But first, a quick note about the MATLAB routine used to create the plots below...

I thought it would be fun to use my recently-purchased copy of MATLAB to create a MATLAB script to let me do a bit of analysis of tuner design -- but rather than analyze power loss (as I'd done in other posts on this blog), I thought I'd look into the "range" of load impedances that a tuner could match to a 1:1 SWR at 50 ohms.

I initially wrote the MATLAB script to plot an outline on a Smith Chart that would

*enclose*the range of impedances that could be matched to 1:1 at a selected frequency. Here's an example of how that plot looked:

(click on image to enlarge)

But I wasn't happy with the "visibility" of the outline, and so I changed the script to show the encompassed area a bit more dramatically by filling it in, like this:

I hope you agree that this second plot is much easier to see.

As for the MATLAB script itself, all it's really doing is stepping the values of the network's two variable components (step size selected by me) over the range of all of their possible values. A 50 ohm load is connected to the network's

*input*and the program calculates the impedance that this 50 ohms is transformed to be when looking into the network's

*output*terminals. This transformed-impedance is calculated at every step of the component values, and it is the

*complex-conjugate*of a load impedance that, when connected to the network's output terminals, would be

__transformed to 50 ohms at the network's input with those same settings of the variable component values.__

**The Nye Viking MB-V-A Antenna Tuner**Let's start off with the Nye Viking MB-V-A. (Note: this tuner was reviewed in the June, 1994 issue of

*QST*).

The Nye Viking MB-V-A tuner is, essentially, an L-Network (series-L, shunt-C), although the 2:1 auto-transformer at the output (which provides a 4:1 impedance transformation) and the 230 pF fixed capacitor at its input might throw you off.

The 2:1 transformer essentially multiplies the load impedance seen by the tuner by four, thus increasing the range of impedances that can be matched (because the series-shunt L-network is good at matching impedances whose resistive component is greater than 50 ohms). E.g. 15 ohms would first be multiplied up to 60 ohms prior to being matched by the network.

Let's take a look at the impedances that can be matched by this tuner. Here's the range of loads that are matchable to a 1:1 SWR at 1.8 MHz:

(click on image to enlarge)

Note the lack of coverage over a significant area of the Smith Chart at 1.8 MHz.

Coverage improves at 3.5 MHz:

(click on image to enlarge)

The range of loads that are matchable to a 1:1 SWR at 7 MHz:

(click on image to enlarge)

The range of loads that are matchable to a 1:1 SWR at 14 MHz:

(click on image to enlarge)

The range of loads that are matchable to a 1:1 SWR at 30 MHz:

(click on image to enlarge)

And here's the MATLAB code I used to calculate the impedances that the Nye Viking tuner can match to 1:1:

(click on image to enlarge)

**Antenna Coupler, Ulrich L. Rohde, DJ2LR/W2, (***QST*, December, 1974)This antenna tuner is also a variant of an L-Network (series-L, shunt-C). It appeared in an article titled "Some Ideas on Antenna Couplers," by Ulrich L. Rhode, DJ2LR/W2, in

*QST*, December, 1974. (And if my memory serves me correctly, I also saw the design published in the September 13, 1975 issue of

*Electronic Design*).

Like the Nye Viking MB-V-A, it also contains a 2:1 auto-transformer (providing a 4:1 impedance transformation). But this design has the auto-transformer at the input of the network, not at the output.

The 2:1 auto-transformer at the network input is essentially multiplying up the impedance it sees by a factor of 4:1. In other words, the goal of the network is now to transform the load impedance to 12.5 ohms, rather than to 50 ohms. The transformer then kicks the 12.5 ohms up to 50 ohms, thus presenting the appropriate load to the transmitter.

The tuning network itself is a series-shunt lowpass L-network, formed by the adjustable 28 uH inductor and 1350 pF capacitor. Per the QST article, the 1 uH fixed across the auto-transformer's "secondary" allows matching loads whose resistive component is less than 12.5 ohms. And the 500 pF series capacitor is to improve the matching range on 160 meters, where the variable shunt capacitor would normally have to be quite large (e.g. 4000 pF, per the article) to match a 50 ohm load. The series cap at the network's output effectively "transforms" an impedance (e.g. 50 ohms) to a higher impedance that can be matched more easily with the 1350 pF variable cap. (Think of the 500 pF series cap in combination with the 1350 pF variable shunt capacitor as forming a "shunt-series" L-network that transforms a low impedance to a high one).

Let's look at some of the bands where the network component values might have their largest impact on coverage of impedances.

First, let's look at the range of loads that are matchable to a 1:1 SWR at 1.8 MHz:

(click on image to enlarge)

The range of loads that are matchable to a 1:1 SWR at 3.5 MHz:

(click on image to enlarge)

The range of loads that are matchable to a 1:1 SWR at 14 MHz:
(click on image to enlarge)

The range of loads that are matchable to a 1:1 SWR at 30 MHz:
(click on image to enlarge)

Here's the MATLAB routine used for the Rohde coupler calculations:

(click on image to enlarge)

Comparing the two tuners, it seems to me that the Nye-Viking model has a wider match range than the Rohde design on the higher bands, and is comparable to the Rohde tuner on the lower bands (although the Rohde design might be better on160 meters).

__Other Tuner Posts:__A quick tutorial on Smith Chart basics: http://k6jca.blogspot.com/2015/03/a-brief-tutorial-on-smith-charts.html

The L-network: http://k6jca.blogspot.com/2015/03/notes-on-antenna-tuners-l-network-and.html

A correction to the usual L-network design constraints: http://k6jca.blogspot.com/2015/04/revisiting-l-network-equations-and.html

A look at highpass T-Networks: http://k6jca.blogspot.com/2015/04/notes-on-antenna-tuners-t-network-part-1.html

More on the W8ZR EZ-Tuner: http://k6jca.blogspot.com/2015/05/notes-on-antenna-tuners-more-on-w8zr-ez.html (Note that this tuner is also discussed in the highpass T-Network post).

The Elecraft KAT-500: http://k6jca.blogspot.com/2015/05/notes-on-antenna-tuners-elecraft-kat500.html

**Standard Caveat:**I could easily have made a mistake in my MATLAB program or in my post above. If anything looks wrong, or if you'd like clarification, please feel free to contact me!

And if you'd like me to apply this MATLAB script to other networks, please feel free to contact me.

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