bandpass filter

Why would it do that? Ever hear of a buffer?

I've done TACAN extractors that, on an O-scope, the signal could not be seen... just hash. ...Jim Thompson

Actually - d(phi)/d(omega) to make the result positive.

I wonder if these engineers spend a lot of time trying to violate the laws of thermodynamics, or do they just specialize in time?

Now, this I really don't understand. Is a capacitor following a resistor a low pass filter? If so, how can it have an output before the input?

Is an RC filter not ideal? Confusion on my part here. Sorry.

I have no idea of how DSP works but I wish to.

This seems to make sense to me. I have written programs that integrate the input. Naturally, the result cannot predict the future input. Is this what you mean? Is it causality?

No, that has been my problem.

An IIR filter?

Ummm... Phil, where can a -100uF capacitor be obtained?

This is cute. Vary R7 and watch the phase plot at SUM.

Version 4 SHEET 1 1392 680 WIRE 512 -64 336 -64 WIRE 688 -64 592 -64 WIRE 784 -64 688 -64 WIRE 848 -64 784 -64 WIRE 992 -64 848 -64 WIRE 1136 -64 992 -64 WIRE 1296 -64 1216 -64 WIRE 1344 -64 1296 -64 WIRE 1376 -64 1344 -64 WIRE 688 -16 688 -64 WIRE 784 -16 784 -64 WIRE 992 32 992 -64 WIRE 688 96 688 48 WIRE 784 96 784 64 WIRE 336 192 336 -64 WIRE 496 192 336 192 WIRE 704 192 576 192 WIRE 784 192 704 192 WIRE 848 192 784 192 WIRE 992 192 992 112 WIRE 992 192 848 192 WIRE 1136 192 992 192 WIRE 1296 192 1296 -64 WIRE 1296 192 1216 192 WIRE 704 224 704 192 WIRE 784 224 784 192 WIRE 336 272 336 192 WIRE 704 352 704 288 WIRE 784 352 784 304 WIRE 336 400 336 352 FLAG 336 400 0 FLAG 688 96 0 FLAG 784 96 0 FLAG 704 352 0 FLAG 784 352 0 FLAG 1344 -64 SUM FLAG 848 -64 A FLAG 848 192 B SYMBOL voltage 336 256 R0 WINDOW 0 75 34 Left 2 WINDOW 3 56 73 Left 2 WINDOW 123 62 105 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V1 SYMATTR Value SINE() SYMATTR Value2 AC 1 SYMBOL res 608 -80 R90 WINDOW 0 71 61 VBottom 2 WINDOW 3 82 60 VTop 2 SYMATTR InstName R3 SYMATTR Value 1K SYMBOL res 592 176 R90 WINDOW 0 79 56 VBottom 2 WINDOW 3 95 58 VTop 2 SYMATTR InstName R4 SYMATTR Value 1K SYMBOL ind 768 -32 R0 WINDOW 0 60 48 Left 2 WINDOW 3 65 81 Left 2 SYMATTR InstName L1 SYMATTR Value 1 SYMBOL ind 768 208 R0 WINDOW 0 61 36 Left 2 WINDOW 3 59 73 Left 2 SYMATTR InstName L2 SYMATTR Value 1.1 SYMBOL cap 672 -16 R0 WINDOW 0 -53 31 Left 2 WINDOW 3 -45 68 Left 2 SYMATTR InstName C1 SYMATTR Value 1 SYMBOL cap 688 224 R0 WINDOW 0 -60 20 Left 2 WINDOW 3 -53 55 Left 2 SYMATTR InstName C2 SYMATTR Value 1 SYMBOL res 1232 -80 R90 WINDOW 0 67 62 VBottom 2 WINDOW 3 77 60 VTop 2 SYMATTR InstName R5 SYMATTR Value 100K SYMBOL res 1232 176 R90 WINDOW 0 -57 56 VBottom 2 WINDOW 3 -49 57 VTop 2 SYMATTR InstName R6 SYMATTR Value 100K SYMBOL res 976 16 R0 WINDOW 0 58 40 Left 2 WINDOW 3 60 73 Left 2 SYMATTR InstName R7 SYMATTR Value 44.9 TEXT 944 272 Left 2 !.ac lin 1000 0.13 0.18 TEXT 904 312 Left 2 ;BP Filter with funny phase shift TEXT 928 352 Left 2 ;J Larkin Aug 7, 2013

An RC is a very "soft" lowpass filter. It gradually attenuates signals as their frequency goes up, but always lets some through.

An ideal lowpass filter passes frequencies below Fc perfectly (no amplitude change, no phase shift, no time delay) and totally cuts off anything above Fc. It's a perfect "brickwall" filter.

A Hilbert transform is a similar case. A Hilbert is an ideal 90 degree phase shifter for all frequencies. It has an impulse response that has tails forward and backwards in time, forever. So you can't make one of them, either. To approximate one, you have to add time delay so that the backward-in-time tail still comes out *after* the input impulse.

Well, there will always be tolerance issues. I can't expect (and can't measure) exactly zero change in phase as a function of frequency. I'd just like it to be a lot better than a vanilla bandpass filter.

I posted one that seems to do what I want... zero phase shift at CF and adjustable +- phase slope in the vicinity. R7 could be a trimpot if one wanted to tweak the phase slope as closely as one has equipment and patience.

Why add a buffer ahead of a high impedance phase detector?

Would a buffer clean up cable reflections in a square wave system?

So did the antenna connect directly to the phase detector? No filtering, no heterodyning, straight wideband connection?

If you're using the EE sign convention for the Fourier transform. I'm a physicist.

Cheers

Phil Hobbs

That's the point. To get an acausal response (i.e. a phase slope opposite to that of a piece of coax), you need a negative capacitor. You can (approximately) make a negative capacitor with a negative impedance converter, and both are superficially OK looking in an AC simulation. However, having the opposite phase slope means that the poles of the transfer function are in the unstable half plane, which becomes apparent immediately in a transient simulation.

The NIC version oscillates, and the fictitious perfect negative capacitor version diverges monotonically to infinite voltage. If you replace the LT1037s with ideal op amps, you'll see the divergence very graphically.

I think it was E. C. Titchmarsh who first proved that the stability and causality conditions were the same. It's certainly not immediately obvious.

Cheers

Phil Hobbs

You just said the phase detector would "introduce all sorts of phase errors as a function of amplitude, waveform, cable reflections".

And a high impedance buffer would do nada.

A PLL IS a BP.

Your usual dose of obfuscation :-( ...Jim Thompson

No worries, this is fun stuff. The causality condition just says that in a cause-and-effect relationship, the cause has to precede the effect. That means that the impulse response of a causal network has to be zero for times t < 0. We need a bit of an arm-waving mathematical detour.

The impulse response h(t) is essentially a scope trace of the circuit's output, when its input is a tall, narrow pulse of unit area, centred at t=0. You can divide the input up into infinitesimally narrow time slices g(t')=Vin(t'). Since the network is linear and time invariant, it responds to each of these slices as though it were the only one, and the output is the sum of all the individual responses. If the slices are dt wide, this summed response is

v_out(t) = integral(-infinity to t) of (g(t')*h(t-t')) dt' .

This is called a convolution, and is a really fundamental operation in essentially all of physics and engineering. (No real circuit is exactly like this, but lots are pretty close, and the theory can be patched up to account for the discrepancies.)

If you take the two-sided Fourier transform of both sides of this equation, it turns into a multiplication

V_out(f) = H(f) G(f)

where V_out, H, and G are the Fourier transforms of v_out(t), h(t), and g(t), respectively. That's how we're used to handling filters and stuff in the frequency domain.

When we impose the causality condition, i.e. we demand that h(t) be identically zero for t < 0 (so that no effect can precede its cause), we get a particular condition on H(f), namely that it shall have no poles in one half of the complex frequency plane. (Which half it is depends on whether you're using two-sided Laplace or Fourier transforms, and whether you're in the EE or physics sign convention. There are four choices in all, but that's not a fundamental issue.)

It is a nontrivial mathematical fact, which as I said earlier was first proved by E. C. Titchmarsh, that the causality condition is identical with the stability condition for filters.

Cheers

Phil Hobbs

Answer the question. Did the antenna connect directly to the phase detector, unfiltered?

Do you even remember?

Recently posted. Turns out that it doesn't need the delay lines.

Of course I remember... that was the circuit that Gardner himself said couldn't work, until he saw me demonstrate it at Hoffman Electronics (El Monte, CA). >:-}

Anyone with half a brain, and an interest in PLL's, has read Gardner's book(s) and knows that an Analog PLL is exactly what you need... because an Analog PLL behaves like a tracking BP (center frequency same as input, with bandwidth a function of loop gain and loop filter corner frequency).

But you're too obstinate (and ignorant) to actually bring a proper engineering discussion to this table. ...Jim Thompson

You refuse to answer the question: in your Tacan system, was the antenna connected directly to your phase detector, with no filtering?

You poor sick puppy! Ask your wife >:-} ...Jim Thompson

What does my wife have to do with this, asshole?

You can't remember anything about that Tacan system, you stupid old fart. You probably only designed a little piece of the system and never understood the rest.