op-amp and math problem

[normad]

Im trying to understand the gain change in a buffer amplifier with a low frequency gain of 1.

I simulated the op-amp on ltspice and according to that the gain does not change with frequency but the phase does..
(i uploaded the ltspice file.. i changed the opamps gbw to 5Meg as we are supposed to do this lab with lf347s)

what i dont understand is..

if there is a phase difference between the input and the output that means the feedback will also have a phase difference.. if there is a phase difference in the feedback shouldnt the difference be amplified? so the gain should either decrease or increase as frequency reaches GBW.. but in the simulation it remains the same..
and when we did this experiment in the lab the gain slightly increased with frequency..

i derived an equation for the gain considering the op-amps input impedance as Rin and the opamp gain as AvΓθ where is the phase difference

and what i got is

Vo Rin*AvΓθ
------ = --------------------------------
Vin (Rin+1) + (2Rin+1)*AvΓθ

doesnt this mean gain depends on phase difference?

please help.. thanks

 

[Electronworks]

Firstly, you have a single pole roll off as the graphs you have supplied give a 45 degree phase difference at the -3dB point. The roll off is a function of the amplifier's internal gain, so although you will get a phase shift in the output that results in a phase shift in the feedback loop, it will not get amplified because the amplifier does not have enough gain to amplify it (it is losing gain due to the internal gain roll off). If it increases slightly in the lab, you probably have some stray capacitance (scope probe?) that is causing an additional phase shift and distorting the natural single pole roll off that you are seeing in your LT SPICE simulation.

Feedback analysis of op amps is tricky, but I think this is what you are seeing

 

[normad]

hmm.. so what you are saying is that the gain achieved by the phase difference in the output is canceled out by the gain lost in the internal gain roll off?

the scope probe was 10X for the oscillator if thats what you're asking.. does that effect the net capacitance?

and is my derivation for the gain correct? the equation looks a bit messed up.. what i meant was

Vo                      Rin*AvΓθ
------ =      --------------------------------
Vin            (Rin+1) + (2Rin+1)*AvΓθ

 

[normad]

i think i made a mistake in my first thread.. The gain does change with frequency in the ltspice simulation.. i hope this doesnt change your first explanation.. i will upload the new graph..
in it

1 ) (V+) - (V-) increases negatively as is reaches the GBW
2 ) The phase difference also increases as frequency reaches GBW
3 ) The Gain decreases with GBW

but in the real lab simulation

1 ) (V+) - (V-) increased with frequency
2 ) The phase difference increased with frequency
3 ) **But gain remained almost the same yet slightly increased from (10V to 10.2~10.4V)

But according to logic the gain should increase as the phase difference creates an input difference.

So from what you said what i can grasp is that

1 ) (V+) - (V-) does increase with frequency
2 ) Internal phase shift does increase with frequency (therefore creating the difference in (1))
3 ) The net gain remains the same because The reduction of gain(as shown in the LT SPICE simulation) is canceled out by the increase of Voltage difference at inputs
4 ) And the slight increase in the laboratory experiment was caused by external capacitance which effects the phase difference

And as for the math part.. going with the logic stated above if i substitute the function of gain interms of ω and substitute a value for ω as Rin approaches ∞ i should get unity regardless of the frequency

 

[normad]

am i correct?

 

[audioguru]

The obsolete LF357 needs a minimum gain of 5 to prevent oscillation. You have it with a gain of only 1.

 

[normad]

we used lf347s not lf357.. is it the same? here what do you mean by oscillation? oscillation of the input difference?

i would really appreciate if someone can explain in detail the questions in my last post why am i getting different results in the simulation and the experiment

 

[audioguru]

Sorry, you don't have an LF457 quad opamp. Your LF347 quad opamp is an ordinary and fairly old Fet-input fairly fast opamp very similar to a TL084.
It has the Opamp Phase Inversion problem like the TL084 where the output suddenly goes high if an input goes closer to the negative supply voltage than the max allowed input common-mode range spec (3V to 4V above the negative power supply voltage).