My thought was perhaps first selecting the six different frequencies might be intuitively understandable which the equations that you gave are not.

Here is the way you determine the pole/zero locations for an equiripple phase difference:
https://archive.org/details/bstj29-1-94

all the broadband phase difference networks with flat amplitude response I know of are based on this - they simply differ in the way they implement the poles/zeroes.

It's not particularly intuitive unless you are familiar with elliptic integrals. I guess these days you could simply throw an optimiser at it to work out the locations - but that doesn't offer any understanding either.

 

In my post #20, I'll retract my last statement about subtracting phase shifting by the lower set of three shifters. That makes sense given that the total phase shift is the difference between phase of the upper and lower sets.

Thanks for your response to my previous post, Tesla23. My knowledge of math is limited, but I do try to understand what I'm building to the extent possible.

 

Mr Al,
My point was that it seems that the designer of the Wideband Active Phase Shifter (the entire circuit) might have gone about designing it by first determining the frequency at which each section should shift the signal by 90 degrees, then solve for component values on that basis. If this is in fact how he proceeded, then the question is how he arrived at the specific 90 degree frequency for each of the 6 sections.

For example from the schematic where you assigned resistor/ capacitor numbers, the first section of the upper three,

1/2*pi*R1*C1 = 1/2*pi*38.46k Ohm*20nF = 206 Hz

where tan(90/2)= 1 (the numerator)

My thought was perhaps first selecting the six different frequencies might be intuitively understandable which the equations that you gave are not. For example, each phase shifting section produces phase lag, yet in your equations of post #15, phase shifting of the bottom three sections subtract from the shifting of the upper three.

Regards and thanks,
Pete

About 1950 three papers appeared describing how to design 90 degree phase shift networks. The papers, authored by Darlington, Saraga, and H. J. Orchard (see this list of references: http://www.home.earthlink.net/~christrask/pshift.html), were followed by others with less high-powered math, in particular Bedrosian's (see the references). In fact, the frequencies in the 7 opamp circuit came from Bedrosian's paper.

There are two errors in the frequencies shown with this circuit: http://www.seekic.com/circuit_diagram/Control_Circuit/WIDEBAND_ACTIVE_PHASE_SHIFTER.html

At the lower left, the frequency 4985 Hz should be 49.85 Hz, and with the top sections, the frequency 1657 Hz should be 1675 Hz.

Here is a graphic showing the phase shift (in radians) vs. frequency of the 6 opamp sections. The top three in blue, the bottom three in red.



Here is the total phase shift through the top 3 sections in blue, and through the bottom 3 sections in red:



Notice that the two phase shift curves are maintaining an approximate constant difference of Pi/2 (1.57) radians, which is 90 degrees.

Neither one of the individual outputs has a constant 90 degree phase shift with respect to the input; the 90 degree phase shift is the difference between the outputs.

Here is a graph of the phase difference between the two outputs. It's not a perfect 90 degrees; it's only an approximation, specifically what is known as an equi-ripple approximation:

 

In my post #20, I'll retract my last statement about subtracting phase shifting by the lower set of three shifters. That makes sense given that the total phase shift is the difference between phase of the upper and lower sets.

Thanks for your response to my previous post, Tesla23. My knowledge of math is limited, but I do try to understand what I'm building to the extent possible.

Hello again,

Yes, the total phase shift is the difference between the two outputs, and i just want to point out that i explained this by noting that the bottom gets subtracted from the top, but you can also subtract the top from the bottom to get a -90 degree phase shift.
What this tells us i think is that each major section (three op amps) ideally provides a 45 degree phase shift, one section +45 and the other -45, so that when subtracted we either get +90 or -90 degrees phase shift.

Also, the equation for the phase for one stage can be simplified into:
Ph1=-atan2(2*w/w1,1-w^2/w1^2)
and that is the simpler form for the phase shift for stage 1 as in the schematic with R1 and C1.
Similarly, stage 2 would have w2 instead of w1 in it where:
w1=1/(R1*C1), and
w2=1/(R2*C2)

So the phase shift for the top section would therefore be:
PhTop=-atan2(2*w/w1,1-w^2/w1^2)-atan2(2*w/w2,1-w^2/w2^2)-atan2(2*w/w3,1-w^2/w3^2)

and that must come out to be +45 or -45 degrees with the bottom section being the opposite.

Of course the alternate form is also possible:
PhTop=-atan2(2*w*T3,1-w^2*T3^2)-atan2(2*w*T2,1-w^2*T2^2)-atan2(2*w*T1,1-w^2*T1^2)

where T1=R1*C1, T2=R2*C2, T3=R3*C3.

and again PhTop=+45 degrees or PhTop=-45 degrees.

So this reduces the problem to a little simpler form, where we just have to fit for three stages, twice.
The next step could be to try doing a least squares fit possibly after weighting the more important frequencies.
The whole problem ends up being a curve fitting problem then, where we have to find three unknowns.
It might be interesting to try this just to see how it comes out, so i'll see if i can get to that later today.

To do it with the AGC circuit and get a response over 20 to 20kHz, we'd need an AGC with a 1000 to 1 dynamic range. This would probably work but it would depend on how fast we needed the output to respond to the input. That also brings up the question of how fast the network with the 7 op amps can respond to a change in frequency on the input.
LATER: It was found that the time to get to 5 percent of the input step is 11.6ms, not exactly super fast.

 

Mr Al and The Electrician,

Thanks very much to both of you for your excellent explanations of the Wideband Active Phase Shifter. These are really top notch responses and I appreciate that you took the time and made considerable effort to explain.

Regards,
Pete

 

Not having ever heard of a syncro control transformer before, and I've been interested in audio electronics for many years, I would bet that such a device is not widely available and also expensive. So I'm not inclined to seek it out, as I'm not certain that constant 90 degree phase shift is a solution for what I'm attempting. But thanks anyway for the reply.

What I'm suggesting should be possible, as I've seen a circuit composed of eight op-amps, and many resistors and capacitors that provides the 90 degree shift with high tolerance and over the entire audio frequency spectrum.

-Pete

synchro control transfoprmers were mostly used in radar displays, the video from the reciever detector was fed into the single phase rotor, and the two 2phase stator windings went into the X and Y of the display. that generated the rotating "sweep" on the screen. there was also a 3 phase version that was used to trim the phase of regular synchros, used in position feedback circuits.

 

Thanks also to Crutschow for providing the link to the constant phase shifter requiring only 6 op-amps. He needs to be thanked too as it is the circuit that he directed my attention to that we have been discussing.