Cascodes & Flexibility
Ugh. I originally meant for this blog to basically answer the question "what did I learn today." While it has wandered a lot, I still feel this is more or less the main goal for me. Interestingly, people actually read it; thus, I have to actually put up readable stuff. For example, my favorite new nugget of understanding for the day involves how cascodes can be used to increase the gain of a current mirror differential amplifier. I'm sure a couple of you think that'd be really cool, but I feel bad for all the others who end up reading. That being said my goal is to write about what I learned so be warned technical stuff follows:
The quick answer is that Rout increases by about two orders of magnitude. Since the differential gain is Rout*Gm, it too increases by about 100. Yay!
To go through it in more detail:
We have two transistors in series that go from Vout to ground. The top transistor is called the cascoding transistor. Pretend for a moment it didn't exist. Rout would now simply be r0 for the cascoded (bottom) transistor due to early voltage. Once the cascode is put back in it gets a bit trickier. Using superposition and source splitting, we can get that changing the replica source on the cascoding transistor doesn't create any currents. Changing the voltage of the replica source on the early voltage resistor, on the other hand, ends up creating two currents. The first one is r0+r0||(1/gs). The other one is a current in the other direction that ends up canceling out part of the first current to yield a total current of dV(1/(r0*(1+gs*r0))). Then we get an Rout of r0(1+gs*r0). Since gs*ro has a typical value of around 100, this means Rout (and thus the differential gain) increases by roughly two orders of magnitude. Yay!
In other news, we learned something today at the Mr./Ms. Olin contest. I think Chandra might've put it best: Flexible men are hot. Keoni and Karst both did talents that involved flexibility; badass limbo and badass yoga respectively. Then, as per Chandra's hypothesis, Keoni and Karst ended up as the finalists. Most intriguing... /me stretches...
4 comments:
Ah, cascodes.
I found my Analog VLSI binder a month or so ago and went through the whole thing relearning all the great designs.
Also, your Mozilla screenshot graphic is refrenced to a file on your hard drive, which us poor readers do not have at the same location on ours.
weird... i see the image location as being hosted on http://bp2.blogger.com/[lots of stuff]... does anyone else have this issue? Does anyone not have this issue? What are the chances of someone reading the comments of a post this old?
The chances are better than you might otherwise expect.
It's the first of two images that I see as pointing to a file on your hard drive. The second one is as you describe.
Interesting. Here's the trick. There's only supposed to be one image. I see the same thing you do actually. Wow. I don't actually use Mozilla for screenshots so I'm a bit confused. I'd fix it, but blogger is a little lame and it'd show up as being new again. anyways. Huge points for reading the comments again.
However. It's been two weeks since you posted your comment. Unless you've got an rss feed, really like browsing or get really luck, I doubt I'll see any more comments here. I challenge you to prove me wrong (again).
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