A new way to teach Ohm’s Law?

I’ve been trying to come up with some short videos that I could post on YouTube that would go over the same material that I do in my one-day Tech classes. In my classes, I basically teach the answers to the questions, but I also try to give a little bit of context, so that they get some idea anyway of the bigger picture.

I start out with the day with electrical principles. That means talking about questions in section T5. Obviously, Ohm’s Law is a big part of section T5. So, I searched YouTube to see what other videos are already out there that explain Ohm’s Law.

In doing this, I ran across a video by a guy named Daniel Sullivan. Apparently, he teaches classes for electricians and industrial technicians. Here’s his video, “Teaching Ohm’s Law to Techs – Part 1″:

One of his main points is that we shouldn’t use the notation E, I, and R when talking about Ohm’s Law. Instead, he says, we should use the notation V, A, and ?. These are, after all, the symbols that we use to denote the units of voltage, resistance, and current, and the symbols that  you see on a meter. If you buy that logic, then the answer to question T5D01 which reads:

What formula is used to calculate current in a circuit?

should be:

Current (A) equals voltage (V) divided by resistance (?).

The more I think about this, the more I like it, and I’ve just e-mailed the Question Pool Committee to see what they think about this. I’d like to know what you think, too.

From the trade magazines: capacitors, inductors, radio architectures

Temperature and voltage variation of ceramic capacitors. Read the data sheet! This tutorial explains how ceramic capacitor type designations, such as X7R and Y5V, imply nothing about voltage coefficients. You must check the data sheet to really know, how a specific capacitor will perform under temperature and voltage.

Circuit measures capacitance or inductance. You don’t need a fancy LC meter to measure capacitance or inductance. This short article show you how to do it with a function generator, multimeter, frequency counter, and an oscilloscope. Hmmmmm. By the time you get that all lashed up, it might have been quicker to just buy one of these LC meters from China.

Understand Radio Architectures. This is the first in a series of excerpts from the book RF Circuit Design, 2e by Christopher Bowick. Even though this appears in an engineering trade magazine, some of this is pretty basic stuff. You even get a schematic for a crystal radio!

From the trade magazines, impedance matching, EMI basics, open-source hardware

elelctronic-design-logoBack to Basics: Impedance Matching. electronic design editor (and amateur radio operator) Louis Frenzel is the author of this short e-book on impedance matching. Note: this e-book was intended for engineers and does use a fair amount of math, but nothing you can’t figure out if you work at it.

EMI Basics. This article  comes from the book Signal Integrity Issues and Printed Circuit Board Design by Douglas Brooks. I like the discussion of how twisted pair wire helps prevent radiation.

Interview With SparkFun’s Director Of Engineering. Peter Dokter is director of engineering for SparkFun, one of the major suppliers of open source hardware. SparkFun designs and sells things useful and interesting to the aspiring electronics tinkerer, including microcontroller boards, Bluetooth, GPS, Wi-Fi, LCD displays, e-textiles components, robots and robotic parts, motors, motor drivers, buttons and switches, tools, and books.

From the trade magazines, selecting crystals, understanding measurement uncertainty, Maxwell’s equations

Another selection of articles from the electronics engineering trade magazines……Dan

Selecting Crystals For Stable Oscillators
Understanding how quartz-crystal resonators operate can lead to designing crystal oscillators with improved stability and better noise performance.

Tutorial on Maxwell’s Equations
There’s a lot of math here, but cracking Maxwell’s equations will give you a lot of insight on how radio works. Registration required.

Understand Uncertainty For Better Test Accuracy
How sure are you of that measurement you just made with your multimeter or wattmeter? This article might open your eyes as to the accuracy of your measurements.


Extra Class question of the day: Smith Chart

NOTE: This is the last installment of the Extra Class question of the day. I’m going to be compiling all of these into the No-Nonsense Extra Class Study Guide. Watch for it real soon now.


Figure E9-3A Smith chart is shown in Figure E9-3 above. (E9G05) It is a chart designed to solve transmission line problems graphically. While a complete discussion of the theory behind the Smith Chart is outside the scope of this study guide, a good discussion of the Smith Chart can be found on the ARRL website.

The coordinate system is used in a Smith chart is comprised of resistance circles and reactance arcs. (E9G02) Resistance and reactance are the two families of circles and arcs that make up a Smith chart. (E9G04)

The resistance axis is the only straight line shown on the Smith chart shown in Figure E9-3. (E9G07) Points on this axis are pure resistances. In practice, you want to position the chart so that 0 ohms is at the far left, while infinity is at the far right.

The arcs on a Smith chart represent points with constant reactance. (E9G10) On the Smith chart, shown in Figure E9-3, the name for the large outer circle on which the reactance arcs terminate is the reactance axis. (E9G06) Points on the reactance axis have a resistance of 0 ohms. When oriented so that the resistance axis is horizontal, positive reactances are plotted above the resistance axis and negative reactances below.

The process of normalization with regard to a Smith chart refers to reassigning impedance values with regard to the prime center. (E9G08) The prime center is the point marked 1.0 on the resistance axis. If you’re working with a 50 ohm transmission line, you’d normally divide the impedances by 50, meaning that a 50 ohm resistance would then be plotted on the resistance axis at the point marked 1.0. A reactance of 50 + j100 would be plotted on the resistance circle going through the prime center where it intersects the reactance arc marked 2.0.

Impedance along transmission lines can be calculated using a Smith chart. (E9G01) Impedance and SWR values in transmission lines are often determined using a Smith chart. (E9G03) Standing-wave ratio circles are often added to a Smith chart during the process of solving problems. (E9G09)

The wavelength scales on a Smith chart calibrated in fractions of transmission line electrical wavelength. (E9G11) These are useful when trying to determine how long transmission lines must be when used to match a load to a transmitter.

Extra Class question of the day: Waveforms and measurements

An electromagnetic wave is a wave consisting of an electric field and a magnetic field oscillating at right angles to each other. (E8D07) Changing electric and magnetic fields propagate the energy is a phrase that best describes electromagnetic waves traveling in free space. (E8D08)

The polarization of an electromagnetic wave is related to the orientation of the wave’s electric field. If, for example, the electric field is oriented vertically, we say that the electromagnetic wave is vertically polarized. Waves with a rotating electric field are called circularly polarized electromagnetic waves.(E8D09)

Peak-to-peak voltage is the easiest voltage amplitude parameter to measure when viewing a pure sine wave signal on an analog oscilloscope. (E8D01) The relationship between the peak-to-peak voltage and the peak voltage amplitude of a symmetrical waveform is 2:1. (E8D02) Peak voltage is a valuable input-amplitude parameter for evaluating the signal-handling capability of a Class A amplifier.(E8D03)

For sinusoidal voltages, the peak voltage is 1.414 times the RMS voltage, and the peak-to-peak voltage is 2.828 times the RMS voltage. The peak voltage of a sinusoidal waveform would be 48 volts if an RMS-reading voltmeter reads 34 volts. (E8D12) If an RMS-reading AC voltmeter reads 65 volts on a sinusoidal waveform, the peak-to-peak voltage is 184 volts. (E8D05) 

120V AC is a typical value for the RMS voltage at a standard U.S. household electrical power outlet. (E8D15) 170 volts is a typical value for the peak voltage at a standard U.S. household electrical outlet. (E8D13) 340 volts is a typical value for the peak-to-peak voltage at a standard U.S. household electrical outlet. (E8D14) 120V AC is the RMS value of a 340-volt peak-to-peak pure sine wave. (E8D16)

The peak envelope power of a radio signal is equal to V2peak/2 x 1/R. Consequently, the PEP output of a transmitter that develops a peak voltage of 30 volts into a 50-ohm load is 9 watts. (E8D04)

Vpeak = 30 V, V2peak = 900 V2

PEP = 900 V2 / 2 x 50 = 9 W.

The average power of a radio signal is equal to V2RMS/R. The average power dissipated by a 50-ohm resistive load during one complete RF cycle having a peak voltage of 35 volts is 12.2 watts. (E8D11)

V2RMS = 35 V / 1.414 = 24.75V

V2RMS = 612 V2

Pavg = 612 V2 / 50 = 12.2 W.

Radio amateurs most often specify the output power of a single-sideband transmitter as peak envelope power and use a peak-reading wattmeter.  The advantage of using a peak-reading wattmeter to monitor the output of a SSB phone transmitter is that it gives a more accurate display of the PEP output when modulation is present. (E8D06) A peak-reading wattmeter should be used to monitor the output signal of a voice-modulated single-sideband transmitter to ensure you do not exceed the maximum allowable power. (E8D10)

Extra Class question of the day: More on coordinate systems

Admittance is the inverse of impedance. So, in polar coordinates, the impedance of a circuit that has an admittance of 7.09 millisiemens at 45 degrees is 141 ohms at an angle of -45 degrees. (E5C16) You calculate it this way:

|Z| = 1/7.09×10-3 = 141 ohms

The angle is the mirror image about the x axis:

θ = 0 – -45 degrees = 45 degrees

Let’s look at another example. In rectangular coordinates, the impedance of a circuit that has an admittance of 5 millisiemens at -30 degrees is 173 +j100 ohms. (E5C17)

|Z| = 1/5×10-3 = 200 ohms

θ = 0 – -30 degrees = 30 degrees

R = |Z| × cos 30 degrees = 200 × .866 = 173 ohms

X (the reactance part of the impedance) = |Z| × sin 30 degrees = 200 × .5 = +j100

Figure E5-2

Now, let’s take a look at some actual circuits.

On Figure E5-2, the point that best represents the impedance of a series circuit consisting of a 400 ohm resistor and a 38 picofarad capacitor at 14 MHz is Point 4. (E5C19) Right off the bat, we know that the only choices are really Points 2, 4, and 6 because the resistance is 400 ohms. Next, we calculate the capacitive reactance:

XC = 1/2πfC = 1/(2 × 3.14 × 14×106 × 38×10-12) ≈ 300 ohms

Because the reactance is capacitive, it’s plotted as a negative value.

On Figure E5-2, the point that best represents the impedance of a series circuit consisting of a 300 ohm resistor and an 18 microhenry inductor at 3.505 MHz is Point 3. (E5C20) The resistance is 300 ohms and the reactance is:

XL = 2πfL = 2 × 3.14 × 3.505×106 × 18×10-6) ≈ 400 ohms

And, since the reactance is inductive, it’s plotted as a postive value.

On Figure E5-2, the point that best represents the impedance of a series circuit consisting of a 300 ohm resistor and a 19 picofarad capacitor at 21.200 MHz is Point 1. (E5C21) The resistance is 300 ohms, and the reactance is:

XC = 1/2πfC = 1/(2 × 3.14 × 21.2×106 × 19×10-12) ≈ 400 ohms

Because the reactance is capacitive, it’s plotted as a negative value.

On Figure E5-2, the point that best represents the impedance of a series circuit consisting of a 300-ohm resistor, a 0.64-microhenry inductor and an 85-picofarad capacitor at 24.900 MHz is Point 8. (E5C23) This problem is a little tougher because it has both capacitive and inductive reactance.

XC = 1/2πfC = 1/(2 × 3.14 × 29.4×106 × 85×10-12) ≈ 63.7 ohms

XL = 2πfL = 2 × 3.14 × 29.4×106 × 0.64×10-6) ≈ 118.2 ohms

X = XL – XC = 118.2 – 63.7 = 55.5 ohms

Because the net reactance is inductive, it is plotted as a positive value, and because the resistance is 300 ohms, the answer is Point 8.

Extra Class question of the day: Filter types and applications

Different types of filters have different characteristics. For example, a Chebyshev filter is a filter type described as having ripple in the passband and a sharp cutoff. (E7C05)On the other hand, the distinguishing features of an elliptical filter are extremely sharp cutoff with one or more notches in the stop band. (E7C06)

Filters have both amplitude and phase-response characteristics. In some applications, both are important. Digital modes, for example, are most affected by non-linear phase response in a receiver IF filter. (E7C14)

The Chebyshev filter was named for Pafnuty Chebyshev, whose mathematical work led to the development of these filters. Sometimes filters are named for their circuit topoology. Pi is the common name for a filter network which is equivalent to two L networks connected back-to-back with the inductors in series and the capacitors in shunt at the input and output. (E7C11) When you look at the circuit diagram for a filter of this type, you’ll see that it looks like the Greek letter pi.

Often, you’ll choose a filter type for a particular application. For example, to attenuate an interfering carrier signal while receiving an SSB transmission, you would use a notch filter. (E7C07)

Today, many of these filters are implemented using digital signal processing. The kind of digital signal processing audio filter might be used to remove unwanted noise from a received SSB signal is an adaptive filter. (E7C08) The type of digital signal processing filter might be used to generate an SSB signal is a Hilbert-transform filter. (E7C09)

Some filters are used almost exclusively in a particular application. A cavity filter, for example, would be the best choice for use in a 2 meter repeater duplexer. (E7C10)

Extra Class question of the day: Impedance plots and coordinate systems

Rectulangar and Polar Coordinates

Most often when we plot values on a graph, we use the rectangular, or Cartesian, coordinate system. The two numbers that are used to define a point on a graph using rectangular coordinates are the coordinate values along the horizontal and vertical axes. (E5C11) In the graph above, point P is at x,y. Rectangular coordinates are often used to display the resistive, inductive, and/or capacitive reactance components of an impedance. (E5C13)

When thinking about how capacitive reactances, inductive reactances, and resistance combine, it’s useful to think in terms of polar coordinates. Polar coordinates are often used to display the phase angle of a circuit containing resistance, inductive and/or capacitive reactance. (E5C14) In a polar-coordinate system, each point on the graph has two values, a magnitude (shown by r in the figure above) and an angle (shown by θ in the figure above).

When using rectangular coordinates to graph the impedance of a circuit, the vertical axis represents the reactive component. (E5C10) To figure out the impedance of a circuit, you first plot the inductive reactance on the positive y-axis and the capacitive reactance on the negative y-axis. The net reactance, X, will be the sum of the two reactances.

When using rectangular coordinates to graph the impedance of a circuit, the horizontal axis represents the resistive component. (E5C09) After you’ve computed the net reactance, you plot the resistance on the x-axis and compute the magnitude of the impedance, shown by r in the graph above. If you consider that r is the third side of a right triangle made up of the sides r, x, and y, r is equal to the square root of x2 and y2.

Let’s take a look at an example. In polar coordinates, is the impedance of a network consisting of a 100-ohm-reactance inductor in series with a 100-ohm resistor is 141 ohms at an angle of 45 degrees. (E5C01) In this example, x=100 and y=100, so

r = sqrt (X2 + R2) = sqrt (1002 + 1002) = sqrt (20000) = 141 ohms.

The cosine of the phase angle θ is equal to x/r, or 100/141, or .707.  If you look up this value in a table of cosines, you’ll find that the angle is 45 degrees.

Here’s another thing to notice. When the value of the reactance is equal to the value of the resistance, the angle will be either 45 degrees or -45 degrees, depending on whether the net reactance is inductive or capacitive.

Now, let’s look at an example with both inductive and capacitive reactance. In polar coordinates, the impedance of a network consisting of a 100-ohm-reactance inductor, a 100-ohm-reactance capacitor, and a 100-ohm resistor, all connected in series is 100 ohms at an angle of 0 degrees. (E5C02) In this case, the inductive reactance and the capacitive reactance are the same, meaning that there is no net reactance. If you plot the impedance of a circuit using the rectangular coordinate system and find the impedance point falls on the right side of the graph on the horizontal axis, you know that the circuit impedance is equivalent to a pure resistance. (E5C12)

Here’s an example with unequal inductive and capacitive reactances. In polar coordinates, the impedance of a network consisting of a 300-ohm-reactance capacitor, a 600-ohm-reactance inductor, and a 400-ohm resistor, all connected in series is 500 ohms at an angle of 37 degrees. (E5C03) Here’s how we got that result:

X = 600 – 300 = 300 ohms

r = sqrt (X2 + R2) = sqrt (3002 + 4002) = sqrt (250000) = 500 ohms

θ = cos-1(x/r) = cos-1(400/500) = 37 degrees

Here are some more examples. I’ll leave the solutions up to you:

  • In polar coordinates, the impedance of a network consisting of a 400-ohm-reactance capacitor in series with a 300-ohm resistor is 500 ohms at an angle of -53.1 degrees. (E5C04)
  • In polar coordinates, the impedance of a network consisting of a 400-ohm-reactance inductor in parallel with a 300-ohm resistor is 240 ohms at an angle of 36.9 degrees. (E5C05)
  • In polar coordinates, the impedance of a network consisting of a 100-ohm-reactance capacitor in series with a 100-ohm resistor is 141 ohms at an angle of -45 degrees. (E5C06)
  • In polar coordinates, the impedance of a network comprised of a 100-ohm-reactance capacitor in parallel with a 100-ohm resistor is 71 ohms at an angle of -45 degrees. (E5C07)
  • In polar coordinates, what is the impedance of a network comprised of a 300-ohm-reactance inductor in series with a 400-ohm resistor is 500 ohms at an angle of 53 degrees. (E5C08)
  • In polar coordinates, the impedance of a series circuit consisting of a resistance of 4 ohms, an inductive reactance of 4 ohms, and a capacitive reactance of 1 ohm is 5 ohms at an angle of 37 degrees. (E5C18)

Extra Class question of the day: AC waveforms: sine, square, sawtooth and irregular waveforms; AC measurements; average and PEP of RF signals; pulse and digital signal waveforms

We use all different kinds of waveforms in amateur radio. It is, therefore, important to know about the different types of waveforms and how to measure their parameters. One of the most important parameters of a waveform is its period. The period of a wave is the time required to complete one cycle. (E8A08) The frequency is the inverse of the period. For example, if the period of a wave is 1 msec, or .001 s, the frequency of that wave is 1 / .001s, or 1000 Hz.

Another parameter that we need to know about a waveform is it root mean square, or RMS, value. The root-mean-square value of an AC voltage is the DC voltage causing the same amount of heating in a resistor as the corresponding RMS AC voltage. (E8A04) Because of this, the most accurate way of measuring the RMS voltage of a complex waveform would be measuring the heating effect in a known resistor. (E8A05)

If the waveform is regular, it’s relatively easy to calculate the RMS value. In the case of a sine wave, the RMS value is 0.707 times the peak value. You use the RMS voltage value to calculate the power of a wave.

The type of waveform produced by human speech is, however, irregular. (E8A09), and  the characteristics of the modulating signal determine the PEP-to-average power ratio of a single-sideband phone signal. (E8A07) This makes calculating or measuring the average power more difficult.

If you know the peak envelope power (PEP), though, you can make a pretty good guess at the average power. The approximate ratio of PEP-to-average power in a typical single-sideband phone signal is 2.5 to 1. (E8A06) Put another way, the average power of an SSB signal is about 40% of the peak power.

It used to be that all the waveforms we used in amateur radio were analog waveforms, but digital waveforms may be even more important than analog waveforms. An advantage of using digital signals instead of analog signals to convey the same information is that digital signals can be regenerated multiple times without error. (E8A13) All of these choices are correct when talking about the types of information that can be conveyed using digital waveforms (E8A12):

  • Human speech
  • Video signals
  • Data

Perhaps the most common digital wave form is the square wave.  An ideal square wave alternates regularly and instantaneously between two different values. An interesting fact is that a square wave is the type of wave that is made up of a sine wave plus all of its odd harmonics is. (E8A01)

Another type of wave used in amateur radio is the sawtooth wave. A sawtooth wave is the type of wave that has a rise time significantly faster than its fall time (or vice versa). (E8A02) The type of wave made up of sine waves of a given fundamental frequency plus all its harmonics is a sawtooth wave. (E8A03)

Digital data transmission is one use for a pulse modulated signal. (E8A11) Narrow bursts of energy separated by periods of no signal is a distinguishing characteristic of a pulse waveform. (E8A10) The waveform of a stream of digital data bits would look like a series of pulses with varying patterns on a conventional oscilloscope. (E8A15)

To make use of digital techniques in amateur radio, such as digital signal processing or DSP, we must convert analog signals to digital signals and vice-versa. Sequential sampling is one of the methods commonly used to convert analog signals to digital signals. (E8A14) When converting an analog signal to digital values, an analog to digital converter measures, or samples, the value of the analog signal at different points, and converts that measurement to a numeric value. Those numbers are then input to a processor or directly into memory.