Last time, I posted a procedure for creating Smith charts by hand. This time, I’d like to continue the process by showing my procedure for using Matlab® or GNU Octave to create these charts. I should note that Matlab® already has a “smithchart” function, that does a pretty good job. But if you’d like to customize the chart or do it in GNU Octave, this process might be better. Matlab®’s function will plot a reflection coefficient for you, while the script presented here does not. Matlab® or Octave, the smithchart function or script doesn’t do the \(Z\) to \(\Gamma\) conversion for you. The function simply draws the circles on in Cartesian coordinates. You still have to convert an impedance to a reflection coefficient. $$\Gamma = \frac{Z - Z_0}{Z + Z_0}$$ where is the basis impedance for the chart. The real and imaginary part of the reflection coefficient will be the and coordinates that to plot. Zero reactance line The zero reactance line is the axis. We just draw a line from -1 to 1. x = linspace (-1, 1, 256); y = zeros (1, length (x)); plot (x, y,'k'); % We don't show the axis, but we need to scale it. axis ([-1.15, 1.15, -1.15, 1.15]); axis off; hold on Zero Reactance Line Resistance Circles We will not plot complete circles for all resistances. This will lead to a very cluttered chart on the right hand side. Instead we will start and stop them at strategic locations on the chart. The complex impedance can be broken down into $$Z=A+jB$ Where is the resistance and is the reactance. In a Smith Chart, all impedances are normalized to one. The reflection coefficients for the circles become A = [.2 .5 1 2]; Blim = [1 2 5 2]; for idx = 1:length(A); B = linspace (-Blim(idx), Blim(idx), 256); rho = (A(idx)^2 + B.^2 - 1 + 2i * B) ./ ... ((A(idx) + 1).^2 + B.^2); plot (rho, 'k'); end Resistance Circles Some resistances can have full circles, namely, the -, -, and circles. However, we will never be able to complete the circles using the technique above. The right hand side of the chart is infinity. Instead, we just make Cartesian circles at those points. It’s easier and saves memory. theta = linspace (0, 2 * pi, 256); A = [0 5 10]; for idx = 1:length (A) cx = A(idx) ./ (A(idx) + 1); rx = 1 ./ (A(idx) + 1); plot (rx * cos (theta) + cx, rx * sin (theta), 'k'); end Full resistance circles at 0, 5, and 10 ohms. Constant Reactance Like resistance, we don’t draw complete circles for the reactances. They start at and end at various resistance circles in the chart. The technique is the same, but we don’t have any reactances that go all the way to the side of the chart. Alim = [.5 .5 1 1 2 2 5 5 10 10]; % Resistance endpoints % for each reactance % line B = [-.2 .2 -.5 .5 -1 1 -2 2 -5 5]; for idx = 1:length (B) A = linspace (0, Alim(idx), 256); rho = (A.^2 + B(idx)^2 - 1 + 2i * B(idx)) ./ ... ((A + 1).^2 + B(idx)^2); plot (rho, 'k'); end Reactance Arcs Resistance and Reactance Markings % Resistance markings are on the zero-reactance line. A = [0.2 0.5 1 2 5 10]; B = zeros (1, length (A)); rho = (A.^2 + B.^2 - 1 + 2i * B) ./ ((A + 1).^2 + B.^2); % Offset the text slightly xoffset = [0.1 0.1 0.05 0.05 0.05 0.075]; yoffset = -0.03; for idx = 1:length (A) text (real (rho(idx)) - xoffset(idx), ... imag (rho(idx)) - yoffset, num2str (A(idx))); end % Let's put the reactance markings outside of the % zero-resistance circle. A = [-0.075 -0.075 -0.075 -.1 -0.125]; rho = (A.^2 + B.^2 - 1 + 2i * B) ./ ((A + 1).^2 + B.^2); for idx = 1:length (B) text (real (rho(idx)), imag (rho(idx)), ... strcat ('j', num2str (B(idx)))); text (real (rho(idx)), -imag (rho(idx)), ... strcat ('-j', num2str (B(idx)))); end % Zero for resistance and reactance. rho = (-0.05.^2 + 0.^2 - 1) ./ ((-0.05 + 1).^2 + 0.^2); text (real (rho), imag (rho), '0'); hold off; Resistance and Reactance Markings Plotting on the Chart To plot a value on the chart, calculate the reflection coefficient for the point and use Matlab’s plot function after issuing the hold on command.
Fall 2010 Applied Arts Workshop on accordion book binding led by Cynthia Katz.
Simple, low component count tone generator. It can be adapted to create a morse code circuit, by adding a switch to the output. How it works: This circuit is based around the 555 timer circuit, used as an astable (free running) oscillator. The frequency (pitch) of the tone is set by the resistors and capacitors in the left side of the circuit. The first one is a potentiometer (variable resistor), this is our pitch control, which is basically all the external components you need. The capacitor to the far left is to reduce as much noise or undesired operation of the potentiometer, getting a smooth pitch change when adjusting. You can find the timer's datasheet by following the link: 555 timer
Store bought deodorants that are truly non-toxic typically lose their effectiveness after a few hours. This homemade deodorant recipe really works!
One of my favorite authors is Edgar Allen Poe. As often as I have read his work, I still keep a dictionary near by as there are so many wor...
Just a random artist with random thoughts and random interests... quite a lot of thoughts and interests actually... welcome to my world :) This is NOT a themed blog... there is no rhyme or reason... glamour will be mixed with rustic country... nature will be mixed with cityscapes etc etc. If I like it, it goes in here. Enjoy! Some of the photos blogged are my own and will be identified as mine... others are not and when possible, they are clickable to the original source. Many of the words are my own, unless blogged as quotes :)
I love to wear skirts! They are so versatile. You can mix and match them with blouses, sweaters, or pair them with jackets. They can be worn with tights and flats or tights and boots. You can change the look by simply changing your shoes from flats to stilettos. Because I love skirts, I am always on the look out for an interesting design and I've found a few that I thought you might like too! I wish I could see a complete front view of this skirt. But regardless, I really like the asymmetrical hem and the side seam welt pocket. A wrap skirt is always lovely. I love how they played with the pattern on this skirt. I'm sure you've seen this skirt on Pinterest. It's a very popular pin. But it derserves to be looked at again as it is such a lovely and dramatic design. Okay, we need Bunny of La Sewista for this one, especially since she is a smocking guru. I REALLY want to know how to do this!!! I don't care for the little buttons, but I do love the technique. Simple, yet so graceful. Here's another interesting wrap. I think this is so pretty. Look closely and you'll see that inside the center of the drape is a zipper. Sadly the zipper looks a bit off, but it's a great idea nonetheless. Since this skirt is in white, it's a little difficult to see, but if you look closely, you'll see that it has very interesting lines. What a lovely take on a pleated skirt. A cute take on a kilt design. This skirt makes me want to throw my sandals on and head for Bermuda!!! It just screams summer. I love how the scalloped edge was taken around the hem and then up the center back to accent the vent opening. Such a comfortable looking skirt. From Eileen Fisher. I believe that Marcy Tilton has a Vogue pattern that is quite similar. I love everything about this skirt. Take a striped fabric and add godets. Lovely. Now for a little comic relief ;) I'll say this, it's interesting!!! I have some fabulous surprises up my sleeve for you this week, so please be sure to check back. Also, the voting for the Get Your Motors Running Contest ends tonight so be sure to get your vote in if you haven't done so already. Have a wonderful day and a great week!!!! Rhonda
Dit kniebeschermingskussen van Nature is een perfecte keuze om je knieën te beschermen tijdens het tuinieren of het doen van een doe-het-zelfproject. Comfortabele ervaring: het kniekussen zorgt voor extra comfort tijdens het tuinieren of klussen.Zacht materiaal: het kniebeschermingskussen is gemaakt van zacht schuim, waardoor een ondersteuningssysteem voor je knieën ontstaat.Praktisch ontwerp: dit kniekussen vermindert ongemak en pijn bij langdurig tuinieren en voorkomt ook dat je broek vies wordt. Bovendien zorgt het extra grote formaat ervoor dat je minder vaak hoeft op te staan om het kussen te verplaatsen.
Voice trainers at Vocal Process have created this ‘Build your own tilting larynx’ template. Such a brilliant idea for teaching the understanding of how the vocal cords wor…
Welcome to the second article on how to make a knitting chart in Excel. Part 1 looked at setting up the spreadsheet so you would have a wor...
I love to wear skirts! They are so versatile. You can mix and match them with blouses, sweaters, or pair them with jackets. They can be worn with tights and flats or tights and boots. You can change the look by simply changing your shoes from flats to stilettos. Because I love skirts, I am always on the look out for an interesting design and I've found a few that I thought you might like too! I wish I could see a complete front view of this skirt. But regardless, I really like the asymmetrical hem and the side seam welt pocket. A wrap skirt is always lovely. I love how they played with the pattern on this skirt. I'm sure you've seen this skirt on Pinterest. It's a very popular pin. But it derserves to be looked at again as it is such a lovely and dramatic design. Okay, we need Bunny of La Sewista for this one, especially since she is a smocking guru. I REALLY want to know how to do this!!! I don't care for the little buttons, but I do love the technique. Simple, yet so graceful. Here's another interesting wrap. I think this is so pretty. Look closely and you'll see that inside the center of the drape is a zipper. Sadly the zipper looks a bit off, but it's a great idea nonetheless. Since this skirt is in white, it's a little difficult to see, but if you look closely, you'll see that it has very interesting lines. What a lovely take on a pleated skirt. A cute take on a kilt design. This skirt makes me want to throw my sandals on and head for Bermuda!!! It just screams summer. I love how the scalloped edge was taken around the hem and then up the center back to accent the vent opening. Such a comfortable looking skirt. From Eileen Fisher. I believe that Marcy Tilton has a Vogue pattern that is quite similar. I love everything about this skirt. Take a striped fabric and add godets. Lovely. Now for a little comic relief ;) I'll say this, it's interesting!!! I have some fabulous surprises up my sleeve for you this week, so please be sure to check back. Also, the voting for the Get Your Motors Running Contest ends tonight so be sure to get your vote in if you haven't done so already. Have a wonderful day and a great week!!!! Rhonda
Dit kniebeschermingskussen van Nature is een perfecte keuze om je knieën te beschermen tijdens het tuinieren of het doen van een doe-het-zelfproject. Comfortabele ervaring: het kniekussen zorgt voor extra comfort tijdens het tuinieren of klussen.Zacht materiaal: het kniebeschermingskussen is gemaakt van zacht schuim, waardoor een ondersteuningssysteem voor je knieën ontstaat.Praktisch ontwerp: dit kniekussen vermindert ongemak en pijn bij langdurig tuinieren en voorkomt ook dat je broek vies wordt. Bovendien zorgt het extra grote formaat ervoor dat je minder vaak hoeft op te staan om het kussen te verplaatsen.
Voice trainers at Vocal Process have created this ‘Build your own tilting larynx’ template. Such a brilliant idea for teaching the understanding of how the vocal cords wor…
Welcome to the second article on how to make a knitting chart in Excel. Part 1 looked at setting up the spreadsheet so you would have a wor...
This month we are doing a lot of water coloring exercises with our students at Art Hours. Although water coloring is immensely fun to work with, Origami is something I cannot keep myself apart from for a long time...so it was just a couple of days back when I was working with Origami Camellias and this week I gave a try to Origami Poinsettia flowers. They took a lot of time to make but the result was so beautiful that I made an Origami Mosaic with some more origami poinsettias. Poinsettias are actually known for its red and green foliage but are not flowers as you would have thought. The red part that you see are actually modified leaves. Well, I will not bore you with more facts. You can surely find more such details about the plant on the internet. These origami poinsettias are based on the modular origami concept, wherein two separate units are made and assembled by inserting into pockets. No glue has been used for assembling it. Below is the origami poinsettia made from two parts. The green leaves are made using 8" square and the red part is made from 6" square paper. The final size of the model is 10" x 10". Poinsettia Red I made some more poinsettias and assembled it without any glue again. The Origami Mosaic that you see below is made using 9 square sheets of paper. The outer four big leaves are made from 6" square and the inner five smaller units are made from 4" square papers. Origami Mosaic with Poinsettias Origami Mosaic with Poinsettias Poinsettias are popular Christmas decorations and are used to decorate homes, Churches, and offices. I haven't seen the foliage for real but a quick search on the internet showed that the origami model is a good resemblance of the original flower. The above model that I made is a slight modification from the original design, which uses three modular units, while I have used only 2 modular units. I plan to use it for home decor. For more details on the design of this origami model, you can visit artisbellus.com which has many diagrams for single sheet origami folding models. Thankyou for visiting this blog. ---
Another three weeks has flown by, but I have a little less progress to show you this time. I finally decided it was time to commit to making my first large rosette, and so I have been slower to wor…
