This course introduces students to the basic components of electronics: diodes, transistors, and op amps. It covers the basic operation and some common applications.

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From the course by Georgia Institute of Technology

Introduction to Electronics

325 ratings

Georgia Institute of Technology

325 ratings

This course introduces students to the basic components of electronics: diodes, transistors, and op amps. It covers the basic operation and some common applications.

From the lesson

Introduction and Review

Learning Objectives: 1. Review syllabus and procedures of this course. 2. Review concepts from linear circuit theory to aid in understanding material covered in this course.

- Dr. Bonnie H. FerriProfessor

Electrical and Computer Engineering - Dr. Robert Allen Robinson, Jr.Academic Professional

School of Electrical and Computer Engineering

Welcome back to Electronics.

Â This Dr. Ferri.

Â This lesson will be a review of impedance.

Â In the previous lesson, we did a review of Kirchhoff's laws.

Â In this lesson, we will look at impedances.

Â In particular, impedance is a,

Â a method that we use for steady-state sinusoidal inputs.

Â In other words, what we call AC, or alternating current, inputs.

Â So we can define the impedance for our basic elements in R, C, and in L.

Â With a resistor, if I look at the voltage current behavior.

Â So, say,

Â this is my voltage across a resistor, and then my current is going in this way.

Â Then if I have it a sinusoidal input or sinusoidal voltage across this resistor,

Â my current's going to be sinusoidal, and in particular it's in-phase.

Â The zero crossings are at the same time, the peak happens at the same time.

Â We often say that, that and that doesn't matter what frequency the input is.

Â So we can say that this is frequency invariant that output is, or

Â the evolved current is always in face with the voltage.

Â Now there's a couple of things that we're going to be needing here so

Â I want to define them.

Â One here is the period.

Â That's how, when it, how long it takes to repeat itself, and we define the frequency

Â as be in hertz, being cycles per second,

Â a cycle being one time that it, it repeats itself.

Â That is one over T, which we're going to define as F.

Â My variable F, as in hertz, is a frequency.

Â There's also a frequency variable, in radians per second.

Â It's a different unit, and it is defined as 2 pi F.

Â Or in terms of T, it's 2 pi over T radians per second.

Â And we use the symbol omega to represent frequency in radians per second.

Â And I need all that once I go to my other variables, my, my C impedance and

Â my L impedance, or I'll call it Z sub C.

Â And I'm going to define it this way.

Â That is, 1 over J omega, omega being the frequency and radiance per second.

Â J being my symbol for the square root of minus 1, and then C is the capacitance.

Â So if I define my voltage this way and my current going in this way,

Â I can represent for a sinusoidal voltage, my steady state current looks like this.

Â Notice that the current, this being the current I and

Â the voltage V, the current leads the voltage.

Â Leads means it comes before.

Â So it comes before this.

Â So that's my impedance for a capacitor.

Â For an inductor, it's J times omega times L.

Â And again, if I plot the voltage current relationship for

Â a sinusoidal voltage, if this is the voltage in this plot, and

Â the current is in this plot, then what we say is that the current lags the voltage,

Â it comes after it, looks like it's delayed.

Â So these are the three impudence's that I'm going to need a great deal when I'm

Â analyzing circuits with an alternating current, another with a sinusoidal input.

Â Let's look at impudence's in series.

Â Here's the good thing about impedances.

Â They're messy because they involve complex numbers,

Â but they use all the same rules that we've already defined for resistors.

Â So, impedances in series, I treat just like they were resistors in series.

Â So, this circuit is equivalent to a circuit.

Â With one impedance, and that impedance

Â is equal to the sum of the other ones, Z1, plus Z2, plus Z3.

Â So, impedances in series, they just add.

Â So it could be 3, it could be a lot more than 3, it's just a summation of

Â all impedances in the series, become our, our equivalent impedance.

Â Impedances in parallel.

Â Well, I treat them just like resistors in parallel,

Â which I get by inverting 1 over each one of them.

Â And it's usually easier to think of it in terms of, if I have two resist,

Â resistors in parallel, in other words if, if this resistance isn't there, if it's

Â if I only have these two impedances, so I'm going to write Z1 in parallel with Z2.

Â If I look at this expression and Z3 is gone, then all I've got is two terms.

Â I can simplify it, to Z1 times Z2,

Â over Z1 plus Z2.

Â So, that's two impedance in parallel with one another.

Â Kirchhoff's Laws still work.

Â Kirchhoff's current law says that all the currents going into

Â a node, have to equal all the current leaving the node.

Â So the currents going in I1, is equal to the leaving, I1 plus or I2 plus I3.

Â And in terms of Kirchhoff's Voltage Law, I can look at a,

Â going around in a loop this way and sum up all my voltages.

Â And in my case, when I sum up voltages around a loop, I use a trick and

Â I just say, in order to get my polarity right,

Â whenever I hit a minus sign first, I subtract that minus VS.

Â And going around, I hit a plus sign, this way, plus V1.

Â Going around this way, I hit a plus sign, plus V2.

Â Going around this way, I hit a plus so plus V3 is equal to 0.

Â In other words, I can rewrite it down this way, right here.

Â So Kirchhoff's Laws still work.

Â The only thing different about all these laws is,

Â now we're working with complex numbers.

Â So again, impedances treat just as if they were resistors.

Â The only thing is, they're going to be complex, complex numbers.

Â Let's look at an example of this.

Â How to analyze this circuit with impedances.

Â The first thing I'm going to do,

Â is replace this circuit with impedances, Z sub R.

Â And 1 over Z sub C, representing the capacitance.

Â I've got my input voltage, and my output voltage.

Â I'm going to use the voltage divider law here.

Â The voltage divider law says that V out is equal to Z sub C,

Â over ZR plus Z sub C, times the input.

Â If I plug in for Z sub C, I get 1 over J omega C.

Â If I plug in for Z sub R, I get R,

Â plus 1 over J omega C times Vi.

Â If I clear my fractions, I will get 1 over RC,

Â J omega plus 1 times Vi, and that gives me V out.

Â So once I know what Vi is, then I can solve for V out.

Â Now let's take a look at a series RLC circuit.

Â First thing I do is redraw the circuit in terms of its impedances.

Â So I get Z sub R, in series with the Z sub L,

Â in series with the Z sub C.

Â And I'm looking for V out, V sub 0, in terms of V sub i.

Â I can use a voltage divider log in.

Â V out is equal to Z sub C over ZR,

Â plus ZL plus ZC times Vi.

Â If I substitute in for Z sub C, I substitute in 1 over J omega C.

Â R is for Z sub R, and J omega L, for Z sub L.

Â And then I've got my other Z sub C.

Â If I clear my fraction here, I'm going to get a one in the numerator.

Â RC, J omega, plus J omega squared, LC,

Â plus 1 in the denominator, times Vi.

Â And remember that J is the square root of minus 1, so J squared is minus 1.

Â So that's 1 over RC J omega minus omega squared LC plus 1,

Â all times Vi is equal to V out.

Â If I know what V sub i is, then I can solve for V out.

Â And the other thing about this,

Â it's implicit in here that I know what omega is.

Â Omega is the input voltage, so

Â if we say Vi is equal to Ai cosine of omega T,

Â that omega is input frequency.

Â Maybe 100 hertz, in which case that would be 2 pi times 100 radians per second.

Â It could be whatever frequency we want, but

Â it is a particular frequency to be able to solve for a particular value of V out.

Â So in summary, we've introduced the KVL and KCL,

Â applied the KVL to parallel elements and series elements.

Â And we solve simple circuits using Kirchhoff's Laws.

Â All of this is applied to circuits with impedances.

Â The bottom line is, an impedance is, acts like a complex resistance.

Â All of our standard laws apply,

Â the only thing is it's messier because it's complex numbers.

Â In our next lesson, we will do a review of transfer function.

Â Thank you.

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