### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# 197 Review Sheet for ECE 20100 with Professor Tan at Purdue

### View Full Document

## 22

## 0

## Popular in Course

## Popular in Department

This 6 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Purdue University taught by a professor in Fall. Since its upload, it has received 22 views.

## Similar to Course at Purdue

## Popular in Subject

## Reviews for 197 Review Sheet for ECE 20100 with Professor Tan at Purdue

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/06/15

ECE201 Linear Circuit Analysis I Prof H Z Tan Topic Complex forcing function 1 Review of Complex Numbers Let j J 1 any complex number can be represented in 3 ways 1 In rectangular coordinates a jb a real part Reajb b imaginary part Imajb magnitude a2 b2 complex conjugate a ijb a jb a ijb a2 b2 magnitude2 Remember j j 1 2 As a vector in rectangular coordinates 1m magnitude Re complex conjugate mirror image wrt Re axis 3 In polar coordinates peie p magnitude 9 angle between the vector and the Re axis ccn Re Real part pcosG Imaginary part psinG complex conjugate pe pe pe p2 magnitude2 short hand notation p 9 2 Conversion between rectangular and polar representation of a complex number Euler Identity Key graphic representation of a vector a b M Euler Identity peje a jb same 2 representations pcosG jpsin9 je Cancelp e cos9jsin9 e e eg e We also get cos 9 and s1nt9 2 2f 3 The Approach 1 Replace input excitation VS cosnt 9 or IS cosnt 9 by their complex counterparts VSeJmHe or Isem e Notice that V cosat H Relem jwt 2 Assume Vmejcm b as the circuit response or Ime 3 Solve for Vm amp I or 1m amp 1 4 The steadystate response ie the response to VS cosnt 9 or IS cosnt 9 is simply Re e 42 or Re Ime 42W Advantage simpler math 4 An Example For the series RC circuit below VSt VS cosnt Determine the steadystate response VCI using complex functions R V40 CR Voa Step 1 Compute the differential equation of the circuit cht 1 1 t t dt RCVc RC Vs Step 2 For the moment let Vst VseJOJt and assume complex form for Vci v00 VmeW Step 3 Substitute vst and Vct in the differential equation V ejmc jm ejm 61m m RC RC Cancel e from both sides 39 V 39 V V 39meJ meJ 5 m J RC RC L 1 me Vs1R CVS Ejw 1a2RC V 1 V eij anil dqcil s 41mRCZejmil Rc 41a2RC2 Graphically V 7 Thus V S I tan 1nRC m 1mRC2 Step 4 Determine the steadystate response v60 ReVme quot1 mRCY V W cosat tan 1aRC V 5 More practice on complex arithmetic Find A and 9 using Euler s identity and complex arithmetic given that A cos3t 6 5 cos3t 30 5sin3t 5cos3t150 2sin3t 45 What you need to know i If y a where a are complex numbers then Re y Rea Re ii sina cosa 90 Can you prove it graphically or mathematically Step 1 Rewrite the given equation converting all sin3t to cos3t functions A cos3t 6 5 cos3t 30 5cos3t 90 5 cos3t150 2cos3t 135 Step 2 Rewrite the above in terms of RecompleX numbers Re die32 a Re e3230 F Re gShm Re ej32150 Re 261327135 Step 3 Rewrite the above using If Re y Rea Re then y 01 Notice that this is only true because Re0c and Im0c are related Aeszw 5692440 Sd32790 Se3z150 283l135 Step 4 Cancel the em in all terms Ae 56309 Sejbgou Semen ZeHw In short hand form A46 5430 54 90 54150 24 135 YOU SHOULD LEARN TO WRITE THE ABOVE EQUATION IN ONE STEP Step 5 Solve for A and 9 from A 9 5430 54 90 54150 24 l35 Goal reduce the right side of the equation to a magnitude and a phase Strategy First use Euler s identity to convert all complex numbers to rectangular coordinate because it is easier to perform addition subtraction using rectangular coordinate Second combine all real parts into one number and combine all imaginary parts into another number Finally convert the result back to polar coordinate in the last step Euler s Identity e cost9 jsint9

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "I made $350 in just two days after posting my first study guide."

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.