# Small signal simplifications: Page 2 of 2

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

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 the signal does not suddenly turn into a distortion fiasco; instead, distortion gradually increases with both amplitude and frequency. We could say that the signal is too large when the distortion is more than the system can tolerate.

So, how do we know if an amplifier is fast enough to handle a signal? First, and as usual, make sure the small signal bandwidth is enough for the desired gain. If it is, then look for a large signal bandwidth specification (or plot) in the data sheet. If not available, the easiest solution is to go to the fundamentals and use the formula:

SR [V/µs] = Peak Amplitude × 6.28 × Frequency [MHz]

A good rule of thumb is to choose an amplifier with 10× more slew rate than required. Then, take a look at the distortion curves on the data sheet at the desired frequency and amplitude to make sure the signal is small enough for the amplifier.

For example, ADA4807-1 as a voltage follower has a slew rate of 225 V/µs with ±5 V supply. Even though the amplifier’s small bandwidth is around 180 MHz, the amplifier wouldn’t be able to exceed 36 MHz with a 2 V p-p signal. And for a 4 V p-p, the same theoretical limit would come down to about 18 MHz. Moreover, slew rate is usually measured with a step, under which internal slew enhancement circuits kick in to improve settling time, but response to sinusoidal signals can actually be a bit slower (the data sheet specifies 28 MHz for large signal bandwidth with 2 V p-p). The distortion plots in the typical characteristics section show the harmonic distortion increase with frequency and amplitude, from which it is possible to determine if you can take your signal citius, altius, and fortius (faster, higher, and stronger).

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[1] That’s a job better suited for computers running simulations, and even then, we opt for simplifications that allow them to reach a numerical solution in a reasonable amount of time.

Gustavo Castro is an applications engineer in the linear and precision technology group of Analog Devices. His main interests are analog and mixed-signal design for precision signal conditioning and electronic instrumentation. Prior to joining Analog Devices in 2011, he worked for 10 years designing high performance digital multimeters and precision dc sources at National Instruments. Gustavo received a bachelor’s degree in electronics engineering in 2000 from Tecnológico de Monterrey, Mexico and his M.S. degree in microsystems and materials from Northeastern University. He holds three patents.