This "devil" circuit reminds me of some of Antoniou's GIC circuits. I spent a lot of efforts to figure out their secrets in this ResearchGate dialogue. Maybe it will help.
As @LFW has noted above, the grounded load resistor of the first NIC (INIC) is replaced by another NIC (VNIC). So, to understand circuit, we need to reveal: first, the role of the second NIC B (VNIC); next, the role of the grounded load resistor of the first NIC A (INIC).
Well, let's begin with considering the second NIC (VNIC) assuming that Z5 is a capacitor. This circuit acts as a negative inductor since the op-amp adds a voltage to the previous circuit (connected to its inverting input) equal to the voltage drop across the grounded resistor Z6... and this voltage represents the voltage drop across an inductor (this is a property of the simple RC circuit where the "complementary" voltage drop across the resistor behaves through time as the voltage drop across an inductor)...
Now about the role of the grounded load resistor Z6 in the VNIC... It acts as an "original" for creation of a "voltage-inverted copy". Briefly speaking about the VNIC operation, the op-amp keeps up the current through the "original element" equal to current through the input source, and "inserts" (adds) a reverse voltage into the circuit equal to the voltage across the "original element". To understand how the op-amp does this magic, think of the VNIC circuit (excluding only the op-amp) as of some kind of a balanced Wheatstone bridge with a varying supply voltage. See more about the topic in this RG question dedicated to NICs and the similar Wikibooks story.
Now about the role of the grounded load resistor of the first NIC (INIC).
It acts as an "original" for creation of a "current-inverted copy": if it has a positive impedance (the usual case), the "copy" will have a negative impedance adn v.v., if it has a negative impedance (our case), the "copy" will have a positive impedance... This op-amp circuit does this "magic":) by inverting the current through the input voltage source; thus the name "negative impedance converter with current inversion" (INIC). In brief, the op-amp keeps up a voltage drop across the "original element" equal to the voltage of the input source, and "pushes" a reverse current through the input source equal to the current through the "original element". To understand how the op-amp does this magic, think of the INIC circuit (excluding only the op-amp) again as of some kind of a balanced Wheatstone bridge with a varying supply voltage. As a result, the whole circuit acts as an "inverted original element"... and, for example, if the "original" is a positive resistor, the circuit will be a negative resistor.
Finally, if we look again at the exotic second Antoniou's circuit, we can see that a negative inductor (the second NIC) is connected in the place of the grounded load resistor... so its negative inductance is converted into a positive inductance... thus the whole GIC circuit acts as a "positive inductor"...So, in this arrangement, the generalized impedance converter (GIC) is an "inverted negative inductor"... or a "double inverted inductor"... what gives a "positive virtual inductor"... or simply an inductor:)... So, we can explain this circuit in a 3-step "scenario:
- Take a "real capacitor"
- By using a VNIC, swap the current through and voltage across the capacitor thus obtaining a "virtual negative inductor"
- By using an INIC, invert the "virtual negative inductor" (more precisely, its current or impedance) thus obtaining a "positive virtual inductor"...
Simply, we can say it in more striking way: "By one swap and next two consecutive negations, the Antoniou's GIC circuit converts a real capacitor into a virtual inductor."
We can add also that while the single NIC is usually a "positive-to-negative impedance converter" while this compound GIC is a "positive-to-positive impedance converter"...
It now remains only to see the connection between this demystified circuit solution and the circuit in the question. It seems there is such a connection since:
- At least, they both contain the same elements (four resistors, one capacitor and two op-amps).
- We can see the differentiating CR (Z5,Z6) circuit that produces the same voltage drop across the resistor as in the case of an inductor
- They both contain a resistor R2 connected between the input source and the circuit (it is used by the circuit to make an impact on the input source so that to simulate an inductor).
- Now let's try to do the most difficult - to see the two NICs; let's begin with the VNIC (the negative inductor). IMO it is implemented by the upper left op-amp with the differentiating circuit (Z5,Z6) connected as a positive feedback, and the resistor Z4 (in combination with the INIC below) connected as a negative feedback. Note the positive feedback is not simply connected to the non-inverting input; it is closed through the other (lower right) op-amp.
- Now only remains to see where the INIC (the negative-inductance inverter) is; it should be composed of the remaining elements. So it seems Z2 is connected as a positive feedback, and Z3 (in combination with the VNIC above) - as a negative feedback. Note again the positive feedback is not simply connected to the non-inverting input; it is closed through the other (upper left) op-amp.