# Can someone please explain phase shifting?

1. Jan 30, 2012

### OysteinJ

Hi guys & gals.

I work as an electronics engineer in an R&D department, and a discussion with a colleague of mine left me a bit dumbfounded.

Let's say I have a circuit where a high-frequency AC signal is lead to two different paths. In one path the signal remains unaltered, and in the other path the signal is passed through a phase shifter circuit, giving e.g. a phase shift of between -45 and 45 degrees.

Exactly *how* would this phase shifting work? Not the mathematics of it, but if I scope before and after the circuit, how would it look one compared to the other?

180 degrees phase shift is easy enough - it's just the signal "turned upside-down". But I'm struggling with grasping how e.g. a 45 degree phase shift would "look" and what has been done to the signal. Ok, if you talk about 45 degree phase shifting of a 1kHz sinus wave, it'd just be the sinus wave crossing the 0 line 1/8 of 1ms earlier or later. But how about an audio signal from a microphone or a CD?

The circuitry in question is part of a high-frequency radio, where of course horizontal and vertical polarization is possible. So I'm trying to picture that it might be some sort of shifting of the polarization phase. But I can't get that to fit either, given that it's just a voltage in a copper PCB trace.

The other option I'm thinking about is a shift in the phase between voltage and current, which I know some electrical components can introduce (e.g. inductors or capacitors, which introduce a 90 degree phase shift one way or the other between voltage and current).

I know I should *know* this, given that I am an electronics engineer already. But digital electronics were always more my strong suit, to be honest...

Thank you for any and all help on this!

2. Jan 30, 2012

### sophiecentaur

Hi
Phase always, explicitly or implicitly, involves a reference phase for comparison.

If you're dealing with HF, it is often to introduce unequal lengths of cable in order to produce a phase shift. (Strictly a time shift, of course, but is is good enough for a narrow 'fractional bandwidth' and works a treat for producing elliptical polarisation using HP and VP antennae.

With 'lumped components' (R,L,C) circuits will produce a shift in phase (not always wanted).

Circuits tend to produce unequal phase shift across the whole band - increasing with frequency. Just think how many degrees a length of line with a given time delay will introduce to a signal with double the frequency of another (i.e. twice the phase shift because it's twice the fraction of a cycle for the higher frequency).

Incidentally, there is often a lot of phase distortion in sound signal processes but we are not too fussy about it because an average room produces a huge mix of signal paths, with a resulting mix-up of the relative phases of signals at all frequencies (sound covers many octaves of frequency, of course) so our brains often tend to 'ignore it'.

Apart from in general terms, I'm not sure what your problem is. But I suppose, if you could ask the right question, you'd probably have a clue about the answer. That's the way it goes. Try to be more specific?

3. Jan 30, 2012

### jim hardy

with a two channel scope look at both waves together on one screen
probably you'll have to use "ALT" trace not chopped since it's HF
so be sure you select trigger from one channel only.

the waves will appear offset on the screen by your phase shift.

phase shift - like the weather lags the sun's elevation angle
DEC 21 sun is lowest in the sky but the coldest time is maybe 6 weeks later.
6/52 = 41.5 degrees phase shift.

with the test equipment you folks have today heaven only knows what you can do,
probably even measure electronically its Laplace transfer function.

old jim

4. Jan 30, 2012

### OysteinJ

Sorry for the imprecise question. I'll recite a little snippet from our conversation to try to clarify my frustration.

This is in regards to a high-frequency radio transmitter that we're making. We were discussing how earlier they were made with analog circuitry, but how much today is done just using a CPU/FPGA combination. I'm not very knowledgeable about radio transmitters, but I'm learning. But he drew up the circuit mentioned above, where the signal was split up into two branches in parallel, and one of them went through a phase shifter circuit, where you could select a phase shift from -45 to +45 degrees.

And I'm just trying to picture what actually happens to the signal. I suppose this works as an illustration for my question (http://web.njit.edu/~gary/728/Lecture7.html). Take a look at the bottom block diagram, where the received signal is passed through a 90 degree phase shifter. What's happening in that phase shifter block?

I apologize for the poorly phrased question. As you say, sophiecentaur, if I could ask the right question, I'd probably have a clue about the answer. And I'm sort of feeling that I in my search for a simple, understandable answer, I'm leaping over the reason for not finding my simple and understandable answer.

5. Jan 30, 2012

### DragonPetter

Basically you have to break down your more composite signals into its component cosine waves using fourier transforms.

A phase shift in the frequency domain is simply a time delay in the time domain. But the amount of time delay is proportional to the frequency of the signal with respect to a given phase shift. So if you phase shift two different frequencies by the same phase shift, they will have different time delays and you will get distortion compared to when they were in phase.

With a microphone for example, when you phase shift the entire spectrum of your signal by 45 degrees, the individual frequency components will be delayed by different times (in proportion to their frequency and the phase shift). Your bass sound will be much more delayed than your treble sounds, and they won't arrive at your ear at the same time as originally intended. This is bad in that it distorts your signal. On the other hand, if you change the phase shift linearly with frequency, you can achieve a constant time delay over the entire spectrum. A linear phase shift over frequency will give a flat group delay, and a flat group delay means no distortion (there can be other kinds of distortion still).

There are circuits or DSP techniques called phase equalizers that adjusts the group delay by adding phase shifts, with the draw back being that it also adds a larger overall time delay
(basically it holds onto the higher frequencies until the low frequencies can catch up).

6. Jan 30, 2012

### OysteinJ

You know, you hit the nail square on the head there. I think what was troubling me was that I was considering the phase shifting in time domain, and couldn't see how it would work.

Thanks a bunch for your feedback. Although your answer didn't help me with my discussion with my colleague, it definitely pointed me in the right direction in regards to what I have to read myself up on. Thanks again!

7. Jan 30, 2012

### DragonPetter

No problem. Are you from Norway by chance?

8. Jan 30, 2012

### OysteinJ

Yep, that'd be correct. Nærmere bestemt Bergen. You, too?

9. Jan 30, 2012

### DragonPetter

Nei, men jeg bodde i Norge for 2 år og studerte i Oslo. Bergen is my favorite city in the world :)

10. Jan 31, 2012

### OysteinJ

I have to agree with you. Moved here half a year ago. :-)

11. Jan 31, 2012

### sophiecentaur

A word of caution. I think the above may be over simplifying and possibly confusing.
A phase shift IS a time domain concept. To describe a 'phase shifted' signal in the frequency domain, you need to use complex notation, such as
V = Ʃ(Ancos(nωt) + iBnsin(nωt). The frequency domain description of a signal (I am pretty sure) uses a common phase origin for all the frequency components (i.e. no time information in the description).

The explicit use of the names 'time' and 'frequency' domains is fairly modern (50s and 60s origin), I believe.

12. Jan 31, 2012

### DragonPetter

http://en.wikipedia.org/wiki/Fourier_transform#Tables_of_important_Fourier_transforms

see row 102, that's specifically what I'm referring to. The time delay (t-a) corresponds to a phase shift a*w in the frequency domain. And yes, you need to use complex notation, but that is required mathematically for it to make sense in the time domain (because when you mulitply a signal by a phase shift in the frequency domain, the complex number attached to it allows the phase to be added into the sine/cosine argument in the exponential).

Last edited: Jan 31, 2012
13. Jan 31, 2012

### sophiecentaur

Can you help me with finding that line (102?). Perhaps you could post a clipping and I could see where you're coming from.

14. Jan 31, 2012

### DragonPetter

Try this one:
http://www.ece.uah.edu/courses/ee426/fourier.pdf

its first page, 2nd row/transform f(t-t0) <=> F(w)e^(-jwt0)

15. Jan 31, 2012

### sophiecentaur

OH, right. That's fine.
But taken on its own, the statement
"A phase shift in the frequency domain is simply a time delay in the time domain."
leaves out the fact that the time / phase relationship is frequency dependent. That bald statement makes it look like the two are synonymous - which would lead to problems.

16. Feb 13, 2012

### Greg-ulate

A phase shift is equivalent to a time delay if you are only considering an exact frequency, correct? I have a little bit of trouble understanding why we say that "capacitors add 90 degrees of phase shift" when talking about amplifier design with feedback. Can anyone help me out with this? I think it is intimately related to the fact that the derivative of Cosine is Sine, which is 90 degrees phase shifted. Since the current is the Capacitance * dV/dt, no matter what the frequency of the current signal you are talking about, the voltage lags it by 90.. i think i answered my own question..

I dont know anything about VH and UH, but I do know that if you multiply signals and take a time average (integral), the result will be zero for any two signals with unequal frequencies. The correlation of signals involves an integral of two signals, one of which is complex conjugated and delayed. Each point in the correlation function represents the evaluation of the integral performed with the corresponding delay.

I am guessing that this type of radio employs a elliptically polarized signal, in contrast to a linearly polarized signal, in which the noise-free signal appears in phase on the different antennas, the signal will be delayed on one antenna with respect to the other. So if you delay the other signal by the same amount, so that now the two are in phase again, what have you accomplished? Well all the noise on each antenna is random and uncorrelated so after multiplying the two together and averaging, nearly the entire frequency spectrum of the noise is filtered away.

Does anyone know if this is anywhere near correct? I'm just guessing.

If my assumptions are correct, a phase correction of +-45 degrees could be used to fine tune the phase relationship of the two. I'm looking at Fig3 of the illustration. I notice that there are two correlation functions, a Sine channel and Cosine channel. If you want the full signal back, you must apply sqrt(Sin^2 + Cos^2). To avoid the need to add these two signals in square, you can fine tune the phase shift between the two signals so that the entire spike lies in one graph or the other. cool! Again, just a guess.