dijkarte said:
I agree, this is what I meant by synthesis. However the example you gave about a power-supply design is more a composition (building from existing components, topologies and tweaking) process than synthesis (starting from scratch). Let me give an example to clarify more what I'm talking about. An engineer is required to design an IC that takes in an analog signal and produces a signal which is the inverse of the original signal's function.
i.e input f(x) = x^2 the result is g(x) = sqrt(x)
Starting from a scratch, using transistors, diodes, and passive elements, how would he/she approach such a problem?
Please note, this circuit probable invented 1000 years ago, I don't know nothing, so my example is just for illustration purpose only. :D
I think I understand. Well, in that case I would say 99% or more of what working analog design engineers do is composition. You only design something from scratch when you have no other choice. Traditionally, progress has been made incrementally with a breakthrough new topology or something only rarely.
To answer your example, it is impossible to do that in any general way using analog techniques. A more tractable question would be "How do you make a circuit that takes a square root". Honestly what an engineer would do first is search the literature and see if there are published circuits to do a square root. In fact there are. There are also very well known circuits to invert a signal. So I would create a first draft circuit combining these two blocks. Then I would see where it needs to be improved (for example, speed, power, etc) and then use my experience and knowledge to address those needs.
Now, since you asked about synthesis assuming I really wanted to design the example circuit from scratch here is what I would do.
First, I would start with a MOSFET since that is the key device in modern analog IC design. Then, I would ask myself, "what is the core operating equation of the MOSFET"? Since it's a square-law device, to first order the drain current is proportional to the square of the difference between the voltage at the gate and the voltage at the source when the device is operating in saturation. Then it would hit me, "well, by simple algebra, then, the voltage between the gate and the source of the MOSFET is proportional to the square root of the drain current!" So, now, I would have the core of a solution. Then, I would figure out what support circuits I need to ensure the MOSFET is biased in saturation under the expected operating conditions. If the input signal is a voltage, I would have to design a simple circuit to convert the voltage to current (I'd use a PMOS device in a common-drain configuration). Also, I would have to consider how to buffer the output signal such that it could drive whatever load was specified.
So, you see, even in the case where I designed the core of the circuit from scratch, there is still a lot of "composition". I'm sure you've heard the phrase "necessity is the mother of invention", one reason for this is why invent something when it already exists!
Incidentally, based on your definition, digital design would be considered "composition", since digital circuits are built using a small number of standard cells such as inverters, AND or OR gates and the like.