A first-order lowpass filter has the frequency response

The frequency at which the frequency response magnitude has dropped to *corner frequency*1. The frequency response magnitude and phase are plotted in Figure 1. It is common to express the frequency response magnitude in units of *decibels* (dB) using the formula

At the corner frequency for a first order lowpass filter, the frequency response magnitude is

A first-order highpass filter is given by

Notice that

This makes sense since a highpass filter can be constructed by taking the filter input

First order filters can be easily implemented using linear circuit elements like resistors, capacitors, and inductors. Figure 3 shows a first order filter based on a resistor and a capacitor. Since the impedance for a resistor and capacitor are

Therefore the corner frequency for this filter is

The corner frequency for the highpass filter is seen to be

Now one might be tempted to apply the results of (Reference) to build a bandpass filter by cascading the lowhpass and highpass circuits in Figures Figure 3 and Figure 4, respectively. Theory would predict that the equivalent frequency response of this circuit is given by

Unfortunately, this is not possible since the circuit elements in the lowpass and highpass filters interact with one another and therefore affect the overall behavior of the circuit. This interaction between the two circuits is called *loading* will be studied in greater detail in the exercises. To get theoretical behavior, it is necessary to use a *voltage follower* circuit, between the lowpass filter from the highpass circuits. The voltage follower circuit is usually an active circuit (requires external power supply) that has very high input impedance and very low output impedance. This eliminates any loading effects which would normally occur between the lowpass and highpass filter circuits.