I read your post a couple of times. My response the first time through was something to the effect of "Eureka! That's it!" But after the 3rd or 4th time through, I am no longer sure that your numbers make sense.
I do that all the time. Sometimes it means there's a problem with the explanation, sometimes it means I have an idea sitting crooked in my head.
mauifan wrote:The short version of that post was basically that I still don't get how the xtal, acting as an inductor, doesn't cancel out the effects of the previous stage.)
You're probably getting caught on the electrical equivalent of a double negative.
Phase shift doesn't depend on the components per se.. it depends on the kind of filter the components make. Low-pass filters always give you a negative phase shift; high-pass filters always give you a positive phase shift.
When it comes to the kind of filter a group of components make, there are two variables in play: the type of component (inductor or capacitor), and its orientation in the circuit (series or shunt). That gives you four possible combinations:
For reactive components in series (upper left, lower right), we care about the part of the input that makes it through the component and reaches the output node. For reactive components in shunt (lower left, upper right), the signal is already at the output node and we care about the part that doesn't
escape through the component to GND.
The upshot is that a series inductor acts like a shunt capacitor, and a series capacitor acts like a shunt inductor.
Don't just take my word for it.. build all four versions and test them on your scope. It'll take maybe fifteen minutes and will give you the experience to bridge the gap between "that's what he says" and "I've seen it happen with my own eyes." That's a hugely important thing.
One of the few nice things about filters is that they 'superimpose', meaning you can basically add the effects of one to the effects of the next (technically it's an operation called 'convolution', but the idea is that they combine in an intuitive way).
If we redraw the two low-pass filters with impedances rather than resistors, then plug in the behavior for an inductor or capacitor, we get this:
In both cases, we get "better than just a fixed value resistor" low-pass filtering.
I know I haven't talked about the RC filter that precedes this part of the ciruit, but the idea of superimposition applies there too. The LC section is a 'second order' low-pass filter (it has two reactive components, so the function that describes it is a second-order differential equation) and the preceding RC section is a first-order low-pass filter.
- The RC stage, being a low-pass filter, gives us a negative phase shift.
- The crystal, acting like a series inductor, keeps high-frequency signals from ever reaching the second capacitor. That gives us a second dose of low-pass filtering, and more negative phase shift.
- The second capacitor shunts higher-frequency signals to GND, for a third dose of low-pass filtering, with still more negative phase shift.
The trick is to add the modifiers 'series' and 'shunt' to the properties of 'inductance' and 'capacitance', and it's really easy to get confused (case in point, the post I disavowed a couple of days ago).
One of the less
attractive things about filters is that everything's symmetric.. if energy flows into a component here, it flows back out over there. A component's shunt behavior is the inverse of its series behavior, and a capacitor's behavior is the inverse of an inductor's behavior. Descriptive words like 'charging', 'dicharging', 'through', and 'across' only apply to specific nodes at specific times, and using them in the wrong context sends you in exactly the wrong direction.
IMO, the best strategy is to study the simple (first-order) filters deeply enough to get a feel for them, then take the rules about combining filters on progressively more faith as the number of stages increases.
When you void a product warrany, you give up your right to sue the manufacturer if something goes wrong and accept full responsibility for whatever happens next. And then you truly own the product.