Simple Low-pass Filter
The simple low-pass filter is shown in Figure 1. This circuit has a 6 dB per octave roll-off after a closed-loop 3 dB point defined by fc. Gain below this corner frequency is defined by the ratio of R3 to R1. The circuit may be considered as an AC integrator at frequencies well above fc; however, the time domain response is that of a single RC rather than an integral.
Figure 1. Simple Low Pass Filter
R2 should be chosen equal to the parallel combination of R1 and R3 to minimize errors due to bias current. The amplifier should be compensated for unity-gain or an internally compensated amplifier can be used.
Figure 2. Low Pass Filter Response
A gain frequency plot of circuit response is shown in Figure 2 to illustrate the difference between this circuit and the true integrator.
1065 09 December 2007
Taking the root of a number using log converters is a fairly simple matter. All that is needed is to take the log of a voltage, divide it by, say 1⁄2 for the square root, and then take the antilog.
The free-running multivibrator shown in is an excellent example of an application where one does not normally consider using an Op Amp.