# Floating simulated inductor design by Bob Pease

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At the 5 minute mark:

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Cheers

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As JT might say - "run the math on that one", yuck.

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to clarify the small-signal math looks OK, but I think you can call this circuit "The Hamstringer" because if you try to use it to simulate a large floating inductance using real-world devices with non-mathematically-small signals it will hamstring itself in some way. And what good is an active fixed inductor that can only simulate _small_ inductances? A real inductor will be cheaper, lower power, and perform better

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Pease's one is 1H. You cold do something fun with that plus a TCA0372.

Cheers

Phil Hobbs

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A minute later Pease says he wants to test it in a circuit that has 2H inductors.

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500 nA max input bias current into 1 Meg resistor into unity-gain buffer driving 1 ohm resistor?
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Did he ever post his results?

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I don't know. I missed most of his articles. But it's 1H already and the theory must be valid. He even recommends a particular op amp, LMV2011.

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Yeah, in a DC application you'd want picoamp input currents with that 1 Meg resistor hung off the non-inverting input but op amps with picoamp input currents generally aren't great at driving 1 ohm loads.

If you reduce the size of the 1 Meg bias resistor to relax the bias current requirement, keeping the capacitor the same you have to increase the 1 ohm resistor in series with the output to maintain inductance, and you hamstring your large-signal output drive. If you keep the series resistor the same and increase the capacitance and reduce the bias resistor you'd start thinking about electrolytics or tantalums, which begets another set of problems. Da Hamstringa

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You don't have to go to the extreme of 1M/1R for the simulated inductor to be a lot better than your average 1H iron.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
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None of my iron core inductors ever disobeyed conservation of energy by having an offset current, :^) but I can definitely corroborate their Q factor is awful. A typical laminated iron choke will turn over from inductance (Q > 1) to diffusion (skin effect and eddy currents, Q ~ 1) to resistance (Q ~ 0) in the low to mid kHz. Even for fine laminations.

The old one-transistor gyrator can easily do better (inductive up to a shelf frequency where bias resistors and finite gain take over).

Tim

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Seven Transistor Labs, LLC
Electrical Engineering Consultation and Contract Design
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Except for the 'floating' bit and working in only one direction.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
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Well yes, comparing with the one-opamp circuit in that case. :^)

Tim

--
Seven Transistor Labs, LLC
Electrical Engineering Consultation and Contract Design
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The reflects a real problem with FET-input op amps.

If you want them to slew fast, you need to feed a lot of current through th em, which means that die get hot and the input FET leakage current get high .

Splitting the job between two op amps can work quite a bit better.

For driving a 1 Ohm load, a unity gain buffer would be really good idea.

My horrid example of the problem was a scan generator designed with the sam e high slew rate FET op amp in the vertical scan generator as in the horizo ntal scan generator. The vertical scan output was a factor of several hundr ed slower than the horizontal scan output, and could be asked to slew slowl y enough that the FET input current was an issue.

If the guy that designed the board had been allowed the time to do the job right, he would probably have used the slow, low-current companion to the f ast FET-input op amp from the same manufacturer for the vertical scan circu it, not that I've talked to him about it - we got back into e-mail contact a few years ago after a twenty-odd year break.

Tantalums are electrolytics (if rather nicer than regular aluminium electro lytics). The equivalent series resistance can be in the ohms range, which c reates it's own problems, but leakage current can be surprisingly low.

--
Bill Sloman, Sydney
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The problem with this one isn't on the "input" side, the input series 1 ohm is nicely bootstrapped for arbitrarily low frequency.

It's on the output where the op-amp has to push current into a load, it falls down trying to drive a low impedance. And if you only want to drive high impedances what do you need such a large floating inductor for? Gyrators can't store energy they can only really be used for signal processing, but "LC" lowpasses with very low cutoff frequencies and large values of shunt capacitance to match definitely aren't happening with this circuit.

The circuit works pretty well in say an LR lowpass filter configuration driving a large R but if your destination impedance is large too why not like, just use an RC filter.

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That is to say its small-signal analysis looks great, but when using op-amps that have the drive capability that usually comes along with input bias currents low enough to avoid DC offset problems on large bias resistors the large signal performance is terrible into anything but high impedances. And if you try to use an op amp with higher drive capability that usually implies higher input bias current, have to reduce the 1 Meg resistors and increase the 1 ohm series resistance to maintain inductance, and cripple yourself yet again.

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I don't think there's any simple way to buffer this topology that wouldn't cause it to cease being a reciprocal network, unfortunately.

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I haven't tried the analysis, but why not bump the R's up by a factor of 20. Say 20 ohms and 20 Meg?

George H.

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