It's not clear what exactly you mean by series versus parallel resistor-capacitor filters. Posting a schematic of each would clarify this.
You probably mean series is something the signal passes thru, and parallel is something that works as a shunt. Note that the same thing that is a low pass filter in series is a high pass filter as a shunt, and vice versa.
Basically a capacitor will block low frequencies and short high ones. If you put it in series with a signal then it is a high pass filter. If you put it accross a signal, it will short the high frequencies thereby making a low pass filter. The value of the capacitance and the resistance it is working against tell you the -3dB rolloff frequency of the filter, whether high pass or low pass. This frequency is:
\$ f = \dfrac{1}{2 \cdot \pi \cdot R \cdot C} \$
When R is in Ohms and C in Farads, then f is in Hertz.
The primary advantage of switched capacitor filters is that they can be easily implemented on an integrated circuit. You can get performance similar to an analog RC op-amp based filter using a switched capacitor topology, while avoiding the need for an ADC, DSP, and DAC on a chip.
Switched capacitor circuits use capacitors and switches to emulate the behavior of resistors. Additionally, the frequency response is determined by the ratio of the capacitors, so even low frequency filters can be easily realized on-chip. The real benefit for IC implementations is that while the absolute value of capacitances and resistances have a poor tolerance, the matching between similar devices is very good. This makes it possible to implement relatively high precision analog filters on a chip.
In an integrated circuit, you would choose a switched capacitor filter for the following reasons:
- Minimizing chip area is a priority
- You will not be doing significant digital processing on the chip
- The output of the DSP would be an analog signal
Practically, you would not use a discrete switched capacitor filter (using op-amps, capacitors, and analog switches) at the board level - you would use an active RC continuous-time filter. There are switched capacitor chips that can provide good filtering results with just a few additional components. Using a general-purpose DSP on a board level design will require additional programming, and may not have analog outputs.
Best Answer
A switched capacitor filter has a "building block" that is made from analogue switches and a capacitor. This building block is equivalent to a variable resistor whose value is modified by the clock frequency. You have to be aware of aliasing so you can't use the "building block" with signals that have frequencies that approach half clock rate.
A significant advantage is that the switching frequency can be altered "on the fly" and you then have a filter whose (for example) cut-off frequency can be swept from one point to another. Quite a useful feature and because capacitors are fairly easy to make on a silicon die they can be integrated too.
Being able to control the frequency allows you to alter two or more resistor values simultaneously and this means that the Q of the filter needn't be affected for instance on a sallen key filter that needs both resistors to remain in the same ratio to keep Q constant.
Given that the "frequency" of the clock can be digitally derived, you can use digital techniques to shift the clock's frequency and thus change analogue values.
A passive LC filter has a Q factor that is largely fixed by the component values. For instance a low pass RLC 2nd order filter might have a response like this: -
This has a cut-off frequency of 1.59 kHz and is a decent approximation to a maximally flat Butterworth response. If I lowered the capacitance from 1 uF to 0.1 uF you would see this altered response: -
The cut-off frequency has changed from 1.59 kHz to 5.03 kHz but the Q factor has gone from 0.707 to 2.236 and now you see a sizable peak in the response and if you look at the transient waveform for a step input, there is clearly more ringing.
Picture calculator source.
An active RC filter like a sallen key 2nd order filter is just as problematic in that (as previously mentioned), to keep the Q constant whilst changing the cut-off frequency, you need to adjust two resistor (or capacitor) values. This makes it difficult to control.