RLC Circuit with a Gyrator as an Inductor

In summary, you are trying to create a resonant circuit with a low frequency resonance. You are using a Gyrator as the inductor and are using C, RL, and L=RL*R*C to create the circuit. You have measured the actual component values and are getting results that are off from the transfer function predictions. You suggest that RL be about 20 times larger and C be about 20 times smaller to get a more accurate result.
  • #1
swraman
167
0
Hi,

Im trying to build a resonant circuit with a ~low frequency resonance (<1kHz). I am using a Gyrator (https://en.wikipedia.org/wiki/Gyrator#Application:_a_simulated_inductor) as the inductor.

300px-Op-Amp_Gyrator.svg.png


Im using:
RL = 100ohm
R = 27kohm
C = 1uF

I put another 1uF capacitor in front of Zin, to form a series RLC circuit with C, RL, and L=RL*R*C

This should give a natural frequency of 96.8Hz and a damped natural frequency of approx the same:

bode.png


But, when I measure the frequency response of the thing using a spectrum analyzer, I get something that is slightly off in frequency:

bode_meas1.png


The frequency is off by over 12Hz. The damping estimates (based on the half power method) are also off by a factor of ~3.

Are there any errors that you can think of that would lead to this? Am I missing something in my usage of the gyrator as an inductor?

Ive tried different resistors and swapped out the capacitors, but they all have the same results. Regardless of what resistors I use, I always seem to get measurements that are off from the transfer function predictions.
 
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  • #2
Not quite sure about your graphs, but in spite of the equivalent circuit you have drawn, you seem to be simulating a parallel resonant circuit. Resonance is defined as the frequency where the phase shift is zero, not the max voltage, and for a parallel circuit the two are different.
 
  • #3
Not all operational amplifiers can handle 100% feedback. I created an equalizer many years ago where I used simple gyrators. Instead of an operational amplifier with 100% feedback, I just used an emitter follower (which also have a gain of +1).
 
  • #4
swraman said:
Regardless of what resistors I use, I always seem to get measurements that are off from the transfer function predictions.
You have measured the actual component values, so you accurately know its theoretical response?

Keep signal amplitude low to avoid overloading the op-amp, and monitor Vout. Your circuit has a relatively low input impedance, so it's loading whatever is driving it.

I'd be happier if RL were to be about 20 times larger and C were 20 times smaller.

https://www.physicsforums.com/attachments/110502.gif
 

1. What is a RLC circuit?

A RLC circuit is an electrical circuit that consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series or parallel. It is used to study the behavior of electrical circuits and is commonly found in electronic devices such as radios, televisions, and computers.

2. What is a gyrator?

A gyrator is an electronic circuit that mimics the properties of an inductor. It is composed of an operational amplifier and other passive components, and it is used to simulate inductance in circuits where a physical inductor is not feasible or desirable.

3. How does a gyrator work as an inductor in a RLC circuit?

A gyrator works as an inductor in a RLC circuit by using negative feedback to create an equivalent inductance. The operational amplifier in the gyrator amplifies and inverts the voltage across the capacitor, creating a voltage across the resistor that behaves like an inductor. This allows the gyrator to replace a physical inductor in a circuit.

4. What are the advantages of using a gyrator as an inductor in a RLC circuit?

One advantage of using a gyrator as an inductor in a RLC circuit is that it allows for flexibility in circuit design. It can be easily adjusted to produce different levels of inductance without physically changing components. Additionally, a gyrator can provide inductance without the bulk and weight of a physical inductor, making it useful in miniaturized electronic devices.

5. Are there any limitations to using a gyrator as an inductor in a RLC circuit?

One limitation of using a gyrator as an inductor is that it is not a perfect replacement for a physical inductor. It has limitations in terms of the maximum inductance it can produce and the frequency range over which it can function effectively. Additionally, the use of a gyrator can introduce noise and distortion into a circuit, which may not be desirable in certain applications.

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