Can passive phase shifters be implemented without a variable delay element? Revisited

What sort of signal do you want to shift the phase of? If it's a sine wave, there are lots of ways to do that.

--

John Larkin         Highland Technology, Inc 

Science teaches us to doubt. 

  Claude Bernard

In radar, we often want to shift a wideband waveform around, where wideband means that the bandwidth is something like 1/10 or 1/8 of the center frequency.

But my original question was more theoretical than practical.

Joe Gwinn

Isn't phase shift defined as a delay in time? A delay of 180 deg can also be confused with inversion.

piglet

That is what I was trying to nail down. A phase shift is just that. Even though many phase shifting devices are implemented as a variable time delay, it turns out that that is not the only way to accomplish a phase shift.

Joe Gwinn

Right.

For instance, in optics it's not too difficult to make a 1/4 wave retarder that's accurate to a few percent over an octave bandwidth (e.g. the visible). You do it by using two polymers with different dispersion, as in an achromatic lens.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC / Hobbs ElectroOptics 
Optics, Electro-optics, Photonics, Analog Electronics 
Briarcliff Manor NY 10510 

http://electrooptical.net 
http://hobbs-eo.com

Hmm. I didn't know that detail. Makes sense.

After my prior reply, it occurred to me that piglet's point about 180 degrees being the same as sign inversion is correct, and I don't know that this switched transmission line can be used to implement something other than 180 degrees, say 90 degrees. I'll have to think about that. Maybe some kind of polyphase clock scheme ...

Joe Gwinn

I am not an optics guy but isn't "dispersion" another way of saying the propagation velocity is frequency dependent - so still involves time delays. Phase and time are intertwined?

To be pedantic 180 deg phase shift is not always the same as inversion, for example it depends on the waveshape. I wrote it can be confused with inversion.

piglet

Time delay makes a linear relationship between phase and frequency, but that's far from the only way of getting a phase shift.

For instance, a lossless mirror phase shifts the reflected wave by pi radians because the tangential E and perpendicular D are zero at the surface. A lossy mirror produces different phase shifts that depend only on mu and epsilon, i.e. not explicitly on frequency or time.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC / Hobbs ElectroOptics 
Optics, Electro-optics, Photonics, Analog Electronics 
Briarcliff Manor NY 10510 

http://electrooptical.net 
http://hobbs-eo.com

Ok so mu and epsilon are what makes the speed of propagation (waving hands in air furiously generalizing) and so that changes the delay experienced by the wave? Isn't that still saying that phase and time are connected?

piglet

Sure, they're connected--frequency is partial d(phase)/partial dt with (x, y, z, etc.) held constant. But there are a lot of other variables that may be involved, such as material properties, boundary conditions, and so on.

In classical electrodynamics, reflecting from a boundary takes zero time--if epsilon and mu are frequency-independent, you get the same phase shift at any frequency. (DC may be a problem.) ;)

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC / Hobbs ElectroOptics 
Optics, Electro-optics, Photonics, Analog Electronics 
Briarcliff Manor NY 10510 

http://electrooptical.net 
http://hobbs-eo.com

OK, thanks.

piglet

Yes but linear increase of phase with frequency results in pure delay, being the group delay for signals of significant bandwidth.

In a dispersive component, an impulse spreads out into a chirp of some kind. This works in both optical and microwave domains. If one can arrange the opposite sign of dispersion, one can use dispersion to compress the chirp back into an impulse.

. .

Yeah. If the signal is a sinewave, inversion and 180 degree phase shift yield the same result.

But if the signal is wideband, not necessarily. For one thing, how would say a random waveform fare? You would think that inverting the waveform would invert all the component sinewaves, so there would be an across the board 180 degree phase change. I'll have to think about this.

Joe Gwinn

No delay either. That's a good example. I kinda remember this from E&M Field Theory, ~50 years ago.

Product mixers also change phase in the sum and difference outputs without requiring a delay or memory of any kind.

Joe Gwinn

Well, one can frequency-mix up, run through a delay line, then frequency-mix down with the same LO, and by varying the LO, that gives a variable phase delay. Is frequency mixing really passive, though?

"Phase" is unambiguously defined as the argument of the complex frequency, or integral of the instantaneous angular frequency.

"Phase shift" is arbitrary it has to be with respect to a reference (the constant of integration.) if you reference happens to be a signal that's

180 degrees out-of-phase then it can be interpreted as inversion.

Cool! So if I take a 1kHz input and upconvert with a 1-2MHz LO and pass through a 125ns delay line [125ns being 45 deg of 1Mhz and 90 deg of

2MHz] and then downconvert with the same LO does the output 1kHz have a phase shift wrt the input that varies from 45 to 90 degrees?

piglet

Yup, plus it's phase that's the operative thing, not time. In principle you can make an arbitrary phase shift with an arbitrarily small time delay by SSB mixing up to some very high frequency, delaying, and mixing back down again.

(Of course the SSB mixers' baseband 90 degree shifts have to come from someplace, but that's at most a fixed delay that doesn't depend on the variable delta-phi.)

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC / Hobbs ElectroOptics 
Optics, Electro-optics, Photonics, Analog Electronics 
Briarcliff Manor NY 10510 

http://electrooptical.net 
http://hobbs-eo.com

A half-cycle delay is not in general the same as inversion, because it's only a half cycle at one frequency. The idea is only applicable to periodic waveforms, of course, because otherwise delaying by half a period makes no sense.

A half-cycle delay at the fundamental becomes an N/2 cycle delay of the Nth harmonic. For odd harmonics, that's an odd number of half cycles, so the delay is the same as an inversion. For even harmonics, though, N/2 is a whole number of cycles, so they don't invert.

Thus it works for periodic waveforms containing only odd harmonics, such as square and triangle waves, but fails for waveforms with even harmonics such as sawtooths and pulse trains with duty cycles other than

50%.

If you phase shift nondispersively, i.e. apply a 180 degree shift to every frequency component, any waveform y(t) becomes -y(t). (An inverting amp is the easiest way to do that, of course.) ;)

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC / Hobbs ElectroOptics 
Optics, Electro-optics, Photonics, Analog Electronics 
Briarcliff Manor NY 10510 

http://electrooptical.net 
http://hobbs-eo.com

Phil, Are the wave plates of which you speak different from the garden variety piece of plastic (or x-tal... mica) with fast and slow optical axes? And if different, what's the name.

George H. (Enjoying the discussion...)