Circuit Analysis Techniques Thévenin & Norton Equivalent Circuits • Circuit simplification techniques that focus on terminal behaviour • • • • Used to represent circuit made of linear elements Replace with VTH and RTH equivalent to original circuit VTH is the open circuit voltage at the terminal RTH is the ratio of the open circuit voltage to the short circuit current •𝑅𝑇𝐻 = 𝑉𝑇𝐻 𝑖𝑆𝐶 Eg. Determine Thévenin Equivalent Eg • Find equivalent Thévenin circuit Eg • Find the Thévenin equivalent circuit Note: short circuit bypasses the resistors. Current source continues to supply constant current! Norton Equivalent Circuit • Derive from Thévenin by source transformation Special considerations • When there are dependent sources, pay attention to the value of the controlling current/voltage. (it is not constant!) I depends on v and vice versa. For short circuit, note that isc is -20i while 𝑣 = 𝑣𝑎𝑏 becomes zero, so the dependent voltage source in first loop goes to zero as well! Note: v= -20i*25 and -5+2000i+3v=0 At short cct: v=0, i= 5/2k, Isc= -20i= -20*5/2k Techniques for quickly determining Rth • If circuit contains only independent sources, ‘zero’ out all sources • Short voltage sources, open current sources. Compute the R looking into the terminals. …II • If circuit has dependent sources • Deactivate the independent sources • Apply a test voltage (or test current source). • Rth is the ratio of test voltage to the current delivered by the test source • Rth= Vt/It PTO → Just to determine RTH Determine VTH as usual – open circuit voltage Determine Thévenin and Norton’s Equivalent Try Assessment Problems 4.17, 4.21 Vth= 8V, RTh = 1ohm, IN=8A Maximum Power Transfer • Comms & instrumentation systems: transfer as much of the signal to the load as possible • Showing that for max power transfer RTH= RL: • Expressing power in RL as fxn of variables: • Find value of RL that maximizes p: Max power transfer….II • Set to zero • Simplifies to RTh= RL • Find value of R for max power transfer Hint: find thevenin equivalent first Also look at full Example 4.12 in NR Superposition • When a linear system is excited by more than one source, the net response is the sum of the independent responses. • Useful in complex circuits. Can simplify no. of equations to solve • Examples to date have been simple. • Following is for illustrative purposes • Find the branch currents in this circuit PTO Find the branch currents • Open I, short V Solution: I1= I1’ + I1’’