He explained that he uses old coax for dummy loads, provided the characteristic impedance is still reasonably close to 50 Ω, since there is near infinite return loss. Also a poor student, he couldn't afford a dummy load that would work well at 70 cm. He got the coax and I never thought of coax loss quite the same way again.
Well, that was a fun story despite being only tangentially related to this article. The relevance is that I determined that an exceptionally long (100,000 meter) transmission line with low attenuation is a good way to emulate a resistive load with EZNEC. I needed it to demonstrate behaviour of L-networks at the feed point of a real antenna. The transmission line is put across the source on a single segment wire that is much too short (0.5 meters) to function as an antenna at 3.5 MHz.
To explore the characteristics of L-network topologies (there are 4 if you care to count them) I combined the aforementioned dummy load with an L-network, putting the source at the 50 Ω port. A virtual wire connects the source to the L-network. For the purpose of this exercise the dummy load is 25 Ω. The L-network was designed using TLW. Wire and L-network components are made zero loss to improve clarity in the calculations; that is, extraneous variables are removed so that we can focus on what is important.
Testing with EZNEC confirmed that the load impedance of the lengthy coax is broadband with a reactance term that is a small fraction of an ohm. Now we can move on to the L-network, an EZNEC example of which is shown above.
TLW supports several topologies of matching networks (tuners), picking the one that meets the stated objectives. Here we have a design frequency of 3.5 MHz using a "low pass" L-network to transform between 50 + j0 Ω and 25 + j0 Ω. Typically the coax is connected to the 50 Ω port and the antenna to the other port. If you want the reverse you simply swap ports. TLW does that automatically for you when you set the source and load impedances accordingly.
Now watch what happens when we plot the SWR from 1 to 15 MHz.
As expected the impedance is a perfect match at 3.5 MHz. The match is not broadband despite the load being a constant 25 Ω; the impedance transformation is frequency dependent. In the plot I chose to highlight the impedance at 14 MHz, as seen at the L-network's input (50 Ω) port. The impedance is very low. But is this consistent with the selected "low pass" topology? Further, what does this mean?
It is no accident that matching networks and filters look alike. Both have two ports and are constructed of inductors and capacitors, often with the same L or Pi (π) topology. The only difference is the design objective, the choice of which determines the result. Which brings us to a fundamental question: what happens to the RF energy that a filter is designed to reject? Physics tells us that energy is conserved so it much go somewhere. There are only a few possibilities:
- It is dissipated in the filter.
- The filter reflects energy back toward the generator.
What does happen, as demonstrated in the above example, is that the filter presents an impedance (high SWR) to the generator that reflects unwanted frequencies. The R component of the impedance of that matching network starts to decrease a little above the design frequency and keeps falling until it is very low indeed. Impedance mismatch is responsible for the filtering function.
As to what happens below the design frequency, well, it's the same as what happens above the design frequency when we choose the high pass topology for the L-network. In the top EZNEC screen capture the L-network is the high pass topology designed with TLW. Here is the SWR plot.
Again the 14 MHz impedance is marked. It's quite different than for the low pass network. As the frequency increases the impedance tends towards that of the dummy load alone. That is, the L-network effectively disappears, and the RF passing through with no difficulty other than a small amount of attenuation. As expected for a high pass filter the impedance declines below 3.5 MHz, reflecting RF back to the generator.
If an L-network is a filter what is happening at the design frequency? The corner frequency of the filter is where the transition between pass-through and blocking occurs. The R and X components of the impedance seen at both ports swings rapidly in the vicinity of this frequency. For a matching network we choose L and C values that give us what we want at the design frequency, often without regard to what happens far below and above that frequency.
In comparison to the dummy load we're using in the example it is never so simple for a real antenna since the load impedance varies with the frequency. Indeed, the antenna is also a species of network that is frequency sensitive! Out of band energy may be reflected while in band energy is matched to the impedance of free space (377 Ω) and radiated.
Sometimes it is possible to design a network that achieves a broader match by designed for frequency sensitive behaviour that in part compensates for the antenna's changing impedance. But hams rarely do this since it is difficult and is very situation specific.
For a receiver filter the impedance swing at the network's corner frequency is responsible for the ringing we hear in our receivers. This is largely due to variable phase shift (reactance change) over a small frequency range. Filter designers try to control for this. Eliminating ringing is more tractable with software DSP than less cooperative analogue filters.
How good a filter is it?
We all want to avoid transmitting harmonics. It is good practice and it keeps us compliant with our country's regulations. For contesters even properly attenuated harmonics are a serious nuisance at operating positions on higher bands (SO2R or multi-op). The question is whether the supplemental filtering function of a L-network can be helpful.
The answer: maybe. In the low pass example above the return loss at 14 MHz, the fourth harmonic, is 0.2 db. This ~14 to 15 db reduction. At 7 MHz, the second harmonic, the reduction is only ~3 db. Clearly we cannot rely on feed point L-networks alone to deal with the problem of harmonic interference. In combination with purpose-built band pass filters the additional harmonic attenuation may be helpful.
Our antennas can also help by being non-resonant on harmonics, which is one reason, although not the most important one, why many contesters look unkindly upon multi-band antennas such as tri-band yagis.
A simple L-network at the feed point of a 20 meter yagi is unlikely to be helpful since the only HF band being protected is 10 meters and then only minimally, ~3 db, since this is the second harmonic. There is no compelling reason to substitute one for a hairpin (beta) match, which is a form of high pass filter (shunt C and parallel L). The hairpin may be better by attenuating the received fundamental energy of adjacent transmitters on lower bands.
If filtering is a really wanted in a matching network it is worth considering a Pi-network which with its additional filter pole (one more shunt component) is a better filter. TLW will happily design for you either high pass or low versions of this more complex network. Pi-networks have been employed in power amplifier circuits for decades, transforming impedance and effectively filtering harmonics. Many tuners also employ the pi topology.
For better filtering a multi-pole filter is required. Although these networks can also transform impedance it is not usually done since optimizing one can come at the expense of the other.
Other reasons to choose an L-network topology
Filtering is not the only secondary criterion when it comes to choosing a matching network for an antenna. When I designed the L-network for my 160 meter antenna I chose the low pass topology since the L and C values were more easily achievable with parts on hand. Both low and high values for coils and capacitors can present difficulties, so picking the topology that best avoids them is attractive. Filtering was a unplanned benefit.
For the same reason I am choosing a low pass L-networks for my new 80 meter vertical yagi. As I write this the matching network is designed but not built. I'll describe it when the project is complete, including the benefits of the selected topology. Once complication I encountered is that at least two L-networks are needed -- one for the yagi (directional) mode and one for the omni-directional mode -- and by careful design I was able to simplify switching between modes.
Unfortunately the choice of a low pass design defeats a benefit. The 80 meter yagi works well as an omni-directional vertical on 30 meters, the third harmonic. It is currently my only effective antenna for that band. Adding a low pass L-network may put an end to that. For multi-band antennas it may be better to select a high pass topology even if you need to switch network elements on one or more bands.
Conclusion
The takeaway is that every network transforms impedance and does so in a manner that is frequency dependent. What we call a "tuner" or matching network is a network that transforms impedance to a desired value at a desired frequency. A filter is a network that passes or blocks desired and undesired frequencies, respectively. Filters and tuners are essentially the same but with parameters adjusted to suit the application. With forethought it can be possible to achieve both.
Simple as they are, L-networks are versatile. There is more to be said about them, some of which I may touch on in the future. None of this will surprise hams who have long experience designing filters and matching networks. For the rest of us there is always more to learn.
The content of this article nibbles at the edges of network design, only highlighting a few interesting points. Hopefully I haven't simplified too much for knowledgable readers. For those of you surprised (or horrified) that I used EZNEC as a network analyzer my excuse is that I stuck with what I know rather than fooling around with more suitable software tools I know less well. EZNEC works when one is careful. With additional effort it'll even handle more complex networks, by chaining L-networks port to port.
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