Sixteen 16-channel multiplexers are used in a data acquisition system as shown in Fig. ex.7.13(a). The 'on' resistance of the switch is 270 Ω the capacitance across the open switch is 1 pF and the output capacitance of each multiplexer is 50 pF. To achieve an accuracy of 0.1% what would be

Question

Sixteen 16-channel multiplexers are used in a data acquisition system as shown in Fig. ex.7.13(a). The 'on' resistance of the switch is 270 Ω the capacitance across the open switch is 1 pF and the output capacitance of each multiplexer is 50 pF. To achieve an accuracy of 0.1% what would be the maximum channel frequency that can be processed with all channels having the same frequency bound? Also calculate the off isolation for the multiplexer at 250 kHz. The access time for each multiplexer is 300 nsec.

Accepted Answer

The delay time is given by

[latex]t_{d}= t_{A} -t_{e}[/latex]

[latex]= 300 imes 10^{-9}-270 imes 50 imes 10^{-12} imes \ln \frac{100-0}{100-(100-0.1)} =207[/latex] nsec

Therefore the total access time

[latex]t_{A}= t_{d} +t_{e}[/latex]

[latex]= 270 imes 10^{-9}+r_{on} imes 16 C_{D(off)} \ln \frac{100-0}{100-(100-0.1)}[/latex]

[latex]=270 imes 10^{-9}+270 imes 16 imes 50 imes 10^{-12} imes 6.9 = 1697[/latex] ns

Therefore the maximum sampling rate per channel is

[latex]\frac{1}{256 imes t_{A} } = \frac{1}{256 imes 1697 imes 10^{-9} } = 2302[/latex]

According to the Nyquist sampling theorem a waveform is fully described by sampling its amplitude at a rate equal to twice the highest frequency present.
Therefore

[latex]2 imes f_{max}= 2302[/latex]

or

[latex]f_{max}= 1151[/latex] Hz

In order to find the off isolation, we consider the circuit shown.

[latex]\frac{V_{out} }{V_{in} } = \frac{\frac{r_{on} imes\frac{1}{j\omega 16 C_{D(off)} } }{r_{on}+\frac{1}{j\omega 16 C_{D(off)}} } }{\frac{1}{j\omega C_{D(off)}}+\frac{r_{on} imes\frac{1}{j\omega 16 C_{D(off)} }}{r_{on}+\frac{1}{j\omega 16 C_{D(off)}}} }[/latex]

[latex]20\log \left|\frac{V_{out}}{V_{in} } ight| =20\log \left|\frac{r_{on}j\omega C_{DS(off)}}{1+j\omega r_{on}[C_{DS(off)}+16C_{D(off)}]} ight| = 20\log r_{on} \omega C_{DS(off)}[/latex]

since

[latex]1\gg \omega r_{on}[C_{DS(off)}+16C_{D(off)}][/latex]

∴ off isolation

[latex]20\log 270 imes 2\pi imes 250 imes 10^{3} imes 1 imes 10^{-12} =-67[/latex] dB

Question 7.13: Sixteen 16-channel multiplexers are used in a data acquisiti...

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