17-08-2013, 05:02 PM
OP-AMP Filter
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OP-AMP Filter Examples:
The two examples below show how adding a capacitor can change a non-inverting amplifiers frequency
response. If the capacitor is removed you're left with a standard non-inverting amplifier with a gain of 10
(1 + R2/R1). Recall that the capacitors impedance depends on frequency (Xc = 1/(2πfC)) and the corner
frequency of an RC filter is fc = 1/(2πRC).
In first circuit the capacitor is placed in parallel with the feedback resistor (R2). At low frequencies
(f << fc) the capacitors impedance (Xc) is much greater than R2 and therefore the parallel combination of
R2 & Xc is about R2 (i.e. R2| Xc = R2 when f << fc ). As frequency increases towards the corner
frequency the impedance of the capacitor decreases and becomes comparable to that of the resistor. This
lowers the impedance of the parallel combination of R2 & Xc and therefore the gain begins decreasing.
When f >> fc, R2| Xc = Xc causing the gain to drop. In this case the gain bottoms out at one since the
gain equation is 1 + R2/R1.
The second circuit has the capacitor in series with R1. When f << fc the capacitors reactance is large and
R1 + Xc = Xc. Therefore the gain is 1 + R2/ Xc which = 1 when Xc >> R2. When f >> fc the capacitors
reactance is small and R1 + Xc = R1. Therefore the gain is 1 + R2/ R1 which = 10 when Xc << R1.
The first circuit is a low pass filter. At low frequencies the capacitors impedance is high, much higher
than R2, and therefore doesn't affect the circuit (XC|R2 = R2). At high frequencies the capacitors
impedance is low, much lower than R2, and therefore limits the impedance of the parallel combination
(XC|R2 = XC). Since the gain equation for a non-inverting amp is –R2/R1 the gain doesn't bottom out at
one. The gain continues to decrease as frequency increases beyond the cutoff frequency.
The second circuit is a high pass filter. At low frequencies (below the cutoff frequency) the capacitors
impedance is high, much higher than R1, and therefore R1 + XC = XC. The gain is therefore R2/XC. At
high frequencies the capacitors impedance is low, much lower than R1, and therefore R1 + XC = R1. The
gain is therefore R2/R1.