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.