If you don't want to deal with the approximations, add an opamp with the resistor from the phase detector feeding its virtual ground. But I recommend you split that resistor in half and add a small shunt capacitor to ground at the midpoint, to keep the amplifier from having to deal with the full spectrum of frequencies present in the detector output. A high frequency pole much higher than the oscillator cycle does not change the loop filter much.
-- John Popelish
I prefer to design PLLs with current output charge pumps, having equal source and sink currents, where the loop filter is analysed as a "trans-resistance" network i.e. current-in, voltage-out. I'm confused by the 4046-style 3-state output. I find this far less intuitive than a current output charge pump. It's not a simple voltage source, since part of the time it's hi-Z. The source and sink currents are not equal, except when the loop filter capacitor voltage is half-rail. Mathematically, how is it justified to model this as a simple voltage source? Is there an assumption about the VCO control voltage being half rail? Is the design really out by a factor of 2 at the tuning range extremes?
TIA Andrew.
Oops, of course I meant "trans-impedance" there, and, I suppose a current-output charge pump is also 3-state, but you know what I mean ....
Answer: there is no *mathematical* justification. It's done that way because it turns this hard-to-solve non-linear circuit into one that's linear and easy-to-solve. The fact that this no longer represents the actual design (or its performance) seems to be lost on most app note authors.
Consider another issue: stray capacitance between the PC2 output and ground will get quickly charged up to the rail when the output is on, then slowly discharge through the resistor in the filter. This leads to another non-linearity in the phase detector characteristic.
If you want predicable performance, use a phase detector with a current source output, such as the (pin-compatible) 9046.
Regards, Allan
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