As an exercise: replace the step voltage source V1 with a square wave source. See what happens as you drive the inverting amplifier at various frequencies from 1 kHz to 1 MHz. If you are relying on a virtual ground, you have to be patient. Unlike a real ground, a virtual ground is only a low-impedance point when you move slowly. This expression includes the open-loop gain A OL which covers DC and low frequencies, and it includes a low-pass filter which drops off following the gain-bandwidth product GBW.
Following the same method we solved in detail in the previous section, the corner frequency can be found by determining where the imaginary part of the denominator is equal in magnitude to the real part. Review that section to see us work through the almost-identical math. Op-Amp Inverting Amplifier - Gain vs. Bandwidth Tradeoff. Try the frequency domain simulation.
Again, the gain-bandwidth product is not magic. Just as we discussed on the non-inverting amplifier , there is parasitic capacitance everywhere, and we have to be most concerned about it at high-impedance nodes like V div. How much parasitic capacitance does it take to start seeing overshoot in the step response? How about ringing?
As the simulation demonstrates, it takes just picofarads of unintentional capacitance to cause serious overshoot or ringing. As an exercise, add ,p to the end of the custom sweep list for C1. Increase the simulation stop time to 40u. What happens to the step response? This demonstrates why this issue is called instability , because the op-amp is very nearly unstable and prone to oscillating indefinitely.
As another exercise, try making both resistors smaller by a factor of 0. Does this help or hurt? As discussed on non-inverting amplifiers , there are a few ways of mitigating this stability problem:. Compensation means modifying the circuit slightly by adding components that counteract the undesired parasitic effects. We demonstrated feed-forward compensation in detail on the non-inverting amplifier.
We can do something similar for the inverting amplifier, adding a capacitor C 2 in parallel with R f :. The simulator is set to try a range of different values for C2. Which value gives the best step response little ringing or overshoot? What happens if C2 is much larger or much smaller than that? It depends on too many factors, including the resistances, the gain-bandwidth product, and the parasitic capacitance.
If C2 is much larger than that, we eliminate ringing, but it also slows down the step response considerably. Somewhere around 0. It may even be present unintentionally due to parasitic capacitance in your physical circuit, simply from the PCB traces of the output and inverting input being in close proximity.
One reason that only a tiny capacitance is required here is because the two ends of the compensation capacitor are connected to voltages that are naturally moving in opposite directions: as V div rises, V out falls because of the op-amp. This means that even a small voltage change at the high-impedance side actually drives a large voltage change across the capacitor. This is called the Miller effect. This can be hard to understand, but to a first order, we can think about the parasitic capacitance C 1 as adding charge stored at the inverting input node V div.
It takes time for this charge storage to happen, which is what causes the ringing and oscillation in the first place. This is discussed in greater detail in the corresponding non-inverting amplifier section. To some degree, we can think of the compensation capacitor C 2 as trying to cancel out or remove that charge so that the circuit behaves overall more like the one without any parasitic capacitance.
This is the Miller multiplication effect at work! If you design op-amp circuits and find you have oscillation, overshoot, or ringing, remember this section and revisit it. My overall advice would be to pay special attention to high-impedance nodes and simulate step responses to quickly see the effects of parasitics and compensation. One common case is in single supply systems, where we have a positive power rail but no negative one.
In that case, you may wish to have everything be relative to a midpoint between ground and the positive rail, in order to maximize the available range symmetric around this new reference midpoint. The midpoint itself could be generated by a voltage divider or by an op-amp voltage reference. However, adding a decoupling capacitor can help reduce resistor noise and improve power supply rejection. An example of a 5V single-supply circuit with a gain-of-negative amplifier anchored at the midpoint is shown here:.
Run the DC Sweep simulation and observe three piecewise-linear segments. Does this shape match your expectation? A ground is always an arbitrary choice of a voltage. Now, we have:. This time constant is quite long. Short-duration high-frequency noise from the resistors, or high-frequency noise from the power supply itself, is substantially reduced by adding the capacitor.
You can try changing it to see the effect that the DC offset has on the output. As an exercise: what happens if you increase the amplitude of signal source V1? We can add a capacitor C in in series with R in. The order does not matter. For a system at DC steady state, no current can flow through a capacitor because the flow of current would cause charge to accumulate, causing a change in voltage, which is disallowed at DC.
At DC, one plate of the capacitor is driven by the DC value of the signal input. The other plate is connected to the virtual ground V div through the resistor R in , but there is no DC current and so no voltage drop across R in. Effectively, the capacitor charges up to perfectly cancel out the DC level of V in. Input signals that change fast enough are allowed to pass through the capacitor, while slow signals are diminished.
In its basic terms a small capacitor is added to the internal elements of the op amp. This has the effect of reducing tendency to oscillate, but it also reduces the open loop bandwidth. Although the open loop bandwidth of the op amp circuit is reduced, once negative feedback has been applied, a sufficient level gain with a flat frequency response can be achieved for most purposes. Negative feedback is used to control the gain of the overall op amp circuit.
There are many ways in which the feedback can be applied when designing an electronic circuit - it may be independent of frequency, or it may be frequency dependent to produce filters for example. It is possible to produce a generalised concept for applying negative feedback. From this the more specific scenarios can be developed. The output voltage can then be calculated from a knowledge of the input voltage, gain and feedback:. Using this generic equation it is possible to develop equations for more specific scenarios.
The feedback can be frequency dependent, or flat as required. The two simplest examples of op amp circuits using feedback are the formats for inverting and non-inverting amplifiers. The circuit for the inverting op-amp circuit is shown below. The op amp circuit is quite straightforward using few electronic components: a single feedback resistor from the output to the inverting input, and a resistor from the inverting input to the input of the circuit.
The non-inverting input is taken a ground point. This op amp circuit uses only two additional electronic components and this makes it very simple and easy to implement. It is easy to derive the op-amp gain equation. This means that any current flowing into the chip can be ignored. From this we can see that the current flowing in the resistors R1 and R2 is the same, because no current is flowing out of the junction between the two resistors.
Hence the voltage gain of the circuit Av can be taken as:. As an example, an amplifier requiring a gain of ten could be built by making R 2 47 k ohms and R 1 4. The circuit for the non-inverting op-amp is shown below. It offers a higher input impedance than the inverting op amp circuit.
Like the inverting op amp circuit, it only requires the addition of two electronic components: two resistors to provide the required feedback. The non-inverting amplifier also has the characteristic that the input and output are in the same phase as a result of the signal being applied to the non-inverting input of the op amp. The gain of the non-inverting circuit for the operational amplifier is also easy to determine during the electronic circuit design process.
The calculation hinges around the fact that the voltage at both inputs is the same. This arises from the fact that the gain of the amplifier is exceedingly high. If the output of the circuit remains within the supply rails of the amplifier, then the output voltage divided by the gain means that there is virtually no difference between the two inputs. We can assume that for the purpose of our calculation, the input to the operational amplifier draws no current as the impedance of the chip inputs will be well above the resistor values used.
This means that the current flowing in the resistors R 1 and R 2 is the same. The voltage at the inverting input is formed from a potential divider consisting of R 1 and R 2 , and as the voltage at both inputs is the same, the voltage at the inverting input must be the same as that at the non-inverting input. Hence the op amp gain equation for the voltage gain of the circuit Av can be taken as:.
As an example, an amplifier requiring a gain of eleven could be built by making R 2 47 k ohms and R 1 4. Op-amp gain is very easy to determine. The calculations for the different circuits is slightly different, but essentially both circuits are able to offer similar levels of gain, although the resistor values will not be the same for the same levels of op amp gain. It is normal to use operational amplifiers in linear applications with negative feedback, although this is not always the case.
This utilises the very high gain of the open loop amplifier to provide repeatable performance governed by the external components.
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The operational amplifiers bandwidth is the frequency range over which the voltage gain of the amplifier is above % or -3dB (where 0dB is the maximum) of. We saw in the last tutorial that the Open Loop Gain, (AVO) of an operational amplifier can be very high, as much as 1,, (dB) or more. The analysis technique was applied to both noninverting and inverting op amp circuits, resulting in a frequency- domain transfer function for each configuration.