The ac-dc converter in Fig. 12.74a is designed for use with a hand-held calculator. Ideally, the circuit should convert a 120-V rms sinusoidal voltage to a 9-V dc output. In actuality the output is
$v_{o}(t)=9+0.5 \sin 377 t \mathrm{~V}$

Let us use a low-pass filter to reduce the 60-Hz component of $v_{o}(t)$ .

Question

The ac-dc converter in Fig. 12.74a is designed for use with a hand-held calculator. Ideally, the circuit should convert a 120-V rms sinusoidal voltage to a 9-V dc output. In actuality the output is

[latex]v_{o}(t)=9+0.5 \sin 377 t \mathrm{~V}[/latex]

Let us use a low-pass filter to reduce the 60-Hz component of [latex]v_{o}(t)[/latex].

Accepted Answer

The Thévenin equivalent circuit for the converter is shown in Fig. 12.74b. By placing a capacitor across the output terminals, as shown in Fig. 12.74c, we create a low-pass filter at the output. The transfer function of the filtered converter is

[latex]\frac{\mathbf{V}_{\mathrm{OF}}}{\mathbf{V}_{\mathrm{Th}}}=\frac{1}{1+s R_{\mathrm{Th}} C}[/latex]

which has a pole at a frequency of [latex]f=1 / 2 \pi R_{\mathrm{Th}} C[/latex]. To obtain significant attenuation at 60 Hz, we choose to place the pole at 6 Hz, yielding the equation

[latex]\frac{1}{2 \pi R_{\mathrm{Th}} C}=6[/latex]

or

[latex]C=53.05 \mu \mathrm{F}[/latex]

A transient simulation of the converter is used to verify performance.
Figure 12.74d shows the output without filtering, [latex]v_{o}(t)[/latex], and with filtering, [latex]v_{\mathrm{OF}}(t)[/latex]. The filter has successfully reduced the unwanted 60-Hz component by a factor of roughly six.

Question 12.35: The ac-dc converter in Fig. 12.74a is designed for use with ...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions