Mathematical methods in electronics – BASIC ELECTRONICS TUTORIAL
Mathematical methods in electronics
Mathematical methods are integral to the study of electronics. To become proficient in electronics it is also necessary to become proficient in mathematics.
Mathematics in Electronic Engineering careers
Electronic Engineering (EE) careers usually include courses in Calculus (single and multivariable), Complex Analysis, Differential Equations (both ordinary and partial), Linear Algebra and Probability. Fourier Analysis and Z-Transforms are also subjects which are usually included in EE programs.
Of these subjects, Calculus and Differential equations are usually prequisites for the Physics courses required in most Electronic Engineering programs (mainly Mechanics, Electromagnetism & Semiconductor Physics). Complex Analysis has direct applications in Circuit Analysis, while Fourier Analysis is needed for all Signals & Systems courses, as are Linear Algebra and Z-Transform.
Basic applications
A number of electrical laws apply to all electrical networks. These include
- Kirchhoff’s current lawthe sum of all currents entering a node is equal to the sum of all currents leaving the node.
- Kirchhoff’s voltage lawthe directed sum of the electrical potential differences around a circuit must be zero.
- Ohm’s lawthe voltage across a resistor is the product of its resistance and the current flowing through it.
- the Y-delta transform
- Norton’s theoremany two-terminal collection of voltage sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor.
- Thevenin’s theoremany two-terminal combination of voltage sources and resistors is electrically equivalent to a single voltage source in series with a single resistor.
- Millman’s theoremthe voltage on the ends of branches in parallel is equal to the sum of the currents flowing in every branch divided by the total equivalent conductance.
- Analysis of resistive circuits.
Circuit analysis is the study of methods to solve linear systems for an unknown variable.
- Circuit analysis
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