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We all know that, there are two assumptions that can be made whe analysing ideal operational amplifers, which are:

V+ = V-

I+ = I- = 0 (no current flows through op amp inputs)

but my question is: "Under what operating conditions are these assumptions valid?"

i am not sure if I'm right, but i said that the input resistor being infinitly big and the output resistor being infinitly close to 0, is this correct?

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  • \$\begingroup\$ The first assumption is not an assumed or real property of any OP-amp real or ideal. It is a property of a circuit. Nor is it required in either a real or an ideal circuit, and there are real circuits out there that don't obey it. \$\endgroup\$ – user207421 Aug 7 '13 at 22:04
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I+ = I- = 0

This is correctly stated as a property of an ideal op-amp. It's roughly true as long as the input voltage stays within the normal operating range (and particularly if the input voltage doesn't go outside the power supply rails). And as long as we don't care about very small currents, in the range of microamps down to femtoamps depending on the op-amp.

V+ = V-

This is not a property of an ideal op-amp.

The property you're thinking of is

  • A = \$\infty\$

If the gain is infinite, and we have a negative feedback configuration, then it will work out that the input voltages are driven to be equal. But if an ideal op-amp is used as a comparator, for example, the inputs will not be equal.

The infinite gain property is limited in real op-amps first because real gains are typically only 10,000 to 100,000. Also, the output voltage of real op-amps can only swing within a limited range. The most this could be is from the lower power rail to the upper power rail, but often it's 1 or 2 volts less on either side.

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Bluntly said, ideal properties are usually true for the opposite case where you would want to use the ideal opamp:

  • output load impedance should be high
  • input source impedance should be low
  • 'configured' gain should be low (set with feedback)

Nice video blogs on non-ideal opamps, introducing:

  • input offset voltage (voltage between V+ and V- is not 0V when connected as amplifier)
  • input bias current (input current is not 0A)
  • input offset current (input current is not 0A)
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The 2 assumptions you list are Ok for most circuits that are only interested in amplifying or processing AC signals. A lot of DC circuits will be OK with them too but understanding input offset voltage errors and input bias and offset currents are not a big-deal to take into consideration.

There are of course other assumptions that can be made: -

  • Open loop gain is infinity
  • Bandwidth is infinity
  • Phase shift is always zero degrees
  • Input resistance/impedance is infinity (I think you alluded to that)
  • Output resistance zero (ditto)
  • Slew rate is infinity
  • Common mode rejection is perfect
  • Power supply noise rejection is perfect
  • Self-generated voltage noise is zero
  • Self-generated current noise is zero

There are probably others I've forgot but all of them either affect dc or ac or both.

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