Matchable Loads from S-Parameters Defined Matching Networks

This post compares two different ways for finding the matchable loads \(Z_L^{'}\) that provide the desired impedance \(Z_G^{*}\) to the generator.

I will show the difference between two approaches, one rigorous and the other approximate, by using a set of S-parameters obtained by a black box network. The only requirement is that the black-box is linear, as the S-parameters requires linearity. For the curious, they are obtained from a binary weighted sweep of a lossy \(LL\) network composed of 1024 states in total from SimSmith.

Tandem Directional Coupler: Circuit Theory Approach

This document discusses the analysis of an ideal “tandem” directional coupler using lumped element circuit theory.

A directional coupler is a four port device that is used to sample the forward and reflected wave in a transmission line. It is a key component of a VNA and can be used to measure power flowing in a transmission line, but it can have countless possible uses. Generally they are built using distributed elements structures, but there are also versions built using lumped elements.

The tandem directional coupler, or also tandem bridge, is one of those directional couplers that is built using a lumped element approach. This kind of directional coupler, famous for radio-hams, has inherently large bandwidth and can handle a lot of power. It is also well suited for low frequency scenarios, down to the kHz range. It is composed of two current transformers, or two transformers with a high turn ratio, and two termination resistors with the desired characteristic impedance \(Z_0\), which can be arbitrary but usually 50\(\Omega\).

Coupled coils and coupling coefficient: from fraction of total flux to inductance definition

It is possible to relate the coupling coefficient \(k\) to both the total (\(\phi_{1}\) or \(\phi_{2}\)) and shared flux (\(\phi_{12}\) or \(\phi_{21}\)) or to the self (\(L_{1}\) and \(L_{2}\)) and mutual (\(M\)) inductances: \[ k = \frac{M}{\sqrt{L_{1} L_{2}}} = \frac{\phi_{12}}{\phi_{1}} = \frac{\phi_{21}}{\phi_{2}} \]

Simple proof:

The Man Who Changed Everything: The Life of James Clerk Maxwell

Basil Mahon wrote a book about Maxwell.
It's a fantastic book on the life of the great Maxwell, that thanks to his discoveries, changed radically the approach to the physics and our's everyday life.
I found it pleasant to read and that passes emotions, the same that James wanted to arouse in his students.
It's really interesting to see the reasoning under the explaining of his theories. Even if it's technically and physically accessible, to fully understand it it's necessary a minimum predisposition to the scientific reasoning and, maybe, some math.
I suggest and i wish to everyone to read it.

Buy it from Amazon.com ! (Even from Amazon.it or Amazon.co.uk)