07-04-2012, 11:42 AM
A 60-Hz Switched-Capacitor Notch Filter
An-SC-Notch-Filter-1303057840.pdf (Size: 3.37 MB / Downloads: 181)
Introduction
The switched-capacitor technique is a clever use of periodic switching of the connections of on-chip small-valued capacitors to realize the equivalent in very high resistances, which would otherwise occupy significant chip real-estate. In particular, it allows the implementation of low-frequency analog active filters when paired with the largest reactive element that can be accommodated on-chip, another capacitor. The two-pole, two-zero, active filter realized here requires only two analog integrators.
Switched Capacitor Fundamentals
A switched capacitor can be used to pass current from one circuit node to another in discrete amounts of charge per clock cycle. For a sustained current flow, the charge in the capacitor must flow in opposite directions every half cycle. This can be achieved in one of two ways: switch both terminals of the capacitor, or just one; switching just one terminal, though economic, is parasitics sensitive, so we’ll avoid that scheme here.
Suitable Active Circuits
The switching requirement, where at least one port of the switching circuit is open-circuited for one half of the period of the clock, rules out the use of differentiators to realize the -domain equation (because the differentiator amplifier feedback would get open-circuited by the SC resistor every half cycle, resulting in unpredictable results at its output).
Asymptotic Behavior
It is interesting to note that, at the higher frequency end of the spectrum, this filter approaches the behavior of an inverting, unity-gain, analog amplifier, independent of the switching frequency, as shown in fig. 9. Its high-frequency response is only determined by that of the opamp under a capacitive load, assuming the latter has a much wider bandwidth than the filter center frequency. The difference to note is that the loads on both the input and output are reactive and equal, and they increase with frequency.
Testing Strategies & Future Improvements
A schematic of the contemplated test setup is shown below. The output impedance of the sinewave source for the input needs to be low: 50 . I may do a frequency sweep and record the frequency response on a programmable instrument to later plot the data and compare it with my simulations. I’ll also test the noise level in the output, either manually or with a THD-measuring instrument. I’ll also do a DC sweep to determine the ICMR at the input and the limits of output swing, as our filter is DC-coupled and has unity gain at DC.