HKN ECE 210 Exam 2 Review

HKN ECE 210 Exam 2 Review
David Jiang
Phasors
 Phasors
 |F| is the amplitude



is the phase shift
is the radian frequency
More Phasors
 To find the phasor of a sine function, convert the sine
function into a cosine function
 KCL and KVL also hold in the frequency domain.
 Derivative Principle of Phasors
 The nth derivative,
phasor
of a co-sinusoid is also a co-sinusoid with
Super position
 Superposition also works with phasors
 Given two co-sinusoidal inputs,
then the weighted linear combination
is
.
with phasors
Impedance of Phasors
 Inductor

 Capacitor

 Resistors

Phasor Exam Questions
 If you see a complex number raised to a large power (or product
of complex numbers, try converting it to phasor notation since
raising an exponential to a power is just multiplying the exponents
and multiplying exponentials is simply adding the exponents
 If you see a complicated sum of phasors (exponentials) of different
frequencies, try converting it to polar form since adding complex
numbers is just basic algebra
 This is usually asked in part of the first question.
Solving Circuits with Phasors
 Given a circuit with sinusoidal input, to find v(t) across an
element, do the following.
 Convert the source into a phasor.
 Write all other elements (such as inductors, capacitors, and
resistors) in terms of their impedance.
 Solve the circuit like you previously have been doing, using
KVL, KCL, CDR, VDR, Ohm’s Law, Superposition, etc… as
necessary.
 This will be probably be asked in some form (Maybe with an
op amp circuit).
Power
 Capacitors and inductors absorb no net power.
 Average Available Power

 Matched Loads
 The matched load impedance is the conjugate of the Thevenin
impedance.
 Matched loads gives us maximum power transfer.
 Power and matched loads usually show up as part of a
question.
Resonance

 At resonant frequency,
 An inductor and capacitor in series becomes an short circuit

 An inductor and capacitor in parallel becomes an open circuit

 A question about resonance usually appears as part of a
question. While you can derive the above results, it’ll be
easier to write this down on your notesheet and just use it on
the test.
Frequency Response

 The frequency response is the product of the magnitude
response and the phase response of a LTI system (such as a
filter).
 When an input goes though an LTI system…


Finding Frequency Response
 If given a circuit
 Convert everything to frequency domain.
 Replace input source f(t) with F, output y(t) with Y.
 Write down the impedances of the circuit elements
 Find an equation to relate F with Y (usually KVL)
 Solve for Y/F.
 If given an ordinary differential equation
 Use the derivative principle
 Replace y(t) with Y, f(t) with F,
 Solve for Y/F.
with
Filters
 Plug in values of 0 and infinity for omega.
 Low pass filter goes to 0 at infinity and 1 at 0

 High pass filter goes to 0 at 0 and 1 at infinity

 Bandpass filter goes to 0 at both 0 and infinity

Fourier Series
 Be familiar with the three forms of the Fourier Series
 Exponential
 Trigonometric
 Compact form
 Table 6.1 (pg. 187) and Table 6.2 (pg.193) has a good summary
of the different forms of the Fourier series and how to find the
coefficients.
 Table 6.3 (pg. 195) has the properties of the Fourier series.
 𝑎𝑛 = 0 for odd functions and 𝑏𝑛 = 0 for even functions.
 There is usually one question about the Fourier series
(finding coefficients).

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