# Complex Impedances Without The Pain

Any grizzled electronic engineer will tell you that RF work is hard. Maintaining impedance matching may be a case of cutting wires to length at lower frequencies, but into the low centimetre and millimetre wavelengths it becomes a Dark Art aided by mysterious and hugely expensive test equipment beyond the reach of mere mortals. A vector network analyser or VNA may be beyond the reach of many, but [Tomasz Wątorowski] is here to tell us about how with some resistors, mathematics, and a bit of lateral thinking its functions may be replicated with a more modestly equipped bench.

It’s not a method for the faint-hearted as the mathematics are of the variety that you probably learned as an undergraduate but let slip from your memory with thanks after the course ended. The method involves measuring the return loss both with and without a resistor of known value in series with the antenna, these figures allow the real and imaginary components of the antenna’s impedance to be calculated. There is a further piece of work though, this method doesn’t determine whether the antenna is capacitive or inductive. Repeating the measurement with either a capacitive or inductive matching network allows this to be determined, and the value of the appropriate matching component to be calculated.

If you are interested in this kind of work, start with a primer on RF design.

Complex impedance matching using scalar measurements, math and resistors

# The \$50 Ham: Dummy Loads, Part 2

In the last installment of “The \$50 Ham” I built a common tool used by amateur radio operators who are doing any kind of tuning or testing of transmitters: a dummy load. That build resulted in “L’il Dummy”, a small dummy load intended for testing typical VHF-UHF handy talkie (HT) transceivers, screwing directly into the antenna jack on the radio.

As mentioned in the comments by some readers, L’il Dummy has little real utility. There’s actually not much call for a dummy load that screws right into an HT, and it was pointed out that a proper dummy load is commercially available on the cheap. I think the latter observation is missing the point of homebrewing specifically and the Hackaday ethos in general, but I will concede the former point. That’s why at the same time I was building L’il Dummy, I was building the bigger, somewhat more capable version described here: Big Dummy.

# The \$50 Ham: Dummy Loads

This is an exciting day for me — we finally get to build some ham radio gear! To me, building gear is the big attraction of amateur radio as a hobby. Sure, it’s cool to buy a radio, even a cheap one, and be able to hit a repeater that you think is unreachable. Or on the other end of the money spectrum, using a Yaesu or Kenwood HF rig with a linear amp and big beam antenna to work someone in Antartica must be pretty cool, too. But neither of those feats require much in the way of electronics knowledge or skill, and at the end of the day, that’s why I got into amateur radio in the first place — to learn more about electronics.

To get my homebrewer’s feet wet, I chose perhaps the simplest of ham radio projects: dummy loads. Every ham eventually needs a dummy load, which is basically a circuit that looks like an antenna to a transmitter but dissipates the energy as heat instead of radiating it an appreciable distance. They allow operators to test gear and make adjustments while staying legal on emission. Al Williams covered the basics of dummy loads a few years back in case you need a little more background.

We’ll be building two dummy loads: a lower-power one specifically for my handy talkies (HTs) will be the subject of this article, while a bigger, oil-filled “cantenna” load for use with higher power transmitters will follow. Neither of my designs is original, of course; borrowing circuits from other hams is expected, after all. But I did put my own twist on each, and you should do the same thing. These builds are covered in depth on my Hackaday.io page, but join me below for the gist on a good one: the L’il Dummy.

# Video: Putting High Speed PCB Design To The Test

Designing circuit boards for high speed applications requires special considerations. This you already know, but what exactly do you need to do differently from common board layout? Building on where I left off discussing impedance in 2 layer Printed Circuit Board (PCB) designs, I wanted to start talking about high speed design techniques as they relate to PCBs.  This is the world of multi-layer PCBs and where the impedance of both the Power Delivery Network (PDN) and the integrity of the signals themselves (Signal Integrity or SI) become very important factors.

I put together a few board designs to test out different situations that affect high speed signals. You’ve likely heard of vias and traces laid out at right angles having an impact. But have you considered how the glass fabric weave in the board itself impacts a design? In this video I grabbed some of my fanciest test equipment and put these design assumptions to the test. Have a look and then join me after the break for more details on what went into this!

# The BNC Connector And How It Got That Way

When I started working in a video production house in the early 1980s, it quickly became apparent that there was a lot of snobbery in terms of equipment. These were the days when the home video market was taking off; the Format War had been fought and won by VHS, and consumer-grade VCRs were flying off the shelves and into living rooms. Most of that gear was cheap stuff, built to a price point and destined to fail sooner rather than later, like most consumer gear. In our shop, surrounded by our Ikegami cameras and Sony 3/4″ tape decks, we derided this equipment as “ReggieVision” gear. We were young.

For me, one thing that set pro gear apart from the consumer stuff was the type of connectors it had on the back panel. If a VCR had only the bog-standard F-connectors like those found on cable TV boxes along with RCA jacks for video in and out, I knew it was junk. To impress me, it had to have BNC connectors; that was the hallmark of pro-grade gear.

I may have been snooty, but I wasn’t really wrong. A look at coaxial connectors in general and the design decisions that went into the now-familiar BNC connector offers some insight into why my snobbery was at least partially justified.

# Putting A Poor Man’s Vector Analyzer Through Its Paces

If anything about electronics approaches the level of black magic, it’s antenna theory. Entire books dedicated to the subject often merely scratch the surface, and unless you’re a pro with all the expensive test gear needed to visualize what’s happening, the chances are pretty good that your antenna game is more practical than theoretical. Not that there’s anything wrong with that — hams and other RF enthusiasts have been getting by with antennas that work without really understanding why for generations.

But we’re living in the future, and the tools to properly analyze antenna designs are actually now within the means of almost everyone. [Andreas Spiess] recently reviewed one such instrument, the N1201SA vector impedance analyzer, available from the usual overseas sources for less than \$150. [Andreas]’s review does not seem to be sponsored, so it seems like we’re getting his unvarnished opinion; spoiler alert, he loves it. And with good reason; while not a full vector network analyzer (VNA) that will blow a multi-thousand dollar hole in your wallet, this instrument looks like an incredible addition to your test suite. The tested unit works from 137 MHz to 2.4 GHz, so it covers the VHF and UHF ham bands as well as LoRa, WiFi, cell, ISM, and more. But of course, [Andreas] doesn’t just review the unit, he also gives us a healthy dose of theory in his approachable style.

[The guy with the Swiss accent] has been doing a lot of great work these days, covering everything from how not to forget your chores to reverse engineering an IoT Geiger counter. Check out his channel — almost everything he does is worth a watch.

# Imaginary AC Circuits Aren’t Really Complex

If you have ever read advanced textbooks or papers about electronics, you may have been surprised to see the use of complex numbers used in the analysis of AC circuits. A complex number has two parts: a real part and an imaginary part. I’ve often thought that a lot of books and classes just kind of gloss over what this really means. What part of electricity is imaginary? Why do we do this?

The short answer is phase angle: the time delay between a voltage and a current in a circuit. How can an angle be a time? That’s part of what I’ll need to explain.

First, consider a resistor. If you apply a voltage to it, a certain current will flow that you can determine by Ohm’s law. If you know the instantaneous voltage across the resistor, you can derive the current and you can find the power–how much work that electricity will do. That’s fine for DC current through resistors. But components like capacitors and inductors with an AC current don’t obey Ohm’s law. Take a capacitor. Current only flows when  the capacitor is charging or discharging, so the current through it relates to the rate of change of the voltage, not the instantaneous voltage level.

That means that if you plot the sine wave voltage against the current, the peak of the voltage will be where the current is minimal, and the peak current will be where the voltage is at zero. You can see that in this image, where the yellow wave is voltage (V) and the green wave is current (I). See how the green peak is where the yellow curve crosses zero? And the yellow peak is where the green curve crosses zero?

These linked sine and cosine waves might remind you of something — the X and Y coordinates of a point being swept around a circle at a constant rate, and that’s our connection to complex numbers. By the end of the post, you’ll see it isn’t all that complicated and the “imaginary” quantity isn’t imaginary at all.