# EE1305/EE1105 Intro to Electrical and Computer Engineering Lecture Week 6

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1 EE1305/EE1105 Intro to Electrical and Computer Engineering Lecture Week 6 Homework Passive Components Capacitors RC Filters fc Calculations Bode Plots Module III

2 Homework- due 2/20 (Najera), due 2/23 (Quinones) SUCCESS POINTS: DESIGN AND ANALYZE YOUR OWN CIRCUITS. PROVE THAT THE CONSERVATION OF POWER IS SATISFIED BY YOUR CIRCUIT. P13 and P14 Pre-Lab Module III Supplies Module II (week of 2/19) will not be allowed in lab without Analog Discovery, Power Supply and Digikey Supplies

3 Homework Questions? P13. (a) Simplify the circuit in P12 in order to, (b) use Voltage Divider to determine the value of V A, and (c) use Ohm s Law to calculate the current through the 5 k resistor. P14. Use any method to (a) determine the voltage drop across the 6 k resistor, (b) the current flowing through it, and (c) the power consumed by the 6 k resistor.

4 xx Intro to Capacitors i(t) = C dv dt C = ε A d i Current C Capacitance V Voltage t Time - Permittivity of free space A Area d Distance between 2 plates Capacitors store charge with applied voltage. Unit for capacitance is the Farad and 1 Farad = 1 Coulomb/Volt or F=C/V. One Farad capacitor stores 1 coulomb of charge per 1 volt. Capacitors DO NOT react instantaneously with changes in voltage. Capacitors are like a bath tub, it takes time to fill them up, and it takes time to empty them.

5 xx Capacitor Simulator

6 Learning Something New Capacitance how is it related to prior knowledge?

7 Voltage. The voltage across a capacitor does not change instantaneously, even after remove power supply the capacitor holds charge, and this keeps the potential drop across the capacitor constant.

8 Current. Connect a capacitor to a power supply the current will flow through the circuit and capacitor until it is fully charged. once the capacitor is fully charged, no more current will flow through the capacitor.

9 What do I need to understand? Assume Capacitor is fully charged. What is current through capacitor? What is V A? What is current through R2? V A R1 R2

10 Visualize How the Capacitor Charges and Discarges

11 See it while it s happening with DC Power. 1. Switch 1 open 2. Switch 1 closed 3. Switch 1 open 4. Switch 2 closed OBSERVE THE CURRENT INCREASING AND DECREASING AS CAPACITOR IS CHARGED AND THEN DISCHARGED

12 See it while it s happening with AC Power. 1. Small frequency 2. Large frequency WHAT HAPPENS TO THE VOLTAGE DROP ACROSS THE RESISTOR IN PARALLEL TO THE CAPACITOR AS THE FREQUENCY IS INCREASED?

13 xx What is a filter?

14 What is a filter? xx a device or material for suppressing or minimizing waves or oscillations of certain frequencies (as of electricity, light, or sound)

15 RC Filters xx How do I make an RC filter?

16 Low Pass and High Pass xx Filter LOW PASS FILTER W1, Ch1+ Ch2+ F Grd, Ch1-, Ch2- Eliminates signals ABOVE the cut-off frequency (fc) HIGH PASS FILTER F W1, Ch1+ Ch2+ R = 5 k Grd, Ch1-, Ch2- Eliminates signals BELOW the cut-off frequency (fc)

17 Low Pass and High Pass xx Filter - Simulation LOW PASS FILTER W1, Ch1+ Ch2+ F Grd, Ch1-, Ch2- Eliminates signals ABOVE the cut-off frequency (fc)

18 Determining the cut-off frequency for RC filters

19 0.01 F (10 nf) xx Low Pass Filter: Cut-off frequency The cut-off frequency for RC circuits is equal to: 10 k f c = 1 2πRC in units of Hz or 1/s

20 0.01 F (10 nf) xx Low Pass Filter: Cut-off Frequency Example Prove that the units for f c = 1 2πRC are Hz (1 Hz = 1/s) 10 k Calculate the critical frequency for filter shown here. Use the following unit conversions: F = C/V A = C/s V = A Hz = 1/s f c = 1 2πRC = 2π x 10 6 F FV C C As A V Hz s 1 = 1592 Hz

21 What is a Bode Plot?

22 COMPARES THE SIGNAL COMING INTO THE FILTER TO THE SIGNAL COMING OUT OF THE FILTER. What is a Bode Plot? Plot used to interpret how the filter affects the input in terms of both magnitude and phase. Logarithm scale of frequency on x axis for both plots Magnitude in units of decibels (db) in one plot PLOT 1 Phase angle in degrees in second plot PLOT 2 Source:

23 Bode Plots LOW PASS FILTER HIGH PASS FILTER Image Source:

24 0.01 F (10 nf) Bode Plot Example xx Analog Discovery 10 k BUILD AND TEST RC FILTER - PROVE THAT fc = 1592 Hz - PROVE IT IS A LOW PASS FILTER

25 Exercise: Solve for R, C or fc to Complete the Table Below Show all calculations, units and unit conversions for each row. R, C, F Cut-off Frequency, Hz 1 x x x x x x x

26 Exercise: Solve for R, C or fc to Complete the Table Below Show all calculations, units and unit conversions for each row. R, C, F Cut-off Frequency, Hz 1 x x x x x x x x x

27 How does a strain gauge work? R = ρl A MODULE I AND II Image Source:

28 How does a strain gauge work? Voltage, Volts Time, seconds MODULE I AND II Signal before filter Signal after filter

29 Homeworkdue 2/27 (Najera), due 3/2 (Quinones) SUCCESS POINTS: REPORT WRITING CHECK TO MAKE SURE EVERYTHING YOU SAY REFER DIRECTLY TO YOUR TABLES AND GRAPHS? P15 and P16 Pre-Lab Module IV Module IV: Build and Analyze 3 types of filters, and add a low pass filter to the output of the Strain Gauge Circuit from Module II.

30 What s Next in Week 6? Will introduce LAB Module III: Strain Gauge II Sensor LECTURE Quiz 3 System of Equations Adding Equtions Analog Discovery Constructing Bode Plots Please bring laptops to all lectures and labs.

31 Questions?

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