## Tuesday, July 29, 2008

### IMPEDANCE SERIES PART 9, Lee week 10

July 30, 2008 Educational Radio Net, PSRG 10th session

This session is the 9th 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 narrative series is an attempt to elevate participants to an intuitive level of electrical understanding without using any serious mathematics as well as provide some review for those of us who have not spent a lot of time on fundamentals lately.

Thus far we have talked about electrical current, voltage, power, resistance, Ohm's Law, DC or direct current, and AC or alternating current. Subsequent parts of the series will introduce capacitance, inductance, then reactance, and, finally, impedance as the combination of resistance and reactance. All discussion material will be reviewed continually and be available on the blog.

Let's review what has been covered up to this point in the series.

Part 1 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.

Part 2 developed 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.

Part 3 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.

Part 4 developed the notion of potential difference and ended with a definition of voltage. If you move 1 coulomb of charge from point A to point B 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 of energy is required to push 1 coulomb through a potential difference of 1 volt.

Part 5 developed the notion of power by using a mechanical analogy. Power is the relationship between energy and time. Specifically power is the change in energy as in work done divided by the change in time to do the work. Conversely, energy is power multiplied by time.

Part 6 developed the notion of resistance by using a simple circuit to compare how well various materials conduct electrical current. We looked at a simple series circuit with fixed voltage, one D cell battery, a fuse, an ammeter, a switch, and a pair of DUT terminals as in Device Under Test. Substituting various materials across the DUT terminals yielded different measurements on the ammeter and we ranked these materials based upon their "conductance". Finally, we learned that resistance and conductance are reciprocals and that high conductance equals low resistance and vice versa.

Part 7 developed the notion of Ohm's Law by using a simple series circuit to illustrate the relationship of voltage, current, and resistance. Ohm's Law states that electrical current through a resistive device is directly proportional to the voltage across the device so, for example, doubling the voltage across the device will double the current through the device. This relationship stated in math terms is I (which is the symbol for current) equals E (the symbol for voltage) divided by R (the symbol for resistance).

Part 8 developed the notion of direct current and alternating current by using a sand filled tube with a scribed fiducial mark. By assuming that the sand particles represented electrons we could watch the action at the mark and deduce if the current, or moving electrons, was AC or DC.

Part 9, tonight's edition, will again contrast direct current and alternating current by measuring the temperature of a resistor with a suitable thermometer and then forming conclusions from observed data.

Ok, on with the heating effect of direct current and alternating current.

We will revert to our simple series circuit to study resistive heating or what is also known as joule or Johnson heating. Let me assert that electrical energy delivered to a resistive circuit by battery or power supply ultimately ends up dissipated as heat energy when all is said and done. As everyone knows heat energy can be measured with a thermometer. Let's select a 100 ohm resistor with a heat dissipation rating of 2 watts. Now attach a thermometer to this resistor in such a fashion that we can collect accurate readings of the resistor temperature. The thermometer could be liquid in glass or, perhaps, a thermocouple device. Remembering that our simple circuit consists of a variable voltage power supply, fuse, ammeter, switch, DUT terminals, and now a voltmeter in the form of a calibrated oscilloscope across the DUT terminals. Let's attach the resistor with associated thermometer device across the DUT terminals. So, we have a fixed 100 ohm resistor attached to the DUT terminals and the switch is off.

Now adjust the variable power supply voltage to +10 volts DC and move the switch to on. Note that the voltmeter in the form of an oscilloscope trace moves upscale to the +10 volt line. Ohm's Law reigns supreme here so we predict that 10 volts DC divided by 100 ohms equals 1/10 ampere or 100 milliamperes. Sure enough the simple circuit ammeter indicates 100 ma. Taking a look at the thermometer we see the resistor temperature rising from room temperature to a much higher value. After a few moments the resistor temperature comes to equilibrium and the thermometer reading is steady. At this point we log the temperature reading and the oscilloscope voltage reading and compute the actual energy dissipation in the resistor by applying Joule's Law wherein we square the current and multiply by the resistor value. So, 1/10 ampere squared times 100 ohms is 1 watt. Our resistor will not burn up since we selected a resistor rated at 2 watts dissipation initially. From this bit of circuit work we conclude that a constant DC voltage will cause the test resistor to heat up to some temperature value and stay at that value as long as the constant voltage is applied to the circuit.

Now, turn the switch off and let the resistor cool down to room temperature. We will make a simple change to our circuit by replacing the DC power supply with a variable voltage AC supply which produces a sine wave output. After the change is made we repeat the above measurements using the variable voltage AC supply. We start with the AC voltage set to zero. Turn the switch on and we notice that nothing happens and the ammeter indicates zero current, the oscilloscope voltmeter shows zero volts, and the thermometer on the resistor indicates room temperature.

Now we advance the AC power supply voltage control such that the peak of the sine wave just touches the +10 volt line on the oscilloscope and things start to happen. The thermometer moves upscale and quickly comes to equilibrium but the indicated temperature is much lower than the reading obtained in the previous DC voltage exercise and the ammeter only shows 70.7 milliamperes. Clearly something is going on here so we slowly advance the voltage control and notice that the resistor temperature continues to rise. Eventually we find the point where the resistor temperature is identical to that which we measured in the earlier DC voltage exercise. Looking at the scope we notice that the peak voltage is 14.14 volts and the ammeter indicates 100 milliamperes.

In terms of the heating capacity we must conclude that 10 volts DC and 14.14 volts peak AC will heat the resistor to the same temperature hence perform the same amount of work. So how do we process the AC voltage sine wave to account for the difference between DC and AC? There is a math process called root mean square, or more definitive, root of the sum of the means squared and, if you apply this process to the 14.14 peak voltage waveform, the answer turns out to be 10 volts rms. So, 10 volts rms in the AC world is the heating equivalent to 10 volts in the DC world. This is only true for AC sine waves. Other waveforms require special treatment to determine equivalency. Fortunately most naturally oscillating voltage sources are sine wave so it is a simple matter to determine the RMS value. Identical DC and AC rms voltages will behave exactly the same with regard to Ohm's Law. Peak AC sine wave voltage times 0.7070 will yield the rms voltage every time.

In summary, if the AC voltage waveform is a sine wave then the rms voltage of that waveform will produce the same heating effect as a DC voltage of the same magnitude. AC rms is AC peak times 0.7070. Most meters, V-O-M or volt/ohm/milliammeter for instance, are calibrated assuming that the waveform being measured is sinusoidal. There are special true rms meters which will measure any complex non-sinusoidal waveform and report correct rms values.

This concludes the set up discussion of AC rms volts vs DC volts. Are there any questions or comments?

Now I have a challenge question for those interested. This question is intended to demonstrate scale. We have been using a coulomb of sand to represent a coulomb of electrons. We know that a coulomb is 6.24 x 10^18 electrons. Given that a cubic centimeter of sand contains about 3000 sand particles figure out how many cubic centimeters would be required to contain 6.24 x 10^18 sand particles. Secondly, express the answer in the number of cubic yards to contain 6.24 x 10^18 particles, and, thirdly, express the answer in the number of cubic miles required to contain this number of particles. What does this tell you about the real size of the electron?

Given, everything you need to know:
One cc of sand contains 3000 particles (more or less depending on sand particle size but we will assume this to be the average)
one coulomb contains 6.24 x 10^18 particles
one inch = 2.54 centimeters
one yard = 36 inches
one mile = 5280 feet

This is N7KC for the Wednesday night Educational Radio Net

### Balanced and Unbalanced Line, and Baluns (Bob, Week 10)

In this week's installment of the ongoing Antenna series we will take a slight detour away from antennas to discuss Balanced vs. Unbalanced Feedlines and Baluns.

Let's briefly review the two types of antennas we have discussed so far.
• The first is the dipole which you will recall is two equal length lines going out in opposite directions from a central feed point. This antenna is an inherently balanced antenna.
• The other type of antenna we discussed is the ground-plane antenna. It is a single line leading away from the center feed point perpendicular to a plane created by a solid conductor or evenly spaced radials. It is an inherently unbalanced antenna.
There are also two main types of feedlines in use in amateur radio.
• Open-wire lines consist of two conductors (wires) kept running in parallel. This is an inherently balanced feedline. It is important to keep the distance between the two lines constant. Other names for this line are parallel-conductor and open-wire. The common types of open-wire line are Twin-lead, window-line and ladder-line.
• Coax cable consists of a central conductor (wire) surrounded by a conductive tube (shield). This is an inherently unbalanced feedline. Like the open-wire line, it is important to keep the tube at a constant distance away from the center conductor by keeping the center conductor exactly in the center.
So, why are these so popular anyway? To answer that we need to know what we want the feedline to do. It may seem obvious but let's talk about it anyway. We want the feedline to efficiently transfer the power from our transceiver to our antenna without changing the signal and without itself becoming an antenna. Any time you send RF signals down a long wire it will radiate. One of the benefits of these feedlines is that they minimize radiation from the line itself but they do it in very different ways.

The open-wire line achieves a low level of radiation because the current flow in the two wires is in opposite directions with equal magnitude or strength. The fields created by the currents along each line are equal and opposite and thus cancel each other. Now they don't cancel completely, even in a theoretically perfect open-wire line. That is because of the separation between the two lines. In order for the fields to cancel perfectly there would have to be no distance between the two lines, in other words, the lines would have to occupy the same space. In practice, what's important is that the distance between the lines should be very small compared to a wavelength. The ARRL Antenna book puts 1% of a wavelength as a maximum and says, "smaller separations are desirable." Several other factors go into the design of good open-wire line but I'm not prepared to go into them yet.

The coax cable achieves a low level of radiation in a very different way. With the coax, the current flows in one direction through the center conductor and the other direction in the conducting tube or shield. A crucial fact of this type of feedline is that due to skin effects, the current flowing "in" the shield, actually flows on the inside surface. In a theoretically perfect coax cable there is no current flow on the outside of the shield and none of the field on the inside penetrates the shield. So the theoretically perfect coax cable does not radiate at all. As with open-wire antennas, there are many factors that go into making a good coax cable and I won't be going into them tonight.

Generally speaking, balanced feedlines work well with balanced antennas and unbalanced feedlines work well with unbalanced antennas as long as the impedance is matched reasonably well. Things get interesting when you try to connect an unbalanced coax to a balanced dipole.

When you connect the coax to the dipole you have the center conductor connected to one side of the dipole and the shield connected to the other. The mismatch between the balanced and unbalanced elements causes a secondary current to flow on the outside of the coax. This secondary current is called common-mode current. This does two undesirable things, it changes the current flow in one half of the dipole, changing it's radiation pattern and even worse, it turns the coax shield into a radiating antenna itself! You may have already guessed how we solve this problem. Enter the balun.

The entire purpose of the balun is to eliminate common mode current. If you do that you will end up with a perfectly balanced signal. So how do you accomplish this? The answer to this would be very simple except that I have jumped ahead of Lee's series on impedance. So let's make this a teaser for his upcoming segments. The way to stop a radio frequency AC current on the outside of the coax is to create a high inductive reactance. After a few more weeks with Lee you will know what inductive reactance is but I will just say that it is a resistance to current flow that makes the current flow more difficult, the higher the frequency becomes. The important thing to note is that we are putting this inductive reactance on the outside of the coax so it will only stop the flow of the current on the outside of the shield which we don't want. It won't affect the normal flow of current on the center conductor and the inside of the conductor. A simple and effective way to make your own balun is to simply coil a few loops of coax near where it connects to the antenna. Of course you can also buy a balun which will do essentially the same job in a more compact space. Another benefit of the store-bought balun, assuming it is a good one is that it will be designed well to do it's job and not have undesirable side affects over a wide frequency spectrum. It is certainly possible to achieve that yourself with a homemade loop but you must take some care in the construction.

## Wednesday, July 23, 2008

### IMPEDANCE SERIES PART 8, Lee week 9

July 23, 2008 Educational Radio Net, PSRG 9th session

This session is the 8th 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 belt to fully appreciate the subject. This multi-part narrative series is an attempt to elevate participants to an intuitive level of electrical understanding without using any serious mathematics as well as provide some review for those of us who have not spent a lot of time on fundamentals lately.

Where are we going with these discussions? So far we have talked about electrical current, voltage, power, resistance, and Ohm's Law. Subsequent parts of the series will introduce DC, or direct current, AC, or alternating current, and 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.

Let's review what has been covered up to this point in the series.

Part 1 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.

Part 2 developed 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.

Part 3 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.

Part 4 developed the notion of potential difference and ended with a definition of voltage. If you move 1 coulomb of charge from point A to point B 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 of energy is required to push 1 coulomb through a potential difference of 1 volt.

Part 5 developed the notion of power by using a mechanical analogy. Power is the relationship between energy and time. Specifically power is the change in energy as in work done divided by the change in time to do the work. Conversely, energy is power multiplied by time.

Part 6 developed the notion of resistance by using a simple circuit to compare how well various materials conduct electrical current. We looked at a simple series circuit with fixed voltage, one D cell battery, a fuse, an ammeter, a switch, and a pair of DUT terminals as in Device Under Test. Substituting various materials across the DUT terminals yielded different measurements on the ammeter and we ranked these materials based upon their "conductance". Finally, we learned that resistance and conductance are reciprocals and that high conductance equals low resistance and vice versa.

Part 7, developed the notion of Ohm's Law by using a simple series circuit to illustrate the relationship of voltage, current, and resistance. Ohm's Law states that electrical current through a resistive device is directly proportional to the voltage across the device so, for example, doubling the voltage across the device will double the current through the device. This relationship stated in math terms is I (which is the symbol for current) equals E (the symbol for voltage) divided by R (the symbol for resistance).

Part 8, tonight's edition, will contrast direct current and alternating current.

Ok, on with direct current and alternating current.

To illustrate the difference between DC and AC think of a clear vinyl tube about 1 foot long and which is filled with sand. About half way down the tube we scribe a "line" across the tube perpendicular to the long axis of the tube. So, we can look at the tube and see the relationship of sand to the scribed line. Assume that particles of sand represent electrons which are free to move if influenced by some motive force such as voltage.

Let's attach a source of voltage, or motive force, across the tube ends by using a battery. Watching the scribed line we notice that the electrons as represented by the sand particles always move slowly to the right (or left if the battery were reversed) with respect to the line. Given that sand represents electrons, or current, this constant motion represents direct current or DC. We know that the number of sand grains in the vicinity of the scribed line is huge. Suppose that we identify 6.24 x 10^18 grains of sand and call the assemblage a coulomb of sand. If our coulomb of sand moves past the scribed line in exactly one second then we can say that one ampere of sand is moving in the tube. Note that the current does not "zip" down the tube quickly from end to end rather the sand "drifts" down the tube and we get our ampere because lots of sand is drifting past the scribed line every second. As long as motive force, in this case a fixed voltage, is applied to the tube ends the sand, or current, continues to move in one direction.

Suppose that we have a second scribed sand tube identical to the first. Suppose further that we have no idea what is connected to the ends of the tube. Looking at the scribed line we notice that sand is drifting to the right, stopping, then reversing its motion to the left, then stopping, then reversing motion to the right. Back and forth with respect to the scribed line in a very regular manner. By carefully counting grains of sand we notice that a coulomb of sand moves to the right past the scribed line in one second then reverses and moves to the left of the line in the next second. We are watching an ampere of alternating sand if you please. Remember from the DC example above that reversing the battery caused the sand to reverse direction. Watching the sand reverse direction regularly suggests that the voltage at the tube ends is reversing regularly as well. Since the sand represents electrical current we are watching alternating current or AC. The sand motion is caused by the motive force at the tube ends so alternating current or AC is caused by an alternating motive force or alternating voltage.

Simple enough but there is a gray area here. Direct current sand may speed up, slow down, or stop completely but the direction never changes. Suppose that the sand mostly goes to the right but on occasion stops and moves a bit to the left then continues on to the right. This would be an example of superimposed AC and DC. If the AC component peak is less than the DC value then the mix of the two will look like unidirectional DC. True AC is generally considered to be periodic and could be produced by a square wave voltage or a sine wave shaped voltage which is symmetric about the zero voltage axis.

If a circuit contains only resistance then Ohm's Law works equally well for both AC and DC. The R for resistance and the Z for impedance are interchangeable. The entire point of this series is to show that impedance is resistance combined with reactance. Reactance is an AC phenomenon hence goes away in the steady state DC world rendering resistance and impedance identically the same.

Next week we will talk about the heating effects of AC vs DC and talk about equivalent waveforms including how various values are calculated.

This concludes the set up discussion of AC vs DC. Are there any questions or comments?
This is N7KC for the Wednesday night Educational Radio Net.

## Wednesday, July 16, 2008

### IMPEDANCE SERIES PART 7, Lee week 8

July 16, 2008 Educational Radio Net, PSRG 8th session

Much like any radio talk show I will "set up" the topic and then allow time at the end for questions or comments. In reality most fundamental ideas in electronics and radio are best described mathematically 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 7th 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 narrative series is an attempt to elevate participants to an intuitive level of electrical understanding without using any serious mathematics as well as provide some review for those of us who have not spent a lot of time on fundamentals lately.

Where are we going with these discussions? Once we have the notions of electrical current, voltage, and power well in hand 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 DC, or direct current, AC, or alternating current, and 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.

Part 1 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.

Part 2 developed 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.

Part 3 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.

Part 4 developed the notion of potential difference and ended with a definition of voltage. If you move 1 coulomb of charge from point A to point B 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 of energy is required to push 1 coulomb through a potential difference of 1 volt.

Part 5 developed the notion of power by using a mechanical analogy. Power is the relationship between energy and time. Specifically power is the change in energy, known as delta P, divided by the change in time, known as delta t. Conversely, energy is power multiplied by time.

Part 6 developed the notion of resistance by using a simple circuit to compare how well various materials conduct electrical current. We looked at a simple series circuit with fixed voltage, one D cell battery, a fuse, an ammeter, a switch, and a pair of DUT terminals. Substituting various materials across the DUT terminals yielded different measurements on the ammeter and we ranked these materials based upon their "conductance". Finally, we learned that resistance and conductance are reciprocals and that high conductance equals low resistance and vice versa.

Part 7, tonight's edition, will deal with the relationship of voltage, current, and resistance in the context of Ohm's Law. We will use the same series circuit as last week but substitute a variable voltage supply for the fixed D battery and also include a voltmeter across the DUT terminals.

But first let's talk about a very interesting question which arose during last week's session.

Someone asked how one would count a coulomb of charge consisting of 6.24x10^18 electrons. Glen, K7GLE, offered an electrochemistry definition of the coulomb and, after due consideration, I think that it will be instructive to talk a little more about how a physical chemist might go about measuring a coulomb of charge using nothing more than a sensitive laboratory balance.

Let's start by thinking about a carbon atom. Looking at a periodic table one finds the atomic weight of carbon to be 12. Now, by definition, the gram molecular weight of carbon is 12 grams and is called a mole of carbon. Checking the periodic table again for silver we find the molecular weight to be 107.87 so one gram molecular weight of silver is 107.87 grams and is called a mole of silver. The interesting point is that both a mole of carbon and a mole of silver contain the same number of atoms. Early researchers worked long and hard to determine how many constituent "things" were in a mole and the number turned out to be approximately 6.022 x 10^23. So, bottom line, a mole always contains the same number of atoms and this number is known as Avagadro's number. I used carbon as the comparison element but, in fact, carbon is the defining element for this number.

Now, let's talk about electroplating with silver. Atomic (or metallic) silver is neutral but if atomic silver loses one electron then it becomes ionic silver and has a charge of +1. Ionic silver is very soluble in water whereas atomic silver is not. Imagine that we have a good, strong, solution of ionic silver and that we insert a couple of electrodes into our silver solution. If we connect a battery to the electrodes then one electrode will be positive (known as the anode) and the other negative (known as the cathode). Now, given that our silver ion has a positive charge of 1, the silver ion will be attracted to the negative cathode which has an abundance of electrons. When the silver ion touches the cathode then an electron is handed to the silver ion and it changes to metallic silver and is plated out on the cathode. As long as the battery is connected to the electrodes and until the solution is exhausted the silver ions plate out on the cathode. Clearly, as time progresses, the cathode will become heavier as more and more silver is transferred from solution to cathode.

If Avagadro's number of electrons, 6.022 x 10^23, were added to the ionic silver then we would plate out 107.87 grams of silver on the cathode. Remember that one ion of silver plus one electron produces one atom of metallic silver. However we are only interested in a coulomb of electrons so, given that there are fewer electrons in a coulomb than "objects" in Avagadro's number we will plate out less metallic silver. In fact, one needs about 96,506 coulombs of charge to equal Avagadro's number. So, dividing 107.87 grams by 96505 gives us the weight of silver per coulomb. The final number is 1.12 mg of metallic silver for every coulomb of charge added to the ionic solution.

So, a bit of cleverness plus a sensitive balance will change the problem from the difficult counting of individual electrons to a much easier weighing of a cathodic electrode.

Note also that if 1.12 mg of silver were deposited every second then we could conclude that the battery plating current is one ampere as in one coulomb per second.

Any questions or comments on this alternate method of measuring charge?

Ok, on with Ohm's Law which deals with the relationship of voltage, current, and resistance.

Let's modify last week's series circuit with which we looked at resistance by changing the D battery to a variable voltage DC power supply and adding a voltmeter across the DUT or "device under test" terminals. Still a simple series circuit but now we have some control over circuit voltage and we can now measure voltage. So, from power supply positive we go to a fuse, then a switch, then an ammeter, then DUT terminals and back to the power supply negative terminal. Finally we add the voltmeter to the DUT terminals.

Now, after poking through a drawer of parts, we find a carbon resistor with the value 1000 ohms marked on it. If you are able to read the color code it would be brown, black, red.

Let's attach this one k-ohm resistor to the DUT terminals, set the supply voltage to 10 volts DC, and flip the switch to on. The ammeter moves upscale to 0.01 amperes or 10 milliamperes. Now double the voltage to 20 volts and the ammeter reads 0.02 amperes or 20 milliamperes. Halving the initial voltage to 5 volts causes the ammeter to drop to 0.005 amperes or 5 milliamperes. Regardless of what values you assign to the supply voltage or DUT resistance you will find that the circuit current is directly proportional to the voltage and inversely proportional to the circuit resistance. In other words higher voltage across a given resistance yields higher current and higher resistance with the same voltage yields less circuit current. This is a straight line curve if plotted and the effect is said to be linear.

The bottom line is this... current is voltage divided by resistance. Double the voltage and double the current... double the resistance and halve the current. That is Ohm's Law in a nutshell.

This concludes the set up discussion of Ohm's Law. Are there any questions or comments?

## Tuesday, July 8, 2008

### IMPEDANCE SERIES PART 6, Lee week 7

July 9, 2008 Educational Radio Net, PSRG 7th session

Much like any radio talk show I will "set up" the topic and then allow time at the end for questions or comments. In reality most fundamental ideas in electronics and radio are best described mathematically 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 6th 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 narrative series is an attempt to elevate participants to an intuitive level of electrical understanding without using any serious mathematics as well as provide some review for those of us who have not spent a lot of time on fundamentals lately.

Where are we going with these discussions you might ask? Once we have the notions of electrical current, voltage, and power well in hand 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.

Part 1 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.

Part 2 developed 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.

Part 3 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.

Part 4 developed the notion of potential difference and ended with a definition of voltage. If you move 1 coulomb of charge from point A to point B 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 of energy is required to push 1 coulomb through a potential difference of 1 volt.

Part 5 developed the notion of power by using a mechanical analogy. Power is the relationship between energy and time. Specifically power is the change in energy, known as delta P, divided by the change in time, known as delta t. Conversely, energy is power multiplied by time.

Part 6, tonight's edition, will deal with the notion of resistance.

Ok, on with the notion of electrical resistance.

Let's design a scheme to study the behavior of moving current. Suppose we use a standard D battery, a simple on/off switch, a fuse, and a pair of terminals to fabricate our "circuit" and also include some means of measuring current such as an ammeter. Let's wire the components in series which means that the various components are daisy chained in a ring. So, the positive terminal of the battery goes to one terminal of the fuse and the other fuse terminal goes to one side of the ammeter. The second terminal of the ammeter goes to one side of the switch and the other side of the switch goes to one of the DUT terminals. DUT is short for "device under test". The second DUT terminal returns to the battery negative terminal. Now we have a series circuit such that we can connect "something" to the DUT terminals and measure moving charge, or electrical current, with a meter. The fuse is the safety valve should something go horribly wrong.

The first interesting thing to note is that without anything connected to the DUT terminals the ammeter shows nothing regardless of on/off switch position. So, an "open" series circuit will pass no current. The second interesting thing of note is that connecting a heavy metal object, for example a spoon, across the DUT terminals and closing the switch will blow the fuse. So, a "short" in this circuit will pass so much current that the protective device is activated. We are interested in connecting objects to the DUT terminals which are not open or short from the viewpoint of the series circuit.

Let's assemble some candidates to study with our series circuit. First we have a piece of plastic that will fit across the DUT terminals. Next we have a piece of very fine wire about a foot long. Finally, we have a piece of what appears to be charcoal that will also fit across the DUT terminals.

With the circuit in front of us let's place the piece of plastic across the DUT terminals and throw the switch to on. The ammeter shows no deflection so we conclude that no current moved through the plastic. Let's try the charcoal next. Repeating the above procedure we find that some current does flow since the ammeter moves a bit upscale. Finally using the wire across the DUT terminals and repeating the procedure we see the ammeter needle move much higher upscale than the previous two readings. Clearly there is a difference in the amount of current that each substance will pass when each is substituted in the identical circuit. We can say that the plastic "conducts" nothing, that the wire conducts very well, and that the charcoal lies someplace in between the two.

We have just demonstrated relative conductivity in a very simple fashion. Relative to charcoal the plastic has low to no conductivity. Relative to charcoal the wire has high conductivity. Relative to the wire both charcoal and plastic have low conductivity.

In the case of the wire with high conductivity we can say that the "resistance" to electrical current flow is low. In the case of the plastic with low conductivity we can say that the resistance to electrical current flow is high. So high, in fact, that it is in a class of material called insulators. Clearly various materials differ in their conductivity hence resistance. Metals tend to be very good conductors with silver being the best followed closely by gold. Carbon is a popular resistance material and most inexpensive resistors are made of carbon. Deposited metal film resistors are more expensive than carbon and tend to be less affected by temperature variations.

Resistance is a physical property of materials. Resistance does not magically pop up in the presence of an electric field rather it is related to the population of free electrons in the material or the ease of producing free electrons if subjected to an electric field. Low conductance is analogous to high resistance and vice versa. In fact, conductance and resistance are reciprocals and their product equals one. Resistance is measured in ohms whereas conductance is measured in mho's or ohm's spelled backwards.

We now have enough information under our belts to move into the relationship of voltage, current, and resistance known as Ohm's Law and we will pursue that next session.

This concludes the set up discussion of electrical resistance. Are there any questions related to the concept of resistance?

This is N7KC for the Wednesday night Educational Radio Net.

## Wednesday, July 2, 2008

### IMPEDANCE SERIES PART 5, Lee week 6

July 2, 2008 Educational Radio Net, PSRG 6th session

Much like any radio talk show I will "set up" the topic and then allow time at the end for questions or comments. In reality most fundamental ideas in electronics and radio are best described mathematically 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 5th 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 narrative series is an attempt to elevate participants to an intuitive level of electrical understanding without using any serious mathematics as well as provide some review for those of us who have not spent a lot of time on fundamentals lately.

Where are we going with these discussions you might ask? Once we have the notions of electrical current, voltage, and power well in hand 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.

Part 1 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.

Part 2 developed 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.

Part 3 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.

Part 4 developed the notion of potential difference and ended with a definition of voltage. If you move 1 coulomb of charge from point A to point B 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 of energy is required to push 1 coulomb through a potential difference of 1 volt.

Part 5, tonight’s edition, will deal with the notion of power.

Ok, on with the idea of power.
Let’s first look at the mechanical side of the picture. Imagine a water tower and let’s say that it is 100 feet tall. There are two ways on this particular tower to get from the ground to the top. The first way is via a ladder from ground straight up the side of the tower to the top. The second way is via a spiral ladder from ground to the top of the tower. Let’s further say that the straight ladder has 100 rungs, or steps, from bottom to top and the spiral ladder has 300 steps from bottom to top. Now imagine identical twins and that both weigh exactly the same. One twin decides to use the vertical ladder to climb the tower and the other prefers the easier route so chooses the spiral staircase. Let’s say that both move along the respective ladders at 1 step per second. The twin traveling up the vertical ladder reaches the top in 100 seconds and the twin on the spiral ladder reaches the top in 300 seconds. Now the question arises… which twin performed the most work going from ground to tower top? Well, given that the twins weigh identically the same and that both traveled the same 100 feet vertically, the answer is that they did identical work to achieve the tower top. Since it took the vertical traveling twin 100 seconds to climb to the tower top and the spiral twin took 300 seconds to achieve the top it is clear that the spiral twin took 3 times longer to make his trip. From this we can conclude that the vertical twin performed the same work as the spiral twin in 1/3 the time so his power output was 3 times that of the spiral twin. The bottom line is that power is a measure of how quickly work is done.

Remember that work and energy are identically the same and that both are measured in units called "joules". So, regardless of whether we are dealing with mechanical or electrical phenomenon, power is the change of energy over time as in joules per second. The unit of power is the watt and one watt is defined as 1 joule per second. In DC, or direct current related phenomenon, electrical "power" is simply electrical current in amperes times potential difference in volts. If comparing a 100 watt transmitter to a 300 watt transmitter you can say that the more powerful 300 watt unit moves 3 times more energy to the antenna than the lesser power unit in the same amount of time. More energy in a given time translates to a stronger radiated field.

Power is power period. Audiophiles will be familiar with the term RMS power as in root mean squared power. There is no such thing in the physical world as RMS power. This is a cooked up term used by audio amplifier manufactures to rate their products. You can plot power as a function of time and then calculate the RMS value of the waveform but the number calculated has no relationship to anything in the real world. We have not talked about AC or alternating current and alternating voltage at this point but let me assert that, in the AC world, power is the product of RMS voltage and RMS current. Power is power is power. Simply the measure of energy changing with time.

Now, let’s consider the kilowatt-hour meter on the side of your house. If power is energy divided by time then it follows from algebra that energy is power times time. So the Kw-H or kilowatt-hour meter measures how much electrical energy you use in your home. At this point in time residential home owners only pay for total energy consumed in the home. Industrial meters also measure what is called "demand" or how fast energy is delivered hence "power" as well as total energy used.

This concludes the set up discussion of power, both electrical and mechanical.. Are there any questions related to the concept of power?

This is N7KC for the Wednesday night Educational Radio Net.