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Basic Summing:  [Setting the Gain Coefficient] [Analog Addition] [Adding a Fixed Constant] 
Variations in Feedback Circuits:  [Integrators] [Differentiators] [Logarithmic Amplifiers] [NonInverting Amplifiers] [A Difference Amplifier] [Increasing the Output Current Capacity] [A HalfWave Rectifier] [A FullWave Rectifier] 
Mixing Analog and Digital Technologies:  [Comparators] [Digital to Analog Conversion] [Analog to Digital Conversion] 
Generating Waveforms:  [A Square Wave Generator] [A Triangle Wave Generator] [A Sine Wave Generator] 
Operational Amplifiers:  [Characteristics of Operational Amplifiers] [Inside the 741] 
Characteristics of Operational Amplifiers 

In analog computers and similar circuits, we make the assumption that the key component of the circuit — the operational amplifier — is perfect and ideal, with an infinite voltage gain and zero input current. Unfortunately, this is not possible in realworld devices. The questions we need to answer, then, are: how close can we come to the ideal, and how much error will be introduced into the results?
A very typical commercial IC op amp circuit is the 741. This IC has been available for many years, and a number of variations have been developed to help minimize the errors inherent in its construction and operation. Nevertheless, the analysis we will perform here using the 741 will apply to any other IC op amp, if you take into account the actual parameters of the device you are actually using. Therefore, we will use the 741 as our example IC op amp.
To the right is a circuit using the 741 op amp IC, with the input and feedback resistors that are required for this circuit to operate properly in an analog computer. Note that there are actually two inputs to the amplifier, designated "+" and "" in the figure. This is because the 741, like all IC op amps of this type, is in fact a differential amplifier. Thus, the output voltage is determined by the difference between the two input voltages. The "+," or noninverting input, is grounded through a resistor as shown. Thus, its input voltage is always zero. The "," or inverting input, is the one that is actively used. Thus, we establish that the inverting input, which is also the junction of the input and feedback resistors, must operate as a virtual ground in order to keep the output voltage within bounds.
So far, so good, but what about the actual voltage gain? It can't possibly be infinite, and if it isn't infinite, there must be some nonzero input voltage to produce a nonzero output voltage. In fact, the typical openloop voltage gain for the 741 is 200,000. This does not mean that every such device has a gain of 200,000, however. What is guaranteed is that the commercial version (the 741C) will have a minimum gain of 20,000. The military version is more stringently selected, and will have a minimum voltage gain of 50,000.
For the 741C, then, with a maximum output voltage of ±10 volts, the maximum input voltage required at the inverting input can never be more than ±10/20,000 = ±0.0005 volt, or 0.5 millivolts. Typical measurement accuracy uses three significant digits, so we would measure voltages from 0.00 volts to ±10.00 volts. The maximum input voltage is more than an order of magnitude smaller than this, and hence is insignificant in a typical analog computer.
But what about input bias current? Surely the IC requires at least some small amount of input current? Well, yes, it does. The 741C requires a typical input bias current of 80 nA (that's nanoAmperes, where 1 nA = 10^{9} A). The maximum input bias current for the 741C is 500 nA, or 0.5 µA.
So how do we use this information to minimize the errors it could cause into insignificance? Well, let's consider the resistance that would be required for this current to cause a significant voltage drop. If we keep the voltage error small enough, we can ignore it as unmeasurable. This means we must keep the values of R_{in} and R_{f} as small as possible, consistent with proper operation of the circuit. At the same time, we cannot make them too small, or the op amp itself will be overloaded. For proper operation, the total load resistance at the 741 output should not be smaller than 2000 ohms, or 2k. This amounts to a maximum output current of 5 mA at 10 volts output.
This means that the output resistance of the op amp is not the desired zero ohms. However, as long as you don't draw too much current from the output, the use of heavy negative feedback has an added benefit: It makes the op amp behave as if it had zero output resistance. That is, any internal resistance will simply mean that the op amp must produce an internal voltage enough higher than the calculated value so that the final output voltage will be the calculated value.
So what if we make our input and feedback resistors about 10k each? Then the current demand on the output is only 1 mA at 10 volts, leaving plenty of capacity for additional inputs. And the voltage caused by the input bias current won't exceed 10,000 × 0.5 × 10^{6} = 0.005 volt. This is half of the least significant digit of our measurement capability, which is not as good as we would like, but will do. Also, this is the absolute worstcase situation; most practical applications won't see an error this big.
In addition, the input bias current applies equally to both inputs. This is the reason for the resistor connecting the "+" input to ground. If this resistor is close in value to the parallel combination of R_{in} and R_{f}, the same voltage error will be generated at the two inputs, and will therefore be cancelled out, or very nearly. Thus, we can relegate this problem to true insignificance by means of correct circuit design and careful choice of component values.
The 741 does also have two error characteristics, called input offset voltage and input offset current, which define the inherent errors which may exist between the two inputs to the IC. However, the 741 also has the means for balancing these variations out, so the actual errors are minimized or eliminated, thus once again removing them from significance.
A problem with any op amp is a limited frequency response. The higher the gain of the complete circuit, the lower the working frequency response. This is one reason an overall gain of 20 is a practical limit. (Another reason is that the input and feedback resistors become too different from each other.) Also, the standard 741 has a slew rate of 0.5 v/µs. This means that the output voltage cannot change any faster than this. The newer generation of op amps, such as the 741S, have a slew rate more like 5 v/µs, and hence can operate over the entire audio range of frequencies without serious problems.


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