Re: Technical Puzzle #22 - Select the right ratio

Folk,

Once again a big 'thank you' to everyone who took part - particularly those brave enough to share their thoughts

Let's dismiss the two easy ones first!

It's good engineering practice to install a balun wherever there is a transition from an unblanced to a balanced part of a sytem. In Pete's situation if there was no balun between the ladderline and the tuner, the ladderline would be severely unbalanced, would carry unequal leg currents, and would radiate. If the balun ratio is chosen appropriately, and the balun is well designed and constructed, it should introduce well under a dB loss; so we can dismiss Answer #4

Answer #1 is more subtle and I often hear it being promoted. The fact is that the impedance at the end of the 450 ohm ladderline feeding this doublet will

never be 450 ohms, no matter what its length; in fact the only time it could be 450 ohms is if the ladderline was connected to a resonant 450 ohm antenna, and you don't find many of those around. Ironic isn't it - the one impedance you're very unlikely to encounter at the end of 450 ohm ladderline is 450 ohms !!

That leaves us with a choice of 4:1 or 1:1.

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The arguments put forward for a 4:1 impedance transformation often assume that the tuner works best when operating with a load impedance close to 50 ohms. That turns out not to be true! This chart shows the losses (%) vs load resistance of a typical T-network tuner on 80m for several values of load reactance; I chose 80m because losses tend to be more evident on the lower-frequency bands.

As we can see the lowest tuner losses occur when the load resistance is in the medium/high range 250ohms-2500ohms; the highest losses occur at low load resistances, particularly where they are accompanied by a large capacitive reactance.

Let's now take the example of Pete's proposed doublet. At modest heights above average ground, the doublet has a feedpoint impedance close to 50 ohms on 80m. That means that the impedance seen at the tuner end of the ladderline could have a resistive component anywhere from 50 ohms to 4050 ohms depending on ladderline length; that range of impedances is indicated by the lower shaded bar in the chart, labelled 1:1. If we now introduce a 4:1 impedance transformation, the range of impedances will be lower by a factor of 4 as indicated by the upper shaded bar labelled 4:1. It's clear that the 1:1 range of impedances will result in the lower overall tuner losses.

In fact, no matter what the antenna impedance, the range of impedances seen at the tuner end of the ladderline would have a āgeometric meanā of 450 ohms - that is they would swing equally below and above 450ohms as the ladderline length is varied, but once we introduce a 4:1 balun the geometric mean will reduce to 112.5 ohms. One look at the loss chart tells you that centering the impedances at the higher value is the preferable option.

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Let's now take a look at the specific losses that would occur with our example 132 doublet fed with 450 ohm ladderline.

The following chart was produced by varying the feedline length from 0Ā° to 180Ā° in 10Ā° steps. At each step I calculated the impedance seen by the tuner first with a 1:1 balun and then with a 4:1 balun, and the tuner losses determined using W9CF's T-network tuner simulator. Of course, beyond 180Ā° the chart simply repeats itself. Ladderline losses were ignored.

Apart from a small range of line lengths between 80Ā° and 115Ā°, where the line is a quarter-wave long and has transformed the 50 ohm feedpoint impedance to a very high value around 4000 ohms, the 1:1 balun is the better option; not only that, the worst case loss never exceeds 14% with the 1:1 balun whereas it reaches 21% with the 4:1 balun.

But what about other bands - the doublet wont be used on just 80m!

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This chart shows the tuner loss plotted against line length for Pete's doublet on 40m. Here the doublet feedpoint impedance is around 4000ohms, so for short ladderline lengths the 4:1 balun shows an advantage. However, as the ladderline length increases and the impedance is transformed to lower values, the 1:1 balun soon shows the lower losses again. Across the whole range of possible ladderline lengths the 1:1 balun is twice as likely as the 4:1 to produce lower losses.

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None of tuner load impedances from this antenna, whatever the ladderline length or whatever the band, was outside the matching range of the T-match with either ratio balun; so matching range is not a consideration.

It's possible that if you ran very high power into a high load impedance there may be an over-voltage problem with the tuner; a 4:1 balun would help in this situation by dropping the load impedance and the voltage, but then the balun would have to be designed to handle the high voltage.

The conclusion seems clear:

if you have to choose just one balun ratio, unless you know that your combination of doublet/ladderline length falls into the minority of cases where a 4:1 balun has the advantage - around a current minimum/voltage maximum - then a 1:1 balun is the preferred choice to reduce tuner losses.This analysis was all about transformation ratios; we'll take a look at some of the other issues - Voltage Baluns vs Current Baluns, Balun losses, etc - in future Puzzles.

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This topic crops up so many times on various forums that I thought it worth devoting a web page to it:

http://www.karinya.net/g3txq/tuner_balun/73,

Steve G3TXQ