Side-by-side comparison
| Parameter | Linear | Non-Linear System |
|---|---|---|
| Superposition principle | Holds: a·x1(t) + b·x2(t) → a·y1(t) + b·y2(t) | Does not hold; output to sum ≠ sum of outputs |
| Homogeneity | Scaling input by k scales output by k | Output may saturate or clip under scaling |
| Impulse response | Fully characterises the system via convolution y = h * x | No single impulse response describes the system |
| Transfer function | H(s) or H(z) exists and is meaningful | Transfer function concept does not apply |
| Frequency components | Output contains only frequencies present in the input | New frequencies (harmonics, intermodulation) generated |
| Real example | Op-amp integrator using LM741 in linear region | Diode clipper, BJT amplifier driven into saturation |
| Analysis tools | Laplace, Fourier, Z-Transform, convolution | Volterra series, describing function, simulation (SPICE) |
| Stability analysis | Poles of H(s) determine stability (Routh-Hurwitz) | Limit cycles, chaos possible; Lyapunov methods used |
| Typical IC | LM741, TL072 (within ±Vsat limits) | NE555 astable, comparator LM393 with hysteresis |
| Output distortion | THD < 0.01% for a good audio op-amp like NE5532 | THD can exceed 10% in a clipping circuit |
Key differences
A linear system satisfies both additivity and homogeneity, which makes convolution y(t) = x(t) * h(t) valid. Non-linear systems generate harmonics — feed a 1 kHz sine into a transistor pushed to saturation and you get 2 kHz, 3 kHz, and higher at the output. An op-amp like the NE5532 is linear only while its output stays between ±(Vcc − 1.5 V); beyond that it clips and becomes non-linear. This is why GATE problems often specify "small-signal" to ensure linearity holds.
When to use Linear
Use a linear system model when analysing amplifier frequency response or filter behaviour — for example, computing the −3 dB bandwidth of a second-order Butterworth filter using its transfer function H(s).
When to use Non-Linear System
Treat a system as non-linear when it operates with large signals or intentional clipping — for example, when designing a square-wave oscillator using the LM393 comparator with positive feedback (Schmitt trigger).
Recommendation
For GATE and university exams, choose the linear model first; only switch to non-linear analysis when the problem explicitly mentions saturation, clipping, hysteresis, or large-signal conditions. Most S&S course problems stay within the linear regime.
Exam tip: GATE papers test linearity by asking you to check superposition with two specific inputs — always verify both additivity and homogeneity separately, and watch for systems with non-zero initial conditions (they are affine, not linear).
Interview tip: A core-company interviewer will ask you to give a real example of a non-linear system and why it cannot be analysed with an H(s); say "a BJT amplifier driven into saturation generates harmonics, so we use SPICE simulation instead of a transfer function."