1. The problem statement, all variables and given/known data We did a lab analyzing this inverting, negative feedback circuit for a 741 op-amp: We measured the closed-loop gain and phase shift of the signal for several values of the input frequency with [itex]R_2/R1=1000[/itex],[itex]R_2/R1=100[/itex] and [itex]R_2/R_1=10[/itex]. The gain curves all looked like horizontal straight lines for low frequencies, and then some sort logarithmic decrease for larger frequencies. The phase shift curves looked sort of similar; they all started with π radian shift for low frequencies with some sort of logarithmic decrease before leveling off slightly near the end. The problem is, I have no idea what the theory is behind the shape of these curves. We know that the ideal case is [itex] G = -\frac{R_2}{R1}[/itex], but the max values of the measured gain weren't even close to that. If someone could point me in the direction of a source that deals with the theory (equations) for this circuit's frequency response, that would be great. 2. Relevant equations Exactly what I need to know. 3. The attempt at a solution I did find one pretty good paper here: http://coe.uncc.edu/~dlsharer/ETEE3212WebCT/SectionH/H7.pdf On page 4 it gives: [tex]G = \frac{G_o}{1 + s/{\omega_o} + {G_o}{\gamma}}[/tex] But I don't think it's for exactly the same circuit as I have, and it doesn't have any equations about phase shifts.
Do you have the datasheet for the LM741 opamp? (You should have it and refer to it as part of this lab work) Look for the plot of the Open Loop Gain & Phase response. Adding the external resistive negative feedback just sets the overall gain lower than the Open Loop Gain, up to the frequency where the Open Loop Gain approaches the Closed Loop Gain. You can also do some reading about "Dominant Pole Compensation" that is used inside opamps like the LM741: http://www.analog.com/library/analogDialogue/archives/31-2/appleng.html .
Thanks for the reply. Yes, I have that. I need a quantitative statement though; if there is no such thing I might just have to come up with some functions that approximate the Open-Loop curves. This talked about a the "transfer function" of the amplifier a lot, which sounds promising, but it never actually said what it was.