Switched Capacitors and Filters

CMOS offers voltage controlled switches of low resistance that never wear out. This makes many things possible, among them a way to get a negative supply from a positive supply, and filters whose frequencies can be easily varied, both of which we’ll observe here.
Sometimes we would like a negative voltage when only a positive voltage is available, such as the 5 V digital logic supply. If we could get -5 V, then op-amps would be easier to use, and analog signals could vary above and below ground. This can be done by first charging a capacitor C to the positive voltage, giving it a charge of CV coulombs. Now we invert the connections to the capacitor, and connect the + terminal to ground. Presto! A -5 V supply. As we drain off some of the charge, we just repeat the operation. Now, this would be hard to do manually, but CMOS can do it 5000 times a second, which makes this simple procedure quite practical.
At the right is shown the insides of an ICL7660 or the more recent LTC1044, a switched-capacitor circuit designed to provide a negative supply, but with many other uses. The flying capacitor C is charged one way, then discharged the other into a storage capacitor C1, which actually supplies the load when C is busy elsewhere. There is an oscillator and divide-by-two circuit that produce signals φ1 and φ2, which are nonoverlapping square waves of opposite phase. These signals operate the CMOS switches, so that the two switches on any one lead are never closed at the same time.
The diagram at the left shows a -5 V supply that you can build and test. Three of the pins are not used. LV is only used for supply voltages less than 3 V, and a capacitor can be connected to OSC to slow down the oscillator, but why do that? “Boost” has uses for which you should consult the data sheets. It is not necessary to connect these pins in this application. The circuit is shown with 10 μF capacitors, which are a reasonable choice. Test the circuit with various load resistors, say 10k, 1k and 470. You’ll find that it supplies about 10 mA before the voltage rises to around -4.5 V, plenty for CMOS chips and op-amps. Leave the circuit built–it will be needed later.
For the next application of switched capacitors, consider the circuit shown at the right. It is an integrator, which adds up or integrates the input voltage. If the input is DC, it just keeps going until the op-amp saturates, but for an alternating input, the output can stay bounded. Note the same two-phase clock that alternately connects C to the source V and to the summing junction of the op-amp, which its output holds at ground by transferring all the charge that enters it to the integrating capacitor C1. The current is, on the average, i = fCV, so the switched capacitor acts like a resistance 1/fC. The beauty of this is that the effective resistance can be changed by changing the frequency.
Active filters can be made from such integrators, and the parameters of such a filter can be changed by changing the clock frequency. These are called state-variable filters. A second-order filter consists of a summer and two integrators in a loop (see the diagram below). The clock frequency is chosen much higher than the highest signal frequency. Usually, the clock and the signal can be separated well enough by a simple RC filter. The MF10 switched capacitor filter contains enough to make two double-pole filters of various types. There is quite a bit of flexibility, arranged by choosing the voltages applied to control inputs, but we shall concentrate on only one mode of operation out of six, with several sub-modes. Mode 1, which we shall study, can give us lowpass, bandpass and notch filters, depending on which output we choose.