Download OP-AMP Filter Examples

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.
Vin
Vout
Vin
Vout
R2
R2
9K
9K
C1
C2
0.1uF
0.1uF
R1
R1
1K
1K
GND
Non-Inverting Amp
Low Pass Filter
GND
Gain (db)
Gain (db)
20
20
Non-Inverting Amp
High Pass Filter
0
0
Freq (Hz)
177
1.77K
Freq (Hz)
1.6K
16K
High and low pass filters can be made by adding capacitors to inverting amplifiers as well.
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.
C2
0.1uF
R2
R2
10K
10K
R1
C1
.
Vin
Vout
1K
R1
.
Vin
0.1uF
Vout
1K
GND
GND
Gain (db)
Gain (db)
Inverting Amp
Low Pass Filter
20
0
Freq (Hz)
160
1.6K
Inverting Amp
High Pass Filter
20
Freq (Hz)
0
160
1.6K
The low pass and high pass filter can be combined into a band pass filter. In the examples below the
corner frequencies were chosen to be the audio band (20Hz – 20KHz). Notice the difference in the gain
outside of the pass band. The gain of the inverting amplifier continues to drop as you get farther away
from the pass band. The gain of the non-inverting amplifier only drops to 1 (0db).
C2
Vin
Vout
80pF
Inverting Amp
Band Pass Filter
R2
R2
100K
9K
C1
R1
C2
.
Vin
0.8uF
Vout
10K
0.9nF
C1
8uF
GND
Non-Inverting Amp
Band Pass Filter
R1
1K
Gain (db)
GND
Gain of 10 in audio band
Gain (db)
20
20
Freq (Hz)
0
0
2
20K
20
200K
20K
20
2
200K
Freq (Hz)
Gain of 10 in audio band
Each gain stage can be combined with another for a larger gain and a steeper roll-off of the frequency.
C2
C4
80pF
80pF
R2
R4
100K
C1
100K
R1
C3
.
Vin
0.8uF
R3
.
10K
0.8uF
Vout
10K
GND
GND
Gain of 100 in audio band
Gain (db)
40
20
Freq (Hz)
0
2
20
20K
200K