## Tuesday, June 17, 2008

### IMPEDANCE SERIES PART 4, Lee week 5

June 18, 2008 Educational Radio Net, PSRG 5th session

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 fundamental ideas verbally.

This session is the 4th in the impedance series. Given that impedance is the combination of reactance and resistance and, further, that reactance is an alternating current phenomenon it is clear that we must have some elemental definitions under our belts to fully appreciate the subject. This multi-part series is an attempt to elevate participants, in narrative fashion, to an intuitive level of electrical understanding without using any serious mathematics.

In part 1, I developed the idea of electrical current consisting of moving charge and defined the ampere as 1 coulomb of charge moving past a fixed point in 1 second. One coulomb was defined as a collection of charge numbering 6.24 x 10^18 electrons.

In part 2, I continued with the notion of mechanical "work" and considered objects at different "potential" levels in a gravitational field. The concept of "voltage", also known as electrical potential difference, and the relationship of voltage to current follows closely with the idea of a mechanical weight being moved between different levels. In both cases work is being done and energy is being manipulated in various ways.

In part 3, I capitalized on Bob’s lightning series to review electrical current in the context of a charged cloud redistributing charge in the form of lightning where modest amounts of charge make a large impression if moved rapidly.

In part 4, this edition, I will return to the notion of potential difference and end with a definition of voltage.

Where are we going with these discussions you might ask? Once we have the notions of electrical current and voltage well in hand I will introduce the notion of "power" in both the mechanical and electrical context. After the power discussion I will introduce the physical property of materials called resistance and then merge the voltage, current, and resistance trio into the workhorse notion of Ohm’s Law. Subsequent parts of the series will introduce AC, or alternating current, and DC, or direct current, followed by capacitance and inductance, then reactance, and, finally, I will introduce impedance as the combination of resistance and reactance. All discussion material will be reviewed continually and be available on the blog.

So… let’s take a look at the notion of electrical potential difference. Remember in part 2 we talked about a box on the floor and considered the mechanical work involved in moving the box from the floor to a table top . In this example the Earth’s gravitational field resisted the elevation change of the box. Recall that the box, if falling from the table top to floor, simply gave up the work done when initially moved from floor to table top. Additionally, while on the floor the box had some potential to fall into the basement. So, clearly, one could measure the difference in potential work required in moving between basement and floor and table top. Given that work and energy are identically the same we can make the claim that the energy stored as a result of the box moving from floor to table top is just the difference in potential energy (or work) between these two levels. What are the units of energy? In the physical sciences the common term used is joule. Less common is the erg. Watt-hour meters also measure energy and are commonly found at the electrical entrance to your home. In subsequent parts of this series we will discuss the relationship between energy, power, and time in detail.

You will not be surprised to learn that charge in an electric field behaves much like a box in a gravitational field. Electric fields are produced by charge separation. For example, the lightning associated cloud, or charge separated cloud, in proximity to the Earth’s surface creates a very significant electric field with respect to the Earth's surface. The bottom line is that charge in an electric field gets pushed around. One of the early investigators of these sort of phenomenon was a fellow by the name of Coulomb and the assemblage of charge in the amount of 6.24 x 10^18 electrons bears his name. Coulomb studied the force of attraction or repulsion between two charges and formulated the equation known as Coulomb’s Law which shows the force to be directly related to the charge magnitudes and inversely related to the separation distance squared. Coulomb’s Law is very similar to the universal gravitational law wherein the attraction force is directly related to the objects mass and inversely related to the separation distance squared. In both laws the force drops off very rapidly with separation distance.

Now, let’s consider charge in an electric field. Suppose the field is directed to the right as in points to the right. A positive charge… also know as "conventional" charge… in this field will move in the direction of this field or to the right. If you choose to push the charge in the opposite direction then you must supply energy or, in mechanical terms, do work on the charge to make it move. Now we can define the volt in terms of the work done in moving charge from point A to point B. If you move 1 coulomb of charge in an electric field such that 1 joule of work is done then the potential difference between points A and B is defined as 1 volt. Another way to state this is that 1 joule is required to push 1 coulomb through a potential difference of 1 volt.

Let’s look at the practical ramifications of this definition. Take a D cell for example where common knowledge says that the available voltage is 1.5 volts. Placing both voltmeter probes on the positive terminal shows zero volts or no potential for doing any work. However, placing one probe on the positive terminal and the other on the negative terminal shows 1.5 volt difference and indicates that the battery can do some work. The battery potential difference of 1.5 volts can push some charge through an external circuit and do some useful work. A D cell can do more work than a AA cell since there is more active material available inside the battery to maintain the terminal voltage.

In summary, gravitational fields and electrical fields behave much the same mathematically. In both cases work is done when moving objects against these fields. Relative or "net" work is the difference in potential work at different locations. Net work in the amount of 1 joule is required to move 1 coulomb through a potential difference of 1 volt.

This concludes the set up discussion of electrical potential difference or more simply voltage. Are there any questions related to the concept of voltage?

Chris Altwegg said...

Don't know if this is relevant to the core discussion, but I'm reading an article about building a 6-meter Yagi and it says I need a 1:1 balun to connect the driven element to the coax feedline. Can't say I really understand the balanced-unbalanced theory entirely, but I'm willing to take it on faith for the time being. I researching baluns online, I ran across this explanation on the Array Solutions website:

A balun's purpose is to allow connecting a BALanced load (e.g., a dipole or driven element) to an UNbalanced line, thus the name. In transmitting antennas, this is accomplished by presenting a high impedance to RF currents flowing outside the coax shield. This forces currents in each side of a driven element to be equal. This is especially important in beam antennas because it prevents distortion of the beam's pattern caused by unequal currents in the driver(s). In a simple dipole, the balun assures that the dipole, and not the feed line, is doing the radiating.

That all makes sense to me, but my question is how RF currents get onto the outside shield in the first place if the center conductor is the full meal deal?

Chris - K7BRK
chris.altwegg@gmail.com

Anonymous said...

Hi Chris-
If you were to connect your unbalanced (to ground) coaxial line directly to the balanced dipole driven element such that the coax center conductor attached directly to one pole of the dipole and the coax braid attached directly to the other pole then you have fashioned what is called a "cobra head" connection. Current to pole from coax center conductor has only one way to go however current from coax inside braid can divide with a part of it going to the pole and part of it traveling back down the outside of the coaxial feedline since, from the shield feedpoint conection, this looks like a parallel circuit. The simple choke balun is not really a true balun device rather just prevents the outside coax branch current from using the entire feedline. Needs to mounted close to antenna to be effective. For a monobander a better choice would be the coaxial 1:1 balun where one leg is lambda/4 and the other 3/4 lamba. The lambda/4 in each leg is the isolating element and the extra lambda/2 on one leg provides the 180 deg phase reversal which makes the assembly look like a transformer to drive the dipole properly. Hope this helps. Lee

Anonymous said...

Correct me if I'm wrong, but...

Due to the skin effect, it seems that the current on the inside and outside of the coax shield are largely independent.

Because of this, we can imagine the shield as two wires---the inside and the outside---and the place where the shield meets the antenna as a junction of three wires: the two for the coax shield plus the antenna itself. When current flows from the inside of the coax shield, some will flow into the antenna, and some will flow back along the outside of the coax. This causes (at least) two problems: the coax will start to radiate; and the leg of the antenna to which it is connected will recieve less power, causing a distorted radiation pattern.

As Lee says, a choke balun prevents current from flowing on the outside of the coax, essentially making it look like an open circuit to RF. With this in place, the current cannot flow back along the outside of the coax, and so it goes into the antenna where it belongs.

Do my reasoning and explanation make any sense?

Cheers,
-Isaac (K7IKK)

Chris Altwegg said...

Thanks, Lee and Isaac, for your responses. It's more clear now thanks to your information. The article I was reading is in the June 2008 issue of Popular Communications. The author wanted to build an emergency quick 6-meter antenna and used the OWA (Optimized Wideband Antenna Yagi concept. In the article, he used a Cal-AV Labs model EB-2 balun.

Thanks again for responses and information. Might just have to try my hand at building one of these things.

Chris - K7BRK

Anonymous said...

Hi Issac & Chris-
Issac, you are perfectly correct in my view. Source current arriving at the junction of antenna monopole and coax braid will divide between the two path choices available. The net impedance of any parallel network is less than the smallest Z. Hence, force the outside braid Z to be very high and then the monopole Z looks much like its twin brother and antenna action proceeds normally. Actually, slightly more complicated since the inherent mismatch between coax Z and dipole Z produces reflected energy which also must divide between inside and outside shield. Chole baluns are brute force but can be wide band... coaxial baluns are more elegant and provide no path for stray currents however limited bandwidth since must be tuned by length. Very pleased that you guys are active in this net. Regrets here that you are, apparently, in the minority.
Lee