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I am trying to design a distributed amplifier in which the parasitic capacitances of a small-signal FET model are linked to inductors to form a distributed line across the drains and gates and I'm frustrated because nothing is matching what I expect from theory.

I know the characteristic impedance of my two lines should be sqrt(L/C) and I've chosen my values as such.. however I am still getting a ringing in my input impedances even when I just simulate a simple LC distributed circuit cell for a transmission line, and there is no real part as can be seen in the graph.

So my questions are - does the characteristic impedance calculation not work in AWR for a distributed element model of a transmission line?

If I measure the S(5,5) or S(1,1) it is resonant at DC, which makes sense because an inductor is a short at DC frequencies, but then what does the resonant frequency wc=1/sqrt(LC) mean and what is its significance in the AWR simulations? enter image description here

Thanks for your time!

-- edit:

so the ultimate goal is the distributed amplifier as it appears below where this cell is repeated five times. The inductors add in series, so at the end there is another L/2 value inductor while between each cell the inductors are value L. The four ports are all terminated in a 50Ohm impedance. I simplified by taking out the fet small-signal model to inspect the input impedance.

By ringing I mean that the impedance value is purely imaginary and oscillates. I guess I'm not surprised that a few LC circuits are not giving an input impedance of sqrt(L/C) but I just can't justify to myself why they disobey this relationship because it should scale with length and number of cells.

enter image description here

I really apologize for the horrible screenshots, I have a cap on how many images I can post.

--edit So I realized I was plotting Z(1,1) instead of ZIN in AWR, which solves a lot of my issue understanding what I'm doing wrong. But thank you for your time and thoughts I really appreciate it!

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    \$\begingroup\$ What is "AWR Microwave Office"? \$\endgroup\$ – Transistor Feb 21 '16 at 21:41
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    \$\begingroup\$ I don't think you can just "throw in" a couple of inductors and capacitors like that and expect them to work as a transmission line. I have a feeling you don't have a clue what you're doing ! The tool will work fine for sure but don't expect that you can just use it in a meaningfull way without following a tutorial or reading the manual. \$\endgroup\$ – Bimpelrekkie Feb 21 '16 at 21:56
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    \$\begingroup\$ Unless you are going to add infinite L-C nodes, it's not going to behave like a transmission line. If you add maybe 100+ you may start to see an ok approximation (that's how things like LTSpice to it), but in no way will it be accurate. Use the built in transmission lines. \$\endgroup\$ – Tom Carpenter Feb 21 '16 at 22:13
  • \$\begingroup\$ A single L/R will not adequately simulate a transmission line, nevertheless your first LCR circuit will produce a 2nd order TF with \$\small \zeta=0.5\$ so the resonance peak will only be 15%. Are you sure you're loading the C with \$\small 50\Omega\$? Is the connection to the output terminal of the port correct? \$\endgroup\$ – Chu Feb 22 '16 at 1:13
  • \$\begingroup\$ @TomCarpenter, in my experience, 100's of sections are not required and even 4 or 5 LC sections is enough to start seeing behavior approximating a transmission line. \$\endgroup\$ – The Photon Feb 22 '16 at 2:16
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Distributed Amps the way you built should be ringing, in theory as well as in practice. To get them to work without ringing, you need an "m-derived network." old Tek manuals from the vacuum tube era show how.

For example, see here http://w140.com/tekwiki/images/3/36/545a_vert.png

the center-tapped inductors are key. Google "t coil network" or "m derived network" for the design equations.


i refer to any of the tapped inductors in the tektronix schematic. for an impedance of Z=1 and a fet capacitance of C=1, we need each half of the inductance to be 1/3 and the mutual inductance to be m=1/2. that gives a 3 db bandwidth of B=2.7 and rise time tr=.79. In theory, a capacitance of C/12 from end to end of the tapped inductor is understood.

so if, for example, Z=50R and C=1.5pF, we get an inductance of 1.25 nH, m=1.875 nH, B=5.7 GHz and tr= 59 ps. Overshoot is less than a percent.

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You need your shunt capacitors at the end of your TL to be C/2 to make the unit cells symmetric c/2--L--C--L--C--L--C/2

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