Inductor simulator

"The Phantom"

** Yep.

See:

and the first link given at the bottom.

...... Phil

That leads us to Elliott's page where he says "A more accurate version of the formula (due to Siegfried Linkwitz) is shown below", giving the same info in the link I gave to Linkwitz's site.

He is just repeating what is found in the Linkwitz .gif I referenced, and that hardly provides proof that Linkwitz's equivalent circuit is correct.

The Phantom a écrit :

I know you can easily do this... so from simple inspection it certainly can't be: make the frequency infinite and you'll see RP can't be R1+R2 (all that with a perfect opamp). It has to be R2-R1 and the right values are Rs=R1, L=C R1(R2-R1), Rp=R2-R1

--
Thanks,
Fred.

simulator:

It doesn't work for large values of C.

amp

This is exactly correct. I wonder why Linkwitz didn't notice.

Now add a small resistor to represent the ESR of the capacitor. Call it R3.

What is the equivalent with the addition of R3?

"Notice that if R3 in the .gif (what you have called Rser) becomes zero, then Rp vanishes (becomes infinite) also.

The inductor simulator in the other thread I posted doesn't have this property. Have you also examined that simulation?"

Then Helmut said:

"Yes, I had simulated it. I now checked it again and found a nice property. OK, it was more empiracilly.

If the capacitor has no series resistance(Rserc=0): Rp=R2-R1

If the capacitor has some series resistance (Rserc>0): Rp=(R2-R1)*(1-Rserc/R1)

Thanks for the discussion of these circuits.

Best regards, Helmut"

Helmut,

Thank YOU for your participation in the discussion. You're the only one who was interested enough to do any work!

Regarding the value of Rp when the capacitor has a non-zero ESR, I find that the value is Rp = (R2 - R1) * R1/(R1 + Rserc).

My multiplying factor is R1/(R1 + Rserc), whereas you get (1-Rserc/R1) If R1 >> Rserc, these two expressions are almost the same. Could you check carefully and tell me which one is *exactly* correct?

The interesting thing is that in this simulator (as opposed to the other one), when the capacitor ESR is zero there is still a parallel resistance branch across the inductor.

In this simulator as in the other, by adjusting the amplifier gain, the parallel branch can be made to vanish.

What gain makes the parallel branch vanish in the two cases, Rserc zero and Rserc not zero? And you'll notice that, unlike the other simulator, when you adjust the amplifier gain to make the parallel branch vanish, the value of the simulated inductance changes; it is no longer C R1 (R2 - R1).

My purpose in initiating a discussion of these two simulators was to show that existing analyses are slightly in error. I searched the web and couldn't find a truly correct analysis anywhere.

I also wanted to point out that the parallel branch can be made to vanish in both simulators by adjusting the amplifier gain slightly, a fact which I have never seen mentioned. This is less important in the other simulator than in this one.

Finally, what are the advantages and disadvantages of the two simulators?

One advantage of the other one is that its parallel branch vanishes if the capacitor ESR is zero, and if the capacitor ESR is very small, the parallel branch, while still present, is less troublesome.

Trying to do a good inductor with a single OpAmp is a waste.

See the various gyrator (two OpAmp) versions on the SED page of my website.

...Jim Thompson

--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC\'s and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
         America: Land of the Free, Because of the Brave

"The Phantom" schrieb im Newsbeitrag news: snipped-for-privacy@4ax.com...

Hello Phantom,

Your formula is correct. The equivalent pasive circuit is now perfectly the same as the active circuit. I will use your formula in the future.

Best regards, Helmut

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While this is indeed true, sometimes there is an cost sensitive application for a not-so-good inductor, and these two inductor simulators fill the bill nicely. The ubiquitous audio graphic equalizer is a prime example.

On 9 Aug, 22:42, The Phantom wrote: [...]

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I loathe transcribing formula but from a 1973 book ... ("W" is omega)

A= R2 . R1^2 . W^2 . C^2+R1 B=1+W^2 . C^2 . R1^2 C=W . R1 . C D=1+W^2 . C^2 . R1^2

(as real,imag)

Zin= A / B + j [C / D x R2-R1]

Q= WC(R2-R1)/ R1.R2.W^2.C^2+1

that

find a

Would you cite the book's title and author, please?

In terms of the s variable it's not too hard to show that the impedance of the op amp circuit (assuming an ideal op amp) is:

R1 + s C R1 R2 Zin = ------------------- 1 + s C R1

If you replace s with jw and rationalize:

(j w C R1 R2 + R1) (1 - j w C R1) Zin = ---------------------------------------- (1 + j w C R1) (1 - j w C R1)

expanding numerator and denominator gives the result you've copied from the book. This is a correct result.

I should have spoken more precisely. I have seen the Zin correctly derived; I just haven't ever seen the passive equivalent circuit correctly derived, and usually that's part of the analysis..

Does the book you're referencing give an equivalent circuit?

[...]

the

"Electronics for engineers". Ahmed and Spreadbury. Cambridge Uni' Press. ISBN0521201144 Sadly, no equiv' circuit was offered, just mention that at HF, Zin moves to R1; which seems logical, given the bootstrapping.

the

derived;

These expressions are identical to those found in the earliest reference to this circuit of which I am aware:

"Inductor Simulation Using a Single Unity Gain Amplifier", S. C. Dutta Roy, IEEE Journal of Solid State CIrcuits, June 1969

Dutta Roy refers to the "equivalent inductance" and the "associated resistance". He doesn't say whether the resistance is in series only, but his expression is for a series resistance. Notice that the expression for the resistance given in your book (and Dutta Roy's paper) has terms that include w (omega). This means that they vary with frequency. This is a consequence of accounting for the resistive part of the simulated inductance with only a series resistance.

If the resistance is given as a series part and a parallel part in the equivalent circuit, then they can be constant, not varying with frequency. This is what I have never seen done correctly. Linkwitz's circuit, shown in the link in the first post of this thread gets the topology correct, but has an error in the value of the parallel resistance branch.

Also, he fails to note that if the gain of the amplifier is made equal to

1+R1/R2, then the parallel branch vanishes, and the impedance of the simulated inductance will continue to increase with frequency instead of asymptotically approaching R2 ohms (assuming an ideal op amp). In fact, I have never seen this modification mentioned anywhere.

There are two resistors, R1 and R2 in this circuit. The required gain to make the parallel resistance branch vanish can be obtained like this: Disconnect the minus input of the op amp from its output. Add two more resistors identical to the existing R1 and R2. Connect another R1 from the output of the op amp in series with another R2, thence to ground. Connect the minus input of the op amp to the junction of those two resistors. The pre-existing R1 still is connected to the output of the op amp. Now the op amp with feedback has a gain of 1 + R1/R2, just what is needed.

If the capacitor has a non-zero ESR with a value of R3, then the gain should be a tiny bit higher yet, namely 1 + (R1 + R3)/R2. The ESR probably varies with frequency so the high-frequency ESR should be used for R3, but this can probably be ignored.

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Yes. Essentially the >1 positive feedback is removing loss terms and the circuit is becoming more and more 'perfect'. A tad more gain though and the circuit is beyond perfection hence unstable :). Myself, I've had practical trouble with these gyrators coupling with source capacitance(usually strays) and forming unintended LC oscillators (or 'incipient' oscillators) such that I'll only use 'em now specifically (with added gain) for an oscillator function. Even then I much prefer the 2 opamp versions, which by nature are pretty perfect in the first place.

Fascinating circuits though. Swap C and R2 and we've created a capacitor! (the "capacitance multiplier"). Add gain, lose R2 and we've a negative capacitor. I sometimes wonder if there's still some useful arrangement of an opamp, couple of resistors and capacitors that has yet to be discovered.