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.

Refer to the ac/dc converter low-pass filter application of Example 8.25. If we put the converter to use powering a calculator, the load current can be modeled by a resistor as shown in Fig. P8.70. The load resistor will affect both the magnitude of the dc component of VOF and the pole frequency. Plot both the pole frequency and the ratio of the 60-Hz component of the output voltage to the dc component of VOF versus RL for 100 Ω ≤ RL ≤ 100 kΩ. Comment on the advisable limitations on RL if (a) the dc component of VOF is to remain within 20% of its 9-V ideal value; (b) the 60-Hz component of VOF remains less than 15% of the dc component. The load resistor will affect both the magnitude of the dc component of VOF and the pole frequency. Plot both the pole frequency and the ratio of the 60-Hz component of the output voltage to the dc component of VOF versus RL for 100 Ω ≤ RL ≤ 100 kΩ. Comment on the advisable limitations on RL if (a) the dc component of VOF is to remain within 20% of its 9-V ideal value; (b) the 60-Hz component of VOF remains less than 15% of the dc component.

Figure P8.70.

Example 8.25:

The ac-dc converter in Fig. 8.59a is designed for use with a handheld calculator. We will ignore the output load for now; it is addressed in Problem 8.70. Ideally, the circuit should convert a 120-V rms sinusoidal voltage to a 9-V dc output. In actuality the output is

v0(t) = 9 + 0.5 sin 377t

Let us use a low-pass filter to reduce the 60-Hz component of v0(t).

SOLUTION

The Thévenin equivalent circuit for the converter is shown in Fig. 8.59b. By placing a capacitor across the output terminals, as shown in Fig. 8.59c, we create a low-pass filter at the output. The transfer function of the filtered converter is

which has a pole at a frequency of f = 1/2πRThC. To obtain significant attenuation at 60 Hz, we choose to place the pole at 6 Hz, yielding the equation

or

A transient simulation of the converter is used to verify performance.

Figure 8.59d shows the output without filtering vo(t), and with filtering, vOF(t). The filter has successfully reduced the unwanted 60-Hz component by a factor of roughly six.

Figure 8.59 Circuits and output plots for ac/dc converter.