Op-Amp Frequency Response Theory

In summary, the conversation was about a lab analysis of an inverting, negative feedback circuit for a 741 op-amp. The measured closed-loop gain and phase shift showed logarithmic decrease for larger frequencies, with the phase shift starting with a π radian shift and leveling off near the end. The problem was understanding the theory behind the shape of these curves, as the ideal case was not reflected in the measured gain values. The attempt at a solution included finding a paper with a transfer function for the circuit, but it was not exactly the same and did not include equations for phase shifts. It was suggested to refer to the LM741 opamp datasheet for the open loop gain and phase response, and to research "Dominant Pole Compensation
  • #1
Screwdriver
129
0

Homework Statement



We did a lab analyzing this inverting, negative feedback circuit for a 741 op-amp:

circuit.jpg


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.


Homework Equations



Exactly what I need to know.

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.
 
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  • #2
Screwdriver said:

Homework Statement



We did a lab analyzing this inverting, negative feedback circuit for a 741 op-amp:

circuit.jpg


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.


Homework Equations



Exactly what I need to know.

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

.
 
  • #3
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.

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.

You can also do some reading about "Dominant Pole Compensation" that is used inside opamps like the LM741:

http://www.analog.com/library/analog...2/appleng.html

This talked about a the "transfer function" of the amplifier a lot, which sounds promising, but it never actually said what it was.
 

What is an Op-Amp and how does it work in frequency response theory?

An Operational Amplifier (Op-Amp) is an electronic device that amplifies the difference between two input signals. In frequency response theory, Op-Amps are used to analyze the behavior of a circuit in response to different frequencies. They are often used in filters, amplifiers, and other electronic circuits.

What is the significance of frequency response in Op-Amp circuits?

The frequency response of an Op-Amp circuit determines its ability to accurately amplify signals of different frequencies. It is important to understand the frequency response in order to design circuits that meet the desired performance criteria. The frequency response also helps in identifying potential issues such as signal distortion or instability.

What are the key parameters used to describe the frequency response of an Op-Amp circuit?

The key parameters used to describe the frequency response of an Op-Amp circuit are gain, bandwidth, and phase shift. Gain is the ratio of output voltage to input voltage and determines the amplification capabilities of the circuit. Bandwidth is the range of frequencies over which the circuit can accurately amplify signals. Phase shift refers to the delay in the output signal in relation to the input signal.

How can the frequency response of an Op-Amp circuit be plotted and analyzed?

The frequency response of an Op-Amp circuit can be plotted using a Bode plot, which shows the gain and phase shift as a function of frequency. The plot can then be analyzed to determine the gain, bandwidth, and phase shift of the circuit. Additionally, the plot can be used to identify any issues such as peaking or rolloff in the frequency response.

How can the frequency response of an Op-Amp circuit be improved?

The frequency response of an Op-Amp circuit can be improved by using different Op-Amp models with better performance characteristics, choosing appropriate feedback components, and designing the circuit with proper compensation techniques. Additionally, using multiple Op-Amps in a circuit can improve the frequency response by increasing the gain and reducing the effects of parasitic elements.

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