Impedance Matching Networks for RF Plasma Thrusters

The source, the load, and the mismatch

In an RF power processing unit the amplifier stage is designed to deliver its power into a defined impedance, conventionally 50 ohms, the impedance its coaxial line and its Class-E output network are built around. The load is an antenna or coil coupled into a plasma discharge. That load is complex, meaning it has both resistance and reactance, and its value depends on gas pressure, RF power, magnetic field and the state of the discharge. It is typically far from 50 ohms and it is not constant. Connect the two directly and most of the power never reaches the plasma. The matching network is the passive circuit between them that transforms the load impedance so the amplifier sees something close to its design value.

Forward power, reflected power and VSWR

When the load is not matched, part of the wave travelling from the amplifier to the antenna is reflected back down the line. Forward power is what the amplifier sends. Reflected power is what returns. The difference, minus network losses, is what couples into the plasma. Reflected power is wasted at best and damaging at worst, since it raises voltage and current stress in the amplifier and can force it to fold back or trip.

Voltage standing wave ratio, VSWR, is the usual single number for how bad the mismatch is. A perfect match is 1 to 1, with zero reflected power. As the mismatch grows the ratio climbs, and the fraction of power reflected rises with it: roughly 1 percent reflected at 1.2 to 1, around 11 percent at 2 to 1, and a quarter of the power at 3 to 1. The job of the matching network is to keep the amplifier-side ratio near 1 to 1 across every operating condition the thruster will see.

L, T and Pi network topologies

Practical matching networks at 13.56 MHz are built from two or three reactive elements, inductors and capacitors, chosen so they are nearly lossless. The three common arrangements:

Plasma matching units are very often a T or a Pi built with two variable capacitors and a fixed inductor, because two independently adjustable elements are the minimum needed to hit an arbitrary complex load and cancel its reactance at the same time. An L network cannot be retuned as the load drifts, which is the core limitation for a thruster.

The unlit-to-lit jump at ignition

Before the discharge strikes, the antenna sees mostly vacuum and a little capacitance to nearby structure. Its impedance is high and almost purely reactive, and it absorbs very little power. A network tuned for the running plasma presents a severe mismatch in this state, so almost all the power reflects and the amplifier cannot deliver the burst needed to ignite. Once the plasma lights, the loading resistance rises abruptly, sometimes by more than an order of magnitude, and the reactance shifts. The network is now far from its tuned point in the other direction.

Handling this transition is one of the hardest parts of the design. Options include a separate ignition circuit, a deliberately detuned start point, a high-voltage strike aided by a keeper electrode, and a controller that steps the network and the power through the transition quickly while protecting the amplifier from the reflected energy. A tunable network with a fast controller can walk from the unlit tuning to the lit tuning in a controlled way.

Losses in the matching network

The network is passive but not lossless. Every inductor has series resistance and every capacitor has an equivalent series resistance and dielectric loss. Because the elements carry large circulating currents, that is currents well above the line current, even a small resistance dissipates real power. Loss is worst when the required impedance transformation is large, which forces high loaded Q and high circulating current, and it is a strong function of inductor quality factor. In a space-grade unit this loss is heat that must be conducted away and it comes straight off the system efficiency, so the network is designed with high-Q air-core inductors, low-loss capacitors, and the smallest transformation ratio the geometry allows.

Fixed versus tunable matching

A fixed network is set once for a nominal operating point. It is simple, light, reliable and lossless in the sense that it has no moving parts or control power. It works only if the plasma load stays within a narrow window, which in practice means a single thrust level and stable conditions. Step the power, change the propellant flow or ride through ignition, and a fixed network reflects power and stresses the amplifier.

A tunable network adjusts its elements, historically motor-driven vacuum capacitors, increasingly solid-state or switched-element designs, to track the load. It keeps VSWR low across the full throttle range and through transients, at the cost of actuators, sensing and a control loop. For a thruster that has to throttle and that must survive ignition every start, tunable matching is usually the only workable answer. The MHz Labs design takes this approach, a real-time adaptive impedance matching network, which is the product companion to this explainer: it measures the mismatch and retunes continuously so the amplifier always sees its design impedance. See that page for the architecture and design targets.

Sources and further reading

• Goebel and Katz, Fundamentals of Electric Propulsion, NASA JPL DESCANSO, for RF coupling and antenna loading.
• Takahashi, Helicon-type radiofrequency plasma thrusters and magnetic plasma nozzles, on antenna-plasma coupling and load behaviour.
• SatNow, What is a Power Processing Unit (PPU) for thrusters, background on the PPU role.