Ensuring Subsystem Independence When Interconnecting Circuits in System Design

When constructing a larger system from interconnecting multiple basic building blocks (circuits), how do we ensure that each subsystem/circuit will maintain its functionality as a separate unit. Is there a rule on how to connect circuits such that the result of analysis on the overall system will lead to the same result as if each circuit is analyzed independently and then combining individual results?

Thanks.

Ah very good questions! Yes typically when function blocks are connected up and on paper it works because say
two - port analysis says it should. Two port- network theory relays on no significant port loading.

This is more or less generalities. When you cUonnect up blocks, each interface must have a specification
in terms of requirements, volts, amps, ohms, signal lever thresjolds and so on. If one can't determine & spec those
requirements, it likely won't work.

Simple case is connecting up a pair of speakers to your sound system, what are the system interface specifications & requirements? More complex, connect up Bluetooth device to your laptop, same approach applies but now you have to throw in the software system interface system spec requirements,

In a nut shell if you connect up two things, you have to understand both devices and the requirements.
You would'n't plug your 120Vac wall wart into 240Vac, unless it indicated it was rated, simple interface spec requirements.

I can imagine this working theoretically on paper where a system is represented by a block, in-out ports, and a transfer function. However in practice, and electric circuits in particular, there are several factors, such as internal impedance of a system, and power supply connections...but what makes me ask this question is one problem I see here, that electric systems are different than other systems, for example mechanical, that the effect happens instantaneously (at the speed of light) through out the whole system, so it's not sequential.

1. Should not be there some kind of separation mechanism that ensures the effect will be per block vs. per the entire system? For instance placing diodes along inter system connections?

2. I would say the superposition theorem may be the answer but what about nonlinear systems?

Despite the speed of light being quite quick, signals do progress at a finite rate (very much less than C) through an electrical or electronic system.

Simplest case: switch on your (incandescent) light bulb, and the filament takes a short fraction of a second to heat up and begin glowing, and time to cool and go dark when you switch off.

Inductance in any electrical circuit slows down the rate at which the current will rise when a voltage is applied.

For many electronic components, their response time is an essential part of the specification data. Old computer memory chips are too slow in response to be used in new computers.

Electronic "blocks" in a system may require separate power supplies, so their output performance depends on (1) the power input, as well as (2) the input signal, and (3) the correct adjustment and functioning of the internal parts.

There are devices which protect one part of a system from problems in another part, such as fuses and circuit breakers. (Which can be specified as slow or fast acting.)
Another example: an amplifier generally has a high input impedance so that it will not adversely affect the signal from the previous device in the chain.
And attach speakers with too little impedance to your sound system, and you blow up the output transistors. (Yup, I've done that :-)

Back to your original question: Yes, successive stages of amplification (whether within a unit or as separate amplifiers) can be multiplied together to obtain the overall system gain.

If we have the theory right, the mathematics will predict the perfomance of the practical system. Does that help to see what's happening ?