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Given an RLC circuit, should I simplify all components to their equivalent admittance/impedance before using nodal analysis?

The circuit in question is below: RLC Circuit

Or should I perform nodal analysis on the circuit as is?

So far, I've attempted to simplify the parallel inductor/capacitor pair, the series inductor/capacitor pair, and the parallel inductor/capacitor/resistor so that I have a single node V1 (image below). The algebra is getting pretty tricky though so I think it might be wrong. enter image description here

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    \$\begingroup\$ I would not combine components the way you have. The goal of circuit analysis is to find all the component voltages and currents. By doing the combinations, you have lost a node and will have a tough time getting all the voltages. With all those one components values the node equations will actually be straight forward. \$\endgroup\$
    – owg60
    May 2, 2017 at 1:29
  • \$\begingroup\$ The usual way to do nodal analsyis is just to enter the circuit into SPICE and click "go". \$\endgroup\$
    – The Photon
    May 2, 2017 at 1:49
  • \$\begingroup\$ @owg60 yeah, thats what I ended up doing. Thanks though! \$\endgroup\$
    – Swoldier
    May 2, 2017 at 3:01

1 Answer 1

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The maths works the same in either case, as long as you keep track of all the variables and signs.

We humans tend to 'simplify' groups of components when working by hand, because it reduces and organises the arithmetic workload, and our visually oriented brains work well picking out patterns of components that will simplify.

We program computers to just mash the entire circuit as is, because it's easy to program them with a general matrix method, it's difficult to program them to group and simplify components and take advantage of the reduction, grouping components loses information that might as well be kept, and the difference in execution time is negligible.

Compare how we were taught to do simultaneous equations in school - recognise the most convenient factors of one of the variables in the two equations and cancel them - and how we program that into a computer - fill in the 2x2 matrix, invert, multiply by the 2x1 vector, regardless of the 'shape' of the problem.

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