Electronic – RLC equivalent model and Impedance Smith Chart

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I have done some impedance measurements on an unknown 1 port device. I have measured its impedance at different frequencies (from 10 MHz to 600 MHz) and I have seen it on the normalized (on 50 Ohm) Impedance Smith Chart:

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At Low frequencies we are at the short circuit point (left). Then, the device offers an inductive impedance, until, at about f0 = 470 MHz, we arrive at the real axis (right). It seems it arrives at the open point but it is not: if you see the following graph you see that the impedance is, obviously, purely real, but not infinite. It is equal to about 471 Ohm (absolute value).

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You may see these results also in the following graphs (the first one contains real and imaginary parts of the impedance, while the second one its absolute value).

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So, at f0 the devices resonates and offers a purely real impedance. Now my question is: which is the equivalent RLC circuit of this device according to this analysis?

Precisely:

  • from the Smith Chart I may get the value of L: I should take the Imaginary Part of Zin at low frequencies (in which the device is almost purely inductive) and divide by 2*pi*f.
  • from the Smith Chart I may get the value of R (it is 471 Ohm, as told before)
  • from the Smith Chart I may get the value of C (at high frequencies, where the device is almost purely capacitive)

So, which is the equivalent model? A parallel RLC, a series RLC?
Moreover, at f0, does the device offer a parallel resonance, or a series Resonance? I have been told that if I measure R,L,C through the Impedance Smith Chart, they are the values of the RLC series model, but I am not sure about it because I can also do my measurements on the Impedance Smith Chart for a device which is not a RLC series circuit. For instance, something like that:

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Moreover, I'd say it cannot be an RLC series circuit, because at low frequency we are at short circuit point, and not open circuit point.

Best Answer

That characteristic looks awfully like a parallel RLC circuit. At resonance the LC part becomes infinity and, because it is shunted with R, the effective impedance is R, possibly a 470 ohm resistor. At DC and low frequencies the inductor dominates with its low impedance and, if you went significantly higher than 1 GHz the parallel capacitance would dominate and start to act as a low impedance shunt.

Below is just a convenient graph I found for a parallel RLC circuit: - enter image description here

The difference between series and parallel resonance is shown side-by-side here: -

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Picture from here.