Monthly Archives: May 2016

Antenna Basics

Over 2600 years ago (and likely well before that) the ancient Greeks discovered that a piece of amber rubbed on a piece of fur would attract lightweight objects like feathers. Around the same time, the ancients discovered lodestone, which are pieces of magnetised rock.

It took a few hundred years more to determine that there are two different properties of attraction and repulsion (magnetic and electric): likes repel and opposites attract. Another 2000 years passed before scientists first discovered that these two entirely different novelties of nature were inextricably linked.

In the early nineteenth-century, Hans Christen Oersted placed a wire perpendicular to a compass needle and saw nothing. But when he rotated the wire parallel to the compass needle and passed a current through the wire, it deflected in one direction. When he passed the current through the wire in the opposite direction, the compass needle deflected in the opposite direction.

A current carrying wire perpendicular to a compass needle causes no movement.

This wire was the first antenna transmitter and the compass needle the first receiver. The scientists just did not know it at the time.

While not terribly elegant, it provided a clue about the way the universe worked—that charges moving through a wire create a magnetic field that is perpendicular to the wire.  (Scientists soon learned the field surrounding a wire is circular, not perpendicular.)

With this information, scientists were able to describe the ways in which electric fields and magnetic fields interact with electric charges and formed a basis of an understanding of electromagnetism.

Shortly after, Nikola Tesla wirelessly lit lamps in his workshop, demonstrated the first remote-control toy boat, and established the alternating-current system we use to transfer electricity throughout the world today.

Less than a full century after Orstead’s experiment, Guglielmo Marconi devised a way to send the first wireless telegraph signals across the Atlantic.

And here we stand, a full two centuries after that first compass experiment, able to capture images from distant planets and send them through the vastness of space to a device we can hold in the palm of our hand—all with antennas.

Electronic Circuits with an Audible Circuit

The Circuit Probe

The Audible Circuit Probe is a handheld audio-oscillator with a sharp probe and an alligator clip for connections to test circuits. Its output tone varies with the component connected between the alligator clip and the probe. It is capable of testing resistors, AC and DC voltage, capacitors, diodes, and transistors.

Inside the tool, the alligator-clip connects to a film capacitor with a 250 V rating (J2), and the probe tip connects to the anode side of a diode (J1).

This is a single-swing blocking oscillator circuit, used to create narrow timing pulses.

Continuity Testing

In the short circuit condition, the probe outputs an approximately 800-Hz tone through a series of rapid pulses.

Tone produced by speaker during short circuit

You can use this audible tone to determine continuity in the same way you might with your multimeter—the audible circuit probe’s tone varies with resistance, whereas your multimeter likely only produces a constant tone. This variable tone allows you to find short-circuits as well as partially conducting paths that your multimeter might miss.

Testing Household Alternating Current

Range: 0-130 Volts Maximum

The tool can be used to check for the presence of AC as well as diagnose certain common problems. When used to probe electrical mains, it produces a very unique sound.

Note: Please do not use this tool to probe energized circuits unless you have been trained to work with household circuits. If you do use it to probe live circuits, wrap the probe shaft in electrical tape or use heat shrink tubing to reduce the exposed metal end down to approximately 1mm. Additionally, if you do probe live circuits, do not change the wiring of a live circuit—always turn off the circuit at the breaker before making any adjustments to wiring.

Note the changing period in the zoomed out trace above

The audible circuit probe has a variety of uses troubleshooting household wiring. I often find it more convenient than a multimeter since most switches and receptacles are several feet off the ground and there is nowhere to place a meter. With this tool, you can keep your eyes on the live circuit at all times and not switch back and forth between looking at a wire and your multimeter.

Household receptacles in the United States have three holes labeled “Hot”, “Common/Neutral”, and “Ground.” The smaller rectangular hole is the one that is supposed to be maintained at 120 V above ground potential.

Many do-it-yourselfers and handymen hook up outlets incorrectly by accidentally swapping the neutral and the hot wires. Unfortunately, appliances will often still work even in this incorrect state, although often more hazardously. Also, it is possible to accidentally break or knock loose wires when closing up a crowded junction-box. These mistakes lead to a variety of issues, from vacuums that shock you when you touch them (caused by reversed hot and neutral) to flickering lights (caused by a loose neutral) to fires.

I suggest using a 3-wire receptacle tester to check all of the outlets in your home if you haven’t done so already. But this only works if you are able to stand directly in front of an outlet. If you are working on a switch in another room, you can use probe leads or alligator clips to attach the audible circuit probe to screws on the receptacle or switch inside the junction box. The audible circuit probe works whether the AC lines are energized or not, so if you accidentally leave it hooked up when you reenergize a circuit, you will not damage it.

I have used the audible circuit probe to diagnose broken switches on live circuits. When attached on either side of a switch, the tone should change between the continuity tone and the AC tone (or no tone) when the switch is flipped.

In my case, overhead lights that worked before would not turn on when I flipped the switch and the circuit breaker had not been tripped. I removed the outlet cover and connected the probe to the screw terminals. There was no change in tone when the switch was flipped, indicating the switch was faulty.

Continuity Tone

DC Voltage Testing

The circuit probe will change frequency when it is connected to batteries and power supplies. The frequency will increase as the potential difference increases to the maximum 130V volts and the frequency will decrease as the potential difference decreases to around -8 V.

The audible signal is not enough for you to deduce a specific voltage, but it does allow you to probe battery compartments to look for loose connections.

Capacitor Testing

Range: 100 µF – 3000 mF

To quantitatively test a capacitor, consider using a quality multimeter instead of this tool.

This tool is my favorite way to demonstrate to students what is happening inside a capacitor.  I compare the movement of charge onto the plates of a capacitor to the movement of air inside an “Air capacitor.”  This is, of course, not a complete description of what is happening, but for someone who is beginning the journey, a complete description would be quite overwhelming.

All About Complex Conjugate Poles

There are two ways to achieve second-order (i.e., two-pole) filter response: cascade two first-order filters, or use a second-order topology. An example of the former is two resistor–capacitor (RC) low-pass filters connected in series, with the output of the first buffered by a voltage follower. Examples of the latter are passive resistor–capacitor–inductor (RLC) filters and active filters, such as the Sallen­–Key.

Of course, this discussion applies also to higher-order filters: a four-pole response can be provided by four cascaded first-order stages or two cascaded second-order stages.

There is an appealing simplicity surrounding the cascade-first-order-stages approach. All you need for a second-order filter is some rudimentary math, an op-amp, two resistors, and two capacitors (three if you include the op-amp’s bypass cap). Why so much ado about second-order topologies, then? Well, the answer to that question leads to an important concept in filter theory: complex-conjugate poles.

Recall that complex conjugates have real parts that are equal in magnitude and sign and imaginary parts that are equal in magnitude and opposite in sign. Let’s visualize this using the s-plane

Here we have complex-conjugate poles on the left side of the imaginary axis (which is where you want the poles, unless you’re designing an oscillator instead of a filter). They have equal distance from the real axis and the imaginary axis, but they are mirrored across the real axis because one has a positive imaginary part and one has a negative imaginary part.

Complex-conjugate poles are important because they allow the designer to optimize a filter such that it exhibits a maximally flat passband, a rapid transition from passband to stopband, or constant group delay (i.e., linear phase response). The problem with cascaded first-order stages is that this configuration cannot provide complex-conjugate poles.

Let’s explore this fact using a unity-gain low-pass filter as an example. The s-domain transfer function is

H(s)=1s+ω0H(s)=1s+ω0

Cascading two of these filters corresponds to multiplying the two transfer functions:

H(s)=1s+ω0×1s+ω0=1s2+2ω0s+ω20H(s)=1s+ω0×1s+ω0=1s2+2ω0s+ω02

The term we are interested in here is the 2ω0s. The denominator of a generalized second-order transfer function can be written as

s2+ω0Qs+ω20s2+ω0Qs+ω02

Thus, we have

ω0Q=2ω0  Q=0.5ω0Q=2ω0 ⇒ Q=0.5

The first thing to notice here is that the Q factor cannot be adjusted so as to fine-tune the frequency response. Two cascaded first-order filters will always have Q = 0.5 (furthermore, Q = 0.5 corresponds to a rather gradual transition from passband to stopband and significant attenuation in the passband).

The second thing to understand is that you cannot have complex-conjugate poles when Q is 0.5. Consider the following diagram

The distance from the imaginary axis to a pole is equal to ω0/2Q, and the distance from the origin to a pole is ω00 is the pole frequency). If Q = 0.5, we have ω0/(2 × 0.5) = ω0, and thus the distance from the imaginary axis will be equal to the distance from the origin. It follows that the pole must be located on the real axis, and consequently there is no possibility for a complex-conjugate pair because the pole location has no imaginary part.

Perhaps we can intuitively conclude from the circuit implementation that cascaded-first-order-stage filters do not allow for optimization. But it is helpful to recognize that this rigidity is bound to the absence of complex-conjugate poles, which can be produced using a true second-order stage and which enable the designer to optimize a filter for a particular application.