Continuing in 11.1 and the subject is “Negative Feedback is Required”—it often is required for op amps.
Negative feedback is the return of a portion of the output signal to the input signal (out-of-phase).
When an op amp has feedback, its operation is closed loop; with no feedback, it is open loop.
Couple of concepts here to consider: Here we have two op amps that are configured to use negative feedback. One is using the inverting input and the other is using the non-inverting input. It's needful to look at the differences in the configuration.
Let's just look at, for example, here we have an input signal. The signal comes in like so. Notice it's inverting, so that signal will be just the opposite of that on the output. Notice the signal comes in and a portion of it is returned to the input. Here we have this signal coming in and the returning signal is the same signal except that it is out-of-phase. This will tend to attenuate the final output.
We mentioned something about closed loop and open loop and often you'll see a term called “AOL,” not for America Online, that is for gain open loop. Gain open loop is kind of like beta was in transistor. The open loop gain, for example, for a 741 can be anywhere from 20,000 to 100,000. We call this gain ACL.
This is for gain closed loop, and that's what we're looking at when we incorporate negative feedback, is gain in a closed-loop configuration. If this resistance wasn't here, you'd feed the input and it'd come out here and there's no loop at all, it's just open loop. When we close this loop, like this, that's why we're calling it gain closed loop. When we do this, we can get a very predictable gain.
The diagrams here, let's see, we're using inverting and non-inverting … Okay, we looked at the inverting, let's look at the non-inverting. In the non-inverting, we're going to send in this input signal and since it's the non-inverting, the output will be the same phase as the input.
Then we have a portion of that is fed back to the inverting input and so, notice, that is coming in like this. It's in the same phase. Recall that an op amp amplifies the difference. If we had the same phase of input on both inputs, then, again, this will tend to attenuate the signal. This idea of negative feedback is that the feedback opposes the original input signal.
Again, this will attenuate the total gain from what we would have in AOL, but, again, it will make for an ACL, which is a closed-loop gain, and it will be an extremely predictable amount of gain.
Since the op amp ideally has infinite input resistance, no current flows into the input. Remember, we've mentioned that several times, that this effectively has infinite input impedance. What we're going to say is that we're going to send in an input voltage and it will go across this resistance.
There's something that we haven't mentioned. There is a concept, sometimes it's referred to as a virtual ground, sometimes a virtual short. In this case, it would be referred to as a virtual ground. At least for calculation of current, we can consider that there is actually a ground between here and … If it was a real ground, we would have no output because simply the signal would come in and go straight to ground, it would never get to the amp. This is a virtual ground but because for calculation purposes and analyzation, it does look like a ground.
If we took this voltage in and we divided it by the resistance here, we would get a current and that current is not going to flow into the op amp because it has infinite resistance. That current will be felt through this resistance up here. Sometimes this is referred to as RF or feedback resistor. The value that flows through that current will develop a voltage and that will result in our output.
We'll look at negative feedback in more detail later, but what we're going to find is that we can get a very predictable gain based upon the sizes of these two components.
The same concept will result down here. We call this a virtual ground. Oftentimes, in this case, it would be called a virtual short because if you calculate the value of this voltage across this component, then we can do basically the same kind of calculation.
The output of an op amp comes from a source internal to it that has an associated series resistance. Here we see the input and we see an associated series resistance that's going to become our output resistance.
The effective resistance is called the output resistance of an op amp. We looked at that back in the transistor section.
Negative feedback lowers the effective output resistance. It is low enough that for practical purposes, we will consider it to be zero.
With the 741, just as an example, it has 25 ohms of resistance with gain open loop and nearly zero with negative feedback. In fact, if we went in and did the formalized calculations for that, we would find that with negative feedback the resistance is usually less than 1 ohm, so for practical purposes, we consider it to be zero.
Output Voltage Swing
The output of an op amp can normally have output voltage swings that are within 2-3 V of the supply voltage.
If the output tries to exceed these limits, it will be distorted. It will result in clipping; we will have saturation in one of the output transistors. Where clipping occurs, it is commonly referred to as the “rails” and we'll get to that in a couple of minutes.
Here we have some examples and here we have an amplifier with, in each case here, the gain is 1,000,000, the supply voltages are +15 and -15. The only thing that is changing is the input and the output. In this case, here we have 1 microvolt of input and so we come in with 1 microvolt, we amplify it 1,000,000 times and so it has 1 volt of output. The input and the output have the same shape except that it's been significant amplified.
Then in the next circuit here, everything's the same except now we're putting in 10 microvolts, so now we're getting 10 volts out.
Next screen, we feed in 15 microvolts and now the op amp is unable to provide that much amplification. We're sending it a signal but the supply voltage are going to limit our output. Notice that we're not getting all the way to 15, in this case we're getting to 12 and this value will actually vary depending upon the size of the load resistance [inaudible 0:08:52]. If you have a very large load resistance, you might get a little more than that. If you have a very small load resistance, you actually might get a little less than this.
In this case, here we have 20 microvolts and, again, now we're having severe attenuation and the output signals going to look kind of like this. It's almost beginning to look like a square wave, no, not quite, but it's getting there.
These signals where it gets clipped off, this would be referred to as the rails of the op amp outputs because it's the limitation where it can't go any further.
Open Versus Closed-loop Gain
We've alluded to this already. An ideal op amp has infinite voltage gain at all frequencies. This isn't going to be true, but we'll just say that's the ideal.
Practical op amps have open-loop gains ranging from 100,000 to over 1,000,000—and notice this—at low frequencies. We will look at a graph in a later presentation.
The internal voltage gain of an op amp decreases at higher frequencies. When we look at this graph we will see the decrease in voltage gain as frequency increases.
We've looked briefly at open- versus closed-loop gain, we looked at output voltage swings, output resistance, and we talked about the concept of negative feedback, which is usually used in operational amplifiers.