Schedule… Date Day Class Title Chapters HW Lab Exam No. Due date Due date 10 Nov Mon 20 Exam Review LAB 7 11 Nov Tue 13.2 – 13.3 12 Nov Wed 21 Boolean Algebra EXAM 2 13 Nov Thu 14 Nov Fri Recitation 15 Nov Sat 16 Nov Sun 13.3 – 13.5 17 Nov Mon 22 Combinational Logic LAB 10 18 Nov Tue Discussion #20 – Exam 2 Review ECEN 301 1
Ask Alma 5:26 26 And now behold, I say unto you, my brethren, if ye have experienced a change of heart, and if ye have felt to sing the song of redeeming love, I would ask , can ye feel so now? Discussion #20 – Exam 2 Review ECEN 301 2
Lecture 20 – Exam 2 Review Chapters 4 – 6, 8 Discussion #20 – Exam 2 Review ECEN 301 3
Exam 2 12 – 16 November (Monday – Friday) Chapters 4 – 6 and 8 15 questions 12 multiple choice (answer on bubble sheet!) • 1 point each 3 long answer (show your work!) • 4 or 5 points each Closed book! One 3x5 card allowed Calculators allowed No time limit Study lecture slides and homework Discussion #20 – Exam 2 Review ECEN 301 4
Exam 2 Review…Overview 1. Capacitors and Inductors 2. Measuring Signal Strength 3. Phasors 4. Impedance 5. AC RLC Circuits 6. AC Equivalent Circuits 7. DC Transient Response 8. Frequency Response 9. Basic Filters 10. Op-Amps Discussion #20 – Exam 2 Review ECEN 301 5
Capacitors & Inductors Inductors Capacitors + C – + L – Passive sign convention i i ( ) di t 1 t ( ) v t L ( ) ( ) ( ) v t i d v t Voltage 0 dt C C t 0 1 ( ) dv t t ( ) ( ) ( ) i t v d i t ( ) i t C Current 0 L L t dt 0 ( ) ( ) di t dv t ( ) ( ) ( ) ( ) P t Li t P t Cv t Power L C dt dt Discussion #20 – Exam 2 Review ECEN 301 6
Capacitors & Inductors Inductors Capacitors 1 1 2 2 ( ) ( ) ( ) ( ) W L t Li t W C t Cv t Energy 2 2 Current Voltage An instantaneous change is not permitted in: Voltage Current Will permit an instantaneous change in: Short Circuit Open Circuit With DC source element acts as a: Discussion #20 – Exam 2 Review ECEN 301 7
Capacitors & Inductors 1. What is the difference between the voltage and current behaviour of capacitors and inductors? Discussion #20 – Exam 2 Review ECEN 301 8
Capacitors & Inductors 1. What is the difference between the voltage and current behaviour of capacitors and inductors? 5.0 0.5 4.0 0.4 3.0 0.3 2.0 0.2 1.0 0.1 0.0 0.0 0.00 2.00 4.00 6.00 0.00 2.00 4.00 6.00 Capacitor current i C (t) Capacitor voltage v C (t) Inductor voltage v L (t) Inductor current i L (t) NB : both can change instantaneously NB : neither can change instantaneously Discussion #20 – Exam 2 Review ECEN 301 9
Capacitors & Inductors 2. find the voltage v(t) for a capacitor C = 0.5F with the current as shown and v(0) = 0 1.2 1.0 current (A) 0.8 0.6 0.4 0.2 0.0 0.0 1.0 2.0 3.0 time (s) Discussion #20 – Exam 2 Review ECEN 301 10
Capacitors & Inductors 2. find the voltage v(t) for a capacitor C = 0.5F with the current as shown and v(0) = 0 1.2 current i(t) in 4 intervals : 1.0 current (A) 0 0 i t 0.8 0.6 0 1 t t 0.4 0.2 1 1 2 t 0.0 0.0 1.0 2.0 3.0 0 2 t time (s) 1 t ( ) ( 0 ) v t id v C 0 Discussion #20 – Exam 2 Review ECEN 301 11
Capacitors & Inductors 2. find the voltage v(t) for a capacitor C = 0.5F with the current as shown and v(0) = 0 1.2 voltage v(t) in 4 intervals : 1.0 current (A) 0 0 0.8 v t 0.6 t 0.4 2 0 0 1 d t 0.2 0 0.0 t 2 ( 1 ) ( 1 ) 1 2 d v t 0.0 1.0 2.0 3.0 1 time (s) 0 ( 2 ) 2 v t 1 t ( ) ( 0 ) v t id v C 0 Discussion #20 – Exam 2 Review ECEN 301 12
Capacitors & Inductors 2. find the voltage v(t) for a capacitor C = 0.5F with the current as shown and v(0) = 0 1.2 voltage v(t) in 4 intervals : 1.0 current (A) 0 0 v t 0.8 0.6 2 0 1 t t 0.4 0.2 2 1 1 2 t t 0.0 0.0 1.0 2.0 3.0 3 2 t time (s) Discussion #20 – Exam 2 Review ECEN 301 13
Capacitors & Inductors 2. find the voltage v(t) for a capacitor C = 0.5F with the current as shown and v(0) = 0 3.5 1.2 3.0 1.0 2.5 current (A) voltage (V) 0.8 2.0 0.6 1.5 0.4 1.0 0.2 0.5 0.0 0.0 0.0 1.0 2.0 3.0 0.0 1.0 2.0 3.0 4.0 time (s) time (s) voltage v(t) in 4 intervals : NB : The final value of the capacitor voltage after 0 0 v t the current source has stopped charging the 2 capacitor depends on two things: 0 1 t t 1. The initial capacitor voltage 2 1 1 2 t t 2. The history of the capacitor current 3 2 t Discussion #20 – Exam 2 Review ECEN 301 14
Measuring Signal Strength 3. Compute the rms value of the sinusoidal current i(t) = I cos( ω t) Discussion #20 – Exam 2 Review ECEN 301 15
Measuring Signal Strength 3. Compute the rms value of the sinusoidal current i(t) = I cos( ω t) 1 T 2 ( ) i i d rms T 0 2 / 2 2 cos ( ) I d 2 0 cos( 2 ) 1 t 1 1 cos 2 2 / ( ) t 2 cos( 2 ) I d 2 2 2 2 0 2 1 I 2 / 2 cos( 2 ) I d 2 2 2 0 1 2 Integrating a sinusoidal waveform 0 I 2 over 2 periods equals zero I 2 Discussion #20 – Exam 2 Review ECEN 301 16
Measuring Signal Strength 3. Compute the rms value of the sinusoidal current i(t) = I cos( ω t) 1 T 2 ( ) i i d rms T 0 2 / 2 2 cos ( 2 ) I d 2 0 1 1 2 / 2 cos( 2 ) I d 2 2 2 0 2 1 I 2 / 2 cos( 2 ) I d The RMS value of any sinusoid 2 2 2 0 signal is always equal to 0.707 1 times the peak value (regardless of 2 0 I phase or frequency) 2 I 2 Discussion #20 – Exam 2 Review ECEN 301 17
Phasors 4. compute the phasor voltage for the equivalent voltage v s (t) v 1 (t) = 15cos(377t+ π /4) v 2 (t) = 15cos(377t+ π /12) + v 1 (t) ~ – + v 2 (t) ~ – + v s (t) ~ – Discussion #20 – Exam 2 Review ECEN 301 18
Phasors 4. compute the phasor voltage for the equivalent voltage v s (t) v 1 (t) = 15cos(377t+ π /4) v 2 (t) = 15cos(377t+ π /12) 1. Write voltages in phasor notation + v 1 (t) ~ – / 4 j ( ) 15 V j e + 1 v 2 (t) ~ – 15 V 4 / 12 j ( ) 15 V j e 2 15 V + v s (t) ~ 12 – Discussion #20 – Exam 2 Review ECEN 301 19
Phasors 4. compute the phasor voltage for the equivalent voltage v s (t) v 1 (t) = 15cos(377t+ π /4) v 2 (t) = 15cos(377t+ π /12) 1. Write voltages in phasor notation + v 1 (t) ~ 2. Convert phasor voltages from polar to – rectangular form (see Appendix A) + v 2 (t) ~ – ( ) 15 ( ) 15 V j V V j V 2 1 12 4 Convert to rectangula r : Convert to rectangula r : ( ) 15 cos 15 sin ( ) 15 cos 15 sin V j j V j j 1 2 4 4 12 12 + 10 . 61 10 . 61 14 . 49 3 . 88 v s (t) j V j V ~ – Discussion #20 – Exam 2 Review ECEN 301 20
Phasors 4. compute the phasor voltage for the equivalent voltage v s (t) v 1 (t) = 15cos(377t+ π /4) v 2 (t) = 15cos(377t+ π /12) 1. Write voltages in phasor notation + v 1 (t) ~ 2. Convert phasor voltages from polar to – rectangular form (see Appendix A) + 3. Combine voltages v 2 (t) ~ – ( ) ( ) ( ) V S j V j V j 1 2 25 . 10 14 . 49 j + v s (t) ~ – Discussion #20 – Exam 2 Review ECEN 301 21
Phasors 4. compute the phasor voltage for the equivalent voltage v s (t) v 1 (t) = 15cos(377t+ π /4) 1. Write voltages in phasor notation v 2 (t) = 15cos(377t+ π /12) 2. Convert phasor voltages from polar to rectangular form (see Appendix A) + 3. Combine voltages v 1 (t) ~ – 4. Convert rectangular back to polar ( ) 25 . 10 14 . 49 V j j + S v 2 (t) ~ – Convert to polar : 2 2 r (25.10) (14.49) 28 . 98 14 . 49 1 tan 25 . 10 + v s (t) ~ 6 – ( ) 28 . 98 V j S 6 Discussion #20 – Exam 2 Review ECEN 301 22
Phasors 4. compute the phasor voltage for the equivalent voltage v s (t) v 1 (t) = 15cos(377t+ π /4) 1. Write voltages in phasor notation v 2 (t) = 15cos(377t+ π /12) 2. Convert phasor voltages from polar to rectangular form (see Appendix A) + 3. Combine voltages v 1 (t) ~ – 4. Convert rectangular back to polar 5. Convert from phasor to time domain + v 2 (t) ~ – NB : the answer is NOT ( ) 28 . 98 V j S 6 simply the addition of the amplitudes of v 1 (t) ( ) 28 . 98 cos 377 v t t and v 2 (t) (i.e. 15 + 15), S 6 and the addition of their phases (i.e. π /4 + π /12) + v s (t) ~ – Bring ω t back Discussion #20 – Exam 2 Review ECEN 301 23
Phasors 4. compute the phasor voltage for the equivalent voltage v s (t) v 1 (t) = 15cos(377t+ π /4) v 2 (t) = 15cos(377t+ π /12) + v 1 (t) ~ – + v 2 (t) ~ – Im ( ) 28 . 98 V j S 6 π /6 Vs(j ω ) 14.49 Re ( ) 28 . 98 cos 377 v t t S 6 + 25.10 v s (t) ~ – Discussion #20 – Exam 2 Review ECEN 301 24
Impedance Impedance : complex resistance (has no physical significance) will allow us to use network analysis methods such as node voltage, mesh current, etc. Capacitors and inductors act as frequency-dependent resistors i (t) i (t) i (t) + + + + + + R v s (t) v s (t) v R (t) v s (t) v L (t) ~ v C (t) ~ ~ L C – – – – – – I(j ω ) + + V s (j ω ) V Z (j ω ) ~ Z – – Discussion #20 – Exam 2 Review ECEN 301 25
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