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Consider the following impedance frequency response for a DC motor :
Its equivalent circuit is :
Clearly, from the response, there exists a capacitor, inductor, and resistor, but my problem is how to determine that the resistor is connected in series with the inductor and all of these elements are in parallel with the capacitor.
Two possible RLC equivalent circuits accommodate the 100 ohm resistance at 0 Hz (below).
The second circuit of the two has a resonant dip at 1 MHz, while the first circuit of the two has a resonant peak at 1 MHz. Furthermore, the first circuit has -20dB slope above 1 MHz, while the second circuit has +20dB slope above 1 MHz.
First circuit meets all the criteria (100 ohms @ DC, resonant peak).
simulate this circuit – Schematic created using CircuitLab
the DC response tells you R must be in series with L which has a slope of +1 (+20 dB/dec) at 100 kHz and then the -1 slope at 1 MHz must be a shunt cap that drops in Xc lower than Xc +R .
Since XL(f) = 0 at DC, the series R must be the DC resistance of the coil.
Since peak Z asymptote is 100 x R you can see the Q is almost 100 at the intersection of XL(f)=XC(f) = 10 kohms.
But this would have to be a “nano-motor” to have this high a parallel resonance, and motors usually have a X/R ratio of 8 to 12 at max RPM or f or as low as X/R ratio of 3 for low surge current AC motors.
