Page 23 - Op Amps Design, Applications, and Troubleshooting

6 BASIC CONCEPTS OF THE INTEGRATED OPERATIONAL AMPLIFIER

through a fixed resistance will produce a corresponding increase in the voltage
drop across the resistance.
Many equations presented in this text appear to be new and unique expres-
sions to describe the operation of op amp circuits. When viewed more closely,
however, they are nothing more than an application of Ohm's Law. For example,
consider the following expression:

Once the subtraction has been completed in the numerator, which is like
computing the value of two batteries in series, the problem becomes a simple
Ohm's Law problem as in Equation (1.2).
For a test of your intuitive understanding of Ohm's Law as applied to series-
parallel circuits, try to evaluate the problem shown in Figure 1.3 without resorting
to the direct use of mathematics. In the figure, no numeric values are given for the
various components. The value of R 3 is said to have increased (i.e., has more resis-
tance). What will be the relative effects on the three current meters (increase,
decrease or remain the same)? Try it on your own before reading the next para-
graph.
Your reasoning might go something like this. If JR 3 increases in value, then
the current (I 3) through it will surely decrease. Since R 3 increased in value, the par-
allel combination of R 2 and JR 3 will also increase in effective resistance. This
increase in parallel resistance will drop a greater percentage of the applied volt-
age. This increased voltage across R 2 will cause J 2 to increase. Since the parallel
combination of R 2 and R 3 have increased in resistance, the total circuit resistance is
greater, which means that total current will decrease. Since the total current flows
through R lr the value of Ij will show a decrease.
This example illustrates an intuitive, nonmathematical method of circuit
analysis. Time spent in gaining mastery in this area will pay rewards to you in the
form of increased analytical skills for unfamiliar circuits.
Ohm's Law also applies to AC circuits with or without reactive components.
In the case of AC circuits with reactive devices, however, all voltages, currents,
and impedances must be expressed in their complex form (e.g., 2 -;5 would rep-
resent a series combination of a 2-ohm resistor and a 5-ohm capacitive reactance).

1.2.2 Kirchhoff's Current Law

Kirchhoff's Current Law tells us that all of the current entering a particular point
in a circuit must also leave that point. Figure 1.4 illustrates this concept with sev-

FIOURE 1.3 How does an increase
in the resistance of R 3 affect the
currents /,, J 2, and / 3?