Electronic – What are the limits & capabilities of Op Amps with AC signals

Why are Op Amps more noisy than other types of amplifiers (BJT and MOSFET, for example)?

I doubt this is true, especially if you consider the noise factor for the same circuit gain (but another answer might give more concrete information).

So, in short, why do OP Amps have electrical noise issues (if at all), and what is the source?

TI has a couple of good app notes on this:

Chapter 10 of Op-amps for Everyone

Noise Analysis for High-speed Op-amps

In short, the feedback resistors and the op-amp's input stage transistors both contribute to noise.

Perhaps Op Amps lack sufficient filtering capabilities that are inherent to BJT and MOSFET design?

Op-amp circuits can be filtered to whatever bandwidth you like. It only requires adding an extra capacitor or two to the op-amp circuit, or for higher-order filtering adding an additional filter stage after the high-gain stage. Which would be equally required for a discrete circuit.

^{simulate this circuit – Schematic created using CircuitLab}

The effect of the decoupling resistor is as follows:

It does not attenuate oscillations - it prevents the start of oscillations. In this case, the keyword again is "loop gain". Together with the finite output resistance r,out of the opamp the load capacitor C forms a first-order lowpass. In many cases this causes an additional phase shift for the loop gain that can bring the opamp (under closed-loop conditions) to its stability limits.

Now - what is the effect of the additional resistor R? It prevents that the loop gain for very large frequencies is approaching zero; instead the loop gain reaches a finite value. This is identical with a phase enhancement which is necessary to avoid instability. In terms of system theory: We have created an additional "zero".

Example: Without such a resistor R the lowpass has the function:

$$ H(s) = \frac{\frac {1}{sC}}{r_{out}+\frac{1}{sC}} $$ $$ H(s) = \frac {1}{1+s(r_{out}C)}$$

With resistor R we have:

$$ H(s) = \frac{R+\frac{1}{sC}}{R+r_{out}+\frac{1}{sC}} $$ $$ H(s) = \frac{1+sRC}{1+s(r_{out}+R)C} $$

$$ \lim_{s \to \infty} H(s) = \frac {R}{r_{out}+R} $$

As you can see, as frequency increases, the lowpass function now approaches \$R/(r_{out}+R) \$

In other words: The lowpass has changed its properties - the phase does not continuously go to -90 deg but increases again towars zero (real voltage division between r,out and R). As a consequence, the phase of the loop gain (including the phase shift of the opamp) does not reach the critical value of -180deg at the cross-over frequency (loop gain 0 dB). This stabilizes the whole circuit.

The value of this additional resistor R should be chosen to produce a zero app at 25%---50% of the cross over frequency (for unity gain feedback identical to the opamps transit frequency).