Lecture 8 PCAP Patterns Primitives Combinations Abstractions Patterns Abstractions reduce complexity by combining multiple primitives into a single entity Buffers with Op Amps Buffers can be used to increase modularity The voltage divided on the left acts as a module that produces 8V regardless of loading of bulb on the right Changing an element changes voltages and currents systematically Consider the changes in V and I when R is changed The equations for the three leftmost elements are linear Check yourself Patterns Correct answer 3 Current Voltage Relations One Ports This is analogous to This is regardless of how many components are in the circuit replacing delays gains and adders with a system function combining a sequence of operations in a procedure call combining diverse data in a list Concept Question Graphing One Ports Correct answer 3 The current voltage relation summarizes all possible behaviors of circuit regardless of what the circuit is connected to We can think about an entire circuit as a single element a one port If a circuit connects to the world via two terminals then that circuit can be represented by a single generalized element called a one port These representations are compositional they replace multiple elements with a single element that can be used in the same way that primitives are used Parallel One Ports Series One Ports Thevenin Equivalents Norton Equivalents If the I V curves for two one ports are both straight lines then the I V curve for the parallel combination is a straight line This is because the sum of two straight lines is a straight line If the I V curves for two one ports are both straight lines then the I V curve for the series combination is a straight line This is because the sum of two straight lines is a straight line If the current voltage relation is linear the current voltage relation is the same as that for a voltage course in series with a resistor From the circuit I If I 0 the V V the x intercept of the plot The rate of growth of I with V is the slope 1 R If the current voltage relation is linear the current voltage relation is the same as that for a current source in parallel with a resistor From the circuit V If I 0 the I I the y intercept of the plot The rate of growth of I with V is the slope 1 R If a one port contains just resistors and currents and voltage sources then its I V relation is determined by two points Open Circuit Voltage and Short Circuit Current First point open circuit voltage Second point closed circuit voltage The equivalent resistance is the slope R Conceptual Value of Equivalent Circuits Equivalent circuits have conceptual values Example Will closing the switch increase or decrease I Replace the parts to the left and right of I by equivalent circuits Equivalent circuit to the right of I depends on the state of the switch Closing the switch decreases equivalent resistance to the right of I Therefore closing the switch increases I Consequences of Linearity If a one port contains just linear elements resistors voltage sources and current sources then the current voltage relation will be linear are it can be represented by a Thevenin or Norton equivalent circuit Linear one ports can be characterized by two points on their I V curve Op Amps as Abstractions We have treated op amps as fundamental building blocks for circuits but op amps are in fact complicated circuits but op amps are in fact complicated circuits that contain dozens of transistors and resistors plus a few capacitors
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