Page 409 - Op Amps Design, Applications, and Troubleshooting

Nonideal DC Characteristics 385

This voltage will be amplified by the noninverting gain of the amplifier and
appear in the output as

It should be noted that this voltage will be negative in our present example, since
we assume that the electron flow was out of the input terminals.
Now let us consider the effect of the bias current for the inverting input
According to the Superposition Theorem, we must set the bias current on the non-
inverting input to 0. Having done this, we see that since no current is flowing
through R B there will be no voltage across it. Therefore, the voltage on the {+)
input will be truly 0 or ground. Additionally, we know that the closed-loop action
of the amplifier will force the inverting pin to be at a similar potential. This means
that the inverting pin is also at ground potential; recall that we referred to this
point as a virtual ground. In any case, with 0 volts across Rj there can be no current
flow through R/. The entire bias current for the inverting input, then, must flow
through RF (by Kirchhoff's Current Law). Since the left end of R F is grounded and
the right end is connected to the output, the voltage across R F is equal to the out-
put voltage. Therefore, the output voltage caused by the bias current on the invert-
ing pin can be computed as

Since current has been assumed to flow out of the (-) pin, we know that the result-
ing output voltage will be positive. Note that this is opposite the polarity of the (+)
input.
Now, continuing with the application of the Superposition Theorem, we
simply combine (algebraically) the individual voltages computed above to deter-
mine the net effect of the two bias currents. Since the polarities of output voltage
caused by the two bias currents are opposite, the net output voltage must be

The manufacturer does not generally provide the individual values of both bias
currents. Rather, the bias current (I B) listed in the specification sheet is actually an
average of the two. In general, the two currents are fairly close in value, so if we
assume that the two currents are equal, the preceding equation becomes