RF cat corner

Switch to Hugo

Sat, 22 Aug 2026 00:00:00 +0000

When I started this website, I decided to use a static site generator because it could run for long periods without maintenance, unlike dynamic websites which are subject to security issues and sometimes need emergency patches. I chose GitHub and Jekyll because it was included.

I was very happy with the result, and at the beginning I found the workflow very convenient.

Then came various inconveniences. First, after any reinstallation, Jekyll stopped working on my computer, and I had to use various workarounds. I remember even using a virtual machine on VirtualBox. I eventually managed to get it working again. This issue now occurs less often because I often work in WSL, where Mistral Vibe works better, but I still had various annoyances, such as the need to run bundler exec.

Gönül's website is awesome

Tue, 18 Aug 2026 00:00:00 +0000

Co-author Gönül Demir has followed my advice to make a website to promote her work. When I first saw it, I was really impressed.

For this reason, I decided to proceed to a relooking of this blog. I have performed a first batch of changes, and more is to come.

Nonlinear impedance (draft)

Thu, 14 May 2026 00:00:00 +0000

Although it is still in draft stage, this document is released before finishing due to its interest. This page is a quick and dirty translation of a previous French document. Various editing issues are susceptible to be present.

A few words on the notion of transistor output impedance

In [PhD thesis section 16.1], we set aside the real behavior of power amplifiers to focus on the behavior of their loads, i.e., the inputs of the power combiner. Power amplifiers operating at high power are nonlinear, which causes particular effects on the behavior of their outputs. We will detail these effects in the following section.

New co-authors

Sun, 29 Mar 2026 00:00:00 +0000

At the beginning, this site had one author, Hadrien Theveneau F4INX. Since some coauthors are now contributing on a more or less regular basis, I updated the title to reflect the introduction of guest authors.

Very welcome to Gönül Demir who up to now has co-authored 2 great pages.

I would like to take this opportunity to welcome all the people who gave me very useful hints for articles, among them Steve Huettner of https://www.microwaves101.com/, where I also posted some material, Chris Basso, who give me lots of advice on active filter topics.

The fine art of (not) doing oscillators

Sat, 14 Mar 2026 00:00:00 +0000

Hadrien Theveneau, Gönül Demir

A day in life…

*Cats fighting, from Wikipedia.*

Riiiiiiiiiiiing.

Hello the ACME labs. What can I do for you ?
We just have two of our enginners injured following a bad fight.
That’s a case for the medical doctor.
Well, we would like to know who was right in this matter.
Well, tell me more…
It involved Andreas “Bullterrier”, our senior electronics enginneer, and Cătălina “Tank”, our field sensor expert.

A (not so) gentle introduction to operational amplifiers.

Sun, 08 Mar 2026 00:00:00 +0000

After some discussions on grounding and various subjects with Gönül Demir, we thought that it could be a good idea to combine our both approaches to make a join page. Indeed I began my series by writing detailed articles about complex points and not by an introduction. We hope that this gentle (or not so) introduction to the topic would fill the gap.

Simple calculations for active bandpass filter with finite GBW operational amplifier.

Wed, 31 Dec 2025 00:00:00 +0000

Many thanks to Christophe Basso for his help in this work.

Introduction

Active filters are a convenient way to implement low frequency bandpass filters, and design equations are commonly available. However, their accuracy is often disappointing, with centre frequency often shifted, because they don’t take into account the finite GBW (gain bandwidth product) of the operational amplifier used, particularly for common and low cost amplifiers with low GBW (gain bandwidth product) like the popular LM324. We propose here simple equations which take this into account and free and open source calculation tools.

Backoff calculations.

Mon, 22 Dec 2025 00:00:00 +0000

Many thanks to my management at Eutelsat who kindly allowed me to republish this document I wrote for internal use here. Many thanks to my fellow colleagues for their help in this document.

Introduction

Power amplifiers have a limit on the maximum power they can amplity while staying linear, that is, keeping distorsion low enough.

For sinusoidal signals, it is straightforward to keep the power of the signal below the maximum linear power. However, for multi-carrier signals, the signal has peaks much higher than its average power, and keeping these paks below the maximum linear power requires to have a maximum power much higher than the average power, which is costly and inefficient in power.

Hilbert transform demo.

Sun, 21 Dec 2025 00:00:00 +0000

The discrete Hilbert transform seems rather mysterious. However, the principle as well as his mathematics are not so complicated: the Hilbert transform is mainly a way to add a 90° phase shift to a signal and its equation can be explained from simple mathematical principles and an Excel spreadsheet.

Pulse

The first step is to start with a discrete unit pulse sampled using 11 points: the center point at 1 and the others at 0. For parity reasons, only 6 sinus are needed in the discrete Fourier transform.

LC ladder impedance matching.

Sun, 21 Dec 2025 00:00:00 +0000

2025-12-21: Replace statically generated plots by dynamically generated and interactive plots using plotly.js. Note the javascript code is also for you: if you need to calculate such structures, feel free to have a look on it.

2025-11-09: Fix roots calculation and change of variables.

2025-10-26: Fix some errors in formulas, add some details about calculations.

2023-06-25: First version.

This blog page is an English translation and adaptation of a part of my PhD thesis. Numbers in brackets refers to the original bibliography, they will be replaced in a future revision.

Equations for terminating a differential amplifier in single-ended input.

Mon, 16 Jun 2025 00:00:00 +0000

Introduction

A few years ago, I had to terminate a differential amplifier in single-ended input. Analog Devices AN-0990¹ gives equations for that. Unfortunately, there are an inaccuracy in these equations. According to this page, the input impedance for balanced differential input signals is given by R_“IN, dm”=2\cdotR_G and for a single-ended input by R_“IN, cm”=R_G/(1-R_F/(2\cdot(R_G+R_F))).

However, in this use case, the last equation is uncorrect. It would have been correct if the -D_IN input were connected directly to ground. However, this is not the case, and instead this input is connected to ground through a resistor of value R_S////R_T to ensure symmetry.

On stability of capacitive loaded op-amps.

Thu, 29 May 2025 00:00:00 +0000

Introduction

Operational amplifiers are often, and for good reason, the go-to building block of many analog functions. They are often used with capacitive loads, for two main reasons. One, when operational amplifiers are used to produce DC voltage supplies, in which cases the capacitive load is used to ensure DC voltage stays constant. Second, when operational amplifiers are used to drive some capacitive load, typically the gate of the transistor of an RF power amplifier, including the capacitors of the biasing network.

IQ modulator and quadrature coupler sign issues.

Tue, 05 Nov 2024 00:00:00 +0000

Update from 2024-11-05: Steve from Microwaves 101 also tackled this topic (https://www.microwaves101.com/encyclopedias/branchline-coupler-port-definition), proposing a different port-naming convention for the branchline coupler. Steve names the direct and coupled outputs in reverse compared to the approach I use. His convention offers some interesting arguments: the output he names "forward" exhibits a higher bandwidth and flatter phase response.

Upon further analysis, it appears that the operating principles of branchline couplers differ significantly from those of coupled line couplers. Consequently, the terms "direct" and "coupled," commonly used for coupled line couplers, no longer carry the same meaning.

Microstrip formulas comparison.

Sun, 07 Jul 2024 00:00:00 +0000

Introduction

The designer has several tools and formulas available to calculate the characteristic impedance of microstrip lines. Some are highly precise but rather complex like the Hammerstad and Jensen formulas¹^,²^,³, while others are rather simple but with questionable accuracy like the IPC-2141 formulas⁴^,⁵^,⁶. While approximations can be useful for the first steps of a design, their accuracy must be evaluated before use. The authors of Qucs³ made some comparison, but this comparison don’t include the common IPC formulas⁵^,⁶. A comparison of the most common microstrip calculation formulas is shown here.

MLCC voltage dependence.

Wed, 24 Apr 2024 00:00:00 +0000

This content was originally published on Microwaves 101 (https://www.microwaves101.com/encyclopedias/capacitor-voltage-effects). Many thanks to Steve for improvements on the original version. Have a look on his website for more interesting content.

This page was suggested by Hadrien, who has had recent experience in MLC capacitor variations with voltage. Did you know your capacitor nominal value can drop 80% when you apply a DC voltage to it? Worse, there does not seem to be any standards for voltage variations like there are for temperature variations.

Calculation of characteristic impedance from S parameters.

Mon, 08 Jan 2024 00:00:00 +0000

Introduction

Suppose one wants to measure or simulate the characteristic impedance of something similar to a transmission line. This can be for example a 75 Ω coax cable or a via structure on HFSS. The characteristic impedance can be calculated form its measured or simulated S parameters references to 50 Ω.

Suppose also that the structure is “symmetric enough” to have the same characteristic impedance on each side (see https://en.wikipedia.org/wiki/Image_impedance)…

Recommended method using ABCD parameters

According to https://en.wikipedia.org/wiki/Image_impedance, and assuming the symmetry hypothesis which allows to simply discard the second result, the characteristic impedance can be calculated as:

Export QGIS maps and terrain height data to Forsk Atoll.

Mon, 09 Oct 2023 00:00:00 +0000

Forsk Atoll antenna planning software is not so hard to use when a suitable map and terrain height data is available for import into Atoll. However such ready to use data is rather hard to find and finding such data is the top question asked in the comments of most Atoll tutorials.

Here is a tutorial to make a pretty convenient map with QGIS, usefull for all needs besides just Atoll, and to export relevant data towards Atoll.

On group delay of antennas.

Sun, 10 Jul 2022 00:00:00 +0000

Many thanks, in the order of appearance in the LinkedIn discussion, to Dr. Pierre-Antoine Garcia, Theunis Beukman, Benoit Derat, Hüseyin Yiğit, Andreas Barchanski for the insightful LinkedIn discussion which led to this post.

Recently on LinkedIn, a fellow colleague asked whether the group delay of an antenna could be calculated by the simulated complex gain. Sure it can, but with the right precautions.

What is tried to be measured ?

A reasonable asumption when dealing with an antenna is that there will be an other antenna facing it. The transmission coefficient S21 between the two antennas can be written as follows, using the Friis transmission equation https://en.wikipedia.org/wiki/Friis_transmission_equation :

Design of a coaxial power combiner with low-impedance inputs and increased isolation.

Mon, 11 Apr 2022 00:00:00 +0000

Hadrien Theveneau, Christophe Gaquière, Romain Lenglet, Matthieu Werquin, Jean-Christophe Joly, and Stéphane Tortel

This post is a mix between an unpublished long article, an article published in IEEE MWCL[^theveneau2017spatial], and further additions. Original articles by the authors in front of this post, revisions by the first author.

This article describes the design, fabrication and measurement of a 2.5 Ω, 8-way, 1 – 6 GHz spatial power combiner using an absorbing material to increase the isolation. Insertion losses are lower than 1.8 dB in the 1 – 6 GHz band, except for a few peaks. Isolation is at least 10 dB for 45° input pairs and better than -15 dB for other pairs. This is the first power combiner to provide wide bandwidth, high isolation, and low input impedances at the same time.

Introduction

More and more applications need to generate very high power pulsed microwave signals, in the order of tens of kilowatts: radars, EM warfare, and so on. These powers are traditionally generated with hyperfrequency tubes: magnetrons, klystrons, TWT, and so on. However, these techniques can have several major drawbacks: poor reliability, short lifespan, fragility, complex waveforms generation difficult and difficult power supplies.

Transfer S parameters.

Wed, 23 Mar 2022 00:00:00 +0000

This content was originally published on Microwaves 101 (https://www.microwaves101.com/encyclopedias/transfer-s-parameters). Many thanks to Steve for hosting the original version. Have a look on his website for more interesting content.

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Transfer S parameters are a convenient way to express S parameters in a way that allows to easily cascade blocks. They have the same principle as ABCD parameters: they express all relevant input quantities in function of all relevant output quantities, contrary to normal S parameters which express all scattered waves in function of all incident waves, and are messy when cascading blocks. They are sometimes more convenient than ABCD parameters, because they work with wave quantities instead of voltages and current, which are very difficult to measure at high frequencies.

Miller effect and solutions.

Tue, 22 Mar 2022 00:00:00 +0000

This content was originally published on Microwaves 101 (https://www.microwaves101.com/encyclopedias/miller-effect). Many thanks to Steve for improvements on the original version. Have a look on his website for more interesting content.

In Scientific Papers of the Bureau of Standards, Volume 15, 1919-1920, John M. Miller published a paper in titled “Dependence of the Input Impedance of a Three-Electrode Vacuum Tube Upon the Load in the Plate Circuit.” For this work, Mr. Miller is forever associated with the “Miller effect” which is still relevant a century later.

RFID coils should not be grounded.

Tue, 22 Mar 2022 00:00:00 +0000

Putting a solid ground plane in a PCB is a good practice. This allows to have good interconnexions between the different grounds of the components, to have a proximity shielding of the lines, and to reduce the cross coupling between the lines. All these effects have one root cause: a ground plane reacts to an electric or magnetic field by generating induced currents which tend to reduce this incoming field.

Why RFID antennas should not be called antennas ?

Wed, 07 Jul 2021 00:00:00 +0000

A friend of mine told me that he was looking for an “expert antenna engineer” to design RFID antennas, but he was not sure he searches well, because the last antenna expert he interview told him that he had designed hundreds of antennas, but never an rfid antenna. Never. Nada.

He tried to search on antenna books some information on rfid antenna to orient his search. He was quickly disappointed. He opened the excellent “Electromagnetic Waves and Antennas” ([https://web.archive.org/web/20240528230718/www.ece.rutgers.edu/~orfanidi/ewa/)) from Orfanidis, and search for RFID and NFC. Nothing! Same thing with “Antenna Theory: Analysis and Design” from Balanis. This starts bad.

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Mon, 01 Jan 0001 00:00:00 +0000

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Sorry, we’ve misplaced that URL or it’s pointing to something that doesn’t exist. Head back home to try finding it again.

About

Mon, 01 Jan 0001 00:00:00 +0000

Hadrien Theveneau, F4INX. Engineer in electronics, radio, high frequencies and microwaves. Ham radio callsign F4INX.

Licence

Mon, 01 Jan 0001 00:00:00 +0000

Contents licences

Parts from both the main author Hadrien Theveneau and co-author Gönül Demir, including both technical content and support source code, is released under the BSD 3-clause licence. See below.

BSD 3-clause licence

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: