Rocket scientist’s guide to RF impedance matching

Article By : Rajan Bedi

Here's a look at impedance matching, which is used to make a load or line impedance equal that of a driving source for maximum power transfer.

Operators are ever more exploiting the benefits of wideband digital payloads, with the aim of delivering the next generation of satellite services. Broadband ADCs/DACs now directly digitise/re-construct IF/RF carriers and impedance matching is required to optimise the integrity of key interfaces and the overall signal path. Once a key skill of RF analogue engineers, digital and mixed-signal members of the avionics design team are now having to grapple with the concept of impedance matching for high-throughput applications.
Impedance matching is used to make a load or line impedance equal that of a driving source for maximum power transfer. If these are not matched, less energy will be delivered, standing waves will develop, and the load will not absorb all of the power sent down the line. Consequently, some of the energy reflects back to the source with the potential to cause damage. For complex impedances, maximum transfer occurs when the load equals the conjugate of the source, i.e. the reactances have the same magnitude but opposite sign.
Within a spacecraft, impedance matching networks have traditionally been used between the receive antenna and the LNA, to connect internal amplifier stages, and also between the power amplifier and the downlink transmitter to maximise power transfer.
Lumped, tuning circuits such as L, Π or T-networks can be used to transform a load impedance into one which is conjugate matched to a source for maximum power transfer. These are narrowband and multiple sections can be cascaded for wider bandwidths.

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Figure 1: Narrowband L, Π and T frequency-tuning networks.

The choice of topology and the position of the inductors and capacitors can be swapped based on the relative sizes of the source and load impedances, the required response and Q, the practical value and size of the components, and whether or not you wish to pass DC.
For microwave frequencies, the values of lumped components become too small and distributed transmission-line structures realised using microstrip or stripline can be used for impedance transformation to eliminate mismatch.
A section of λ/4, low-loss transmission line can be inserted between a source and an arbitrary real load to match their impedances, where Z0 for the matching section becomes √(Zsource*Zload). Broadband matching can be achieved by cascading multiple λ/4 lines with various passband characteristics.{pagination}
To avoid the use of a different characteristic impedance, a stub can be connected in parallel to a main transmission line to prevent reflections reaching the source. For example, a short-circuit of appropriate length is placed at a specific distance from the load allowing standing waves from the terminated stub and reflections from the load to completely cancel each other. The admittance seen beyond the stub equals Y0<img alt="
As an example, let's assume our satellite needs to process 500MHz of bandwidth centred at 2.35GHz. Typically I enter my schematics using Mentor's xDxDesigner which allows me to re-use the circuit entered for PCB design for simulation and analyses. Layout extraction using Hyperlynx Boardsim allows me to add the effects of traces, vias and connectors to predict the overall post-layout |S11| or |S22| of the load to be matched.

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Figure 2: λ/4 and shunt-stub transmission-line impedance-matching structures.

Once the load impedance has been calculated, I like to use a Smith Chart to develop a tuning circuit to optimise RF match and minimise reflections. Today, because of time-to-market pressures, I use Keysight's Genesys software to quickly synthesise a compensation network. This is a really cool piece of software, which has saved me a lot of time and someone has even posted a nice video tutorial. Once you enter your required bandwidth, the source and load impedances, the tool can generate lumped tuning topologies or distributed, transmission-line structures such as stubs or a ?/4 transformer. The software can be trialled free-of-charge if you would like to have a play.
The following EZwave plots show how Hyperlynx Analog has been able to extract the input match of the mixed-signal front-end for a telecommunication payload. Genesys was used to synthesise a suitable tuning network, which was subsequently added to the receiver circuit within xDxDesigner and re-simulated. The pink trace is the uncompensated input match and the green is the post-layout |S11| after tuning.

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Figures 3 and 4: Input match for a 500MHz bandwidth, S-band satellite transponder.

This post has briefly introduced RF impedance matching for space applications, and there are limits on how good a match can be achieved over a specified bandwidth and the complexity of the tuning network as defined by Bode-Fano. If you would like to learn more about narrow and wideband tuning as well as the advantages and disadvantages of the various topologies and techniques, this is a topic I teach on my Mixed-Signal course. I also demonstrate the Hyperlynx and Genesys tools, as broadband matching has become a major challenge for many satellite OEMs wanting to offer the benefits of high-throughput digital payloads to spacecraft operators.

About the author
Rajan Bedi is currently CEO of Spacechips. Rajan worked at Astrium (now Airbus) for twelve years developing and researching space-grade electronics for telecommunication, navigation, Earth-observation and science missions. As Head of the Mixed-Signal Design Group, Rajan's team developed the hardware for the award-winning, channelising payload currently operating on-board the Alphasat telecommunication satellite.

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