network analysis

the basic connections are series and parallel. series and parallel combinations are described in terms of nodes, branches, and loops. component characteristics and changes in circuit state may also render an open or short circuit.

the electric power in watts associated with a complete electric circuit or a circuit component represents the rate at which energy is converted from the electrical energy of the moving charges to some other form, e.g., heat, mechanical energy, or energy stored in electric fields or magnetic fields. for a resistor in a dc circuit the power is given by the product of applied voltage and the electric current, measured in watts:p = v * i

potential difference, voltage, across an ideal conductor is proportional to the current through it.material that obeys ohm's law is called "ohmic" or "linear" because the potential difference across it varies linearly with the current.

we need to solve every circuit problem with mathematical statements that express how the circuit elements are interconnected. said another way, we need the laws that govern the electrical connection of circuit elements. First of all, the places where circuit elements attach to each other are called nodes.electrical engineers tend to draw circuit diagrams—schematics— in a rectilinear fashion. Thus the long line connecting the bottom of the voltage source with the bottom of the resistor is intended to make the diagram look pretty. This line simply means that the two elements are connected together. kirchhoff's laws, one for voltage and one for current, determine what a connection among circuit elements means. these laws are essential to analyzing this and any circuit.

the superposition theorem for electrical circuits states that the response (voltage or current) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, while all other independent sources are replaced by their internal impedances.to ascertain the contribution of each individual source, all of the other sources first must be "turned off" (set to zero) by:1. replacing all other independent voltage sources with a short circuit (thereby eliminating difference of potential. i.e. V=0, internal impedance of ideal voltage source is ZERO (short circuit)).2. replacing all other independent current sources with an open circuit (thereby eliminating current. i.e. I=0, internal impedance of ideal current source is infinite (open circuit).

the condition of "rest", after all the changes/alterations were made. may imply, for examples, that nothing at all happens, or that a "steady" current flows, or that a circuit has "settled down" to final values - that is until the next disturbance occurs.if the input signal is not time invariant, say if is a sinosoid, the steady state wont be invariant either. the response of a system can be considered to be composed of a transient response: the response to a disturbance, and the steady state response, in the absence of disturbance.the transient part of the response tends to zero as time since a disturbance tends to infinity, so the steady state can be considered to be the response remaining as t goes to infinity.

analysis in the frequency domain proceeds exactly like dc analysis, but all currents and voltages are now phasors (and so have an angle). impedance is treated exactly like a resistance, but is also a phasor (has an imaginary component/angle depending on the representation.)(In the case that a circuit contains sources with different frequencies, the principle of superposition must be applied.)note that this analysis only applies to the steady state response of circuits. for circuits with transient characteristics, circuits must be analyzed in the laplace domain, also known as s-domain analysis.

the way to think about circuits is to locate and group parallel and series resistor combinations. resistors not involved with variables of interest can be collapsed into a single resistance. this result is known as an equivalent circuit: from the viewpoint of a pair of terminals, a group of resistors functions as a single resistor, the resistance of which can usually be found by applying the parallel and series rules.

resistors can be connected in series; that is, the current flows through them one after another. the current through each of the resistors is the same.resistors can be connected such that they branch out from a single point, a node, and join up again somewhere else in the circuit. this is known as a parallel connection. resistors in a parallel circuit must have the same voltage.

the node method begins by finding all nodes--places where circuit elements attach to each other--in the circuit. we call one of the nodes the reference node; the choice of reference node is arbitrary, but it is usually chosen to be a point of symmetry or the "bottom" node. for the remaining nodes, we define node voltages that represent the voltage between the node and the reference. these node voltages constitute the only unknowns; all we need is a sufficient number of equations to solve for them. the very act of defining node voltages is equivalent to using all the KVL equations at your disposal. the reason for this simple fact is that a node voltage is uniquely defined regardless of what path is traced between the node and the reference. because two paths between a node and reference have the same voltage, the sum of voltages around the loop equals zero.

current through 26 gauge copper wire that, for example, splits at a node into three paths, is subject to kirchhoff's current law. the three resulting currents' sum are equivalent to the initial current before it experienced current division. this junction, split, or node, leaves the current no choice but to distribute as evenly as possible at the node and then through the three paths that follow the node. the sum of all four currents, before and after the node will equal zero.

sum of voltages across a closed loop series circuit shall be zero. this understanding is crucial when voltage division becomes a necessary element in the circuit analysis process.voltage across a parallel circuit will, at each resistor, be the same as the voltage source.