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Many texts talk about 180 degree phase shift as a function of the inverting opamp.

Is that correct? It seems to me inverting is happening almost immediately but phase is related to time and period and time delay between the input and output.

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    \$\begingroup\$ Phase is making sense for periodical sinusoidal signals, where phase shift of 180 degrees is equivalent to multiplication by -1. For other signals it is not the same. \$\endgroup\$
    – Eugene Sh.
    Jan 22 '19 at 18:12
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    \$\begingroup\$ But thats an illusion for the sine case, it just “looks like” phase shifted. Correct? \$\endgroup\$
    – GNZ
    Jan 22 '19 at 18:17
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    \$\begingroup\$ Yes it is an "illusion" but if it is a pure sinewave, you will be unable to tell the difference so it does not matter, the resulting signal is the same whether you invert of phase-delay. \$\endgroup\$ Jan 22 '19 at 18:19
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An inverting op-amp inverts the signal; it does not phase change the signal at the output by 180 degrees although, if the input waveform were a sinewave, then it would look like 180 degrees of phase shift.

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  • \$\begingroup\$ So it “looks like” as if it is phase shifted but actually it is not. There is a nuance here. \$\endgroup\$
    – GNZ
    Jan 22 '19 at 18:16
  • \$\begingroup\$ @Genzo indeed and a lot of EEs will use the terms interchangeably (including me but I always try and correct these bad habits of mine). \$\endgroup\$
    – Andy aka
    Jan 22 '19 at 18:17
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    \$\begingroup\$ More specifically inverting is equivalent to phase shifting every constituent sine wave in the Fourier representation of the signal by 180 degrees. So in that sense it is equivalent, but potentially miselading in cases where there are other "phases" of interest, such as modulated signals where "invert" is not necessarily the same as phase shifting the modulation by 180 degrees. This is where people get tripped up, phase actually means slightly different things in different contexts. \$\endgroup\$
    – Evan
    Jan 22 '19 at 18:36
  • \$\begingroup\$ Filters have phase shift and group delay. Inverters have 180 deg inversion \$\endgroup\$ Jan 22 '19 at 18:50
  • \$\begingroup\$ Another situation where it matters is if the voltage and current are out of phase. \$\endgroup\$ Jan 22 '19 at 20:31
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How an opamp behaves depends on how you configure it in a circuit.

But the opamp is actually irrelevant to your actual question.

I think that your actual question is:

Is inverting a signal the same as phase shifting it by 180 degrees

What we mean by inverting a signal is multiplying the signal by -1, so +33mV becomes -33 mV and -0.5 V becomes +0.5 V.

A 180 degree phase shift is indeed related to time but since phase is also coupled to frequency we only tend to use phase when talking about a single frequency. The only signal that contains a single frequency is a sinewave. Now for a sinewave inverting it (multiply it by -1) or phase shifting it 180 degrees will result in the same signal.

So yes, for sinusoidal signals, inverting and phase shifting with 180 degrees is the same thing.

Also for periodic signals like square waves and sawtooth signals, which consist of a base frequency and harmonics, inverting and phase shifting with 180 degrees is the same thing. Then the phase is only related to the base (lowest) frequency.

For non-periodic signals (these do not have a base-frequency) this isn't the case.

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    \$\begingroup\$ "Also for periodic signals like square waves and sawtooth signals, which consist of a base frequency and harmonics, inverting and phase shifting with 180 degrees is the same thing." That makes it sound like it's true of all periodic waves. It's only true of odd waves (i.e. nothing but odd harmonics). \$\endgroup\$ Jan 22 '19 at 20:37
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Inverting a signal is the same as a phase shift of 180 degrees at all frequencies.

If you take the Fourier transform of a signal, and compare it to the Fourier transform of the inverted version of the signal, you will see that the latter has the phase shifted by 180 degrees at every frequency.

This means if you invert a sine wave you get a shifted sine wave, but also if you invert the sum of two sine waves, for example, you get the sum of two sine waves that are each shifted by 180 degrees.

You can describe this in either the time domain or the frequency domain. Obviously it is more intuitive in the time domain ("it multiplies the signal by -1").

You are correct that the frequency at a single point in time doesn't make sense to talk about - but we are not talking about inverting a single point in time, because the circuit will invert the signal at all points in time. Or at least, all the points between turning it on and turning it off.

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