Page 241 - Op Amps Design, Applications, and Troubleshooting
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High-Pass Filter  223


        5.3.2 Numerical Analysis
               Let us now extend our look at the high-pass filter shown in Figure 5.7 to a numer-
               ical analysis. There are three primary characteristics that we will want to deter-
               mine:

                  1. Cutoff frequency
                 2. Q
                 3. Input impedance

               Cutoff Frequency. The cutoff frequency for a high-pass filter is the fre-
               quency that causes the output voltage to be 70.7 percent of the amplitude of sig-
               nals in the passband (i.e., the higher range of frequencies in this case). We can
               determine the cutoff frequency for the circuit in Figure 5.7 by applying Equation
               (5.9).








               For the values in our present circuit, the cutoff frequency is computed as






               Filler Q. The Q of the circuit shown in Figure 5.7 is computed with Equation
               (5.10).








               For the values given in Figure 5.7, the Q is computed as







               If the resistor values had an exact ratio of 2:1, the Q would equal 0.707 and the
               passband response would be maximally flat.

               Input Impedance. The input impedance of the circuit shown in Figure 5,7
               varies inversely with the input frequency. The limit, however, is established by Rj
               in parallel with the input impedance of the voltage follower. Therefore, for practi-
               cal purposes, the limit is established by the value of Rj. In our present case, the
               minimum input impedance will be 47 kilohms.
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