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Active filter

Weak signals require special attention. The techniques of separating signal from noise vary depending on the nature of the signal and of noise. There are no general easy prescriptions.

When the frequencies of the signal and of the noise differ, one way to increase the signal-to-noise (S/N) ratio is to restrict the bandwidth of the amplifier in such a way that only the signal frequencies are transmitted. This principle is illustrated using an active filter device.

The AF100 universal active filter is a versatile active filter device. It has high-pass (HP), low-pass (LP), and band-pass (BP) outputs simultaneously available and an uncommitted summing amplifier for making notch filters. The centre frequency is tunable from 200 Hz to 10 kHz with two resistors. The quality factor (Q) is variable from 0.01 to 500 by changing two additonal resistors. The AF100 can be used in either an inverting or a non-inverting configuration.

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The pinout and the schematic diagram of an AF100 ar...
..._0 = \frac{50.33 \times 10^6}{R_{\rm f}}, \qquad {\rm in Hz} \end{displaymath}}$

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Wire up the non-inverting mode filter using extern...
...$R_{\rm in} = R_{\rm Q}
= 100$k$\Omega$. Use precision resistors if possible.
}$

These external resistor values should give a centre frequency of $\sim 500$Hz and a Q of slightly greater than unity. Connect the FG output to $R_{\rm in}$ and use the scope in the two-channel mode to observe both the FG output and the bandpass output of the filter. Connect the FG TTL output to the digital counter for a readout of frequency. Set the FG for a 1V peak-to-peak sine wave. Observe the bandpass output as the FG frequency is varied through the centre frequency, $f_0$.

What happens to the bandpass output at $f_0$?

To measure $f_0$ accurately, switch the scope to produce an $xy$-plot (Lissajous figure) of filter output vs. filter input. At the centre frequency the bandpass output should be exactly 180$^\circ$ out of phase with the input signal. Use the Lissajous figure to adjust the FG exactly to the centre frequency (see Experiment 1, and/or Malmstadt p.43 or Brophy p.63, for a discussion of Lissajous figures).

Now switch the scope back to the dual trace mode and measure the peak-to-peak output voltage of the bandpass filter as a function of FG frequency over a range of $20 $Hz to $20 $kHz. Record 10-15 values in this range including several near $f_0$.

Calculate and plot the filter gain in dB vs. log frequency.

From the graph, determine the rolloff rate of the filter in dB/decade, on both sides of $f_0$.5.1 Comment on the values you obtain.

Now connect the scope to the low-pass filter output. Convince yourself that the device acts as a low-pass filter. Accurately measure and record the $3 $dB frequency where gain $G = 0.707 \times G({\rm low frequency})$, and the phase shift at the $3 $dB frequency.

Repeat for the high-pass filter output.

To get a filter with a higher Q, use $R_{\rm in} = 20 $k$\Omega$ and $R_{\rm Q} = 1 $k$\Omega$. Set the FG to give a sine wave with $V_{p-p} \simeq 0.5$V. Observe the bandpass output.

Measure and plot the gain in dB vs. log frequency for the high-Q bandpass filter.

Estimate the Q of the two bandpass filters you have investigated. Q can be measured as the ratio of the centre frequency $f_0$ of the bandpass output to the bandwidth (the difference in frequency between the upper and the lower $3 $dB points).

Return the AF100 to the low-Q state, ( $R_{\rm in} = 100$k$\Omega$, $R_{\rm Q} = 100$k$\Omega$). Vary the feedback resistors and measure the centre frequency of the bandpass output.
    $R_{\rm f1} = R_{\rm f2}$       $f_0$, predicted       $f_0$, measured       % error   
10k$\Omega$      
50k$\Omega$      
200k$\Omega$      
       


next up previous contents
Next: Notch filter Up: Active filters and tuned amplifiers Previous: Active filters and tuned amplifiers

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Last revised: 2007-01-05