# Investing amplifier gain frequency response matlab

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This example assumes the use of an uncompensated op amp with 2 poles at frequencies w1,w2 and high dc gain a0. Assuming this op amp is operated in its linear mode not saturated , then its open-loop transfer function can be represented as a linear time-invariant LTI system, as shown above. Though higher-order poles will exist in a physical op amp, it has been assumed in this case that these poles lie in a frequency range where the magnitude has dropped well below unity.

Next, you want to create a transfer function model of this system using Control System Toolbox. First, define the Laplace variable, s, using the TF command. Then use 's' to construct the open-loop transfer function, a s :. Right-click on the plot to access a menu of properties for this Bode Diagram.

Left-click on the curves to create moveable data markers which can be used to obtain response details. Hold the mouse over the settling time marker to reveal the exact value of the settling time. This feedback network, b s , is simply a voltage divider with input Vo and output Vn. Solving for R2 yields:. The use of negative feedback to reduce the low-frequency LF gain has led to a corresponding increase in the system bandwidth defined as the frequency where the gain drops 3dB below its maximum value.

Since the gain is now dominated by the feedback network, a useful relationship to consider is the sensitivity of this gain to variation in the op amp's natural open-loop gain. The inverse relationship between S s and L s reveals another benefit of negative feedback: "gain desensitivity".

The very small low-frequency sensitivity about dB indicates a design whose closed-loop gain suffers minimally from open-loop gain variation. Such variation in a s is common due to manufacturing variability, temperature change, etc. However, the step response now displays a large amount of ringing, indicating poor stability margin. The resulting plot indicates a phase margin of less than 6 degrees. You will need to compensate this amplifier in order to raise the phase margin to an acceptable level generally 45 deg or more , thus reducing excessive overshoot and ringing.

A commonly used method of compensation in this type of circuit is "feedback lead compensation". This technique modifies b s by adding a capacitor, C, in parallel with the feedback resistor, R2. The capacitor value is chosen so as to introduce a phase lead to b s near the crossover frequency, thus increasing the amplifier's phase margin. You can approximate a value for C by placing the zero of b s at the 0dB crossover frequency of L s :. To study the effect of C on the amplifier response, create an LTI model array of b s for several values of C around your initial guess:.

We can overlay the frequency-response of all three models open-loop, closed-loop, compensated closed-loop using the BODE command:. I would offer that the characteristics are those of a complex conjugate pole pair. The characteristics that show up in my modeling, are in agreement with the described effects of input capacitance on the inverting negative input of an inverting amplifier in this TI application report on the effects of parasitic capacitance on op-amp circuits.

My question, is whether it is reasonable to conclude from the absence of an amplitude peak, and the sudden degree phase shift, characteristic of capacitance at the inverting input of the op-amp, that such parasitic capacitance at the op-amp input plays a negligible role in the frequency response observed in the circuit which lacks the explicit capacitor?

Perhaps I am missing something. Edit: Perhaps I could put my question in another way. Some factor or factors cause the bandwidth of the op-amp circuits to be limited. One possible limiting factor is the input capacitance together with the circuit resistors. However, when bandwidth is limited by input capacitance combined with circuit resistors in models , the models show tell-tale signs, especially an amplitude peak and a sudden degree phase reversal.

If the frequency response of a circuit does not appear to have these features, is it reasonable to conclude that some other factor or factors are limiting the bandwidth? Is it reasonable to conclude that, although the input capacitance may play some role in the frequency response, it does not play the dominant role?

Or would that reasoning be faulty? The peak has moved to about kHz. It is wider and with less amplitude, but still quite noticeable. The peak here is almost at the kHz -3dB bandwidth found earlier. If the capacitance is made even smaller, the "peak" will disappear into the roll-off caused by the op-amp's internal compensation capacitor.

There is a roll-off with a break frequency of around 15kHz. I do not doubt that this initial roll-off is due to capacitance somewhere in the op-amp. However, the absence of a peak suggests to me that the capacitance that is causing the roll-off is likely elsewhere than at the inverting input. I wouldn't be surprised to learn that this higher frequency break is caused by capacitance at the inverting input. Perhaps I am wrong in my hypothesis, but I have not seen the "peak" disappear except into the high frequency roll-off which is generated by the op-amp's compensation capacitor.

So, if there is something that suggests my guess is wrong, I am still unaware of it. With no cap and no load, other things inside the op-amp seem to add a delay of a couple hundred ns to the -1 gain configuration. So this looks a lot like the graph of the first model CircuitLab?

I don't know what's going on in that Spice model. Also used a smaller input with 51ohm termination. This did not change the results without C1 cap much shaved another 25ns off the delay. But it made a big difference once C1 was added below. It seems this was because of the output stage again. Rload going to Vee fixed it. It also turns on the output quite a bit more 10mA DC. The following 3 graphs show it. The delay values are also picked to line up with variations from the output load conditions described above.

This seems to extend the model out from Kish to Kish. I suspect more modern op-amps don't have these issues in ordinary cases, since the LM is nearly 50 years old, and process of that time used fairly slow transistors on the IC.

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Modified 1 year ago. Viewed times. The model which I wish to consider is this: simulate this circuit The frequency response of this circuit looks like this: I have simulated this circuit with multiple different resistor values, multiple different capacitor values, and multiple different op-amps.

Now, please compare what has been seen above with the frequency response in the prior question. Notice that the 3dB cutoff frequency is around kHz, and notice the 90 degree phase shift. Notice the peak at about 4kHz and the phase shift.

With smaller resistors, the same sequence is observed, except at different capacitance values. Now in the next graph, there is NO observable peak. Math Keeps Me Busy. You also connect the non-inverting input directly to ground with zero impedance, while in the other simulation connected it to 0V via 50k impedance. Nor does adding a power supply unless it is very low voltage affect the simulation. Would you expect either of these to alter the characteristics of that are evidenced by input capacitance, i.

Perhaps it would be time to question the op-amp model itself? It is basically "unnoticed" there, because op-amps are generally not operated in that region.

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Investing amplifier gain frequency response matlab | That other question asks why a particular op-amp behaves the way it does. The resulting plot indicates a phase margin of less than 6 degrees. Select a Web Site Choose a web site to get translated content where available and see local events and offers. Note how the addition of the compensation capacitor has eliminated peaking in the closed-loop gain and also greatly extended the phase margin. It generally needs to be beyond the unity gain frequency to ensure stability. Sign up using Facebook. We can overlay the frequency-response of all three models open-loop, closed-loop, compensated closed-loop using the BODE command:. |

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Investing amplifier gain frequency response matlab | Perhaps I am wrong in my hypothesis, but I have not seen the "peak" disappear except into the high frequency roll-off which is generated by the op-amp's compensation capacitor. Stack Overflow for Teams — Start collaborating and sharing organizational knowledge. So, here, I have simplified the circuit to a unity gain inverting amplifier:. Post as a guest Name. This seems to extend the model out from Kish to Kish. I suspect more modern op-amps don't have these issues in ordinary cases, since the LM is nearly 50 years old, and process of that time used fairly slow transistors on the IC. And that limits open loop bandwidth. |