ABSTRACT
The circuit just analyzed could be described as a passive low-pass filter, passive because it includes no power sources or amplifiers. An alternative design with the same generic first-order response is shown in Fig. 7-31. This is an active low-pass filter since it uses an op-amp (which has its own power supply). Recall that two basic op-amp assumptions are that the node n is essentially at ground potential (0 volt) and that the amplifier input current is negligible. Applying Kirchhoffs current node Jaw at node n we get
e; - 0 e0 - 0 C d ( O) O --+--+ -eo-=
The negative value of steady-state gain K means that an input voltage of positive polarity produces an output voltage of negative polarity. If this is unacceptable we can connect an op-amp inverter at e0 • Its transfer function of -I gives the combined circuit a gain of +R2/ R1• Remember that most op-amps are cheap and small; popular integrated circuit devices may provide 4 op-amps on one "chip" at a total price of about a dollar. Circuit designers thus don't hesitate to use "extra" op-amps to provide desired functions. Let's assume our active filter circuit includes the inverter, giving the positive gain desired.
