Version 4
SHEET 1 1664 908
WIRE 48 144 -48 144
WIRE 176 144 176 96
WIRE 176 144 48 144
WIRE 336 144 176 144
WIRE 480 144 336 144
WIRE 768 144 480 144
WIRE -48 240 -48 144
WIRE 176 240 176 144
WIRE 336 240 336 144
WIRE 480 240 480 144
WIRE 48 256 48 144
WIRE 48 624 -48 624
WIRE 176 624 176 576
WIRE 176 624 48 624
WIRE 336 624 176 624
WIRE 480 624 336 624
WIRE 736 624 480 624
WIRE 768 624 736 624
WIRE -48 720 -48 624
WIRE 176 720 176 624
WIRE 336 720 336 624
WIRE 480 720 480 624
WIRE 736 720 736 624
WIRE 48 736 48 624
FLAG 176 320 0
FLAG 48 320 0
FLAG 336 320 0
FLAG 480 320 0
FLAG 768 144 o
FLAG 176 16 0
FLAG -48 320 0
FLAG 176 800 0
FLAG 48 800 0
FLAG 336 800 0
FLAG 480 800 0
FLAG 768 624 o2
FLAG 176 496 0
FLAG -48 800 0
FLAG 736 800 0
SYMBOL cap 32 256 R0
SYMATTR InstName C1
SYMATTR Value {C}
SYMBOL ind 160 224 R0
SYMATTR InstName L1
SYMATTR Value {L }
SYMBOL res 320 224 R0
SYMATTR InstName R1
SYMATTR Value {R}
SYMBOL bi2 480 240 R0
SYMATTR InstName B1
SYMATTR Value I=atan(V(o))/R*G
SYMBOL current 176 16 R0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName I1
SYMATTR Value PULSE(0 1m 1n 0.2u 0.2u 0.05u)
SYMBOL current -48 320 R180
WINDOW 0 24 88 Left 0
WINDOW 3 24 0 Left 0
WINDOW 123 -58 88 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName I2
SYMATTR Value ""
SYMATTR Value2 AC 1
SYMBOL cap 32 736 R0
SYMATTR InstName C2
SYMATTR Value {C}
SYMBOL ind 160 704 R0
SYMATTR InstName L2
SYMATTR Value {L }
SYMBOL res 320 704 R0
SYMATTR InstName R3
SYMATTR Value {R}
SYMBOL bi2 480 720 R0
SYMATTR InstName B2
SYMATTR Value I=atan(V(o2))/R*G
SYMBOL current 176 496 R0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName I3
SYMATTR Value PULSE(0 1m 1n 0.2u 0.2u 0.05u)
SYMBOL current -48 800 R180
WINDOW 0 24 88 Left 0
WINDOW 3 24 0 Left 0
WINDOW 123 -58 88 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName I4
SYMATTR Value ""
SYMATTR Value2 AC 1
SYMBOL res 720 704 R0
SYMATTR InstName Rload
SYMATTR Value {Rl}
TEXT 248 0 Left 0 !.param C=500p f=1e6 L=1/(4*pi*pi*f*f*C)
TEXT -64 0 Left 0 !.tran 1000u
TEXT 392 -40 Left 0 !.options plotwinsize=0
TEXT 576 32 Left 0 ;I.e.: R=31.831k
TEXT 248 32 Left 0 !.param Q=100 R=Q/(2*pi*C*f)
TEXT -64 -40 Left 0 ;.ac lin 5000 0.7e6 1.3e6
TEXT 224 360 Left 0 ;I=sgn(V(o))*SQRT(abs(V(o)))/R\n; LTspice won´t calculate the derivative from this at 0\n; -> feedback would be neglected in .AC\n; ( function works when a DC offset is added )
TEXT 848 32 Left 0 !.MEAS tran Vo rms V(o) from 0.8m to 0.9m\n.MEAS tran Vl rms V(o2) from 0.8m to 0.9m\n.MEAS TRAN Ri param (Vo/Vl-1)*Rl
TEXT 872 584 Left 0 ;2.)  Ri as a measure of output sensitivity to\nload variations (Magnitude of Ri):\n------------------------------------------------------------------\nFrom .TRAN: \n/Ri/=Rl*(V(o)/V(o2) - 1) = 43.03k\n( see Error Log )\nThis considers effective loop gain\nat varying output voltages. For a check by\ncalculation the sensitivity to V(o) of the 1st\nfourier coefficient of the sinewave distorted\nby the nonlinear transfer function would be\nneeded (did not find the integral).
TEXT 864 160 Left 0 ;1.)  Ri@f from .AC, output fed by I2:\n-------------------------------------------------------------------\nfrom Plot: Ri=V(o)/1A= -21.22k (phase= 180 deg)\nThis results from the linearized loop gain at 0 volts\nusing dATAN(x)/dx = 1/(1-x**2) :\n1/Ri=1/R-dI(B1)/dVo=1/R-G/R ->Ri= -21.22k\nA real oscillator will reach a stable oscillating\nstate due to nonlinearity/finite output swing.\nThen loopgain is 1 and Ri is (negative) infinite.\n-> the above Ri gives the minimum load resistor that\ncan be connected (theoretically) before oscillation\nstops.\nSimulation is correct only if the transfer function\ncan be differentiated at the given OP !
TEXT 40 -96 Left 0 ;Measuring Output Impedance Ri of an LC-Oscillator?       G.M. jan-08
TEXT 848 -8 Left 0 !.param Rl=400k
TEXT -16 536 Left 0 ;Kick off pulse
TEXT 16 856 Left 0 ;Copy of the oscillator, required because .MEAS\ndoes not evaluate across .STEPs
TEXT 848 -56 Left 0 !.param G=2.5  ;loopgain at 0V