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Consider the following impedance frequency response for a DC motor :

enter image description here

Its equivalent circuit is :

enter image description here

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.

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2 Answers 2

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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).

schematic

simulate this circuit – Schematic created using CircuitLab

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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.

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  • \$\begingroup\$ please explain in more details why R must be in series with L? Even if R is parallel with L the response will increase. \$\endgroup\$
    – John adams
    Apr 6, 2019 at 20:31
  • \$\begingroup\$ if it were in parallel then DCR =0 ( DC resistance ) All motors and inductors have a DCR spec which is a series R value at DC and ZL(DC)=0 \$\endgroup\$ Apr 6, 2019 at 20:36

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