System Reponse and Stability


The system response is the output produced by an electronic system when stimulated by a valid input signal. In the context of electronics, the systems of interest often take the form of voltage regulators, analog filters, audio amplifiers, transducers, or analog-to-digital data converters. These systems can exhibit various types of responses, such as time-domain decay, transfer function gain, frequency response, phase response, or harmonic distortion. 

Two example responses

Visuals are provided below to illustrate the step and impulse reponses:

In essense, the system response is the output of the system due to excitation from the input. In the above illustration, the input signal are step function and impulse function respectively, and the output on the right are the corresponding system responses. Here, think of the system as a "black box" that takes an input signal, processes it, and gives an output signal. 


Both Step and Impulse signals in the frequency domain contain wide spectral content over a large spread of bandwidth. It is often used to evaluate system response stability, such as overshoot, undershoot, oscillatoring ringing, etc., with this specfic input test. This simulates real-world conditions where sudden changes in current load are common.

Stability in a system refers to the property of the output response remaining bounded when subjected to a bounded input signal. This concept is commonly referred to as BIBO (Bounded Input, Bounded Output) in technical terms. A practical example of stability in electronics is observed when output audio amplifiers do not exhibit clipping.

Below is a visual aid illustrating this idea:

Left: Bounded Input Signal, Center: Stable Output (BIBO), Right: Unstable Output.

In simpler terms, stability ensures that the system's output stays within set limits, even if the input signal varies within a specific range. For example, in audio amplifiers, a stable system will keep the output signal within a desired range without distortion or clipping. Stability is key for accurately reproducing the input signal without introducing unwanted artifacts or distortions in the output.

You may wonder what causes instability and how to correct it. Briefly, systems with feedback are prone to instability. By carefully designing the feedback network, one can mitigate unstable behavior in the output.