# Matching Network Efficiency

## Matching Network Efficiency

Your company has paid a large sum of money for a piece of complex RF process equipment and your RF power supply is rated to 1% accuracy. That will give you great confidence that the process will be reliable and repeatable.

However, if 10 – 50% of that accurate power is lost in the matching network does that change things?   Would you like to know how efficient your matching unit is?

So, even if 50% of the power is lost in the matching unit; you can probably learn to live with that as long as it is the same every time, Right!  But, what if the match efficiency is not constant and changes every time you change the process gas flow, the gas type or the chamber pressure, that would not be so good, would it?

So let’s measure a typical matching network and establish the efficiency and see how good it is and if it is stable or does it change with other parameters?

### First, let us define what efficiency, Eff is; it is the power out divided by the power in. The measurements used here were described in detail on a previous blog where we measured the rf matching network range in nine easy steps.  We will use the same data in our analysis here. So if you want to collect your own data then follow the steps outlined in the previous post.

### A bit of background first

The components of a matching network are designed as pure reactance in order to have no power dissipation within the matching network. However real reactive components are lossy, and so will dissipate some power. Inductors are typically one or two orders of magnitude more lossy than capacitors, and it is usual to assume that all lost power in the matching unit is dissipated in the inductor. The figure above shows that the power measured by a power and impedance meter before and after the matching network over the full range (extremes) of operation of the matching network.  Note that the power in both power meters are quite different.  This is often a shock to an engineer who views the matching network as ideal.  The suspicion is caste on the meters.  Most power meters do not work when the load is not matched, but the real reason that the powers are different is the match efficiency and internal resistance Ri of the matching network.

So using this power in and power out data we can measure the efficiency. It is clear that the efficiency changes with the match position, in other words with the process impedance.  The data is measured at the extremes of the operating range so for this matching network the maximum operational efficiency is 80% and the minimum is 50%. The problem posed at the beginning of the post is very real and will happen. As much as 50% of the input power will be lost in the matching unit, and that figure will change at different process impedance values.  That means a +/- 23% variation of delivered process power for a fixed set power.  The least you can do is know about this and how it might impact your process.

But can we trust the power meter?  These data were taken with a power and impedance meter so that it can record power in an unmatched line but the power accuracy is a function of the phase of the load. The power meter used is 1% accurate near zero phase.  So the efficiency changes that are measured at low phase angles are indeed accurate, the 50% to 80% changes are real.

### The cause of variable efficiency

The main cause of power loss is the coil resistance or wiring resistance on the load side where the higher currents flow.  This is because we are matching 50 ohms to a lower real impedance.  As the process switches on the Q is a maximum and would be expected to reach a minimum at the highest power, but this depends on the load dynamics.  So the efficiency varies rapidly even during a single process step.

The ratio of load to source resistance determines the Quality Factor of the matching unit.  We have already determined that the Q within this matching network’s operation range is 2-4.  This was also done in a previous post in this series, matching network quality. Where Rl and Rs are the load resistance and source resistance (normally 50 Ohm). We will  now show that efficiency is determined by this Q factor.  We do this by measuring the internal resistance of the matching network. The efficiency of the match is determined by the internal match resistance, mostly in the coil.  If Ri remains constant then as Q changes so most the Efficiency, Eff.  Ri will change with heating of the coil but this effect is usually much less that the changes due to the variation of Q which is determined by the load impedance. The value of Ri can be determined from the measured efficiency. Because of the mono accuracy the best values for Ri will be obtained at the lowest absolute phases, for this match Ri = 0.7 Ohms.

### Conclusions

Over the series of three posts we have examined how to measure the matching network operating range, quality factor and efficiency.

The quality factor depends on the load resistance and it determines the current amplification needed.

The higher current amplification creates more losses in the output section of the matching network.

The power set at the generator does not determine the power delivered to the process as the Q and efficiency can modulate the power by +/- 23% .

Please comment on this post, questions are very welcome and if errors are spotted please let us know.

Previous posts in this series

rf matching network range