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In the following picture, the second circuit is a non inverting opamp, the gain of which is well known to be \$A_v = 1 + R_3/R_4\$ and the demonstration of this formula can be easily found on many websites.

My problem is with the first circuit in the figure which makes me a little bit confused as it looks different from the second one, furthermore the voltage gain I calculated is \$A_V = 1/(1 + R_1/R_2)\$, but I found on some web sites that still this configuration is a "non inverting opamp" with a gain \$A_V = 1 + R_1/R_2\$.

If I am right, and this is not a non inverting opamp, still I found such configuration in some other cases such as in instrumentation amplifiers. So the question is: is this another well known opamp configuration?

enter image description here

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    \$\begingroup\$ It's a unity gain buffer with a 50 ohm load. \$\endgroup\$
    – user16324
    Feb 13, 2021 at 21:41

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In the first circuit there is almost zero current flowing through R1 so the voltage at IN- = the voltage at the top of R2. It is the same as OP2 with R3 = 0. You have created a unity-gain voltage follower with an unnecessary load on the output.

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    \$\begingroup\$ Both circuits will not work because the 50 ohm resistor values are much too low. most opamps have a minimum allowed load of 2k ohms. \$\endgroup\$
    – Audioguru
    Feb 13, 2021 at 21:26
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    \$\begingroup\$ @Audioguru: Agreed but I felt it was out of scope of the question. \$\endgroup\$
    – Transistor
    Feb 13, 2021 at 21:29
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    \$\begingroup\$ @Audioguru Not necessarily. APEX makes op amps that can drive a 50 ohm load. It's always dangerous to generalize like that. \$\endgroup\$
    – Elliot Alderson
    Feb 13, 2021 at 21:40
  • \$\begingroup\$ even out of the main issue, still the resistores dimensioning is an interesting topic. I argue I should have to figure out the range of resistances from the datasheet, isn't it? \$\endgroup\$
    – Stefano Fedele
    Feb 13, 2021 at 22:05
  • \$\begingroup\$ While he is the king of such out-of-scope statements, he said "most opamps", which is correct. The world consumes more LM324/358's in a week than Apex's entire product line sells in a year. \$\endgroup\$
    – AnalogKid
    Feb 13, 2021 at 22:06

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