Circuit Analysis: Understanding Kirchhoff's Laws and Impedances in Electrical Engineering , Study notes of Basic Electronics

Download Circuit Analysis: Understanding Kirchhoff's Laws and Impedances in Electrical Engineering and more Study notes Basic Electronics in PDF only on Docsity! 1 Phys 351, Fall 2008 Lecture 2 1 Circuit analysis Kirchoff’s Laws Voltage Law (conservation of energy) = KVL Current Law (conserve charge & momentum) = KIL Series impedances Parallel impedances Voltage dividers Thévenin equivalent circuit Norton equivalent circuit Phys 351, Fall 2008 Lecture 2 2 OMG! How am I going to solve that? I don’t know how! It’s too hard! It’s not fair! Phys 351, Fall 2008 Lecture 2 3 Where do I start ?!? Start at the beginning, go until you reach the end. Or vice versa. Phys 351, Fall 2008 Lecture 2 4 Impedances and voltage drop R1 30ohms V1 10Vdc R2 10ohms 0 Batteries push charge “up hill” so charges gain P.E. The charges lose P.E. as they “fall” back down hill through impedances Loss is encoded as “voltage drop” V = IR 10V Phys 351, Fall 2008 Lecture 2 5 Kirchoff I Voltage Law (KVL) Sum of voltage drops around any closed loop is zero ΣiVi = 0 So: Vin = V1 – V2 = V3 – V4 = V3 – V5 – V6 – V4 etc Z B Vin ZA R Vout 1 2 3 4 5 6 7 8 NO APPROXIMATIONS ON THIS Phys 351, Fall 2008 Lecture 2 6 Any loop, every loop V1 R2R1 R3 R4 R5 2 Phys 351, Fall 2008 Lecture 2 7 Kirchoff II Current Law (KCL or KIL) Sum of currents into any circuit node is zero ΣiIi = 0 I1 I2 I3 I4 I1+I2+I3 = I4 NO APPROXIMATIONS ON THIS Phys 351, Fall 2008 Lecture 2 8 Series impedances Impedances in series with each other Ztotal = Z1 + Z2 + Z3 + … + ZN = 1.0kΩ 100kΩ V R1 R2 ! k k Z • Kirchoff I, II: • V = IReff = I1R1 + I2R2 = I(R1 + R2) • Notice! • If Zn >> Zk, then Ztotal ≈ Zn • total resistance R = 1×103 + 1×105 = 101kΩ ≈ 100kΩ Phys 351, Fall 2008 Lecture 2 9 Parallel impedances Impedances in parallel with each other 1/Ztotal = 1/Z1 + 1/Z2 + 1/Z3 + … + 1/ZN 1kΩ 100kΩ R1 R2 V I I • I = V/Rtotal • 1/Rtotal = 1/R1 + 1/R2 • Rtotal = R1R2 /(R1 + R2) • total resistance Rtotal = 108/(103 + 105) ≈ 108/105 = 1kΩ • If Zn << Zk, then Ztotal ≈ Zn • Resistors in parallel: same game • at nodes: I = I1 + I2 = V/R1 + V/R2 Phys 351, Fall 2008 Lecture 2 10 Voltage divider: Everything is a voltage divider Total impedance is R1 + R2 “ground,” “common,” “earth.” … This choice (bottom of battery) is COMPLETELY ARBITRARY • Total current is I = Vin/(R1 + R2) • Output voltage • Vout = IR2 = VinR2/(R1 + R2) • H = Vout/Vin = R2/(R1 + R2) R1 R2 Vout I I I = 0 Vin • (Implicit assumption: Rload >> R2) Phys 351, Fall 2008 Lecture 2 11 All circuits contain 1 – input signal 2 – circuitry 3 – output terminals Since 1 and 3 are generically voltages referred to ground, so can redraw with essentials only: All voltages are referred to ground. Schematic short(er) hand: implied reference to ground R1 R2 Vin R1 R2 Vin Vout Phys 351, Fall 2008 Lecture 2 12 Measurements Believe nothing until you understand the measurement technique. All instruments have their own impedances and their own limits. Main questions about instrument: 1- Does it perturb the circuit (change the current paths noticeably)? 2- How fast does it respond (what’s the bandwidth)? 3- How accurate is it (and how do you know)?