Op amp and 3-db frequency problem

[Alex Santos]

Homework Statement

An inverting amplifier with the DC gain of -9 (V/V) is built with an op amp having its
DC gain of 10⁵
and corner frequency of 30 rad/s.
▪ Determine the 3-dB frequency of the inverting amplifier.
▪ Sketch the magnitude Bode plot of the voltage transfer function of the inverting amplifier.

Homework Equations

X

The Attempt at a Solution

X

Hello.
So I am dealing with this homework and I have absolutely no idea how to approach this problem.
Just to clear things out I do not want someone to do this for me as you'll all guess. But I am kinda asking for help on how to approach and start this problem. Also I am not sure what the question is. I know that that 3-db frequency is the half power point but because this is a DC gain I would think that I am dealing with a DC circuit and therefore I would not expect any frequency in this problem (but I am probably wrong). I am also having a hard time understanding why there are 2 given gains, the -9 V/V and the other 10⁵
What are the difference in those gains. So far we've learned that an op amp can be represented with a simple circuit consisting of 2 resistors and Voltage-Controlled-Voltage source (VCVS).

So basically my question is how do I approach this and am I suppose to simplify the op amp with a simple amplifier circuit with 2 resistors and VCVS?

Thanks in advance.

 

[berkeman]

Homework Statement

An inverting amplifier with the DC gain of -9 (V/V) is built with an op amp having its
DC gain of 10⁵
and corner frequency of 30 rad/s.
▪ Determine the 3-dB frequency of the inverting amplifier.
▪ Sketch the magnitude Bode plot of the voltage transfer function of the inverting amplifier.

Homework Equations

X

The Attempt at a Solution

X

Hello.
So I am dealing with this homework and I have absolutely no idea how to approach this problem.
Just to clear things out I do not want someone to do this for me as you'll all guess. But I am kinda asking for help on how to approach and start this problem. Also I am not sure what the question is. I know that that 3-db frequency is the half power point but because this is a DC gain I would think that I am dealing with a DC circuit and therefore I would not expect any frequency in this problem (but I am probably wrong). I am also having a hard time understanding why there are 2 given gains, the -9 V/V and the other 10⁵
What are the difference in those gains. So far we've learned that an op amp can be represented with a simple circuit consisting of 2 resistors and Voltage-Controlled-Voltage source (VCVS).

So basically my question is how do I approach this and am I suppose to simplify the op amp with a simple amplifier circuit with 2 resistors and VCVS?

Thanks in advance.

The high gain is the open-loop low-frequency gain. The -9V/V is the closed loop low-frequency gain with the negative feedback. Show us the Bode plot for the open loop gain of an opamp (find it via Google Images or scan your textbook). Then show us how that open-loop Bode plot of gain is altered when you close the loop with negative feedback...

 

[Alex Santos]

This is the only thing that was given in the problem. There is no image or anything else. But shouldn't I first determine the 3 db frequency before sketching up the Bode plot?

Also I am not quite sure how to draw the circuit. I've completed one sketch but I am not sure if it is the right thing to do.
I will link the sketch that I've drawn.

 

[berkeman]

This is the only thing that was given in the problem. There is no image or anything else. But shouldn't I first determine the 3 db frequency before sketching up the Bode plot ?

I was just asking for some visual support for this problem. It helps a lot to see the Bode plots of opamps with and without feedback when working this type of problem. As I said, use Google Images or some other way to find some Bode plots that you can use to help you illustrate and work this problem... :-)

 

[rezeew]

Hello,

Firstly, the two different gains (DC gain of -9 V/V and DC gain of 105) represent the open-loop gain and closed-loop gain of the op amp, respectively. The open-loop gain is the gain of the op amp without any feedback, while the closed-loop gain takes into account the feedback from the output to the input. In this case, the DC gain of -9 V/V is the gain of the op amp without any feedback, while the DC gain of 105 is the gain of the inverting amplifier with feedback.

To approach this problem, you can start by drawing a circuit diagram for the inverting amplifier with the given information. You can then use the standard formula for the closed-loop gain of an inverting amplifier, which is -R2/R1, where R2 is the feedback resistor and R1 is the input resistor. You can also use the formula for the corner frequency of a low-pass filter, which is 1/RC, where R is the resistor and C is the capacitor in the circuit.

Once you have calculated the closed-loop gain and the corner frequency, you can use them to find the 3-dB frequency of the inverting amplifier. This can be done by using the formula 3-dB frequency = corner frequency * closed-loop gain. This will give you the frequency at which the output power is half of the input power, which is the definition of 3-dB frequency.

To sketch the magnitude Bode plot, you can use the calculated 3-dB frequency and the corner frequency to plot the curve. The Bode plot is a logarithmic plot, so you will need to use logarithmic scales for both the frequency and the magnitude. The magnitude Bode plot should start at the DC gain of -9 V/V and gradually decrease until it reaches the 3-dB frequency, after which it should decrease at a rate of -20 dB/decade.

I hope this helps. Good luck with your homework!