BME/ISE 3511 Bioelectronics - Test Three Course Notes Fall 2016 Delta & Y Configurations, Principles of Superposition, esistor Voltage Divider Designs Use following techniques to solve for current through and voltage across a network resistor: Equivalent esistances Kirchoff s Voltage Law Kirchoff s Current Law Principle of Superposition Thevenin Equivalent Norton Equivalent Sketch Series esistors Voltage Divider (including voltage source) Calculate voltage across load resistor Voltage Divider (esistors in Series with Voltage Source) V 2 V ( 2 / ( 1 + 2 ) Sketch Parallel esistors Current Divider (including current source) Calculate current through load resistor Current Divider (esistors in Parallel with Current Source) I 2 I ( 1 / ( 1 + 2 ) Design Voltage Divider Network (10% rule for two resistors and voltage source) given output requirements Convert Delta configuration to equivalent Wye configuration Convert Wye configuration to equivalent Delta configuration Solve Voltage Source & Current Source Circuit Network Problems (using Superposition) Attachments: Delta & Y Configurations and Conversions (Figures & Equations) Five esistor Equivalent Y to Delta & Delta to Y Practice Conversion Problems Principle of Superposition Example Problem Principle of Superposition (Figure 30-3 Giorgio izzoni 2009).pdf Voltage Divider Design Notes & Practice Problem
Y to Delta & Delta to Y Conversions a b c 2 c 2 b a Y to Delta Conversion Delta to Y Conversion + + a b b c a c 1 3 1 a c + 2 + 2 + + a b b c a c 1 2 b a + 2 + + + a b b c a c 2 3 3 c b + 2 +
Calculate the equivalent resistance for a five resistor network (See Figure 1.) Step 1. Divide into two parts. Delta( 5 ) and "V"(2 ) 5 5 2 2 Figure 1. Step 2. Convert Delta( 5 ) to Y(c a b) c 5 b a Step 2. Delta( 5 ) to Y(c a b) - continued Step 3. Combine Delta( 5 ) with "V"(2 ) Note: otated and eflected Labeling c. + + 5 b 5. + + 5 a 5. + + 5 c b a Step 4. b in Series with therefore b b + a in Series with 2 therefore a2 a + 2 Step 5. b in Parallel with a2 (b) x ( a2) (b) + ( a2) Step 6. c in Series with Parallel b a2 Step 7. eq c + Parallel b a2 2
Y to Delta & Delta to Y Practice Problem Conversions 1. Write closed-form solutions for each of the following configurations. 5 5 2 2 2 Figure A Figure B Figure C 2. For Figures A, B, C, Find single equivalent resistive values for 1 5, 2 7, 3 8, 4 3, 5 4 3. Answers: Figure A. eq 5.74 Figure B. eq 2.36 Figure C. eq 5.66
Solving Voltage and Current Circuit Problems Using the Theory of Superposition The overall effect for two or more stimuli to a linear system is equal to the sum of individual effects. efer to Figure 1. Objective: a. Calculate V Load b. Calculate I Load Given: I 3 A V 9 V 1 3 Ω 2 4 Ω Load 2 Ω 2 I 1 Load V Figure 1. Procedure: I. Short all Voltage Sources Calculate V Load (Generated by Current Sources) V Load 2.77 V II. Open all Current Sources Calculate V Load (Generated by Voltage Sources) V Load 2.08 V III. Calculate overall results by adding results from Step I and Step II V Load 2.77 + 2.08 4.85 Volts Calculate I Load V load / Load 4.85 V / 2 Ω 2.43 Amps
Fundamental of Electrical Engineering, Giorgio izzoni, McGraw-Hill, 2009
Voltage Divider Design Note (10% ule) - Minimizes I 2 Heat Loss Given values for voltage source and Load voltage and current specifications (V Load & I Load ); Determine values for Bias esistor ( 1 ) and Bleed esistor ( 2 ). 1 (Bias) V V Supply 2 (Bleed) Load Step 1. Calculate Load esistor ( V Load / I Load ) Step 2. Calculate I 2 (Bleed Current) 10% I Load Step 3. Select 2 (Bleed esistor) based on I 2 such that 2 V 2 / I 2 (Note: V 2 V Load ) Step 4. Calculate I Total I Load + I 2 Step 5. Calculate 1 (Bias esistor) (V S - V Load ) / (I Total ) Example Problem: Given: V S 12 volts V Load 7.5 V @ 50 ma Find: Load 150 Ohms Bleed esistor 1500 Ohms Bias esistor 82 Ohms Check esults: Note - by design I Total 1.1 x I Load 55 ma I Bleed 0.1 x I Load 5 ma Bleed 10 x Load 1500 Ohms V Bleed Bleed x I Bleed 1500 x 5 x 10-3 7.5 V Sanity Check: V Bleed V Load 7.5 V!!!!! Sanity Check: V Bias V S - V Bleed 12-7.5 4.5 V V Bias I Tota l x Bias 55 x 10-3 x 82 4.5 V!!!!!!!!! Short Cut Closed Form: Bias (V S - V Load ) / (1.1 x I Load) (12-7.5) / (1.1 x 0.050) 4.5 / 0.055 82 Ohms Bleed V Load / (0.1 x I Load ) 7.5 / (0.1 x 0.050) 7.5 / 0.005 1500 Ohms