Inverting Amplifier: How to analyze component variation?

[maktoomi]

Hi,

Consider following fig. showing an inverting opamp configuration-


Suppose (the input 'Vi' is just some DC voltage and ) R2 fluctuates very very rapidly - may be
R2 depends on some external environment condition that causes it to show such behavior.
Is the output still -Vi(R2/R1) or I will have to do a frequency response analysis?

Thanks.

 

[crutschow]

The equation holds but you have to substitute the time varying value for R2. What is the frequency of this varying value?

 

[maktoomi]

Thanks for responding.
At this moment this is just a hypothetical problem. Say the frequency is 10KHz. And this opamp is single-pole 741 type.
If I ground Vin (as its DC) for ac analysis, then how could possibly I will get any output. Hence, I think that I should replace
the DC input with an AC source and proceed. But, will that give me correct result as I am only intersted in output due to fluctuations in R2, given a DC input?
Any suggestion will be greatly appriciated as everything looks so confisung.
(Later, I also wish to simulate this problem using SPICE. Hand calculation will help me 'think' in that term.)

 

[crutschow]

If you want noise output due to the R2 variation with a DC input then you need to apply a DC on the input, not ground it. With a grounded input the value of R2 has no effect on the output since it is also 0V.

 

[D.A.(Tony)Stewart]

This is known as computing the Sensitivity factor which is a partial derivative of the transfer function with respect to the variable..

In this case the Sensitivity is 1
meaning a 1% tolerance yields a 1% change in gain. or 1:1.

 

[maktoomi]

@crutschow: No, I am not interested in noise (at least for now). I am interested in output volatge when (time-) rate of change of R2 is very high, given fixed DC value of Vin.

@SunnySkyguy: Sorry, but I would disagree. It is NOT sensitivity. Sensisitivity is change in something when some related parameter changes. There isn't any consideration of time-rate/frequency of the parameter variation.

 

[Borber]

When R2 is a function of an independent variable then the Vo is allso function of that variable.

R2(t)=f(t)

Vo(t)=-R2(t)/R1*Vi

f(t) modulates output voltage


You may want to analize your circuit in Pspice using Monte Carlo analysis. It will give you set of output curves for variation of R2.

 

[maktoomi]

Hello Borber (and others) , sorry for not being able to explain the problem clearly.
I am basically interested in perhaps frequency response- I want to see how
output varies if rate of variation of R2 keeps on increasing. So it will be a plot Vout vs frequency where frequency shows the rate of fluctuation of R2.
Higher the frequency on horizontal scale, more rapid the variation in the value of R2.

 

[Borber]

Analyzing such problem with ideal operation amplifier make no sense because equiation Vo=-R2/R1*Vi is valid regardless of frequency of signal or a frequency of change of R2. Changing R2 causes only a change in gain of inverter and it does not matter how fast it is.
For analysis you take a real operational amplifier with specific gain-bandwidth parameter and phase characteristic for open loop that is use real transfer function. Write gain equiation of inverter with real parameters and use for R2 it's function over frequency (R2(f)). Then resolve gain equation as a function of frequency.

 

[maktoomi]

Expressing R2 as R2(f) is perhaps not suitable in this case. one doesn't write for example, a sinusoid voltage as V(f) because sinusoid is a single
frequency signal. so consider R2 as a single frequency 'signal'. Just as you plot Bode to know how the output voltage changes as the frequency of
input voltage changes, I wish to know how the output will changes if the frequency of variation of R2 changes.

To show that output does depend on frequency of R2 (and it very mcuh make sense), here is an spice simulation in time doamin:



Simulation uses ua741 macromodel and R2 is modeled as a sinusoid : green-10KHz, blue- 100KHz, red-1MHz.

simulation setup in LTspice:

 

[FvM]

So what do you see from the simulation results?

The OP output voltage is affected by slew rate limitation of the 741 OP, resulting in an about triangular waveform. You would get a simiar output waveform when connecting an AC voltage to the amplifier input or modulating R1 instead of R2. When modulating R2, you get an additional shift of average voltage.

Just for curiosity, what's the purpose of analyzing this (I agree) completely hypothetical problem?

 

[godfreyl]

OK, so you want to generate Bode plots showing output vs frequency, where the "input" is a varying resistance.

Ideally you want a voltage controlled resistor, where the resistance between the 2 main terminals depends on the input voltage on a separate control input.

Then you could just replace R2 with the voltage controlled resistor, and connect your AC source to it's control input.

Now all you need is the voltage controlled resistor. Fortunately, someone much smarter than me figured out how to make one in spice. It's explained here: http://www.ecircuitcenter.com/Circuits/vc_resistor1/vc_resistor1.htm

 

[maktoomi]

Dear FvM, Thanks for your expalnation of distortion (atributing to SR and/ finite UGF).
But that unfortunately doesn't solve my problem. To rephrase, I wish to know how could I genearte this same information in
frequency domain as I were able to do that in time-domain by performing '.tran' in spice.
Purpose of this circuit problem is educational as well as to look for possible research direction (of course a long way to go, as I have to learn about sensors,too).

- - - Updated - - -

godfreyl, Thanks for your VCR idea . I will give it a try (it should take perhaps not more that a line in LTspice).Meanwhile, see if you could suggest a method for hand calculation to get a 'transfer function' sort of thing.

 

[D.A.(Tony)Stewart]

@crutschow: No, I am not interested in noise (at least for now). I am interested in output volatge when (time-) rate of change of R2 is very high, given fixed DC value of Vin.

@SunnySkyguy: Sorry, but I would disagree. It is NOT sensitivity. Sensitivity is change in something when some related parameter changes. There isn't any consideration of time-rate/frequency of the parameter variation.

a parameter derivative can be a function of any time or tolerance. the gain or sensitivity result is the same just faster.

In any case, what is your resistor? a Photodetector? or? Are there capacitance changes from motion in this Resistor? or just leakage?
Can you explain with pictures? schema? p.n.?

 

[maktoomi]

a parameter derivative can be a function of any time or tolerance. the gain or sensitivity result is the same just faster.

In any case, what is your resistor? a Photodetector? or? Are there capacitance changes from motion in this Resistor? or just leakage?
Can you explain with pictures? schema? p.n.?

Thanks for your points but at this moment I will not go into discussion of sensitivity, gain etc.
What is that resistor physically, is perhaps immaterial. Well, imagine that to be some kind of vibration sensor. Rapid vibrations causes its resitance (modeled by R2) to change.

 

[D.A.(Tony)Stewart]

it is difficult to separate voltage due to gain dependant resistance changes from motion and piezo electric effects.

Most ceramic capacitors have this effect but I have not seen this in resistors, could it be tri-electric effects?

Actually the type of sensor is important due to other physical property effects when not in a benign state.

e.g. modulation of cable capacitance on a charge amplifier is another example of noise voltage with vibration.

The most difficult problem I solved was a plastic once used in the ends of magnetic air bearings of hydro power meters. We had a 1GHz radio inside which only detected noise when it was transmitting and the rotor was moving and it looked and sounded like crackling noise. It turned out the plastic had very high dielectric constant but poor loss tangent and the rotor movement modulated the flux density enough to cause a very low level dielectric breakdown due to Tx excitation with antenna not even that close. We changed the plastic end-stop to the magnetic air bearing and all the noise disappeared.

 

[FvM]

Dear FvM, Thanks for your expalnation of distortion (atributing to SR and/ finite UGF).
But that unfortunately doesn't solve my problem. To rephrase, I wish to know how could I genearte this same information in
frequency domain as I were able to do that in time-domain by performing '.tran' in spice.
Purpose of this circuit problem is educational as well as to look for possible research direction (of course a long way to go, as I have to learn about sensors,too).

There should be no problem to measure a transfer function in AC analysis. But by nature of AC analysis it's a small signal response respectively the response of an idealized linear system.

 

[maktoomi]

Dear FvM, Thanks for your expalnation of distortion (atributing to SR and/ finite UGF).
But that unfortunately doesn't solve my problem. To rephrase, I wish to know how could I genearte this same information in
frequency domain as I were able to do that in time-domain by performing '.tran' in spice.
Purpose of this circuit problem is educational as well as to look for possible research direction (of course a long way to go, as I have to learn about sensors,too).

- - - Updated - - -

godfreyl, Thanks for your VCR idea . I will give it a try (it should take perhaps not more that a line in LTspice).Meanwhile, see if you could suggest a method for hand calculation to get a 'transfer function' sort of thing.

godfreyl, idea of a VCR may not work at all as even considering an AC value for the controlling voltage will set input DC reference voltage , Vi to zero during AC analysis.

 

[Borber]

While time domain spice analysis give output signal for various amplitude and frequencies of R2 the only relation to frequency domain is FFT of output signal. Use harm or distortion function in time domain to get frequency spectrum of output signal for diferent R2 cases. You will manually transfer results point by point to frequency domain graph.
You actually need something similar to load pull analysis used for RF and microwave devices which I think does not exists.

 

[godfreyl]

godfreyl, idea of a VCR may not work at all as even considering an AC value for the controlling voltage will set input DC reference voltage , Vi to zero during AC analysis.

No, the reference voltage won't be set to zero. If it was , you'd never be able to do AC analysis of any amplifier circuit because the power supply voltage would be set to zero.