# Circuit analysis on very complex circuit

I am studying circuit analysis.

Problems contain only 5-6 components. I wonder how can we analyse very complex circuit like a radio reciever which has 30-40 components or some circuit like that. Do I need to solve 30-40 unknown variable from equations (node,mesh analysis,) or there are other means?

Can I break circuits down into smaller modules and analyse each of them?

• No one I know would use circuit analysis on a radio receiver, treated blindly as a mathematician might do, in order to solve all of the unknown variables. It would tell you very little of use and you'd be buried under equations that carry lots of terms and where their real purpose would be almost impossible to ferret out. It's lots easier to understand a circuit in highly interwoven pieces (subsystems) that connect to others via only a few wires and to apply reasoned simplifications in terms of their interconnections. Last question is now answered as: yes. – jonk Sep 26 at 18:39
• To see how difficult your first case might be, try and completely solve with closed equations, the circuit of just a simple resistor in series with a diode, sharing a common ground but with the signal applied across the two in series and the output taken at the shared node with reference to ground. There's only one node to worry about and only one equation. But if you include all of the details with respect to how a diode functions (and I mean temperature, etc.) you'll find the result "interestingly complex to solve." Try it sometime. – jonk Sep 26 at 18:44
• For example, see here. And this doesn't deal with including saturation current variations with temperature, by the way. It's highly simplified. If you do this just a few times on your own, you will quickly find other, more preferred, ways to solve circuit problems. Real circuits with any more than just a few components cannot even be solved (with current knowledge) with closed equations. – jonk Sep 26 at 18:46
• Yes. Pretty much that's how everyone solves them. When the DC equilibrium state of one subsystem would interact in unwanted ways with the DC equilibrium state of another, it's common to insert a capacitor between them in order to isolate one's DC state from the other's. You'll learn all this stuff as you begin to recognize subsystems. – jonk Sep 26 at 18:51
• Would you study the ecology of a meadow by studying the quantum mechanical behavior of particle wavefunctions? No, you would not. You would treat it as subsystems (plant species, daily sun, weather types, soil types, etc.) Still, the meadow actually works as a result of the interaction of particle wavefunctions, just the same. That's what drives the system. But it is way too complex to solve. Nor would it help you understand the meadow, even if you could. – jonk Sep 26 at 18:53

can i break circuit down into smaller modules and analyse each of them?

Yes, that's how we all do it. In fact we design a radio by designing small sections, the RF pre-amp, the local oscillator, the mixer, the first IF, the audio amplifier etc etc, and putting them all together.

We usually design each stage to work between known terminations, like 50 Ω or 75 Ω so that when we put them together, they'll still work as intended. This is such a common practice, that test gear like signal sources and spectrum analysers also use these standard terminations, so we design, measure, test and assemble bigger systems keeping to the same impedances.

There is a type of instrument called a network analyser, that although it makes it convenient to quickly measure the transfer function of a subcircuit, its unique measurement feature is that it will measure the input and output impedances of the subcircuit. Sometimes we use it to tell us how near the I/O impedances are to 50 Ω (so return loss better than, for instance, -20 dB), sometimes we use it to tell us what the I/O impedances are, so we can design to the precise impedances.

Problems can arise when we've synthesised each of these sections to work in isolation to the others, and then we find that when we put them all together, the isolation between sections isn't as good as we thought. For instance we may get RF leaking along a common power supply line to another block1, or the audio amplifier pulling the power rail down at each audio peak upsetting the local oscillator. Not all unwanted coupling goes through the power supplies, RF leaking from the thing the IF amplifier drives back to something driving its input can make life very tedious. Making a successful radio is often about making sure the sub-circuits are as isolated in the final product as they were when we designed each to work by itself.

Why do design projects take longer than we all expect? Getting the intended behaviour from subcircuits is often the easy bit, taking the time we estimated. Getting rid of the unintended behaviour when we integrate them into a system usually takes two or three times as long again, as these are unknown unknowns. Why don't we plan extra time for this stage? We do, but optimism, failure of imagination, and management and timescale pressure gets us every time. I never fail to be surprised at how nature can find ways to subvert our best intentions.

1. I had a power supply line about 50 mm long, connected at one end to a capacitor to ground, and at the other with a series ferrite bead whose impedance went up to 1 kΩ, both components intended to stop RF, and it leaked RF when its length was a λ/4 resonator at IIRC 914 MHz. The cure, very late in the project when a re-layout was not possible, was to change the ferrite bead to one with an impedance of 50 Ω, which terminated the line and prevented the resonance.
• when we put small sections together there is current flow between them so voltage and current through components of each section are changed when compare with isolation design in first place.it may cause unwanted result like lower output power etc.how do we do with these changed circuit characteristics? do we need to build real circuit and measure them with oscilloscope to see unwanted result? – Jittinan Suwanrueangsri Sep 27 at 1:37
• @JittinanSuwanrueangsri Important point, added to my answer – Neil_UK Sep 27 at 5:34
• can you recommend a circuit design process book ? – Jittinan Suwanrueangsri Sep 27 at 13:43
• @JittinanSuwanrueangsri No, unfortunately not. I would recommend designing a circuit, then another one, then a few more, ideally while having conversations with other people also designing circuits, and debuggin them and getting them to work. Good design comes from experience. Unfortunately, experience usually comes from bad designs. I have done an embarrassingly large number of bad designs in my life. Now retired from designing for a living, I have enough experience to make some good designs. – Neil_UK Sep 27 at 15:35
• @JittinanSuwanrueangsri Let's see if I can be more helpful. Pick a small function. Write a specification for it. Design something for it. Then post it here asking for comments. In your post include the specification, your design schematic, and a list of the reasons you chose the architecture and component values. That last bit is very important, as what you want from this exercise is not a circuit to do something, but your thought processes to be capable of making good circuits. I'll try to spot your posts and comment if I can. – Neil_UK Sep 27 at 17:15