In all ΟΤA problems, the specifications are: gm − IABC sensitivity = 20, maximum gm = 1 mS...

In all ΟΤA problems, the specifications are: gm − IABC sensitivity = 20, maximum gm = 1 mS with range of 4 decades.

Referring to Example 8.28, design a notch filter for the tape deck for use in Europe, where power utilities generate at 50 Hz.

Example 8.28:

The circuit in Fig. 8.66a is called a notch filter. From a sketch of its Bode plot in Fig. 8.66b, we see that at the notch frequency, fn, the transfer function gain is zero, while at frequencies above and below fn the gain is unity. Let us design a notch filter to remove an annoying 60-Hz hum from the output voltage of a cassette tape player and generate its Bode plot.

SOLUTION

Figure 8.66c shows a block diagram for the filter implementation. The tape output contains both the desired music and the undesired hum. After filtering, the voltage Vamp will have no 60-Hz component as well as some attenuation at frequencies around 60 Hz. An equivalent circuit for the block diagram including a Thévenin equivalent for the tape deck and an equivalent resistance for the power amp is shown in Fig. 8.66d. Applying voltage division, the transfer function is found to be

After some manipulation, the transfer function can be written as

We see that the transfer function contains two zeros and two poles. Letting .s = jω, the zero frequencies, ωz, are found to be at

Obviously, we would like the zero frequencies to be at 60 Hz. If we arbitrarily choose C = 10 μF, then L = 0.704 mH.

The Bode plot, shown in Fig. 8.66e, confirms that there is in-deed zero transmission at 60 Hz.

Figure 8.66 Circuits and Bode plots for 60-Hz notch filter.