ECE 202: Ideal Transformers
Charity Pettis
March 29, 2004
Objectives
Establish relationships between the
primary and secondary sides of an ideal
transformer
Define the turns ratio of an ideal
transformer
Work an example problem using circuit
analysis a
LECTURE 19: Graphical Convolution
Part 1: INTRO
1. The Notion of Flip and Shift
Increasing t
2. RECALL: y(t) = h(t) * f (t) = f (t) * h(t) means
y(t) =
h(t ) f ( ) d = h( ) f (t ) d
Lecture 19 Sp 15
2
R. A. DeCarlo
3. What is the meaning of the convolut
LECTURE 18: THE JOY OF CONVOLUTION
Part 1: INTRO
1. Just because no one understands you, doesnt mean youre an artist.
Rich Hebda. I am reminded of this quote every time I talk about convolution.
2. WORDS:
CONVOLUTED: folded in curved or tortuous windings.
LECTURE 17: IMPEDANCE AND FREQUENCY SCALING-Worksheet
Part 1: Impedance Scaling
1. Basics of Impedance Scaling
(a) Impedance scaling or magnitude scaling by a factor K m :
Z new (s) = K m Zold (s) and Ynew (s) =
1
Y (s)
K m old
(b) Let us visit the little
LECTURE 17: IMPEDANCE AND FREQUENCY SCALING
Worksheet Approach
Part 1: Impedance/Magnitude Scaling
1. A Problem Example 1: Consider the op amp circuit below which is to
realize a transfer function H (s) =
1
which is a normalized LP Butterworth
s +1
filter
Lecture 12: Response ClassificationA Unification
Intro. The definitions
Zero-input Response: due only to the initial conditions.
Zero-state Response: due only to the input signal.
Complete Response: sum of the zero-input and zero-state responses.
Steady S
Lectures 11 and 12. Boost Converter Circuit (will not be covered on
exams): Switch closes at t = 0, opens at t = 1, closes at t = 2, and the
process repeats. The following circuit represents a CHARGER for a
SUPERCAPACITOR used on a bus in Shanghai for exa
Lecture 15: Sinusoidal Steady State (SSS) Analysis
or Phasors without the Phasor
1. Definition. A signal f (t) is periodic with period T > 0 if f (t) = f (t + T ) ;
the smallest such T > 0 is the fundamental period.
2. Memories from the corners of ECE-201
Lecture 12: H(s)Poles-Zeros & BIBO Stability
1. Introduction
(a) What are poles and zeros? Answer: HS math and calculusreview.
(b) What are nice inputs? Answer: nice inputs are bounded inputs;
if you excite a circuit with a nice bounded input, like a step
Lecture 12: Switched Capacitor NetworksWorksheet Approach
1. Introduction
(a) What are switched capacitor circuits/networks? Resistorless and
inductorlessonly capacitors, switches, sources, and op amps.
(b) Can they be all that the other circuits can be?
Lecture 11: Switching in RLC Circuits
Question: Why consider switching circuits?
Answer: a circuit with switches that never switch,
never switches its behavior, and is equivalent to a
circuit without switches: circuits without switches
are a spec
LECTURE 20: Butterworh & Chebeyshev
BP Filters
Part 1: Series and Parallel RLC CircuitsAgain
1. RLC Admittance/Impedance Transfer Functions
EXAMPLE 1: Series RLC H (s) .
1
s
I out (s)
1
L
H (s) =
= Yin (s) =
=
1
R
1
Vin (s)
R + Ls +
s2 + s +
Cs
L
LC
EXAMP
WORKSHEETCOUPLED INDUCTORS AND TRANSFORMER MODELS
1. True-False. The wire across the top of the coupled coils in the circuit below makes
no difference to any of the usual calculations. _
2. The value of the mutual inductance for the coupled coils in the c
LECTURE 31: Basics of Magnetically Coupled
CircuitsPart 1
1 Question 1: What is meant by a magnetically coupled circuit?
A changing current (derivative is not constant) enters inductor L1 (which
continues to act like an inductor with inductance L1 ) induc
Quiz 20 ECE-202
(20 points)
Name: (3 pts) _
November 10, 2014
Construct only part of the op amp observable form realization of
H (s) =
Vout (s) 4s 2 5s + 6
.
= 2
Vin (s)
s + 2s + 3
(a) (3 pts) Using the political operator D =
d
, write down the differenti
Quiz 19 ECE-202
(20 points)
Name: (3 pts) _
November 7, 2014
(a) (12 pts) Construct the op amp controllable form realization of
H (s) =
Vout (s)
1
= 2
Vin (s) s + 4s + 16
as follows:
(i) Construct the diff eq in vout (t) and vin (t) associated with H (s)
EE-202/445, 3/31/15
9-1
R. A. DeCarlo
BIQUADRATICS AND
STATE SPACE REALIZATIONS
I. Introduction
1. The biquadratic transfer function is simply a transfer function having a 2nd
numerator and a 2nd denominator:
z
2
s +z
Qz
b0 s 2 + b1s + b2
H (s) = 2
=K
p
Lecture 28. Passive HP Filter Design
1. High Pass Specs: ( p , Amax ) , ( s , Amin ) , p > s :
STOPBAND: 0 s in which dB loss Amin
TRANSITION BAND: s p
PASSBAND: p in which dB loss Amax
REMARK:
Lecture 27. Active Sallen & Key Butterworth Filter Design
1. Sallen and Key LP Circuit
2. Sallen and Key Circuit Transfer Function
H SK ( s ) =
Vout ( s )
Vin ( s )
=
K
R1 R2C1C2
1
1
1 K
1
s2 +
+
+
s+
R1 R2C1C2
R1C1 R2C1 R2C2
where K = Vout Va = 1 +
Quiz 17/EE-202
(20 points)
Name: (3 pts) _
1. The filter transfer function of the circuit below is H LPcir (s) =
November 3, 2014
4/3
.
1
s2 + s + 1
Q
1
1
R
, R2 =
, C1 = 3 Q , C2 = 1 F, R = RA , and RB = ; R can be
Q
3
3
scaled independently of the rest
LECTURE 24: Resonance and Coupling for
Maximum Power Transfer
Definition: Input and output voltages/signals are in phase.
1. RLC Admittance/Impedance Transfer Functions
CONSEQUENCE: Yin ( j ) AND Z in ( j ) ARE REAL AT = r , THE
RESONANT FREQUENCY.
EXAMPL
LECTURE 22-23: Approximate Analysis of
Near Bandpass Circuits
Part 1: Practical and Ideal Capacitors
IDEAL
PRACTICAL-One form
1
YC, prac ( j ) =
+ j C
Rp
YC ( j ) = j C
1. Question: How ideal is practical? How can we tell?
1
(a) YC ( j ) = j C ! YC, prac
Lecture 10: That Pesky Modified Nodal and
Modified Loop Analysis
1. Hey Professor Ray, cant we just use supernovas,
or supernodes, or something?
ANSWER: (Inspired by Bread and Jam
for Francis by Russell Hoban)
Nodal is what makes SPICE run,
But su
Lecture 9: Transfer Function Ideas
ContinuedAND the Initial and Final Value
Theorems
1. Hey Professor Ray, how does loop analysis work
in the s-world?
ANSWER: Example 1. Computation of a circuit
transfer function using loop analysis.
Step
Quiz 25.1/EE202
(10 ptS)
Name: April 21 , 2016
With reference to the two port below, assuming 31 1 = 4s compute V2(s) and v20)
assuming V1(s) = j . Quiz 25.1/EE202
(10 pts)
Name: April 21 , 2016
With reference to the two port below, assuming y : 25 comput
R. A. DeCarlo
Quiz 21.2/EE202 (MW)
(10 points)
Name: (3 ts) \" V M "' D) A Iil 15, 2016
p p
In the circuit below, suppose there is a dot at position A, k = 0.4 , L1 2 L2 = 5 H, and R L 2% Q, then
Y
in
(S) = : (simplest form)