ABSTRACT
At the end of this chapter you should be able to: • understand and use Thévenin’s theorem to analyse a.c. and d.c. networks
• understand and use Norton’s theorem to analyse a.c. and d.c. networks
• appreciate and use the equivalence of Thévenin and Norton networks
33.1 Introduction
Many of the networks analysed in Chapters 30, 31 and 32 using Kirchhoff’s laws, mesh-current and nodal analysis and the superposition theorem can be analysed more quickly and easily by using Thévenin’s or Norton’s theorems. Each of these theorems involves replacing what may be a complicated network of sources and linear impedances with a simple equivalent circuit.A set procedure may be followed when using each theorem, the procedures themselves requiring a knowledge of basic circuit theory. (Itmay beworth checking somegeneral d.c. circuit theory in Section 13.4. page 140, before proceeding)
33.2 Thévenin’s theorem
Thévenin’s theorem states:
‘The current which flows in any branch of a network is the same as that which would flow in the branch if it were connected across a source of electrical energy, the e.m.f. of which is equal to the potential difference which would appear across the branch if it were opencircuited, and the internal impedance of which is equal to the impedance which appears across the open-circuited branch terminals when all sources are replaced by their internal impedances.’ The theorem applies to any linear active network (‘linear’ meaning that the measured values of circuit components are independent of the direction and magnitude of the current flowing in them, and ‘active’meaning that it contains a source, or sources, of e.m.f.).
