8.5. Amplification 493
8.4.B HighPassFilter
The CR differentiator circuit shown in Fig.8.3.4(a) is a high pass filter. Its output
voltage is given by
Vout=Vin2 πRC
√
1+(2πfRC)^2, (8.4.5)
where, as before,Vinis the input voltage andfis the input signal frequency. Let us
write this relation in terms of the decibel notation by first taking base-10 logarithm
of both sides and multiplying by 2. This gives
2log(
Vout
Vin)
=2log[
2 πfRC
√
1+(2πfRC)^2]
=2log[
1
√
1+1/(2πfRC)^2]
. (8.4.6)
This relation shows that the response of the system is inversely proportional to
the logarithm of the frequency. As in the case of the low pass filter, substituting
f=1/ 2 πRCin this relation gives
2log(
Vout
Vin)
=− 3 dB. (8.4.7)This frequency at which the response is -3dBis called the cutoff frequency or
the breakpoint. Below this frequency the attenuation becomes high and increases
rapidly at a rate of 6dBper octave of frequency change. The circuit can therefore
be said to effectively block the low frequencies. At frequencies much higher than the
cutoff value the second term in the denominator of the right hand side of equation
8.4.6 can be neglected, giving
2log(
Vout
Vin)
≈ 2log(1) = 0⇒Vout ≈ Vin.This shows that for frequencies much higher than the breakpoint, the output voltage
of the CR filter is approximately equal the voltage at its input.
8.4.C BandPassFilter
A band pass filter can be constructed by connecting a low pass filter with a high
pass filter in series as shown in Fig.8.4.2(a). A realistic RC-CR band pass filter is
shown in Fig.8.4.2(b). The values of the individual resistances and capacitances can
be chosen according to the cutoff frequency requirements. It should be noted that
here there will be two cutoff frequencies or breakpoints corresponding to the low
and high pass filters.
8.5 Amplification
The two main purposes of the preamplifiers we discussed earlier are to amplify the
low level signal as it comes out of the detector and to match the detector and