Exam 1 Review Dr Holbert February 15 2006

Exam #1 Review Dr. Holbert February 15, 2006 ECE 201 Exam #1 Review 1

Circuit Analysis Techniques • • While Obeying Passive Sign Convention Ohm’s Law; KCL; KVL Voltage and Current Division Series/Parallel Impedance combinations ECE 201 Exam #1 Review 2

Sign Convention • Passive sign convention : current should enter the positive voltage terminal I + Circuit Element – • Consequence for P = I V – Positive (+) Power: element absorbs power – Negative (-) Power: element supplies power ECE 201 Exam #1 Review 3

Ohm’s Law V=IZ I The Rest of the Circuit + Z ECE 201 Exam #1 Review V – 4

KCL (Kirchhoff’s Current Law) i 1(t) i 5(t) i 2(t) i 4(t) i 3(t) The sum of currents entering the node is zero: Analogy: mass flow at pipe junction ECE 201 Exam #1 Review 5

KVL (Kirchhoff’s Voltage Law) + v 1(t) + – v 2(t) – + v 3(t) – • The sum of voltages around a loop is zero: • Analogy: pressure drop thru pipe loop ECE 201 Exam #1 Review 6

KVL Polarity • A loop is any closed path through a circuit in which no node is encountered more than once • Voltage Polarity Convention – A voltage encountered + to - is positive – A voltage encountered - to + is negative ECE 201 Exam #1 Review 7

In General: Voltage Division Consider N impedances in series: Source voltage(s) are divided between the elements in direct proportion to their impedances ECE 201 Exam #1 Review 8

In General: Current Division Consider N impedances in parallel: Special Case (2 impedances in parallel) ECE 201 Exam #1 Review 9

Equivalent Impedance If we wish to replace the two parallel impedances with a single impedance whose voltage-current relationship is the same, the equivalent impedance has a value of: Parallel elements share the same 2 end nodes ECE 201 Exam #1 Review 10

Phasors • A phasor is a complex number that represents the magnitude and phase of a sinusoidal voltage or current: ECE 201 Exam #1 Review 11

Complex Numbers Polar: z q = A = x + jy : Rectangular z y imaginary axis real axis q • • x is the real part y is the imaginary part z is the magnitude q is the phase angle x ECE 201 Exam #1 Review 12

Impedance • AC steady-state analysis using phasors allows us to express the relationship between current and voltage using a formula that looks likes Ohm’s law: V=IZ • Z is called impedance (units of ohms, W) • Impedance is (often) a complex number • Impedance depends on frequency, w=2 f ECE 201 Exam #1 Review 13

Impedance Summary ECE 201 Exam #1 Review 14