quick Smith chart question [h/w]

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This is for school. I'm trying to match a single transistor 1GHz amp output stage (common emitter) with a double-stub tuner. A 10mm-20mm TL (length L2) runs between the collector and 1st stub, then 1/8-wavelength TL between the stubs, then some length connects to a chip cap (DC block; 0.1uF), then ~10mm to the SMA connector.

Zout = 143.14 @ -35.14deg
--> y_out = 0.286 + j0.201 (normalized output admittance to 1/50Ω)
wavelength = 166.99mm

Question is really about Smith chart usage, but I know you techies like details ;) .
I've rotated y_out towards the load, and rotated the g=1+jb circle towards the generator (it's at the top of the chart, now), and now have to follow constant real admittance lines to intersect that circle. Do I go clockwise or counter-clockwise? My textbook [Pozar] and a few online examples indicates that I can go either way; common-sense tells me to go clockwise, but I've always matched input circuits (wrt. a load), not output circuits (wrt. a source).

scan of Smith chart solutions with L2 = 10mm, 15mm, and 20mm:
[75dpi; 1 MB] or [300dpi; 15 MB]
Question pertains to the blue arrows, between the A's and B's, and the green arrow (on the g=1+jb circle), between the C's and g=1.

Related, how do I get stub length?

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My understanding of Smith Chart is fuzzy at best. Mostly used it with discrete parts (impedance matching networks) and never with stubs. So, no help from here.

Jim

Jim Wagner Oregon Research Electronics, Consulting Div. Tangent, OR, USA http://www.orelectronics.net

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To match a load with discrete parts, you'd use an inductor to decrease susceptance or capacitor to increase (either, in parallel/shunt), corresponding to going counter-clockwise to decrease and clockwise to increase. Does this convention reverse when matching an output impedance to a line?
[edit: fudged up my directions, which really doesn't help matters.]

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Shouldn't you start from the complex conjugate Zout* ? That is what you should see when looking from the output port of your transistor towards the matching network.

You can go both ways with the blue lines, but if you are only allowed to use open ended stubs, the length of the stubs will be over 0.25*lambda when going "the wrong way".

To get the length of an open ended stub you start from the point where admittance is zero (the open end) and rotate towards generator until the normalized susceptance matches that of your blue line. The length of the stub can be calculated from the wavelengths shown in the figure by subtraction.

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Thanks Tuomas!

The prof set me straight. I am to treat the output impedance as a load and match it just like the input.
Determining the length of the stubs can be done with the Smith chart: first, get the change in susceptance required. You can then look at the stub as a TL with either a short-circuited or open end. I'm using open ones, so I start at the edge of the chart where y=0+jB (RHS on immittance or admittance chart; LHS on impedance chart flipped* through Z0). Short open stubs are capacitive, or add susceptance, so follow the y=0+jB along the positive susceptance line (clockwise for all Smith chart versions) until you intersect the y=jB line corresponding to the change in susceptance required -- mark it. Most charts have 2 wavelength notations on the outermost edges. Using the one that increases in the clockwise direction, determine the change in fraction of wavelengths (the y=0+j0 point will likely be at 0.00 or 0.25) -- this is the length of your stub.
*'flipping' an impedance chart maps admittances to it, allowing you to use a simple impedance chart. This is done by rotating your ZL point 180-degrees, like a quarter-wavelength TL. The new impedance point is actually the admittance of the original ZL, and all lines and directions on the chart can be treated as admittance parameters (conductance, susceptance).

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Yep, that's the way I learnt it as well, but I didn't want to confuse you because you had chosen to treat it as the generator.

Both methods are correct and yield the same result. When you think of the output of the transistor as the generator, and you are looking from the generator towards the load, you just need to match the complex conjugate of the output impedance to the load.

It is actually the same thing with the method your professor chose to teach you. Because the impedance of the actual load (Zl) is pure real, the complex conjugate Zl* = Zl . Zl* = 50Ω is what you are trying to achieve with the matching network.

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RF and transmission lines are beyond me.

After you did the calculation, did you construct the physical network?

And most importantly, did it electrically match with your theoretical geometry?
How much different was the real life match?

David.

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I get to hook it up to the VNA on Tuesday. I'm going to try to 'calibrate' my assumptions with this unmatched version, as all I'm using now is a SPICE model (though it seems to be pretty close):

(Extra pads are just for biasing.) I'm thinking that differences in the FR4 permittivity is going to be the biggest factor, but I'm usually wrong in these cases. This is a snap of the actual network:

At the last minute I extended the stubs to the edges of the board (as long as possible) so I can just cut them by hand later.