Gyrator circuit discussion

What do you guys think about the following gyrator circuit ?

Someone told me the following:

Let's put a voltage on v(in) and see the current drawn by that voltage. The inverter is high impedance, so none goes into that, so it will be just the current out of the diff pair. At DC, We get a current out of the inverter Iinv = Gm1*V(in). That current is multiplied by the output resistance of the inverter Ro,inv to give V(b) = V(in)*Gm1*Ro,inv. Then we multiply by the diff pair Gm2, so Iout = Gm2*V(b) = V(in)*Gm2*Gm1*Ro,inv. Rtest = Vin/Iout = 1/(Gm2*Gm1*Ro,inv).

The cap on node Vb makes the impedance at that point go down with frequency, making Ro,inv get smaller. But the Ro,inv term is in the denominator of our Zin equation, so it makes the test impedance get bigger as frequency increases. Replace Ro,inv with the impedance of the cap, and you have a rough approximation of the impedance of the gyrator.

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Anyone up for a discussion regarding the mosfet sizing ?

Someone told me that I could draw up a parasitic model of the gyrator (active inductor) using only 4 discrete components resembling the following AC plots

Note: the magnitude plot has a peak at 500MHz

Could anyone advise ?

Yes, I see how your gyrator circuit places a capacitor so that it attenuates high frequencies. It diverts them to ground. It's a similar result as placing an inductor in series so the choke effect attenuates high frequencies.

This gyrator circuit (a demo included with a simulator) is built around an op amp. It simplifies circuit construction although it takes some watching to see what are the key principles of operation. And it's not obvious how to adapt the demo circuit to produce high power.



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So I experimented a while wondering whether the op amp was absolutely necessary to make a gyrator. In fact the RC network can produce a similar waveform as the inductor. However the RC network provides almost no power at the frequencies (low frequencies) where the inductor performs well. Besides that the RC network introduces power factor error. However we can power a low frequency load if we attach an amplifier (similar to the concept of your schematics).



A practical use for the above amplifier might be to drive a woofer at bass frequencies. It has no massive crossover coil. Theoretically it delivers 16W to a 4 ohm load. (8V * 2A) (To achieve this the bias voltage had to be increased in amplitude.)

I am not sure how I am going to increase input impedance at low frequencies from 60 Ohm to 10 kiloOhm ?

promach said:

I am not sure how I am going to increase input impedance at low frequencies from 60 Ohm to 10 kiloOhm ?

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To create 10k impedance requires a large amount of Henries. Bulky, heavy, expensive. To surface thought it seems counter-intuitive that electronic components would work that way, but we cannot change the laws of physics.

So that's where an active inductor shines. The op amp derives the waveform from an RC network, and mimics the same waveform as produced by an inductor. Small and inexpensive. Compatible with low power and low current.

The simulation below borrows from diagrams in post #3 except the right-hand circuit is the op amp gyrator. The 1k resistor is repositioned instead as a load to ground. It works in simulation.

I installed 10k input resistance to show that the incoming signal only needs to provide minuscule current to the active inductor.

Someone told me that I could draw up a parasitic model of the gyrator (active inductor) using only 4 discrete components resembling the following AC plots

Click to expand...

Yes.



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I am not sure how I am going to increase input impedance at low frequencies from 60 Ohm to 10 kiloOhm ?

Click to expand...

The circuit in post #1 has 28 ohm rather than 10 kohm low frequency input impedance. If you are asking for the equivalent RLC circuit of a different active design, you didn't clarify what it is. Did you possibly confuse phase and magnitude plots?

@FvM

How do you exactly arrive at that parasitic model circuit arrangement with the right values for each passive components ?

Please do not tell me : through trial and error.

R1 and R2 can be directly derived from minimal and maximal impedance magnitude, resonance frequency is given, resonator impedance (L/C ratio) is set to match the bandwidth.

@FvM

R1 and R2 can be directly derived from minimal and maximal impedance magnitude

Click to expand...

I do not understand this. Could you tell more about this minimal and maximal impedance ?

See the following, another similar parasitic model from others.

What do you think about the following circuit + frequency response with regards to your own circuit arrangement topology ?

Minor differences, both can be used.