## Tuesday, June 10, 2008

### IMPEDANCE SERIES PART 2, Lee week 3

June 4, 2008 Educational Radio Net, PSRG 3rd session

One of the topic suggestions from Dave, KE7RJI, was impedance and antenna matching. This is a great topic but one of enormous scope and complexity. After some thought I felt it appropriate to serialize the topic and spread it over several weeks so that we can deal with the component subjects in more detail. To this end we must all speak the same language so a discussion and review of elemental concepts is essential so that we can use them for building blocks. My intent is not to "whip" you into engineers but rather give you the tools to listen to engineers and have a good intuitive understanding of just what is going on.

Impedance is one of the corner stones of electrical theory in general and radio systems in particular. To really grasp the significance of the symbol "Z" requires at least some understanding of the big three circuit elements... resistance, inductance, and capacitance plus some understanding of electrical current and voltage. Last week we started the narrative by discussing the most elemental idea in electrical physics... that of "charge", both moving and stationary. This week we will review "charge" and add the notion of "voltage". In the weeks following we will address the circuit elements in turn and then review and, finally, merge them together into some coherent structure.

Much like any radio talk show I will "set up" the topic and then allow time at the end for questions or comments. Truth be known this subject is a mathematical adventure but, given that we do not have a "white" board for graphic illustration, I will attempt to convey simple ideas verbally.

So, lets get started with the review of "charge".

In the formative years of electrical theory it was understood that something clearly moved when influenced by electrical forces. That hypothetical "something" was given the name "charge" and considered to be positive due to the direction it would move when in the presence of some motive force provided by a, so called, electric field. Modern electrical theory has shown that charge is an electron and, in fact, the elemental electronic charge is negative. So, from a historical perspective, the early and assumed positive charge became known as "conventional" theory in contrast to the now better understood "electron" theory of charge composition.

The electron is very tiny and is normally attached to some atom... helium or hydrogen or some metal such as copper for example. When agitated by forces yet to be discussed the electron can break free of the "mother" atom and become a free electron in contrast to being a "bound" electron before agitation. One free electron bumping along a wire would be impossible to locate or measure without some fancy laboratory instruments however large numbers of moving electrons are readily detected by nanoamp, microamp, milliamp, and just plain ammeters.

There are some very important definitions which are associated with charge.

First. Charge is identically the charge of an electron and is assigned the symbol Q.

Second... the coulomb. This is simply a fixed number of electrons. In fact 1 coulomb is defined as an assemblage of 6.24 x 10^18 electrons and is assigned the symbol C.

Third... the ampere. The ampere is charge in motion and which constitutes electrical current. One "ampere" is defined as 1 coulomb moving past a point in 1 second and enjoys the electrical symbol "I". In the sciences, something per time is known as a "rate" so electrical current... charge in motion... is an example of rate. Other examples are miles/hour, feet/second, apples/minute, coulombs/second, speed, etc.

So, there you have it... a coulomb, with symbol C, is just a known quantity of charge... in a bag for example... and electrical current is just a known quantity of charge moving past a fixed point. A coulomb sitting around doing nothing is electrostatic charge whereas a coulomb marching down a wire is electrodynamic charge and which is the same as electrical current and is measured in amperes.

This concludes the review of charge, moving charge known as electrical current, and the definition of the ampere.

Let's move on to the notion of voltage.

First we need to understand a few things about "work". If you have a box on the floor next to a table and you pick up that box and place on a table then you have done some work. You have moved a box vertically through a gravitational field to do this work. If the box had been in the basement and you moved it to the upstairs table then you would have done more work than just moving it from the upstairs floor to the table. Had you been on the Moon and done the same box moving exercise over the same distances then you would have done less work since the Moon's gravitational field is not as strong as the Earth's. Had you used a lighter box, then you would have done less work on either the Moon or Earth. So, apparently, the amount of work done seems to be related to the "heaviness" of the box, the strength of the gravitational field, and the distance moved.

Now, suppose the box falls from the table to the floor. If you did some work moving the box from floor to table then the box must have also done some work moving from table to floor. In effect the falling box reversed your previous work effort. Apparently the box had some "potential" for doing work while sitting on the table. In like fashion, while sitting on the floor, the box has some potential to fall to the basement. The box actually has the potential to fall to the center of the Earth.

Now we have the ability to define how much work is done in these circumstances. The work you do in moving the box from floor to table is the difference in the two potentials of box on floor and box on table. This is a sneaky way of introducing the notion of potential difference which we can relate directly to voltage potential difference in later segments of this series. Let me just state that "work" and energy are identically the same. We will soon find out that moving electric charge, also known as electrical current, behaves pretty much the same in an electric field as does the moving box in a gravitational field and that voltage is really a measure of electrical potential difference or the ability to do some work.

This concludes the introduction to the concept of voltage. We will develop this voltage notion further and offer a formal definition in the next segment of this series.