ISL's first digital chip, a CDMA receiver was completed and tested very recently. Today, there was a small presentation for sharing this success with other faculty members of the department and other departments. In the process, the next project, an analog design was also communicated. It went on fine with Dr. PVR and the project team sharing their experiences, learnings from the project. The role of alumni in funding this effort (Esp. Class of 1983 and Chandru of C2001, now at Rutgers) and in transferring the tech know-how (esp. one Mr.Vijayabhaskar) was acknowledged and appreciated. The meeting was completed with some refreshments.

Reddy, formerly my class mate and (unfortunately for him, still) a close buddy and currently with IITM doing his M.S. in Analog IC design had also come. Reddy has some design experience in A/Ds and so he shared it with us after that in an informal way. Inspite of me having completed B.E., I have little clue as to how these devices work. (Don't think I am being humble. It is just a question of time before I learn these ) So, I would listen to their discussion intently until I got bored and then go do some other thing before coming back again.

All others except this discussing group had left. So I joined them since I got nothing to do. As usual, Reddy was drawing one of those scary little MO(n)Sters... I mean MOS transistors, with some adjoining circuitry. Suddenly Reddy said some sort of a generalization, a theorem which got me in directly since these abstractions I generally understand intuitively. (albeit, at a non rigorous level)

Reddy had drawn a black box, three input lines and one output line. And he said, the poles of this system whatever path you see from is the same. For me this was a counter intuitive result and I was damn convinced that it should be only for a certain class of circuits. This was because, I argued that, between any point and another, if the transfer network has certain poles, then from another input to the output, since the signal path is different, the time constant and hence the poles should have been different.(sorry for this stupid sentence. hope u got it)

Here is where a fallacy entered our argument. Somebody had related the bandwidth and the poles. Hence the discussion veered in the wrong direction. Then, Kiran/Reddy took some Thevenin's theorem argument and proved that theorem. But me, a weak student when it comes to such standard jumps, was not convinced. Reddy's result was very obvious for the MOS circuit he had drawn. But for me, something non-trivial existed about this class of circuits.(other than, their linearity)

Then MARS (a.k.a MS Arvindraj), the physics whizkid tried to explain this from a mechanical perspective. Showing how a system of pendulums will always settle into its natural frequency of oscillations even if one excites it from different points. This was an important result in convincing me partly. (I was the only one there, not very satisfied with that result. Others had convinced themselves) But MARS pointed the flaw of this system, it could model only real systems i.e. along the jw axis on the s-plane. So the vedalam erified the murungai maram again.

Previously, I had thrown up a challenge to reddy and others asking them to derive the respective poles for different transfer functions of a MISO system which I considered would provide a counter intuitive example. Lazy, as I am, I generally don't do these trivial derivations, you see. (That I know, is one of the reasons I have failed consistently) Shankamanka, the backbone and reddy finally derived the poles and proved that they are the same. No-confidence motion defeated!

Now everyone was in a really confused state. Reddy did one more thing. He wrote a general linear differential equation representing this MISO system. Seeing that, I was partially convinced that the poles were indeed the same and that bandwidth was changed by the zeroes as well. But, me and kiran, had one common question that left it open again.

Agreed that this set of equations could not have modified poles between each input and output. Agreed that the poles of a system (the natural response argument) didn't depend on the input of the system. But shouldn't it depend on the places where we feed the inputs? Are viewing these transfer functions in the wrong sense? If you consider a vector of inputs, modified by the transfer function to give the output, then the poles will remain the same. If you consider it as a set of N systems with some coupling between?? Also if the zeroes are modified in such a way that they cancel out with some poles, then wouldn't the poles for each path be different? To this, nobody had any answer since nobody had any theoretical standing in systems. We closed the day offering a few more reasons why our education is not enough and all that. Huh!!

This might seem a futile exercise but this is how one learns. You know, UGs don't need to solve problems at the forefront. They can't. To get to the forefront though, they can take up these already solved problems, the standard textbook ones and non standard stuff like the above and think randomly to get a solution. In the process, one refreshes the basics, reinforces certain math, refers a few books and gets a deal wiser.

---

Precisely, why I am gonna take up DSP by Proakis to see the effect that poles and zeroes have on the transfer function!! Teachers there... don't think I am trying to teach you. This is just a point to be taken from an objective point of view. Unconventional teaching is the need for the hour. Your linear methods won't work because it assumes the interest of the students. Student interest, is unquestionably needed for any activity. But there are so many fields today, that they don't get interested because they are not taught in the right ways. Time to introduce a few non-linear methods as these to accelerate learning. You know, an engineer must know better to optimize the system for various parameters. It should happen with engineering learning too. Probably your electromagnetics course shouldn't start with that uninspiring chapter on static fields (for the UG student, that is.) Instead, see the first lecture from Dr.Lewin's MIT OCW course on Electromagnetics.Dr.PVR is a class apart when it comes to such non-linear yet rigorous courses.

---

P.S: I thot we sorely missed the math whizkid, Sreeram. He could have provided some simple math intuition to see whether what was being posited is right or not.

---

In the course of the above, I probably re-invented some old quote:

A proof is not good enough, if it isn't/can't be made intuitive!