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I've recently been learning about FET amplifier circuits and I'm looking for some information that can help explain why the calculated and simulated Gain Values can differ by up to 15% in some cases.

this image is an example of the first FET amp. http://www.electronics-tutorials.ws/amplifier/amp14.gif which gives the following values calculated Gain = -11.8 simulated Gain = -13.4 difference = 12.698% any help explaining this difference will be greatly appreciated.

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"A simulation" is a series of calculations which are hidden and which you supply input parameters for. The simulation "models" the target device by embodying assumptions which may or may not be visible and/or explicitly stated.

"A calculation" (or a family of associated calculations) that can be used to arrive at a solution to the operation of a circuit is essentially a manual or visible simulator - you are "modelling" the circuit with numerical equivalents. Assumptions are usually explicit in the form of constants, transfer functions and formulae.

Your statement is that the calculated and simulated values can differ by up to 15%. You did not mention the vitally important 3rd member of the family of explain how results from the other two compared in accuracy. The important 3rd member is reality.
ie you have calculated, simulated and actual results. The degree to which simulation and calculation differ from reality is what is important. Both differ from reality because the "model" of the device(s) that they use also differ from reality.

At an informed guess I'd expect a simulation to be closer to reality because it embodied a "model" which more closely matched reality. It is easy for the simulation maker to use formulae, lookup tables, piece wise approximations and more.
Calculations are liable to involve not much more than Use of much more than one or a number of formulae and so cannot match the theoretical and/or empirical detail of a simulation.

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If you measure the gain, there is usually some variability in the measurements. This means that you would have to measure enough times to get a statistic distribution for the gain. The computed value should be equal to the mean of the distribution.

What I'm also curious about: is the gain given in Decibels (dB)?

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