Lesson+27

Lesson+27 - Lesson 27 Challenge 26 Power/RMS 16:6-7...

This preview shows pages 1–14. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Challenge 26 Power/RMS 16:6-7 Challenge 27 Exam #2 average ~ 85 2 Lesson 27 Lesson 27
Challenge 26 3 0 1 2 3 4 2 1 0 0 1 2 3 4 0 - /2 - What is the compact Fourier series ? x(t)= 2 + 2 cos(2t - )+ 1 cos(3t- /2 ) What is the trigonometric Fourier series ? = 2 – 2 cos(2t)+ sin(3t) Given Lesson 27

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Power 4 Instantaneous power Average power Special case: Sinusoidal signals T d i v T P t i t v t P 0 ) ( ) ( 1 ) ( ) ( ) ( Lesson 27
5 Average Power and RMS Power Calculations for sinusoids. Assume: T n n n n n n d i v T P t n I I t i t n V V t v 0 0 1 0 0 1 0 1 τ τ τ ω ω ) ( ) ( ) cos( ) ( ) cos( ) ( (Average Power) Lesson 27

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
6 Average Power and RMS Power Calculations for sinusoids Combining  T m n m n n n T n n n T m m m T dt t m t n T I V dt t n T V I dt t m T V I d I V T P 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 ) cos( ) cos( ) cos( ) cos( ω ω ω ω τ 0 0 0 if m n Sum and difference frequencies cos(a)cos(b)=1/2cos(a-b)+(1/2)cos(a+b). Lesson 27
7 Average Power and RMS Power Calculations ) cos( 2 1 1 0 0 n n n n n I V I V P (You can replace peak values with RMS values) ) cos( 2 2 1 0 0 n n n n n I V I V P Remember power factor? Lesson 27

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
8 Average Power Calculations ) cos( 2 1 1 0 0 n n n n n I V I V P Consider the RL circuit shown (C=2, R=10) with i(t)=2+10cos(t+10 )+6cos(3t+35 ) C=2 R=10 I(t) v(t) i(t) Lesson 27
9 Average Power Calculations i(t)=2+10cos(t+10 )+6cos(3t+35 ) 0 th Harmonic C=2 R=10 I(t) ) ( tan ω ω ω 20 400 1 10 2 1 1 1 IZ V Z j 20 2 10 0 2 )) ( ( ; V I Lesson 27

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
10 i(t)=2+10cos( t +10 )+6cos( 3t +35 ) Only odd harmonics exist, 3 rd Harmonic 1 st Harmonic C=2 R=10 I(t) 77 5 10 10 V I ; ) 54 3 cos( 1 ) 77 cos( 5 20 ) ( t t t v Lesson 27 i(t)=2+10cos(t+10 )+6cos(3t+35 ) ) ( tan ω ω 20 400 1 10 1 V 54 1 ; 35 6 V I
11 Average Power Calculations W 3 41 05 0 25 1 40 54 35 6 1 2 1 77 10 10 5 2 1 2 20 . . . ) cos( ) )( ( )) ( cos( ) )( ( ) ( V I P Use 3 rd harmonic as a stopping rule: Lesson 27 Power factor angles

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
12 Consider the periodic signal V m x(t) What is the signal’s CTFS? 0 T/6 T/3 T/2 2T/3 5T/6 T The signal has odd symmetry and half wave symmetry, This means that A n =0 and only odd harmonics (B 2n+1 ) exist. (Lesson 25) AP16.3 3 12 0 5 3 1 2 2 ) sin( ) / sin( ) ( ,... , , t n n n V t x n m ω π π Lesson 27
13 V m x(t) Derivation 0 T/6 T/3 T/2 2T/3 5T/6 T odd n 3 1 12 8 6 8 8 0 2 2 4 6 0 6 0 0 4 0 0 odd n m T T m T m T n n n n

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern