This is not a Wein bridge oscillator, though it's trying a bit to look like one.
I've redrawn it slightly, to emphasise the 'Wein' components R6, C2 in series and C1 and R1 in parallel to ground. This schematic is from LTSpice.
U1 with R2 is a virtual ground amplifier, presenting a short circuit to the bottom of R1. It's a transconductance amplifier with a gain of R2, producing a voltage at its output of 100k x -I(R1). It's basically measuring the current in R1.
The R4/5/D1/2 network around U2 is intended to produce an effective feedback resistance of 100k at the correct output level. At a lower level, D1/2 stop conducting and the feedback resistance rises, and vice versa. This creates a feedback network together with R3.
U2 is a differential amplifier, with inputs from both V(mid_point), and U1. It can be analysed by fixing one input, computing the gain for the other, and then superposing the two results.
With U1 output fixed, the output of U2 is 2 x V(mid_point).
With V(mid_point) fixed, the output of U2 is -1 x U1 output, or 100k * I(R1).
It seems to me that the V(midpoint) and I(R1) will always be in phase. It appears that it's the phase shift through R6 and C2 into the C1/R1 load that controls the resonant frequency.
That's as far as I'm going to go with a verbal description. It needs somebody to do nodal analysis and write down the phase shifts and amplitudes to demonstrate that there is a resonant frequency where all the phase shifts are zero and the gains unity.
Simulating the circuit in LTSpice, I get the following approximate frequencies
| R1(Ω) | freq(Hz) |
|---|---|
| 1k | 10k |
| 10k | 3k |
| 100k | 1k |
| 1M | 300 |
So it's not behaving like a Wein Bridge oscillator with a linear dependence on tuning resistance, it's going as the square root of R. The circuit appears to be behaving as if it's synthesising an LC, with the value of one of them linearly related to the tuning resistance. It's an interesting circuit though. As R1 needs to swing over such a wide range, it's of limited usefulness. I'd be inclined to use a state variable oscillator if I needed a wide range oscillator and could afford multiple opamps.
The vital part that some people miss when trying to simulate an oscillator in Spice is the .ic Initial Conditions. When Spice first analyses a circuit, it does a DC analysis to find the operating voltage of all the capacitors. Now settled, the circuit has no stimulus to start oscillating, unlike a real oscillator which starts from noise. Setting an initial voltage on one of the capacitors forces an initial transient into the circuit.
I've included my LTSpice file below for your simulating convenience.
Version 4
SHEET 1 912 836
WIRE 720 -224 -64 -224
WIRE -64 -176 -64 -224
WIRE -64 -48 -64 -96
WIRE 240 48 176 48
WIRE -64 112 -64 16
WIRE 16 112 -64 112
WIRE 176 112 176 48
WIRE 176 112 16 112
WIRE 480 112 176 112
WIRE 720 128 720 -224
WIRE 720 128 544 128
WIRE -64 144 -64 112
WIRE 16 144 16 112
WIRE 480 144 416 144
WIRE 416 240 416 144
WIRE 480 240 416 240
WIRE 720 240 720 128
WIRE 720 240 560 240
WIRE 16 272 16 224
WIRE 80 272 16 272
WIRE 208 272 160 272
WIRE 256 272 208 272
WIRE 416 272 416 240
WIRE 416 272 336 272
WIRE 624 320 576 320
WIRE 720 320 720 240
WIRE 720 320 688 320
WIRE 16 352 16 272
WIRE 80 352 16 352
WIRE 416 352 416 272
WIRE 480 352 416 352
WIRE 576 352 576 320
WIRE 576 352 560 352
WIRE 208 368 208 272
WIRE 208 368 144 368
WIRE 80 384 16 384
WIRE 576 400 576 352
WIRE 624 400 576 400
WIRE 720 400 720 320
WIRE 720 400 688 400
WIRE -64 432 -64 208
WIRE 16 432 16 384
FLAG -64 432 0
FLAG 16 432 0
FLAG 720 -224 Output
FLAG 240 48 mid_point
SYMBOL OpAmps\\opamp 112 304 R0
SYMATTR InstName U1
SYMBOL OpAmps\\opamp 512 192 M180
SYMATTR InstName U2
SYMBOL cap -80 144 R0
SYMATTR InstName C1
SYMATTR Value 1.5n
SYMBOL cap -80 -48 R0
SYMATTR InstName C2
SYMATTR Value 1.5n
SYMBOL res 0 128 R0
SYMATTR InstName R1
SYMATTR Value 1Meg
SYMBOL res 176 256 R90
WINDOW 0 0 56 VBottom 2
WINDOW 3 32 56 VTop 2
SYMATTR InstName R2
SYMATTR Value 100k
SYMBOL res 352 256 R90
WINDOW 0 0 56 VBottom 2
WINDOW 3 32 56 VTop 2
SYMATTR InstName R3
SYMATTR Value 100k
SYMBOL res 576 224 R90
WINDOW 0 0 56 VBottom 2
WINDOW 3 32 56 VTop 2
SYMATTR InstName R4
SYMATTR Value 102k
SYMBOL res 576 336 R90
WINDOW 0 0 56 VBottom 2
WINDOW 3 32 56 VTop 2
SYMATTR InstName R5
SYMATTR Value 2Meg
SYMBOL res -48 -80 R180
WINDOW 0 36 76 Left 2
WINDOW 3 36 40 Left 2
SYMATTR InstName R6
SYMATTR Value 100k
SYMBOL diode 624 336 R270
WINDOW 0 32 32 VTop 2
WINDOW 3 0 32 VBottom 2
SYMATTR InstName D1
SYMATTR Value 1N4148
SYMBOL diode 688 384 R90
WINDOW 0 0 32 VBottom 2
WINDOW 3 32 32 VTop 2
SYMATTR InstName D2
SYMATTR Value 1N4148
TEXT 296 -144 Left 2 !.lib opamp.sub
TEXT 296 -104 Left 2 !.ic V(mid_point)=1u
TEXT 294 -60 Left 2 !.tran 1