Why the theoritical gain in operational amplifier is different from experiment?

Question

With an inverting version, the gain is given as:

Vo = -Vi x (Rf/Ri)

but when I did an experiment, the gain is different from the gain that I calculate from the formula , why is that?

Is it because of the resistor getting hot and then the value changed?

Answer 1

If you specify what resistor values you used, we could tell better what the problem is likely to be.  In addition to what other people have said, there is a range of resistances that are practical to use for an op amp.  If you use too low a value, the calculations do not apply because the amplifier cannot supply enough current.  The resistors should be at least a few thousand ohms.  Also, if you are trying to get a high value of gain, like 1000X, the actual gain will be somewhat lower because the open loop gain is not actually infinite, like the calulations assume.  And if your output voltage swing is close to the power supply voltage, it will be limited to the maximum swing available, which is at least a volt or so lower than the power supply voltage in most cases.  As somebody else said, looking at the input and output with an oscilloscope is a good way to find out what is going on.

Answer 2

A few more details about the experimental setup would have been useful.

One thing to bear in mind with an inverting amplifier is that in a practical circuit Ri is effectively in series with the internal resistance of the input source.  Depending on your setup, the effective value for 'Ri' can be bigger than you think.

Answer 3

Unless there was something seriously wrong with the op-amp, the feed back resistor should not have gotten hot. Over driving the op-amp is a slim possibility, but it is possible.

The frequency used could have caused the error, your actual resistor values could have been different. Unless you used 1% or better tolerance resistors, and everything at a fixed temperature, then your theoretical and practical values will not be the same. Just because a resistor is marked as "x" resistance does not mean that it actually is that value. A resistor with a silver band on it for the +/- % value is a 10% resistor. It's value can be high or low by that value of tolerance. What did you use to measure Vi? If it was not an oscilloscope, then that could also cause the error that you are asking about.

Answer 4

How much different?  Are you off by a factor of ten or like 0.5%?  If you're off by a small amount it could be many things.  The amplifier has an offset, could be a few microvolts or could be a few millivolts depending exactly which op amp is used.

All resistors have a tolerance so the actual resistance will be different than the stamped nominal value.  An extra step would be to measure the resistors with a DVM.  But even then, the DVM measurement is subject to some error.

If the feedback resistors are too small the op amp may not be able to drive them and the output voltage will be much less than expected.  Check the manufacturers data sheet for recommended values and output drive capability.

If you're running at a high frequency you may be beyond the amplifiers bandwidth capability.

Answer 5

How much different? what are the numbers?

If the resistor is getting hot, you are making some mistake.

Typical values to use with an ordinary opamp are:

Ri = 10k, Rf = 20k, which will give you a gain of 2. If you use 0.1% accurate resistors, the gain will probably be almost that accurate at DC and low frequencies.

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Answer 6

Four things you could check.

1. is the circuit oscillating? The presence of oscillations on the output will give you a different output voltage reading to what you expect.

2. are the resistors you used actually the value you think they are? Use a ohm-meter to check.

3. Are you using dual power supplies? Applying AC to an amplifier around ground will cause the +ve side to attempt to output a negative voltage. To enable it to do this you will need a -ve supply.

4. Are you over-driving it? The output voltage must be within the range of the op-amp.

Answer 7

One thing that others have not mentioned that I thought I should is that the gain equation you give assumes an ideal op amp. You are using a real op amp and real resistors, the resistors themselves could change the gain by up to 10% (although probably not that much).  Then the fact that your omp amp does draw a little bit of current at its inputs will change things. If you are operating in a frequency outside the omp amps bandwidth things will be different. If you are using the opamp to power a low resistance that will reduce the gain as well. Lots of things are at play here. The main thing to realise is that electronics never do exactly what they should theoretically.

Answer 8

I suspect you are using a non-inverting opamp amplifier instead of inverting, where the gain is Vin * (Rf/Rin +1).