Electronic Devices and Amplifier Circuits with MATLAB Computing, Second Edition
Emphasizing operational amplifiers and integrated devices used in digital circuits, this text presents a thorough discussion of state-of-the-art electronic devices.
TABLE OF CONTENTS Electronic Devices and Amplifier Circuits with MATLAB Computing, Second Edition
Appendix E: Substitution, Reduction, and Miller s Theorems
This appendix discusses three additional theorems that are especially useful in the simplification of circuits containing dependent sources. In our previous studies [*] we discussed the superposition principle and Thevenin s and Norton s theorems.
E.1 The Substitution Theorem
The substitution theorem states that if the voltage across a branch with nodes x and y of a network is v xy and the current through this branch is i xy, a different branch may be substituted in its place in the network provided that the voltage across the substitute branch is also v xy and the current through it is also i xy. The most common use of this theorem is to replace an impedance by a voltage or current source, or vice versa. The substitution theorem can best illustrated with the simple circuit and the substitute branches shown in Figure E.1.
Figure E.1: Illustration of the substitution theorem
For the simple resistor circuit of Figure E.1(a) we find by series-parallel resistance combinations that v=6 V and i=3 A. According to the substitution theorem, the 2 ? resistor across terminals x and y can be replaced with a source with a 6 V source as shown in Figure E.1(b) and the rest of the network will be unaffected. The current in the branch will be 3 A as before.
Other substitutions are possible also. For instance, the substitute branch may consist of a resistance of 1 ? and a voltage source of 3 V...
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