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I now understand that a common emitter amplifier produces an inverted amplification. I am asking this question because for a bit, I was hung up around the frequency with which I heard it explained as having an output that is “180 degrees out-of-phase” with its input. While I was still wrapping my head around the fundamentals, this seeming contradiction caused me a bit of frustration.

I recognize that while analyzing consistent sinusoidal curves that the “out of phase” quality is visually self-evident, but if you were analyzing signals that were changing, then describing them as 180 degrees out-of-phase would also be obviously incorrect.

Is this correct? Am I misunderstanding anything or simply reacting to semantic details that are taken for granted as obvious?

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Whether you say that a signal is inverted, or phase shifted by 180°, depends on context.

In the context of frequency response, where we are interested in the output of a system in respsonse to an input sinusoid at any given frequency, the concept of inversion wouldn't be used to describe behaviour. Take this filter for example:

schematic

simulate this circuit – Schematic created using CircuitLab

If you were to input a sinusoidal signal of frequency 0.1Hz to this system, the output would be another sinusoid of almost exactly the same phase, but at 1kHz the output would appear "inverted" with respect to the original. We wouldn't say it's "inverted", though, since at frequencies in between, the phase relationship between an input sinusoid and the output sinusoid would fall somewhere between those extremes of 0° and 180°, with a somewhat smooth transition as frequency changes.

It's not clear whether that filter inverts on not, it depends on frequency. Furthermore, for signals that are not sinusoidal, like square or sawtooth waveforms, which consist of many sinusoids in superposition (harmonics), some of them will be phase shifted more than others, and the output may not resemble the input at all. From this perspective, "inversion" is not a meaningful description of behaviour of such a system, which could alter wave shape in much more varied ways than "flipping upside down".

In this context, the concept of phase is very apposite, but the concept of inversion is not.


But, there exist systems that only "flip upside down", such as the common-emitter transistor circuit you mentioned, or this one:

schematic

simulate this circuit

For these circuits, whatever frequency of sinusoid you apply at the input, the output will be another sinusoid exactly 180° phase shifted from the input. In other words, any sinusoid at any frequency (below the bandwidth of the op-amp) is "inverted".

Importantly, the output is a "flipped upside down" copy of any input waveform, be it sinusoidal, square, sawtooth, or even aperiodic. In that sense, this amplifier can truly be said to "invert", because it does not discriminate between frequencies or shapes. The term "inverting" would be a very appropriate description of its behaviour under all input conditions.

You would not be wrong to say it shifts phase by 180°, but that description wouldn't be telling the whole story.


One last example might help. Let's say you have a rectangular PWM waveform, and a copy of that waveform delayed by a half-cycle:

enter image description here

Those waveforms are clearly not inverted with respect to each other, and yet they could be described as being 180° out of phase with each other. The harmonics that comprise this waveform will all be phase-shifted by some amount other than 180°, though. Whatever circuit that took the orange wave, and produced the blue wave in response, cannot be called inverting, and yet it does produce a delay of 500μs, which some might call a phase shift of 180°. I personally never would. I prefer the term "500μs delay", since it avoids the implication that all harmonics are equally phase shifted.


Your common emitter transistor amplifier inverts, and produces 180° phase shift for all harmonics of any input waveform, so in this sense it is not misleading to use either description, though the term "inversion" implies both anyway.

I recommend you use the term "invert" strictly in the sense of "flipping a waveform upside-down", and the term "phase" strictly in the context of sinusoids. There are always exceptions, though, and as long as people understand what you mean, I suppose you can use them interchangeably in certain circumstances.

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  • \$\begingroup\$ In my opinion, we can talk unambigously about the concepts of phase and phase shift not only for sinusoids, but for all signals x(t) with a given period T (or equivalently, with a given fundamental frequency or a given Fourier series). Only on non-periodic signals does the concept of phase fall apart, in my opinion (at least in this context of phase shifts). A phase shift of 180° on a periodic signal makes all harmonics phase-shift by a different amount, but time-shift by an equal amount. See this answer for a detailed explanation/proof. \$\endgroup\$ Commented Dec 31, 2023 at 15:11
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"out of phase" maybe if you are only using sinusoidal inputs or square waves, something purely symmetrical but inverted in shape.

  • also known as (AKA) "Inverted phase" or "opposite phase"
  • not to be confused with "out of shape" the human condition, the opposite of what we would like to be (mild humour)

It is more accurate to say "inverting output", because in both the Analog sense(AC+DC) or Digital (lo/hi) sense, a common emitter (CE) amplifier from base-to-collector is always inverting for changes in voltage.

When many stages are cascaded, it becomes common-practise to think by counting the inversions to see if the overall polarity is normal or inverted.

It is inherently non-linear for the large signal but there are various ways to make it more linear with emitter resistors and negative feedback from collector to base, smaller signal excursion and negative feedback to correct for errors on a larger number of stages such as Operational Amplifiers. (Op Amps)

More background maybe found on a Wiki page.

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  • \$\begingroup\$ pour s'amuser tinyurl.com/28zrjdz3 CE amp simulation with mouse & wheel interactive values to affect high linear gain of 35. \$\endgroup\$ Commented Jun 16, 2023 at 3:48
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It's misleading when you're an absolute newbie, but as soon as you learn how to think in terms of frequency responses it makes as much or more sense than saying the signal is inverted.

As with a lot of other notions in engineering, it's helpful to be able to think about things using either paradigm -- because sometimes thinking of the signal as "inverted" will make more sense (or make the math easier), and sometimes thinking of the signal as "180 degrees out of phase" will make more sense.

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