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The concept of feedback has extremely wide applications to other fields of study, including mathematical biology and economics. For example, predator-prey relationships rely upon several feedback loops that determine the stable size of populations. If the number of predators the system's output increases, then the number of prey animals the input will decrease.

The negative feedback in this system occurs because an increase in the output predator population results in a decrease in the input prey population. There will in general be an equilibrium ratio of populations as a result of the stabilizing influence of the negative feedback, with, of course, many other factors entering in to establish their exact sizes.

In another example, computerized trading of stocks on the stock market represents a prime example of the pernicious effects of positive feedback. Extremely large investors, such as pension funds, can buy and sell stocks using computer programs set to make trading decisions based on the behavior of a market index, such as the Dow Jones Industrial Average. These trading decisions are the system's inputs. When the stock market index the system's output begins to drop, these programs are designed to quickly sell off stocks in order to minimize investor's losses.

However, a large investor can further depress the stock market index by selling off its stocks i. This system can lead to wild oscillations, or even a crash, should many large investors use such programs during a period of sharply falling prices.

The Securities and Exchange Commission decided to regulate computerized trading after this practice was implicated in the major crash of One can show mathematically that the results of feedback in op-amps circuits are summarized by two "golden rules", which we will take as our starting points for figuring out how op-amp circuits will function:.

That's the function of high gain of the amplifier and the negative feedback; if the output voltage rises too much, it drives the input voltage difference down. The voltage difference between the inputs is so close to zero that we can assume that it really is zero in analyzing circuits. Figure 3: Inverting amplifier circuit the triangle at the bottom denotes power supply ground.

Using the golden rules, the negative feedback "inverting amplifier" circuit shown in figure 3 can be analyzed. The inverting input isn't actually connected to ground, rather the internal circuitry of the op-amp labors to keep it very near ground. We call such a voltage a virtual ground. From golden rule number 2, all of the current through R 1 must flow through R F , because no current flows into the op-amp inputs. We arbitrarily take the direction of the conventional positive current to be to the right.

Then applying Kirchoff's laws gives. This means that you can choose the gain by selecting the values of the resistors! Also, the gain is not dependent on the details of the particular op-amp e. The largeness of A 0 is the underlying justification for Golden Rule 1. Since the output is negative for positive inputs, the amplifier called an inverting amplifier.

You will be using the LF op-amp in today's lab. The F refers to the original manufacturer, Fairchild, and the other numbers specify one of many different integrated circuits made by this company. The LF has been inserted into your breadboard for you. Figure 4: Connections for the LF op-amp top view. The "offset null" connections will not be used here; their purpose is to allow the user to make small adjustments if desired so that the output is precisely zero when the input voltage difference is precisely zero.

Figure 5: Open loop circuit the triangle at the bottom is power supply ground. Notice that the output voltage is far from zero because of the very high open loop gain of the op-amp. Try adjusting the input and sketch the output voltage as a function of the input voltage.

Explain briefly why your graph looks the way it does. Figure 3 presented earlier employs negative feedback from V out to V - to give a stable gain that is controlled by the ratio of two resistors. In this portion of the lab you will construct an op-amp circuit with negative feedback. Use your function generator's sine wave setting and the LO output set to a very low voltage to supply V in.

The feedback is set up by connecting pin 6 to pin 2 with R F. You should start with an extremely low amplitude input signal to see a clear sine wave output. Sketch this display, carefully noting the amplitudes and phase relationships of the two signals. Determine the gain of your circuit from this data. How large an input is required to do this? What determines whether the output is saturated? Op-amps can be used to do mathematical computations.

For example, they can be used to compute the sum of many inputs, with each one multiplied by a selectable gain. For example, the output of the circuit shown in figure 6 is given by the following expression:. This can easily be generalized to an arbitrary number of inputs by adding terms to the equation.

Figure 6: Weighted summing circuit. Another useful function of an op-amp is to compute the integral or derivative of an input signal. It may be surprising to realize that all the integrals we compute mathematically can be calculated electronically by the simple op-amp circuit shown above.

Figure 7 shows an op-amp circuit for which the negative feedback is now through an RC circuit rather than just a resistor. From the golden rules, the current flowing through R and C must be equal just as for the resistors in figure 3 above. It is there to discharge the capacitor for very long times when the input voltage is turned off, or if the function-generator has a DC offset.

Otherwise, charge will build up gradually and saturate the op-amp. Therefore, the output voltage at a given time is the integral of the input voltage from some initial time when the feedback was connected to the present time t.

However, in this case a small deviation from ideal behavior in the op-amp can cause problems. As you will have noted earlier, there can be a small offset voltage between the inputs of an op-amp even when the output is zero. In an amplifier circuit e. In an integrator, however, it is a real problem, because the small constant offset voltage will be integrated to produce a gradually growing output that eventually dominates over the desired integration of the real input signal.

This linearly increasing spurious output is manifested by a gradual accumulation of charge on the capacitor. The function of R S is to allow this charge to leak off slowly. A differentiator can be constructed by small modifications of this circuit, but we shall not do so here. Apply Eq. Compare the amplitudes of the input and output against the theoretical prediction. Be sure to try out sine waves and triangle waves too. The total gain of non-inverting amplifier is;.

If the feedback resistor in removed i. Terms used for Differential Amplifier formulas. If all the resistors used in the circuit are same i. This type of Operational Amplifier provides the output voltage which is directly proportional to the changes in the input voltage. The output voltage is given by;.

This amplifier provides an output voltage which is the integral of the input voltages. Related Formulas and Equations Posts:. Your email address will not be published. Notify me of follow-up comments by email. Notify me of new posts by email. Table of Contents. Electrical Technology 0 3 minutes read. Show Full Article.