Digital Electronics: Principles, Devices and Applications

494 Digital ElectronicsR 2R 3CV INR 1−A 2R 4−+A 2+R FBOut 1DACV refOut 2−A 1V OUT+Figure 12.26Low-pass filter with a programmable time constant.Also, the transfer function for this low-pass filter is given byV out /V in = −R 2 /R 1 1/1 + jR 1 + R 2 R DAC C/R 1 D (12.12)The cut-off frequency can be made independent of R DAC by using the D/A converter as a programmablegain element, as shown in Fig. 12.25. In this case, the cut-off frequency is given byand the transfer function is given by = R 3 D/R 2 R 4 C (12.13)V out /V in = −R 2 /R 1 1/1 + jR 2 R 4 C/R 3 D (12.14)If it is required to have a proportional adjustment of the filter time constant rather than its cut-offfrequency, the circuit of Fig. 12.25 is rearranged and the D/A converter is connected in the dividerconfiguration as shown in Fig. 12.26. The time constant is given byTime constant = R 2 R 4 CD/R 3 (12.15)