*Sallen-Key Low-Pass Filter*
CIRCUIT
OPSALKEY1.CIR
Download the
SPICE file
Suppose you had a large interfering signal you needed
to get rid of. To get lots of attenuation, you could cascade several RC
filters. Unfortunately, the impedance of one RC section affects the next.
This means that the “knee” or transition between the pass and stop bands
won’t be very sharp. A sharp knee helps you reduce the interfering signal
without degrading your desired signals. In this situation, the Sallen-Key
active filter can save the day. This circuit implements a 2-pole filter.
Cascading several stages can give you a steep attenuation curve with a very
sharp knee.
LOW-PASS FILTER DESIGN
Although there are many filter types and ways to
implement them, here’s an active low-pass filter that’s greatly simplified
if R1=R2 and the op amp stage is a unity gain follower (RB=short and
RA=open). Designing a 2-pole Butterworth filter requires just a few steps.
1. Choose a cutoff frequency fo (Hz).
As an example, select fo=10 kHz to reduce a noise
signal at 50 kHz and pass your desired signals below 5 kHz.
2. Pick a convenient cap value C2 between 100pF and 0.1
uF.
Suppose you’ve got plenty of 1000pF caps in stock,
select this value for C2.
3. Make C1 = 2 x C2
C1 = 2 · C2 =
2000pF
4. Calculate R1 = R2 = 0.707 / (2
·
π · fo
· C2)
R1 = R2 = 0.707 / (2 ·
π
· 10kHz ·
1000pF) = 11.2 K ohms
CIRCUIT ANALYSIS
Take the Sallen-Key for a test drive and watch the frequency
response at the output V(5). To get a better view of the attenuation past
10kHz, change the Y axis to a log scale. How fast does the curve decrease as
the frequency increases by a factor of 10?
Just how much of an advantage does a 2-pole filter have
over a single pole filter? There’s a simple RC filter (R10,C10) in the SPICE
file for comparison. Both filters have a cutoff frequency of 10kHz. Add the
output of the simple RC filter V(10) to your plot. Is there a difference in
the attenuation of the stop bands? Another advantage of the active filter is
that the knee hasn’t lost its sharpness.
HANDS-ON DESIGN
Pick a different cutoff frequency for a low pass filter. Design
your new filter and take a look at the output V(5).
FILTER LIMITS
In theory, the response in the stop band should keep
decreasing as frequency increases. Instead, the response actually will begin
rising again at some high frequency. Why? A properly functioning op amp is
essential to the filter’s operation. However, real world op amps lose voltage
gain at some frequency due to their finite bandwidth.
CIRCUIT INSIGHT
Extend the frequency range of the analysis to 100 MHz via the
command
.AC 10 100
100MEG
At what frequency does the curve depart from the ideal?
This should be near the Gain Bandwidth Product GBP of the op amp.
HIGH-PASS FILTERS
HANDS-ON DESIGN
Its easy to convert a Sallen-Key low-pass filter to a high-pass
filter. Just swap the resistor and capacitor locations – R1 with C1 and R2
with C2. Here are the components with the exchanged node numbers.
R1
3 0 11.2K
R2 2 5 11.2K
C2 2 3 1NF
C1 1 2 2NF
Try out the high-pass circuit and plot the output V(5).
Essentially, this response should be a mirror image of the low-pass flipped
about the cutoff frequency. Again, due to the finite bandwidth of the op amp,
the response is the pass-band (ideally flat) takes a nose dive beyond the
GBP.
SINGLE POLE FILTER
If you need less attenuation in the stop band, try a
single-pole RC low-pass filter with op amp buffer.
SIMULATION NOTE
To create a unity gain amplifier with XOP1, the circuit
requires RB = (short circuit) and RA = (open circuit). To do this, the
resistors were given small and large like RB=10 ohms and RA = 100MEG.
Another way to open or remove a component is to place a "*" in the beginning
of the statement. SPICE ignores these statements.
Be careful of using resistor values covering large
ranges in the same circuit such as 1 Pico (1e-12) ohm and 1 Tera (1e+12)
ohm. The computation required may be beyond the mathematical precision of
the computer. To be safe, a range spanning 12 decades (say 1ohm to 1 Giga
ohm) should be safe for double precision math.
SPICE FILE
Download the file
or copy this netlist into a text file with the *.cir
extention.
OPSALKEY1.CIR - OPAMP SALLEN-KEY LOW-PASS FILTER
* 2ND-ORDER BUTTERWORTH
*
VS 1 0 AC 1
*
R1 1 2 11.2K
R2 2 3 11.2K
C1 2 5 2000PF
C2 3 0 1000PF
*
* UNITY GAIN AMPLIFIER, RA=OPEN, RB=SHORT
RA 4 0 100MEG
RB 4 5 1
XOP 3 4 5 OPAMP1
*
* SINGLE RC FILTER FOR COMPARISON
R10 1 10 15.9K
C10 10 0 1000PF
*
* OPAMP MACRO MODEL, SINGLE-POLE
* connections: non-inverting input
* | inverting input
* | | output
* | | |
.SUBCKT OPAMP1 1 2 6
* INPUT IMPEDANCE
RIN 1 2 10MEG
* DC GAIN (100K) AND POLE 1 (100HZ)
* GBWP = 10MHz
EGAIN 3 0 1 2 100K
RP1 3 4 1K
CP1 4 0 1.5915UF
* OUTPUT BUFFER AND RESISTANCE
EBUFFER 5 0 4 0 1
ROUT 5 6 10
.ENDS
*
* ANALYSIS
.AC DEC 10 100 1MEG
* VIEW RESULTS
.PLOT AC V(5)
.PROBE
.END
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