Utility of Node Analysis in Designing Circuits Step-by-Step

Question

Question: Does node analysis have any utility when designing a circuit step-by-step, or must the entirety of the circuit be known before node analysis is useful? Here's an example to illustrate what I mean.

Suppose that I have a 12V power supply, but I only want to have 6V across my lightbulb. So, when I go to design a circuit, I think through the steps I want the circuit to take:

1. Reduce the 12V to 6V.
2. Send those 6V across the lightbulb.

To tackle step 1, I decide that I will use a voltage divider. Thus, I build the following circuit:

If I perform a node analysis on this voltage divider alone, then I will find that I do indeed have the 6V that I was seeking at my output node. However, when I move on to step 2, I'll find that my circuit will not work because I neglected the fact my lightbulb has some resistance. (We'll say 100 ohms.)

Now, when I add my lightbulb, there will only be 4 volts across it. Thus, it seems that my previous node analysis was unfruitful because I had yet to determine all of the components of my circuit.

Yet, it seems that, in most literature, node analysis is performed on "incomplete" circuits. Does this imply that node analysis can still be useful before a full circuit is determined? Or is it just a shortcut taken to avoid wasting time with extraneous information?

Answer 1

The most important utility of nodal analysis is that it is relatively easy to program a computer to do. So whenever you use SPICE, or most any other circuit analysis program, to simulate a circuit, you're using nodal analysis.

For hand calculations, nodal analysis might sometimes be appropriate, but as soon as your circuit makes nod analysis difficult, there's no reason not to switch to some other analysis method (whether mesh analysis or simply an ad hoc mix of node and loop equations).

Does this imply that node analysis can still be useful before a full circuit is determined?

It doesn't matter whether you use node analysis, mesh analysis, ad hoc methods, or whatever, if you analyze an incomplete circuit, you only get information about the incomplete circuit, not the complete circuit.

The problem here isn't the choice of node analysis. It's the choice to try to analyze the incomplete circuit, regardless of what method you choose.

in most literature, node analysis is performed on "incomplete" circuits.

It's not clear what you mean by this, but one "incomplete" circuit analysis is when you find the Thevenin or Norton equivalent of a source circuit. Node analysis is often used for this purpose.

If you had done a complete analysis of your "6 V source" to find its Thevenin equivalent, rather than just found the open-circuit output and stopped there, you would have found it is equivalent to a 6 V source, with a 50 ohm series resistor. Knowing that, you could predict exactly how much its output will drop for any given DC load (i.e. about 1 V for every 20 mA of load current).

Then you wouldn't have been surprised to find your source is a very bad way to deliver 6 V to a load requiring any kind of significant power, even though you used nodal analysis to find the Thevenin equivalent of your source.