Circuit Analysis - Basic Techniques and Principles

Circuit Analysis is an important part of electrical engineering. It is often one of the first classes that an EE major will take. We use Circuit Analysis in the real world to help design circuits as well as determine what components are needed in a specific type of circuit. A circuit is considered completely solved when all of the node voltages and branch currents are known.

Basic terms to know

Current - a flow of electrons. The unit is the Ampere (A). We always say that a current goes through something.

Voltage - the difference of electric potential between two elements or nodes on a circuit. Voltage is measured in Volts (V). We say that a voltage is across something.

Node - a point on a circuit where the voltage is the same throughout. They usually connect other elements on a circuit but do not pass through said elements.

Branch - nodes often split off into branches. Each of these branches has their own respective current.

Loop - A closed circuit that could be part of a greater circuit.

Resistance - The measurement of how much an element in a circuit resists the current that is going through it. The unit is the Ohm. You can imagine what a resistor does by picturing them as light bulbs being lit up as a current goes through them.

Source - Sources are the elements on a circuit that provide a voltage or current. Therefore, the two main types of sources are voltage and current sources. There are many variations of these two main types but we won't go into details here.

Power - the measurement of work done by a current. The unit is the Watt (W). Power can be found by multiplying the Voltage by the Current (P = VI) or equivalently (I^2)*R.

Basic Principles

Ohm's Law - This is the most important law in Circuit Analysis. It is used in every analysis technique and is entirely necessary to know when even looking at a circuit. Fortunately, it is rather simple. Ohm's Law states that the Voltage is equal to the Current multiplied by the Resistance. V = IR

Kirchoff's Voltage Law (KVL) - KVL states that the voltages around a closed loop add up to zero. This forms the basic principle behind the technique known as mesh analysis.

Kirchoff's Current Law (KCL) - KCL is much like KVL, only instead of voltages, it deals with currents. KCL says that all the currents entering (or leaving) a node will add up to zero. KCL is used in nodal analysis.

Techniques

Circuit analysis techniques are almost impossible to explain using only text, so here are a few brief summaries of the main techniques.

Mesh Analysis - Usually, one uses mesh analysis when there is a circuit that involves several loops where one or more loop currents are not known. One would then use KVL to find the voltages across each of the elements on the circuit to derive an equation for the unknown loop currents.

Nodal Analysis - Nodal analysis is used when one wants to find (or already has) a node voltage. KCL would then be used to find the branch currents coming out of that node to derive an equation for the unknown element.

Superposition - The theory behind superposition is that each source on a circuit will provide a certain amount of current or voltage to an element. Thus, using superposition involves 'turning off' every source on a circuit except one and finding the effect it has on the said element. Each source will have a turn being analyzed this way, and in the end we can add up each source's effect on said element.

Thevenin and Norton Equivalence - This technique says that for each complicated circuit you can design, there is an equivalent circuit with a voltage source in series with a resistor or a current source in parallel with a resistor. This is the technique one would use when looking for the maximum power a resistor can dissipate in a specific circuit.