It seems an easy question but I just can find out how I'm supposed to do it: what frequency is needed so that Vin and Vout have a 90° phase shift.

(picture below just as a matter of an example circuit) enter image description here

  • \$\begingroup\$ wait, do you need to know the frequency for this circuit, or do you know what a 90° phase shift is in general? \$\endgroup\$ Jan 25, 2021 at 16:20
  • \$\begingroup\$ I need to find the frequency of a circuit so that the phase shift between Vo and Vi is 90° but I don't know how to use/ what the requirement for a 90° phase shift is to get the frequency \$\endgroup\$ Jan 25, 2021 at 16:25
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    \$\begingroup\$ Well, what circuit? For example, the circuit you've posted isn't linear nor stable, so it doesn't have a fixed output/input relationship, as far as I can tell, and hence also no phase response which you could solve for 90°. \$\endgroup\$ Jan 25, 2021 at 16:27
  • \$\begingroup\$ Are you sure that you didn't flip the (+) and (-) symbols on the op-amp? \$\endgroup\$ Jan 25, 2021 at 16:55
  • \$\begingroup\$ You made exactly the same mistake in your previous question AND you were informed about this in a comment right under your question. \$\endgroup\$
    – Andy aka
    Jan 25, 2021 at 17:09

2 Answers 2


In general, you'll need write down an equation for the output voltage of your circuit, and then find the phase of that in relation to your input. There's no single way of doing that – it depends on the circuit.

For example, the circuit you've posted doesn't have that property – a fixed frequency at which the output has 90° shift relative to its input, since it has positive feedback only, and both for low and for high frequencies is pretty much instable.

  • \$\begingroup\$ Suppose this were a trick question; of course whether it is or not - hard to tell, too much mediocre teaching going around to tell clever apart from ignorant. Suppose you had actually made such a circuit, with some reasonable values of inductance and resistance. Even if the op-amp was saturated, there will be some leakage from input to the output :) But I'm 99.9% sure that question wasn't about that. But if it was shown exactly as in the question, that's what I'd answer - I'd substitute the op-amp with, say, a 60dB pad with some parallel capacitance to ground and series inductance :) \$\endgroup\$ Jan 25, 2021 at 17:03
  • \$\begingroup\$ Yes the exercise was to calculate Vo, I(t), complex power of R1 etc whilst Vi and other values were given and didn't understand the subquestion about finding the frequency for which the phase angle would be 90°. exercise was purely based on calculations not legitimacy I suppose, but really thanks for the extra info! always better to know more :) \$\endgroup\$ Jan 25, 2021 at 18:37

It depends if you can tolerate 90 deg or close to that as the ratio of impedances for 2pif*L/R determine how far below the ratio of 1 when the magnitudes are equal where you get 45 deg.

Reusing a nomograph from my other answers for RLCFZ variables, let’s choose an example where all R=1k and all L = 100uH. The breakpoint for this value is ~2MHz, thus 1 decade down in frequency the current will be close to 90 deg at 200kHz and closer below this.

enter image description here

You can slide the signal frequency here and watch the circle slant go from a 90 deg circle above 200kHz towards 2MHz . The scope can be resized and maximized with mouse.


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