# Network Analysers: The Electrical Kind

Instrumentation has progressed by leaps and bounds in the last few years, however, the fundamental analysis techniques that are the foundation of modern-day equipment remain the same. A network analyzer is an instrument that allows us to characterize RF networks such as filters, mixers, antennas and even new materials for microwave electronics such as ceramic capacitors and resonators in the gigahertz range. In this write-up, I discuss network analyzers in brief and how the DIY movement has helped bring down the cost of such devices. I will also share some existing projects that may help you build your own along with some use cases where a network analyzer may be employed. Let’s dive right in.

# Network Analysis Fundamentals

As a conceptual model, think of light hitting a lens and most of it going through but part of it getting reflected back.

The same applies to an electrical/RF network where the RF energy that is launched into the device may be attenuated a bit, transmitted to an extent and some of it reflected back. This analysis gives us an attenuation coefficient and a reflection coefficient which explains the behavior of the device under test (DUT).

Of course, this may not be enough and we may also require information about the phase relationship between the signals. Such instruments are termed Vector Network Analysers and are helpful in measuring the scattering parameters or S-Parameters of a DUT.

The scattering matrix links the incident waves a1, a2 to the outgoing waves b1, b2 according to the following linear equation: $\begin{bmatrix} b_1 \\ b_2 \end{bmatrix} = \begin{bmatrix} S_{11} & S_{12} \\ S_{21} & S_{22} \end{bmatrix} * \begin{bmatrix} a_1 \\ a_2 \end{bmatrix}$.

The equation shows that the S-parameters are expressed as the matrix S, where and denote the output and input port numbers of the DUT.

This completely characterizes a network for attenuation, reflection as well as insertion loss. S-Parameters are explained more in details in Electromagnetic Field Theory and Transmission Line Theory but suffice to say that these measurements will be used to deduce the properties of the DUT and generate a mathematical model for the same.

# General Architecture

As mentioned previously, a simple network analyzer would be a signal generator connected and a spectrum analyzer combined to work together. The signal generator would be configured to output a signal of a known frequency and the spectrum analyzer would be used to detect the signal at the other end. Then the frequency would be changed to another and the process repeats such that the system sweeps a range of frequencies and the output can be tabulated or plotted on a graph. In order to get reflected power, a microwave component such as a magic-T or directional couplers, however, all of this is usually inbuilt into modern-day VNAs.

In a laboratory grade VNA, we have two or four ports where a DUT is connected and the software does everything else for you. The only downside is that these instruments are very very expensive and price varies depending upon the range of RF frequencies or RF band coverage.

# A DIY Scalar Network Analyzer

Let’s simplify things a bit. Say I have a simple filter I want to characterize in which case phase may not be necessary for my particular applications. I would just like to obtain the frequency-attenuation plot for the circuit so that I can use it correctly. In such cases, the DIY approach is the best and I would like to highlight a project on Hackaday.io for beginners. The idea is simple and involves using the Analog devices AD9851 to generate the desired signals.

The received signal power levels are converted into a voltage using the AD8307 logarithmic amplifier (datasheet, PDF). This voltage is read by a microcontroller and the results, in this case, are plotted using a Python script. Another restriction to this design is the 70 MHz upper limit though it may work for a lot of people getting started with such projects.

In my quest for a simple experiment, I purchased some AD9850 modules, op-amps, and other tidbits from eBay and made a PCB in KiCAD. I built the project in the Arduino UNO shield layout because my intention was to test it on an Arduino and then move up to an STM32 Nucleo which was also bought on the cheap. My revision 1.0 had some basic bugs so it is still a work in progress but I am sure it will work the same as the above project. Feel free to explore it and make one for yourself. Mine is shown below in OshPark Purple.

I did salvage the connectors from an old DVR board I had lying around so I suggest you replace that footprint with whatever you intend to use in your build.

# More serious projects

If you are more comfortable with RF circuits and want a more serious project, there is another by [Henrik Forstén] that works from 30 Mhz all the way up to 6 Ghz. The difference here is that his design uses a lot of planning as well as specific RF chips to do the job.

The AD985x is replaced by the MAX2871 and the detector is replaced by an LMH2110. All the files are available on GitHub for our experimentation pleasure though this may not be everyone’s cup of tea. Though if you are getting a little bit interested in this stuff, be sure to check out the website for all the nice info provided.

# Vector Network Analysers

The Vector Network Analyzer is able to generate phase relationships in addition to the magnitude measurements. This allows us to generate complex math models for the components under test and helps identify the capacitive and inductive properties as well. In addition to the above-mentioned applications in the DIY field, VNAs are important tools for analysis of dielectric properties of materials as well. When working with materials such as ceramics in a research environment, a simple method is to apply the silver paste to opposite faces and then use a network analyzer to measure the various parameters. This method is commonly known as capacitance method for measuring complex permittivity.

For higher frequencies where the EM wave needs a waveguide, transmission/reflection methods are preferred. In this method, the material under test is placed inside a waveguide and there is no electrical contact between the terminals and the DUT. This method is commonly called the transmission/reflection line method and is usually employed in the laboratory.

It’s also possible to extend this to make free space measurements, where horn antennas are employed and the DUT is suspended in free space. This allows for the material to be heated or cooled without affecting the instrument or the antennas and is commonly used for temperature analysis of materials.

# Measurement Methods for Materials

Once S-parameters are obtained from experiment, this data can then be converted into dielectric properties. Some conversion methods (PDF) are:

• Nicolson-Ross-Weir method,
• NIST iterative method,
• New non-iterative method,
• Short circuit line method.

The most common parameter evaluated is permittivity or more specifically complex relative permeability (mu-r). The real part is the dielectric constant which is a measure of the amount of energy from an external electrical field stored in the material. The imaginary part is the loss factor and is the amount of energy lost due to external fields. The dielectric constant usually varies with the frequency which means that the same electrolytic capacitor won’t behave the same at all frequencies.

There has been a lot of research invested in creating new materials that will behave favorably at higher frequencies. Today there is a variety of materials being employed to create these devices and research involves characterization of the materials involved.

Another important term is loss tangent (tan delta) and is the ratio of the two. If you are interested in the subject, then I recommend reading the Rhode and Schwarz application note linked just above, as well as papers here and here.

Note: I have not tried to discuss methods like cavity perturbation though it may be of interest to some and can be explored on its own. Take a look at this application note from Keysight (PDF) for more information on the subject.

# A short note on VSWR

To complete this write-up, I am going to talk a bit about VSWR which is more associated with antenna and radio setups than materials and VNA. A scalar network analyzer used in HAM radio setups is used to measure a number of things including the Voltage Standing Wave Ratio or VSWR. This parameter is a ratio of energy that was put into an antenna or RF line and the amount of energy that bounced back out of it due to imperfect matching. So essentially, the standing wave ratio (SWR) is a measure of how efficiently RF power is transmitted from the power source, through the transmission line, and into the load. It is ideal to have all the signal converted into RF energy or EM waves at the antenna, however, practically if the impedance of the amplifier and antenna are mismatched, some part will be reflected back just like we discussed in the initial sections. A scalar network analyzer can measure these as well as impedance at various frequencies. RF couplers assist in reducing the mismatch and improving performance in these cases.

# What next?

The idea was to explain network analyzers and their applications in brief. You can extend this article by diving into radios and antennas, RF instrumentation, or get into microwave materials for high-frequency applications. For someone working with such materials, a VNA is indispensable as it does the heavy lifting of analysis and presents results in a very straightforward manner.

We are moving into ceramics that have a low-temperature coefficient i.e. the dielectric constant remains constant over temperature and LTCC or Low-Temperature Co-fired Ceramics. LTCC allow us to layer components together enabling high-density electronics manufacturing. All that requires analysis which is possible thanks to a combination of advanced instrumentation as well as mathematical algorithms.

# An Unconference Badge That’s Never Gonna Give You Up

When your publication is about to hold a major event on your side of the world, and there will be a bring-a-hack, you abruptly realise that you have to do just that. Bring a hack. With the Hackaday London Unconference in the works this was the problem I faced, and I’d run out of time to put together an amazing PCB with beautiful artwork and software-driven functionality to amuse and delight other attendees. It was time to come up with something that would gain me a few Brownie points while remaining within the time I had at my disposal alongside my Hackaday work.

Since I am a radio enthusiast at heart, I came up with the idea of a badge that the curious would identify as an FM transmitter before tuning a portable radio to the frequency on its display and listening to what it was sending. The joke would be of course that they would end up listening to a chiptune version of [Rick Astley]’s “Never gonna give you up”, so yes, it was going to be a radio Rickroll.

I evaluated a few options, and ended up with a Raspberry Pi Zero as an MP3 player through its PWM lines, feeding through a simple RC low-pass filter into a commercial super-low-power FM transmitter module of the type you can legally use with an iPod or similar to listen on a car radio. To give it a little bit of individuality I gave the module an antenna, a fractal design made from a quarter wavelength of galvanised fence wire with a cut-off pin from a broken British mains plug as a terminal. The whole I enclosed in a surplus 8mm video cassette case with holes Dremmeled for cables, with the FM module using its own little cell and the Pi powered from a mobile phone booster battery clipped to its back. This probably gave me a transmitted field strength above what it should have been, but the power of those modules is so low that I am guessing the sin against the radio spectrum must have been minor.

At the event, a lot of people were intrigued by the badge, and a few of them were even Rickrolled by it. But for me the most interesting aspect lay not in the badge itself but in its components. First I looked at making a PCB with MP3 and radio chips, but decided against it when the budget edged towards £20 ($27). Then I looked at a Raspberry Pi running PiFM as an all-in-one solution with a little display HAT, but yet again ran out of budget. An MP3 module, Arduino clone, and display similarly became too expensive. Displays, surprisingly, are dear. So my cheapest option became a consumer FM module at £2.50 ($3.37) which already had an LCD display, and a little £5 ($6.74) computer running Linux that was far more powerful than the job in hand demanded. These economics would have been markedly different had I been manufacturing a million badges, but made a mockery of the notion that the simplest MCU and MP3 module would also be the cheapest. Rickrolling never gets old, it seems, but evidently it has. Its heyday in Hackaday projects like this prank IR repeater seems to have been in 2012. # Piezomagnetic Trick Shrinks 2.5 GHz Antennas To a ham radio operator used to “short”-wave antennas with lengths listed in tens of meters, the tiny antennas used in the gigahertz bands barely even register. But if your goal is making radio electronics that’s small enough to swallow, an antenna of a few centimeters is too big. Physics determines plausible antenna sizes, and there’s no way around that, but a large group of researchers and engineers have found a way of side-stepping the problem: resonating a nano-antenna acoustically instead of electromagnetically. Normal antennas are tuned to some extent to the frequency that you want to pick up. Since the wavelength of a 2.5 GHz electromagnetic wave in free space is 120 cm mm, most practical antennas need a wire in the 12-60 cm mm range to bounce signals back and forth. The trick in the paper is to use a special piezomagnetic material as the antenna. Incoming radio waves get quickly turned into acoustic waves — physical movement in the nano-crystals. Since these sound waves travel a lot slower than the speed of light, they resonate off the walls of the crystal over a much shorter distance. A piezoelectric film layer turns these vibrations back into electrical signals. Ceramic chip antennas use a similar trick. There, electromagnetic waves are slowed down inside the high-permittivity ceramic. But chip antennas are just slowing down EM waves, whereas the research demonstrated here is converting the EM to sound waves, which travel many orders of magnitude slower. Nice trick. Granted, significant material science derring-do makes this possible, and you’re not going to be fabricating your own nanoscale piezomagnetic antennas any time soon, but with everything but the antenna getting nano-ified, it’s exciting to think of a future where the antennas can be baked directly into the IC. Thanks [Ostracus] for the tip in the comments of this post on antenna basics. Via [Science Magazine]. # Doppler Module Teardown Reveals the Weird World of Microwave Electronics Oscillators with components that aren’t electrically connected to anything? PCB traces that function as passive components based solely on their shape? Slots and holes in the board with specific functions? Welcome to the weird and wonderful world of microwave electronics, brought to you through this teardown and analysis of a Doppler microwave transceiver module. We’ve always been fascinated by the way conventional electronic rules break down as frequency increases. The Doppler module that [Kerry Wong] chose to pop open, a Microsemi X-band transceiver that goes for about$10 on eBay right now, has vanishingly few components inside. One transistor for the local oscillator, one for the mixer, and about three other passives are the whole BOM. That the LO is tuned by a barium titanate slug that acts as a dielectric resonator is just fascinating, as is the fact that PB traces can form a complete filter network just by virtue of their size and shape. Antennas that are coupled to the transceiver through an air gap via slots in the board are a neat trick too.

[Kerry] analyzes all this in the video below and shows how the module can be used as a sensor. If you need a little more detail on putting these modules to work, we’ve got some basic circuits you can check out.

# Attack Some Wireless Devices With A Raspberry Pi And An RTL-SDR

If you own one of the ubiquitous RTL-SDR software defined radio receivers derived from a USB digital TV receiver, one of the first things you may have done with it was to snoop on wide frequency bands using the waterfall view present in most SDR software. Since the VHF and UHF bands the RTL covers are sometimes a little devoid of signals, chances are you homed in upon one of the ISM bands as used by plenty of inexpensive wireless devices for all sorts of mundane control tasks. Unless you reside in the depths of the wilderness, ISM band sniffing will show a continuous procession of chirps; short bursts of digital data. It is surprising, the number of radio-controlled devices you weren’t aware were in your surroundings.

Some of these devices, such as car security keys, are protected by rolling encryption schemes to deter would-be attackers. But many of the more harmless devices simply send a command in the open without the barest of encryption. The folks at RTL-SDR.com put up a guide to recording these open data bursts on a Raspberry Pi and playing them back by transmitting them from the Pi itself.

It’s not the most refined of attack because all it does is take the recorded file and retransmit it with the [F5OEO] RPiTX software. But they do demonstrate it in action with a wireless lightbulb, a door bell, a wireless relay, and a remote-controlled switched socket. Since the data in question is transmitted as OOK, or on-off keying, the RPiTX AM mode stands in for the transmitter.

You can see it in action in the video below the break. Now, have you investigated the ISM band chirps in your locality?

# Sorry US; Europeans Listen to Space with GRAVES

In Europe, the GRAVES radar station beams a signal on 143.050 MHz almost straight up to detect and track satellites and space junk. That means you will generally not hear any signal from the station. However, [DK8OK] shows how you can–if you are in Europe–listen for reflections from the powerful radar. The reflections can come from airplanes, meteors, or spacecraft. You can see a video from [way1888] showing the result of the recent Perseid meteor shower.

Using a software-defined radio receiver, [DK8OK] tunes slightly off frequency and waits for reflections to appear in the waterfall. In addition to observing the signal, it is possible to process the audio to create more details.

Why is there a giant vertical radar transmitter in the middle of France? The transmitter uses a phased array to send a signal over a 45-degree swath of the sky at a time. It makes six total steps every 19.2 seconds. A receiver several hundred miles away listens for reflections.

Even the moon reflects the signal when it is in the radar’s path. If you are interested in a moon bounce, you may be able to build a station to hear the reflections without being in Europe.

Of course, if you can transmit yourself, you might want to bounce your own signal off airplanes. If you want to do it old school, you could emulate [Zoltán Bay].