Network Theory
Network Theory carries high weight in the ECE prelims. It asks for steady-state and transient solutions of linear networks via KCL/KVL and mesh or nodal analysis, and for the standard theorems: superposition, Thevenin, Norton, reciprocity and maximum power transfer.
Rules to apply
- Superposition holds only for linear circuits: each independent source is applied alone, while dependent sources are never switched off.
- Thevenin and Norton equivalents may contain dependent sources; the resistance is then found by applying a test source, because the open-circuit/short-circuit ratio is invalid.
- Maximum power transfer occurs at RL = Rth, where efficiency is only 50%.
- First-order transients use τ = ReqC or L/Req; the variable moves 63.2% of its final change in one τ and is essentially settled in 5τ.
Worked example
A 10 V source with a 2 Ω series resistor feeds a node into which a 2 A current source injects; a 6 Ω load is connected at that node. Remove the load and apply KCL at the node voltage V: (V − 10)/2 − 2 = 0, giving V = 14 V - the injected current pushes the node above the source voltage. Rth = 2 Ω because the ideal current source becomes an open circuit. Reconnecting the 6 Ω load gives VL = 14 × 6/(2 + 6) = 10.5 V.
Traps
Computing Vth with the load still attached; reversing the sign of an injected current in KCL; using V/I at a port that contains dependent sources; and forgetting that inductor current and capacitor voltage cannot change instantaneously.