Context - Linear Electrical Networks

A ‘network’ refers to any interconnected set of objects. An ‘electrical network’ is an interconnection of ideal electrical elements such as resistors, inductors, capacitors, transformers, diodes, sources, controlled sources and switches. Linear electrical networks are interconnections of linear electrical elements including resistors, inductors, capacitors, independent sources, controlled sources, amplifiers and Op Amps.

The linear electrical network elements, resistor, capacitor and inductor, satisfy simple voltage-current (V-I) relationships.  These simple V-I relationships, multiplication by a constant, integration and differentiation, enable us to perform a variety of signal processing functions, like improving the signal-to-noise (S/N) ratio of signals and signal conditioning. The S/N ratio was improved initially using linear networks comprising capacitors and inductors between the non-ideal source and a predominantly resistive load.  A variety of networks based on capacitors and inductors, known as filters, were developed to reduce noise outside the pass band to the minimum possible value. Practical capacitors and inductors have losses and also their size increases with the power levels they are required to handle. 

Active components like controlled sources were introduced to reduce the size of the signal processing circuit and for adequate signal power delivery to the load.  Active components enable separation of processing function from power amplification using DC power sources. Active network elements include independent sources, controlled sources, amplifiers and Op Amps. 

The size, poor tolerance, non-linearities and high sensitivity to temperature variations being the dominant characteristics of passive circuit elements in present day monolithic integrated circuits, the signal processing is done using mostly active components and symmetric circuit topologies.  With no limitation on the number of active components used for signal processing, the focus is shifting back to passive components, but with values a few orders of magnitude lower in comparison to passives used some years ago.  We turn to processing signals in digital form to avoid using passives.  However, we need to be concerned with passives until we convert analog signals into digital form and digital signals to analog form, and when we need to send a digital signal at high speeds from one active device to another in a chip or on a board.

One of the main competencies that an electronic engineer has to acquire is to design passive and active linear electrical networks that improve signal-to-noise ratio of signals, do signal conditioning, and generate signals at different frequencies and in different contexts. All the network configurations explored through Linear Electrical Networks can eventually be realized as analog circuits using either discrete passive and active devices or as integrated circuits.

The course on Linear Electrical Networks deals with analysis and design of one-port and two-port passive networks, and active networks that use active network elements like independent sources, controlled sources, amplifiers and Op Amps. One-port or two-terminal passive networks can be made up of series or parallel combination of passive network elements like resistor or conductor, capacitor and inductor. Such network obeys basic network theorems like Kirchoff’s current and voltage laws resulting in node and loop equations. Tellegen’s theorem is also another general way of explaining the basic behavior of a network. Other theorems like superposition theorem, Thevinin’s theorem, Norton’s theorem and reciprocity theorem arise as corollaries to these basic theorems. Combination  of independent sources on one side and passive network elements arranged in series or parallel to form complex  one port networks on the other side of a pair of terminals  is  the focus of the Module on one-port passive networks. These networks can then be characterized by impedances or admittances of the network. Their response to excitations can be understood in terms of their transient and steady state response got by solving the differential equations that they constitute. Poles and zeros of admittance or impedance (immittance) functions of these passive networks are then investigated.  The one-port passive networks can be of series configuration, parallel configuration and series-parallel configuration.  Their time-domain and frequency-domain behavior is studied in detail, using simulation.  Once input-output relationships are thoroughly explored, it is possible to synthesize one-port networks to meet the stated specifications.

A network can have an input port and an output port. Input ports are terminals that get connected to independent sources and output ports are those terminal pairs where loads are connected. One port on the other hand has only one independent source connected to a pair of terminals to which the entire network is connected. Such two-port networks are characterized by self admittance or impedance functions at the input and output ports, and feed-forward and feed-back parameters from input to output and vise versa respectively. Study of these parameters with respect to time and frequency then form the major topics of the Module on two-port passive networks.  Simulation will greatly help is exploring the behavior of networks.  Synthesis of two-port passive networks can then be undertaken to meet the specified input-output specifications either in time-domain or frequency-domain.

One port active network and two port active networks their characteristic and application in signal-processing form the topic of discussion in the other two Modules.  The primary one-port active component which is negative resistance is discussed with its ability to give power gain and to synthesize oscillators, which are signal generators. Issue of stability of amplifiers is also highlighted.  Role of poles and zeros of characteristic equation of the network in shaping the response to a forcing function is explained with examples

The study is continued for the controlled sources, which constitute the so called amplifiers is continued in the final chapter. This chapter essentially forms the ground on which next courses on Analog circuits will be built upon.  Therefore all signal processing a, signal conditioning activities possible using these active devices in combination with suitable passive networks are discussed here. This includes sign al generation also. The equivalent of Operational Amplifier as an ideal active element in terms of nullator-norator pair (two-port or four-terminal) is highlighted.  Transistor, FET or BJT, as special case of Op Amp with common terminal between input and output is brought out.