DESIGN AND DEVELOPMENT OF MEDICAL ELECTRONIC ...

50/60-Hz NOTCH FILTERS 65where z is an offset input. In the tunable filter of Figure 2.16, the AD633 is configured suchthat the apparent impedance between x 1 and the output is proportional to the control voltageat y 1 . This makes the cutoff frequency of the high- and low-pass filter outputs, as wellas the center frequency of the bandpass section,f c c ontrolvoltage20π(R3)( C1)PSpice simulation results shown in Figure 2.17 demonstrate the effect of varying the controlvoltage presented to the y 1 inputs of the AD633s. Although the circuit is shown set upfor PSpice simulation, it can be built using real components. Output buffering using Burr-Brown BUF634 buffers make this a very useful stand-alone lab instrument that can be usedto filter amplified biopotential signals selectively prior to recording. A digitally programmableversion of the tunable filter can be made by substituting two multiplying D/A convertersfor the AD633s. In this case, the control voltage is replaced by a digital controlword supplied to the input of the D/A converters.50/60-Hz NOTCH FILTERSProbably the most common problem in the detection and processing of biopotential signalsis power line interference. Sixty hertz (50 Hz in Europe) and its harmonics manages to creepinto low-level signals despite the use of differential amplification methods and active bodypotential driving which attempt to eliminate common-mode signals. Unfortunately,50/60 Hz falls right within the band where biopotentials and other physiological signalshave most of their energy. The usual solution to reject unwanted in-band frequencies is thenotch filter.As shown in Figure 2.18, simple implementation of a notch filter known as a twin-T filterrequires only three resistors and three capacitors. If C1 C3, C2 2C1, R1 R3, andR2 R1/2, the notch frequency occurs where the capacitive reactance equals the resistance(X C R) and is given by1f notch 2π(R1 )(C1)As such, the twin-T notch filter works by phase cancellation of the input signal. When thephase shift in the two sections is exactly 90 and 90, the tuned frequency is canceledcompletely. Signals passed by the filter will experience some distortion since the twin-Tnotch shifts the phase of low-frequency components ( f notch ) by 90 and high-frequencycomponents (f notch ) by 90. The insertion loss of the filter will depend on the load thatis connected to the output, so the resistors should be of much lower value than the load forminimal loss. The depth and width of the response can be adjusted somewhat with thevalue of R2 and by adding some resistance across the capacitors.Twin-T notch filters can achieve very good suppression at their center frequency.However, the use of precise and tightly matched components is extremely important toyield a deep notch at the required frequency. The depth of the notch is defined as the outputsignal ratio between an out-of-notch component and a component at the notch frequency.In practice, a twin-T notch built with tightly matched components can yield prettygood notch-frequency attenuations. Passive notch filters can be built into small enclosuresand placed between equipment stages. For example, the notch filter of Figure 2.19 wasbuilt inside a Pomona Electronics model 2391 box, which comes with BNC connectors oneach end, making it easy to place it at the input of oscilloscopes and signal recorders.For most practical applications, however, an op-amp needs to be added to the twin-Tnetwork to increase its notch depth as well as to make it insensitive to the impedance of