The tank losses in the form of leakage resistances are causing the oscillations to damp down.
So, the effective parallel leakage resistance can be cancelled by putting the same magnitude negative resistance in parallel.
After doing this we get undamped or sustained oscillations at tank's resonant frequency.
Resistance in parallel at resonance is
Rp = -(1+Q^2)×Rs;
Where Q is the quality factor of the tank.
With the component values used in schematics:
Rp ~ -Q^2× Rs
~ -100^2×10m
Rp = -100 ohm.
Toggle the switches in the below order to see the operation. ( switches are named from left to right in schematic. )
SWITCH2 : CLOSE; to charge the capacitor with 1V supply.
SWITCH2: OPEN.
SWITCH1 : CLOSE; to see the DAMPING(dying) sinusoidal oscillations from LC tank.
SWITCH3 : CLOSE; to see that there is NO DAMPING, i.e. SUSTAINED oscillations.
Which is due to -ve resistance offered by OPAMP circuit.
