characteristic categorization?

Firstly, a linear bilateral network is a network in which the components in the system exhibit a linear relationship, and yet simultaneously, the magnitude of the current is separate from the polarity of the voltage. Secondly, you can also consider a bilateral network as linear if the circuit meets the following criteria:

1.   The network follows Ohm's law, which states that the current through a conductor between two points is directly proportional to the voltage across the two points.

2.   The network follows the Superposition theorem, which states that, in any linear complex network having several sources, the response on a particular element can be determined as the algebraic sum of the reactions caused by the individual sources acting alone, while the other sources are non-operative.

Finally, an example of a linear bilateral network is a circuit or network that consists of only independent sources and resistors.

Green printed circuit board with electronic components

After finalizing the validation of your linear bilateral network, you can anticipate a well produced board.

 

A linear bilateral network is a circuit or network that exhibits two distinct characteristic behaviors. Furthermore, these behaviors afford functionality that ordinarily would not be possible due to the limitations of the two characteristics alone.

With Cadence’s suite of design and analysis tools, any design team will be sure to rest easy implementing the use of linear bilateral networks in any PCB design. Allegro PCB Designer is the layout solution you’ve been looking for, and it can make linear bilateral network design strategies in your current and future PCB designs a breeze.

If you’re looking to learn more about how Cadence has the solution for you, talk to our team of experts and us

About the Author

Cadence PCB solutions is a complete front to back design tool to enable fast and efficient product creation. Cadence enables users accurately shorten design cycles to hand off to manufacturing through modern, IPC-2581 industry standard.

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