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Chapter 30: Introduction to Network Analysis

Date: 13/7/19

Introduction

Network Analysis is any structured technique used to mathematically analyse a network of interconnected components. This is when they are too complex to simply be analysed by Ohm’s Law. In such cases other means are required. This and the subsequent chapters present some techniques for analysing such complex circuits.

Network analysis is used in modern electronic and communication systems where these systems are coming from increasingly complex systems. As there is a demand for systems with more information content, there is a concern with getting signals from one point to another with maximum efficiency and clarity, and minimum power.

30.1 Laws of Network Analysis

The laws which determine current and voltage drops in ac networks are:

  • i = v / z, where z is the complex impedance and v is the voltage drop across the impedance.
  • The laws for impedance in series and parallel, i.e., total impedance Zt = Z1 + Z2 + Z3 + … + Zn for impedances connected in series, and 1/Zt = 1/Z1 + 1/Z2 + … + 1/Zn for impedances connected in parallel.
  • Kirchhoff’s Laws:
    1. At any node in an electrical circuit, the phasor sum of the currents flowing towards that junction is equal to the phasor sum of the currents flowing away from that junction.
    2. In any closed loop in a network, the phasor sum of the voltage drops (the products of current and impedance) taken around the loop is equal to the phasor sum of the electromotive forces acting in that loop.

Kirchhoff’s laws can be used to determine the voltage and current at any point in the circuit or by related analysis called mesh current and node voltage analysis.

More Complex Theorems for D.C. and A.C.

These are circuit theorems that can be used as alternatives to Kirchhoff’s laws to solve problems involving both D.C. and A.C. electrical networks. They include:

  • The Superposition theorem
  • Thevenin’s theorem
  • Norton’s theorem
  • The Maximum power transfer theorem

In addition to these theorems, star-delta (T-π) and delta-star (π-T) transformations provide methods of simplifying certain circuits before applying the theorems. All above laws require the use of complex numbers and apply to linear circuits which contain impedances whose values are independent of the direction and magnitude of current flowing through them.

30.2 Solutions to Simultaneous Equations Using Determinants

For n loops in a circuit, n simultaneous equations with n unknowns are formed using Kirchhoff’s laws. One way to solve this is by elimination and substitution. The other way is by using Determinants.

30.3 Network Analysis Using Kirchhoff’s Laws

If the current flowing through each branch is required, the following three-step procedure may be used:

  1. Label branch currents. The direction is arbitrary but it is useful to assume they are in the direction the voltage is leaving the positive voltage end.
  2. Divide the circuit up into loops and then apply KVL to each loop in turn. The choice of loop direction (clockwise or anticlockwise) is a matter of choice. The direction does not have to be the same as that used for the first loop.
  3. Solve the simultaneous equations.