# Small signal simplifications

Gustavo Castro discusses what constitutes a small signal in an analog system and the implications for some design approximations and simplifications.

Q: The data sheet for the amplifier that I’ve chosen for my application specifies a small signal bandwidth along with a large signal bandwidth, and they are quite different specs. How do I determine if my signal qualifies as small or large?

A: When we talk about the bandwidth of an amplifier, we are really talking about the frequency response of the amplifier using the small signal model. This model is derived assuming the circuit is linear around a bias point or, in other words, its gain remains constant independent of the applied signal. If a signal is small enough, the model works very well and its deviation from reality is impossible to detect.

Everybody likes working with this model because it simplifies the design and analysis process. If we were to use large signal models – that is, include all the nonlinear equations – circuits would get awfully complicated, at least for mortals like myself. 1 Therefore, small signal models and sinusoidal signals bring the complexity to a manageable level.

Strictly speaking, though, even the smallest practical signal changes the bias point of a transistor circuit (for example, an op amp) by a little. The larger the signal, the more difficult it gets to ignore nonlinear effects, which most evidently manifest as distortion. At some point, the signal gets too fast and so large that the amplifier reaches its slew rate limit – equivalent to the maximum rate of change of the amplifier output, and typically expressed in volts per microsecond (V/µs).

When the slew rate is limited, the amplifier falls behind, it does not reach the signal peak before the signal starts to ramp down, and the overall result is that the signal amplitude is smaller than expected. At that point, the amplifier has about reached the large signal bandwidth. Normally this happens at frequencies below the small signal bandwidth, and the signal is most definitively distorted. But