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So I have a lab practical with the instructions

"Demonstrate an operational amplifier circuit which may consist of one or two op amps with a gain of X (±10%) and a -3dB frequency exceeding Y kHz. The sign of gain can be + or -. "

I understand the operation and build of an amp and this is actually the second time doing this lab as I screwed it up the first time. The first time I was asked to design an amplifier with a gain of 80 with a frequency of around 1kHz. I used a circuit similar to the one depicted below to do this. Obviously my resistor values were different because I required a different gain.

enter image description here

As my understanding, depending on the sign of the gain dictates whether I used the noninverting (-R2/R1) or the inverting equation (1+R2/R1). Using these equations and the desired gain I can choose resistor values that give my desired gain. I also understand that if the desired gain is high enough I will have to cascade op amps. What I'm confused about is designing around the desired -3dB frequency. I guess I would like someone to explain where the -3dB frequency comes in to play in designing an op amp circuit.

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  • \$\begingroup\$ You do realize that the circuit shown has a gain of 20, not 80. And that a feedback resistor value of 460\$\Omega\$ is a bit low for most op-amps. \$\endgroup\$
    – TimWescott
    Nov 24, 2018 at 18:06
  • \$\begingroup\$ Yes I didn't use any of the values shown in that picture. I just used a similar model for my circuit. \$\endgroup\$ Nov 24, 2018 at 18:21

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What I'm confused about is designing around the desired -3dB frequency

I think the question is trying to test you on your understanding of the open-loop gain for an op-amp and how the 3dB point changes as you lower the gain with feedback resistors. For instance: -

enter image description here

In the example above, the feedback and input resistors are chosen so that the "closed-loop" gain at DC is 20 dB (a real number gain value of 10). At this level of amplification you can see that the op-amp will run-out-of-steam at a frequency about 50 kHz. This is the approximate 3 dB point (half power point). If we chose a closed loop gain of 55 dB (G = 560), the 3 dB point would be much lower at 1 kHz.

As an aside, this introduces the concept of the op-amp having a numerically fixed (well, fairly fixed) value of gain x bandwidth often called the GBWP or gain-bandwidth-product. G = 10 and BW = 50 kHz is pretty close to G = 560 and a BW of 1 kHz. I'm sure with a better picture of the open-loop gain it would be numerically quite close in both scenarios.

So, with two cascaded op-amps, the best (highest) 3 dB point you can get is when both have the same gain because, if one had a much smaller gain than the other, the device operating at the higher gain would dictate the 3 dB point and this will inevitably be lower than if both gains (and both op-amps) are the same.

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  • \$\begingroup\$ So what is exactly the correlation between the resistor values and the 3dB point? Fundamentally everything you said makes perfect sense but I'm am still a bit confused about choosing the correct resistor values with a specific 3dB point in mind. \$\endgroup\$ Nov 24, 2018 at 18:02
  • \$\begingroup\$ That graph is different for each model of op-amp so the 3 dB point only correlates to resistor values when you know the specific op-amp. Read about gain-bandwidth product. \$\endgroup\$
    – Andy aka
    Nov 24, 2018 at 18:05
  • \$\begingroup\$ Once you're using high enough resistor values there's not much correlation between resistor value and the 3dB point. The correlation is between the circuit's DC gain and the 3dB point. \$\endgroup\$
    – TimWescott
    Nov 24, 2018 at 18:05
  • \$\begingroup\$ The only way to "see" the effects is to calculate and observe. Design a stage with X gain, and observe the frequency rolloff. Design another with Y gain and observe. Now mulitply the two and see what you get. Do this for other combinations of gain. Stop guessing asking for other people to explain things. \$\endgroup\$ Nov 24, 2018 at 18:20
  • \$\begingroup\$ Warning ----- the total of capacitances on the Vin- pin (the virtual ground) may set the bandwidth. And expect phase-shifts to cause extending settling or ringing or oscillation. Photodiode circuits often have this problem; the cure is a 1pF or 5pF or 20pF feedback capacitor. \$\endgroup\$ Nov 24, 2018 at 19:04

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