Smith chart question [h/w]

[tyblu]

This is part of a homework/lab circuit. I'm trying to match the output of a single transistor 1GHz amp (common emitter) to a 50 ohm line, using a double-stub tuner (microstrips). The output, the collector, has a TL of length (L2) 10mm to 20mm connected to the 1st stub, then 1/8 wavelength between the stubs. Some length after the 2nd stub there is a chip capacitor (DC block; 0.1uF), then 10mm to the SMA connector.

Zout = 143.1 @ -35.1deg
--> y_out = 0.286 + j0.201 (normalized admittance wrt. 1/50 S)
wavelength = 166.99 mm

This question is really about Smith chart usage, but I know you techies love details.
I've rotated y_out towards the load (ccw) to wavelengths corresponding to L2, and I've rotated the y=1+jb circle towards the generator (cw; it is now at the top of the chart). Now I need to follow the susceptance lines from the translated y_out point to intersect the translated y=1+jb circle to determine the susceptance change required and hence the length of the stub. Which way do I go: clockwise or counter-clockwise? Normally, when matching a load, you'd go clockwise - is it reversed in this case, matching an output stage to a line? My book [Pozar] implies that I can go either way, which doesn't really make sense to me, as the length of the arc corresponds directly and linearly to the length of the stub. That brings me to my second question: how do I determine the length of the stub, in this case?

can 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.

[Excavatoree]

This brings back some memories.  I'll try to find my notes .

[Time]

This day has finally come - someone on the EEVBlog forum asking for homework help.

[krapht]

Is that good or bad? 

[GeoffS]

At least it's asking for help with homework rather than asking someone to do their homework for them 

[tyblu]

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).