esign and simulate a Butterworth, low-pass Sallen-Key active filter
Just Click on Below Link To Download This Course:
http://bit.ly/2K7CY7g
ECET 350 Topic 1 Lab DeVry
ECET 350 Topic 1 Lab 1 Sallen Key Active Filter Design
Objectives
- Design and simulate a Butterworth, low-pass
Sallen-Key active filter
Tools Needed
- Multisim Software
Introduction
Active filters are key elements in both analog and
digital signal processing. In this lab, you will first design, and using
Multisim, simulate a Butterworth type, Sallen-Key low-pass filter comparing the
design specifications against the simulation. Next, you are to actually
construct the designed Butterworth and test its response measured against the
design specifications, noting any differences between the simulated filter and
the actual filter.
Deliverables
Answer all questions, complete all tables, and paste all
figures and graphs in the Week 1 Lab Cover Sheet here (Links
to an external site.) .
Submit your Week 1 Lab Cover Sheet.
You can also download the Week 1 Cover Sheet for the Week
1 Lab in the Files section of the Course Menu.
Required Software
Multisim and Excel
Lab Steps
STEP 1: Butterworth, Low-Pass Sallen-Key Active Filter Design
In this part, you will design an active
low-pass filter with the following specifications.
Second-order low-pass filter, 3-dB ripple at
the cut-off frequency of 3 kHz, type: Butterworth, circuit topology (VCVS):
low-pass Sallen-Key circuit
The second-order, low-pass prototype for
Butterworth type is given as
HP(s)=Hos2+1.4142s+1HP(s)=Hos2+1.4142s+1where
HoHois DC gain to be determined, and the cut-off frequency
ωC=2π.3000ωC=2π.3000rad/s.
1. Determine the transfer function using
low-pass to low-pass transformation:
s=sωCs=sωC. Include your answer in the Lab cover report and from
the transform function, identify the b0 and b1 coefficients.
H(s)=H(s)=bo=bo=
b1=b1=Choose the second-order, Sallen-Key low-pass filter shown
in Figure 1.
Figure 1: Second-Order, Sallen-Key Low-Pass
Filter
Based on circuit analysis, the circuit
transfer function of the Sallen-Key low-pass filter shown in Figure 1 is given
below.
G(s)=VoutVin=Gbos2+b1s+boG(s)=VoutVin=Gbos2+b1s+boWhere
G=1+R4R3,bo=1R1R2C1C2G=1+R4R3,bo=1R1R2C1C2b1=1R1C2+1R2C2−R4R2R3C1b1=1R1C2+1R2C2−R4R2R3C1To solve for
circuit parameters, one of the solutions could be determined using the
following conditions.
C1=C2=0.01μFC1=C2=0.01μFand
R1=R2R1=R2.
2. By matching coefficients of the
Butterworth filter transfer function,
H(s),H(s),with the Sallen-Key circuit transfer function
,G(s),G(s), the design formulas are found below. Calculate values
for the circuit parameters, and include your answers in the Lab cover report.
R1=R2=√1boC1C2=R1=R2=1boC1C2=For a Butterworth response, the ratio of
R4R3R4R3may be set at 0.586. If R3 is selected to be 10 kΩ,
calculate the value for R4 and copy all calculation and values for R1, R2, R3,
and R4 in the Week 1 Lab cover report.
R1=R2=R3=R4=R1=R2=R3=R4=3. Calculate the theoretical filter gains, and complete
the calculated entries in Table 1 in the Lab cover report for verification.
Note: The pass band ripple, Ap, for this type of Butterworth filter you may
assume is approximately 3 dB.
Ho=G=1+R4R3=G(dB)=20logG=Ho=G=1+R4R3=G(dB)=20logG=ϵ2=10Ap(dB)10−1=ϵ2=10Ap(dB)10−1=MC=Ho√1+ϵ2=MC(dB)=20logMC=MC=Ho1+ϵ2=MC(dB)=20logMC=Roll-off
rate:
RR≅−20N=RR≅−20N=(dB/decade) where N is the order of the filter.
Where
G(dB)G(dB): the filter DC gain
MC(dB)MC(dB): the gain at
ωCωC(radians/sec)
ωCωC: the cut-off frequency
APAP: the passband ripple (dB)
HoHo: the filter passband gain
RRRR: the roll-off rate (dB/decade)
4. Use MultiSim to simulate the designed
Sallen-Key circuit and verify DC gain, gain at the cutoff frequency, and
roll-off rate from the Bode plotter. Copy the Multisim schematic of your
filter, and paste it into the Week 1 Lab cover report. Next, copy the steady
state frequency response from the Bode-plotter, and paste it into the Week 1
Lab cover report, as well.
Complete the measured entries in Table 1 in
the Week 1 Lab cover report.
Note that for the low-pass filters, the estimated
roll-off rate is
RR(dbdecde)=G1(dB)−G2(dB)logf1−logf2=G1(dB)−G2(dB)log(f1f2)RR(dbdecde)=G1(dB)−G2(dB)logf1−logf2=G1(dB)−G2(dB)log(f1f2)where
G1G1at frequency
f1f1and
G2G2at frequency
f2f2are two measured gains beyond the cutoff frequency. You
may also want to modify the Bode output window to record measurements over a
wider range of frequencies and magnitudes.
Figure 2: Multisim Example of Filter Simulation—Values
Are Not Correct for This Lab
Comments
Post a Comment