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

I should also add that total internal reflection also produces a phase shift that is not based on a time delay and is nondispersive if the refractive index is flat with wavelength.

That's an example of a boundary-condition phase shift. Bouncing off a metal waveguide below cutoff works the same way.

Cheers

Phil Hobbs

The baseband 90 degree shift (or Hilbert) needs to have a delay of at least a quarter cycle on the lowest frequency component of the baseband, to be causal.

Good point? Hmm. For a single sine wave, don't you start generating another sine wave immediately, regardless of phase? Such as in a product mixer.

I don't recall what Hilbert's assumptions were. I bet Phil Hobbs knows.

Joe Gwinn

While the above is true, the question came from the other direction: If one inverts the sign of a voltage waveform, do all the fourier componets of that waveform invert their magnitudes?

Joe Gwinn

Would not a band-block filter to eliminate the undesired sideband eliminate the filter delay, at least in theory?

Joe Gwinn

Joe Gwinn

You do not know the signal before it arrives. If you start to generate a single sinusoid, you do already know its amplitude, frequency and phase.

The magnitude is by definition a positive entity. The sign information is in the phase. The signs of the complex components do change.

It would, if the desired sideband were far enough out to be unaffected. I picked the SSB method 'cause I thought it was easier to visualize.

Cheers

Phil Hobbs

Sure, but the point is that it's fixed, whereas the phase shift can be anything you like, for an arbitrarily small additional delay.

Cheers

Phil Hobbs

Yes. Without going too far into the math weeds (and probably getting myself in trouble in the process), the FT of a given signal is

Int[-inf,inf] dt y(t) exp(-j2pi f t)

If you multiply y by -1, you can take that out of the integral, so all the Fourier coefficients change sign.

Cheers

Phil Hobbs

Yes, of course; the Fourier transform is a linear transformation, so multiplying inputs by -1 has the effect of multiplying outputs by -1.

The GH effect is specifically due to TIR, and as you say, the physics of the waveguide effect is the same: given the EM patching conditions at the boundary, the phase shift in the reflection coefficient has to be nonzero in order to account for the nonzero (exponentially decaying) field on the low-index side of the interface.

Cheers

Phil Hobbs

The Hilbert transform phase-shifts all the positive frequencies by pi/2, all the negative frequencies by -pi/2, and deletes DC.

Thus when you multiply it by j and add it to the real spectrum to get the analytic signal, the following rules apply

1. Leave DC alone.

1. Set all negative-frequency components to 0.

2. Double all positive-frequency components.

This works great, as all frequency-domain test gear will demonstrates. Dealing with exp(j omega t) instead of sines and cosines saves a whole lot of algebraic blunders, which is a huge win. However, when you need to do some nonlinear thing such as computing signal power, you need to go back to sines and cosines instead of the analytic signal.

Cheers

Phil Hobbs

So you can make an arbitrart phase shift by SSB delay un-SSB for arbrarily small delay.

but doesn't the initial SSB step need a quadrature signal in addition to the main signal.

And with the quadrature signal you can make any phase shift you want with just a summing amplifier. it seems to me that nothing is gained by the SSB, but a layer of obfuscation.

Yes, as I pointed out in my first post on the subject. SSB mixers need quadrature networks on the IF and one of the other two ports (generally the LO--divide-by-4 Johnson counters are useful for that).

Well, to each his own taste. I was trying to illustrate that the connection between phase and time delay is not altogether simple, which was the point at issue.

Cheers

Phil Hobbs

Huh, how the heck do they do that?

Oh I've used some of the american polarizer wave plates. ~200nm retardation. Those I understand. The retardation is approximately constant... you've got to tilt the plate to get 1/4 wavelength at different wavelengths. There must be some special tricks in the Thor labs spendy ones.

I wanted to make a general comment. Which I think applies to a lot of wave phenomena. There can be two types of responses. The first is direct, happens right away.. like a time delay to a phase shift. It's part of the transient solution. The other type of things you can see are built up from having many coherent waves. Maybe calling it the homogenous solution (as opposed to transient) makes sense. For this case the easiest example for me to think about is the phase shift in a (decent Q) bandpass filter. Here you can sit on the maximum and then change the frequency to either side and watch the phase shift both ways. But it's not instantaneous, you have to what for it to build up in the filter.

And then we sometimes run into problems (make a mistake) when we forget that it is (or is not) a transient solution.

An example for me is I tried to make an AR impedance matching layer in some ultra sound experiments. (Ultra sound was kinda nice 'cause I could make a single sine wave.. one period... and send it into the medium.) With a single period sinewave there was no AR effect. And only by making many periods could I see it work.

I guess this is all to say that in complex media there are transient, homogeneous and general solutions, and we should try and not confuse them.

George H.

PS.. I reread Feynman's 'Origin of the refractive index' Great stuff for any physics types or wanna be's

Yup. I haven't looked into it though--maybe there's some patent marking that would lead to illumination. (so to speak)

Well, that's redefining a pre-existing term in differential equations, which I expect might cause more confusion than it solved. The key distinction seems to be between broad- and narrow-band excitation.

Sure, because it was too narrowband for a single-cycle pulse, which has a fractional bandwidth of 100%.

Cheers

Phil Hobbs

Quadrature networks or filters, anyway. They used the latter for the optional phase modulation feature in the HP 8663A. The 320-640 MHz carrier is upconverted to 4.3-4.6 GHz and downconverted back to 320-640 using the same LO with a splitter to drive both mixers. One arm of the LO splitter goes through the phase modulator:

It's a legitimate-enough SSB mixing application, just not at baseband. I always thought it was an elegant approach since it fit on a single plugin module. Given the single LO frequency, a true SSB image-reject mixer might have been used on the input side to suppress the RF-LO response near 8 GHz. But it would've been more expensive than the 1 GHz LPF they went with, I'm sure.

-- john, KE5FX