arbitrary resistor network analysis

On Thu, 08 Apr 2004 12:58:03 +0100, Alex Hunsley

Quote:

>I'm aware of the basic rules for calculation resistance networks where you have

>resistors in series, and in parallel combinations, but is this knowledge enough

>to calcuklate the resistance between two points in an arbitrary network (or

>think connected graph!) of resistors?

>For example, take the following graph where every edge represents a resistor:

>(needs to be viewed in a propertional font like courier)

> A

> /|

> / |

> / |

> R0 / | R1

> / |

> / |

> / R2 |

> ---------

> \ |

> \ |

> \ |

> R3 \ | R4

> \ |

> \ |

> \|

> B

>What is the effective resistance betwen A and B in terms of R0, R1 etc?

>Or, to put another way, can I analysis this circuit just thinking in terms of

>parallel and series resistors?

>thanks

>alex

The general solution, as has been noted, is to write the loop

equations and solve them simultaneously, or use equivalent matrix

methods.

You can also do this by simple breakdown:

Apply 1 volt at A and ground B.

Ignoring R2 for a bit, compute the Thevenin equivalent voltage and

resistance at the R0:R3 junction (call that Vx, Rx), and repeat for

the R1:R4 junction (Vy, Ry.) Now add in R2. The two Thevenins and R2

make a simple voltage divider string, and you then get "loaded" values

for Vy and Vx. Knowing these, the supply current is apparent and the

effective net resistance is just its reciprocal.

More fun than solving simultaneous equations.

Interestingly, it's often easier to design networks than to analyze

them, especially since you have the option of picking ones that are

easier to think about. I once designed a duty-cycle DAC that had two

trimpots to set gain and offset. The interactions were so bizarre that

*nobody* could set the pots.

John