BMME 207 Circuit Analysis

Nodal pair

One voltage

KCL equations

Numbers of nodes minus 1 (reference)

KCL analysis

i in = i out

KCL with Ohm’s

i = vin - vout/R

Adding current sources

Parallel

Adding voltages sources

Series

Same current

Series

Same voltage

Parallel

Reference node

If unassigned, should be node with most branches for easiest calculations

Nodal analysis

Based on KCL

Supernode

Node around a voltage source (no resistor for ohm’s law) that can not include the reference node

Supernodal analysis

Done using standard equation set up, but instead of current in and out of a resistors, it’s current in and out of a supernode, so that the current across the voltage source can be ignored

Mesh analysis

Based on KVL and only works for planar circuits

Planar circuit

Possible to draw without any branches overlapping, even if this means lengthening wire

Mesh

Loop that does not contain any other loop within it

Mesh current

Flows around the perimeter of a mesh

Mesh analysis procedure

Identify all meshes, assign one internal loop current to each mesh, and write KVL and Ohm’s law equations (sum of voltages converted to ir) with the current across a resistor being either a singular or multiple mesh currents

Supermesh

Has a current source on the shared boundary of two meshes. which can be fully enclosed using a loop combining the two meshes

Supermesh analysis procedure

Create KVL equations for non-supermeshes, create KVL for any supermeshes, which should add or subtract the voltage source depending on the direction if along the mesh, last equation is relating the current source value to all contributing currents of the supermesh.

Voltage division

Used to calculate voltage drop of a single resistor within a series of resistors

Voltage division equation

vn = (Rn/Req)*vin

Current division

Used to calculate current fraction across a single resistor within a parallel group of resistors

Current division equation

in = (Req/Rn)*i in

Sinusodial wave form

A*sin(2*pi*f0*t), where A is amplitude and f0 is frequency of oscillation

Sinusoidal period (T0)

T0 = 1/f0

Graphing sin waves

Start at origin with one full positive and negative peak per period