# How do people estimate node voltage and branch current by observing a circuit?

The question might sound silly, but I hope experts can guide me on that particular issue. I am struggling for the last few months. I am a beginner in analog circuit design. When I follow a tutorial, I found that by observing a big transistor (MOS)-level circuit, they can say about node voltages, branch current, input and output resistance, and sometimes gain. My question is, without drawing a small-signal model of those circuits, how do people do that? Is this because they already solved many circuits by hand (I mean not using any simulator), and that is why a concept was built? Even when I try to draw a small-signal model for a big circuit I get lost due to the circuit's complexity. What is a good way to approach this kind of circuit?

I added the figure as an example circuit!

Figure reference: https://www.hindawi.com/journals/apec/2014/274795/ • Run a sim as I did here for BJT’s with Falstad’s web tinyurl.com/y2o5pjn2 Jan 15, 2021 at 4:33

A lot of it is simply seeing/solving circuits and subcircuits often, and being able to pull out those structures and consider their behavior in isolation. Even complex circuits tend to often decompose to a number of simpler elements, allowing a lot of behavior to be qualitatively described quickly, saving mathematical analysis for unfamiliar or unusual sub-structures.

These understandings of common subcircuits, of course, come from mathematically solving those subcircuits for behavior, typical operating point, input/output impedances, etc.

As an example for this circuit, one path of analysis that comes to mind is to:

1. Assume all MOSFETs in saturation.
2. Notice that Mk (likely strongly inverted) is giving a constant bias voltage to M3/M4 gates thus making M3/M4 matched cascodes for M1/M2.
3. Attempt to pattern-match M1/M2 to a current mirror, noting that the gates don't connect to the drain so I might not be able to immediately make that simplification.
4. Hand-wavily consider M1/M3 as if it were a single transistor with very high output impedance because a cascode structure behaves that way under the assumed conditions. Same for M2/M4.
5. Now the two sides match a current mirror structure, with high output impedance thanks to the cascode.

At each step, I redraw the circuit (mentally or otherwise) and continue making simplifications/equivalences that seem to simplify it further.

Knowing the circuit's rough structure and behavior allows me to decide what stimuli make sense for it--it can now be simulated to supplement and verify the analysis. If I get unexpected results, I revise my analysis, simulate again, and so on until my understanding and expected/actual results converge.

• thanks a lot for taking the time to answer my question. I got the idea.
– Shu
Jan 15, 2021 at 15:31