You were asked to examine this circuit (below) in two different ways.

• You built this circuit in the laboratory, and explored what went on.
• You should have found that this circuit "emphasizes" a band of frequencies around a "resonant" frequency.
• That is the same kind of frequency behavior that you found in the RLC circuit you examined earlier.
• That's this circuit (below)
• 
• So, you should reasonably expect that the frequency response function (i.e. V_o/V_in) should be of the same general form.  And any insight that you have generated for the RLC circuit should carry over to the op-amp circuit above.
• You were asked to analyze the circuit so that you could calculate various aspects of the performance of this circuit.  Those aspects include the following.
• The resonant frequency - i.e. the frequency at which the peak response occurs.  You were able to do that for the RLC circuit, and should be able to get this one - but you have to be able to analyze the circuit and get that frequency response function.
• The bandwidth - this is more of a challenge for you.  You have to define the problem - i.e. figure out what it is that you are looking for - and then apply your mathematical skills to get a solution.  The hard part of this problem seems to be to realize that you are looking at when the magnitude of the frequency response function drops to 0.707 of the value at the resonant peak.  You have to get that magnitude thing in there, and that means that you better understand the idea of the magnitude of a complex number.
• The gain at the resonant frequency is also important.  You should be able to calculate that.  It will be different for the two different circuits.

• First, we will put together a quick list of the things that you need to do.  Click here for E. J.'s list.
• Secondly, we need to think about what we should look for in all of this.
• IMPORTANT ITEM #1  here is that you can make predictions for several of the circuit performance measures - resonant frequency, bandwidth and gain at the resonant frequency.
• IMPORTANT ITEM #2 is that you have laboratory measurements that you can compare to your predictions.
• A short philosophical note on items 1 & 2:  Making predictions is what engineers do.  If you are designing a spacecraft or an airplane, you need to predict how it will function.  If your predictions are off when someone finally rides in your vehicle you won't have a job for very long because you may have killed someone.  Making correct predictions is the most important thing that you do as an engineer.  The second most important thing is to be able to communicate those predictions effectively.  The engineers at Three Mile Island made correct predictions but failed to communicate clearly.  You MUST get both of those correct.
• Your report should include the following.
1. Predictions of performance measures
2. Measurements of performance measures
3. Comparison of predictions and measurements
4. Explanation - as best possible - of discrepancies.  You need to explain discrepancies analytically (i.e. show where your analysis and physical reality do not match up) and numerically (i.e. show that a corrected analysis would yield the numerical results you actually obtained).
• IMPORTANT ITEM #3 is that you need to learn how to anticipate where your analysis and model might not be as trustworthy as you would like.  There is at least one problem in one of the two circuits, and it is the kind of problem that you need to learn about - i.e. a model that doesn't match up with reality as well as you might like.