Electronic – Why does this parallel->series rewrite change the AC simulation results a little

acimpedanceltspice

Here are two circuits I've simulated. Both have a current source of \$\sin(\omega t)\$ mA with \$\omega=1000\$. They should be equivalent but give different simulation results.

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Here are the simulated currents across R1:

I(R1):   mag:  0.0672338 phase:   -137.752°  device_current
I(R1):   mag:  0.0673282 phase:   -137.783°  device_current

Here is how I calculated the new R2 and L1: The total complex impedance of R2 and L1 in parallel is \$1/( 1/R_2 + 1/(j\omega L_1)) = 1/(1+1/j) = 0.5 + 0.5j\$ which can be written as the series resistance and inductance \$0.5+j\omega \times 0.5\times10^{-3}\$.

So my question is: where did this calculation go wrong? Are the circuits not equivalent or have I missed something in the simulation?

I don't think this is a numerical error since the current is wrong in the third significant digit whereas the model should be accurate to the floating-point precision.

Best Answer

The problem arises from the 1mohm that's in series with the inductor:

Inductor Properties

When I calculated the current through R1 with the extra 1mohm added my calculations line up perfectly with the simulation results. Alternatively, you can force the series resistance to be 0. Doing this also gave me equivalent results for both circuits from LTSPICE.

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