1.2.1.1 Low-Pass Frequency Scaling Procedure
1.0 Application Notes (Continued)
The actual component values represented in bold of Figure 5
were obtained with the following scaling procedure:
1. First determine the frequency scaling factor (FSF) for
the desired cutoff frequency. Choosing fc at 3 kHz, pro-
vides the following FSF computation:
3
=
=
FSF 2π x 3 kHz (desired cutoff freq.) 18.84 x 10
2. Then divide all of the normalized capacitor values by the
FSF as follows:
=
C1’
C(Normalized)/FSF
3
3
−6
−6
=
=
=
C1’ 0.707/18.84 x 10
37.93 x 10
75.05 x 10
=
C2’ 1.414/18.84 x 10
(C1’ and C2’: prior to impedance scaling)
3. Last, choose an impedance scaling factor (Z). This Z
factor can be calculated from a standard value for C2.
Then Z can be used to determine the remaining compo-
nent values as follows:
−6
=
=
=
Z
C2’/C2(chosen) 75.05 x 10 /6.8 nF 8.4k
−6
=
=
=
C1 C1’/Z 37.93 x 10 /8.4k 4.52 nF
(Standard capacitor value chosen for C1 is 4.7 nF )
=
=
=
R1 R1(normalized) x Z 1Ω x 8.4k 8.4 kΩ
=
=
=
R2 R2(normalized) x Z 1Ω x 8.4k 8.4 kΩ
DS012830-47
(Standard value chosen for R1 and R2 is 8.45 kΩ )
FIGURE 4. THD+Noise Performance of LMC6035 and
“Benchmark” per Circuit of Figure 1
1.2.2 High Pass Active Filter
Figure 4 shows the superior distortion performance of
LMC6035/6 over that of the benchmark op amp. The heavy
loading of the circuit causes the AVOL of the benchmark part
to drop significantly which causes increased distortion.
The previous low-pass filter circuit of Figure 5 converts to a
high-pass active filter per Figure 6.
1.2 APPLICATION CIRCUITS
1.2.1 Low-Pass Active Filter
A common application for low voltage systems would be ac-
tive filters, in cordless and cellular phones for example. The
ultra low input currents (IIN) of the LMC6035/6 makes it well
suited for low power active filter applications, because it al-
lows the use of higher resistor values and lower capacitor
values. This reduces power consumption and space.
DS012830-49
Figure 5 shows a low pass, active filter with a Butterworth
(maximally flat) frequency response. Its topology is a Sallen
and Key filter with unity gain. Note the normalized compo-
nent values in parenthesis which are obtainable from stan-
dard filter design handbooks. These values provide a 1 Hz
cutoff frequency, but they can be easily scaled for a desired
cutoff frequency (fc). The bold component values of Figure 5
provide a cutoff frequency of 3 kHz. An example of the scal-
ing procedure follows Figure 5.
FIGURE 6. 2 Pole, 300 Hz, Sallen and Key,
High-Pass Filter
1.2.2.1 High-Pass Frequency Scaling Procedure
Choose a standard capacitor value and scale the imped-
ances in the circuit according to the desired cutoff frequency
(300 Hz) as follows:
=
=
=
=
C
Z
C1 C2
1 Farad/C(chosen) x 2π x (desired cutoff freq.)
=
1 Farad/6.8 nF x 2π x 300 Hz 78.05k
=
=
=
R1 Z x R1(normalized) 78.05k x (1/0.707) 110.4 kΩ
(Standard value chosen for R1 is 110 kΩ )
=
=
=
R2 Z x R2(normalized) 78.05k x (1/1.414) 55.2 kΩ
(Standard value chosen for R1 is 54.9 kΩ )
1.2.3 Dual Amplifier Bandpass Filter
The dual amplifier bandpass (DABP) filter features the ability
to independently adjust fc and Q. In most other bandpass to-
pologies, the fc and Q adjustments interact with each other.
The DABP filter also offers both low sensitivity to component
values and high Qs. The following application of Figure 7,
provides a 1 kHz center frequency and a Q of 100.
DS012830-48
FIGURE 5. 2-Pole, 3 kHz, Active, Sallen and Key,
Lowpass Filter with Butterworth Response
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