Circuits 2 Overview January 11, 2005 Harding University Jonathan White.

Circuits 2 Overview

January 11, 2005

Harding UniversityJonathan White

General Overview of Class• 3 tests and a comprehensive final

– The first test should be easy if you remember last semester.

• Homework for each chapter• Small quizzes to reinforce new concepts or if I think

you are sleeping• Lab every Thursday except tomorrow

– Some labs will be for presentations– Some may be needed for test review

• Final projects:– Team build of an FM transmitters– Team presentation and report on any circuits topic

• After the first 3 chapters, the material covered is more difficult due to the math involved.– Also, some memorization of formulas will be required.

Chapter 9 – Sinusoids and Phasors

• Impedance: ratio of phasor voltage to phasor current.

• Z = V/I -- similar to Ohm’s Law, R=V/I• Impedances are combined exactly like resistors.• For resistors, Z = R• For inductors, Z = jwL• For capacitors, Z = 1/(jwC)

– To solve AC circuits, convert every element to an impedance value and treat like a resistor.

• We will practice some phasor mathematics, and how to use your calculator to solve.

Chapter 9 - Problems

• Find I0 in the circuit below:

Obtain Zin for the circuit below:

5 6 2 8

3 4 5 4 6

j j

j j j

240 75 160 30 60 80

67 84 20 32

j

j

Simplify and write in rectangular and polar form:

Chapter 10 – AC Steady-State Analysis Techniques

• Nodal analysis• Mesh analysis• Superposition• Source transformation• Thevenin/Norton equivalents

• Should be a good review of last semester. Make sure you can do nodal analysis.

Ch. 10 Problems:• Use nodal analysis to find vo in

the circuit below:

Find the mesh currents if v1 = 10cos(4t) V and v2 = 20cos(4t – 30o) V

Find the Thevenin equivalent from a to b

Ch. 11 – AC Power Analysis

• Power in a circuit is still p = v*I– However, the power in an AC circuit

changes continually. We use average power.

• PAVG = ½ VmImcos(θv – θi)

• Resistive loads absorb power all the time. Reactive loads don’t.

• RMS values of currents/voltages• Power factors

Ch. 11 Problems:

Find the average power absorbed by each element if vs = 8cos(2t – 40o) V

Find the RMS value of the waveform below:

Ch. 12 – Three Phase Circuits

• Used in high power applications• Used in power generation plants• Used in alternators/generators• Typically consists of 3 voltage sources

spread out by 120o in phase– Wye or Delta Connections

• Table 12.1 (page 518) summarizes about everything about 3 Phase circuits.

Ch.12 Problems

For the - circuit below, calculate the phase and line currents:

Ch. 13 – Magnetically Coupled Circuits

• Also known as transformers

• You’ll be spending about 2 months on this in physics

• The number of windings in the coils affect the produced voltage and current.– This is the summary for this chapter.

Ch. 13 Problems

Find the average power delivered to the 4 Ohm resistor:

Ch. 14 – Frequency Response and Filters

• Variation in behavior of a circuit with a change in signal frequency.

• Bode plots– Only a little

• Resonance– We’ve done this before in lab

• Quality factor and bandwidth• Passive filters:

– Lowpass/HighPass/Bandpass/Bandstop

• Active filters with Op Amps• This is a very long, but very important chapter.

– It is also very understandable and useful.

Ch. 14 - Problems

Calculate the resonant frequency, the quality factor, and the bandwidth for the circuit below:

Chs. 15 & 16 – Laplace Transforms

• A way of solving sinusoidal and non-sinusoidal problems

• Lets use do algebra instead of calculus– Make the RLC problems just a few steps instead

of 15.• Works by transferring the whole problem

from the time domain into the frequency domain, solving the problem algebraically, and then doing an inverse Laplace transform at the end to get back to the time domain.– Laplace makes solving complex problems much

easier• Covered in the differential equations class.

Chs. 15 & 16 problems

Find the Laplace Transform of:

f(t) = te-2tu(t – 1)

Find the inverse Laplace transform of:

1 2( )

1F s

s s

Find v0 using the Laplace Method:

Chs. 17 & 18 – Fourier Transforms

• These are difficult, and we will only cover them if we have time at the end of class– They are covered in the differential equations

class and in control systems.

• Fourier transforms are used to express non-sinusoidal sources as an infinite sum of sinusoids.– We can then apply the methods we’ve used in

AC analysis.

• Page 764 has a great picture of what the Fourier transform does.