Low-pass filter

In this part of the experiment we compare the relative importance of various sources of error: systematic errors due to differences between nominal and actual component values, instrumental errors, random scatter, etc.

$\parbox{2.0in}{\raisebox{-1.4in}{\includegraphics[height=1.4in]{FIGS/fig1.2.ps}}}$ $\parbox{3.5in}{% Wire the circuit shown. The FG and scope should be ... ...ectors (with BNC connectors, the connection to common is automatically made).}$

Measure the input and output amplitudes as a function of frequency, [at least] for the frequencies shown in the table below. An easy way to do this is to set the scope time base so that dozens of cycles appear on the screen. The signals then appear as horizontal bands whose height is a measure of the signal amplitude. The FG output can be adjusted if necessary, to keep the Ch1 amplitude constant. Use an FG amplitude of 5 to $10$V. Express the gain $G=\mbox{$V_{\rm out}$}/\mbox{$V_{\rm in}$}$ in decibels (dB).^1.1

Frequency, $\nu$	log$_{10}(\nu)$	$V_{\rm in}$, V	$V_{\rm out}$, V	$\vert\mbox{$V_{\rm out}$}/\mbox{$V_{\rm in}$}\vert$, dB
10 Hz
30 Hz
100 Hz
300 Hz
1000 Hz
3000 Hz
10 kHz
30 kHz
100 kHz

If you are using a computer program to do your calculations, fill only the two middle columns of the above data table.

Plot the absolute value of the gain, $\vert G\vert$, in dB vs. log frequency. Determine the cutoff frequency and the attenuation slope (in dB/decade) at high frequencies.

Review Simpson, Sec. 2.10. Using the nominal (marked on the component) values of $C$ and $R$, calculate and add to your plot the line representing the expected frequency response of this low-pass filter.

Treat $\tau = RC$ as a parameter and, starting with the initial value given by the nominal component values, fit a theoretical curve to your data. Add this curve to the same plot. Explain any differences observed.