Real inductor multiplier

[mac]

I need a simple circuit to multiply the value of a real inductor, floating or grounded.

>--()()()()--circuit--()()()()()()()()()()()()-->

I'm googling but I see only gyrators.

mac

[Rob Strand]

You might be able to find something under the field of instrumentation.  Maybe for LCR calibrators.

I do remember some tricks multiplying and dividing resistances for the old computer joysticks.

The general circuit for the grounded case is,

            input  ->   Buffer   --> divider  by k  -->  Buffer

The inductor connects to the input (of the first buffer) and the output of the second buffer.

The idea is to reduce the current through the inductor in a way which is opposite to the Miller effect.

If the input voltage is V  the voltage across the inductor is V*(1-k).
The current through the inductor will be I_L = V*(1-k)/(sL)   ; s = complex frequency
So the impedance to ground looking into the input is,

Z   = V_in / I_L  = V / [V* (1-k)/(sL)]  =    sL / (1-k)   = L_new

Where L_new = L/(1-k)

so when k is just below 1 you get a large inductor.
I suspect trying to multiply by 1000 is going to be a disaster but you might get away with x10.

That's the idea.   I don't know what evil behaviour the circuit has when you start considering stability and
limited opamp bandwidth.

If you use a high-impedance divider before the first opamp you can remove  the second opamp.

[Rob Strand]

In the back of my mind there might be a way to do this using the idea of a current divider.   Maybe what I posted was it. Let me think about it.

OK, here's yet another way using the method I mentioned above,

http://www.seekic.com/uploadfile/ic-circuit/s200971231137907.gif

Here's the way using a the current divider,  (Section, Higher-Ratio Impedance-Multiplier Circuits )

http://www.tubecad.com/2009/09/blog0171.htm

[mac]

Thanks Rob,
I'll run a spice model before going to the breadboard, and report back.

>--()()()()--circuit--()()()()()()()()()()()()-->

There is an error in my drawing. I mean this,

>--()()()()--circuit-->   =   >--()()()()()()()()()()()-->


mac