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Characterizing Two Analog Op Amp Filters
Using LabView of National Instruments or VEE
of Hewlett Packard
Ralph and Rachel Rosenbaum and Avraham Semenkee
Computer and Electronics Laboratories
School of Physics and Astronomy
Shenkar Building, Room 301
Ramat Aviv 69978
Useful book reference: Operational Amplifiers and Linear
Integrated Circuits by Robert F. Coughlin
and Frederick F. Driscoll, pages 265 thru 271
and Appendix 1, pages 329 thru 337
Introduction
In class we have discussed band pass filters designed to pass signals only in a
certain band of frequencies centered about a resonant frequency fr while rejecting all
signals outside this band as illustrated below. We can either build the band pass filter
using digital signal processing DSP techniques or reverting back of op amps, resistors
and capacitors. Both techniques work well and have their advantages and
disadvantages. In this lab, we will “solder together” the circuit using standard
components, which give us the opportunity to learn soldering techniques and the
satisfaction of testing a circuit. The band pass circuit is shown below. We will measure
its frequency response using either LabView or VEE software for data acquisition.
In class we also discussed the notch filter in which undesired frequencies are
attenuated in the “stop band” centered about the resonant frequency fr. For example, it
may be necessary to attenuate a 50 Hz or 400 Hz noise signals induced in a circuit by
motor generators. The circuit diagram and frequency response are shown below.
Vin
Vout
Circuit Diagram for Band Pass Filter
Low 0
Hi
Frequency Response for Band Pass Filter
Theoretical Predictions for the Band Pass Filter
In a home work problem, we derived the output response of the band pass
filter as a function of frequency. Referring to the above circuit diagram, we found:
Vout/Vin = 1/{2R1/R2 + j[2R1Cf – (R1 + R3)/(2R2R3Cf)]
.
(1)
The magnitude is:
Vout/Vin = 1/{[2R1/R2]2 + [2R1Cf – (R1 + R3)/(2R2R3Cf)]2}1/2 .
(2)
By setting the imaginary part to zero, we find the resonant frequency fr where the
band pass filter has its peak output Ar:
Vout/Vinmax = Ar = R2/2R1 at
(3)
fr = [1/(2C)]*[(R1 + R3)/(R1R2R3)]1/2
.
(4)
Note: In the definition of the “Q” of the circuit, we can use either frequency f
(cycles/sec = Hz) or angular frequency  (radians/sec). In using the expressions
presented by Coughlin and Discoll, we must define the bandwidth B in angular
frequency! Thus, we must convert our specified resonant frequency fr to a resonant
angular frequency r = 2fr. The “Q” is defined as (you specify its value, say 20):
Q = fr/B = fr/(fHi - fLow) = r/(Hi - Low)
Then,
.
(5)
B = band pass = r/Q = 2fr/Q
and
(6)
R2 = 2/(BC)
and
(7)
R1 = R2/2Ar ,
(8)
where you specify the amplification Ar at the resonance frequency fr to be, say,
typically 20. Finally,
R3 = R2/(4Q2 – 2Ar) .
Equation (9) is really a disguised version of Equation (4) !!
If you choose C1 = C2 = C = 0.01 uF and if you choose a typical audio
frequency of 1590 Hz for fr, then typical values for the resistors are R2 = 400 k,
R1 = 5 k and R3 = 263 .
(9)
Theoretical Predictions for the Notch Filter
In an exam problem, we derived the output response of the notch filter as a
function of frequency. Referring to the circuit diagram
Vdiv
Vin
Vout
Circuit Diagram for Notch Filter
Frequency Response for Notch Filter
we found:
Vout = Vdiv – (Vin – Vdiv)/{2R1/R2 + j[2R1Cf – 1/(2R2Cf)]} ,
(10)
or as a magnitude:
Vout= Vdiv – (Vin – Vdiv)/{[2R1/R2]2 + [2R1Cf – 1/(2R2Cf)]2}1/2 .
(11)
Again the “notch” or huge attenuation will occur at the resonance frequency fr
where the imaginary part of Equation 10 vanishes, namely at
fr = [1/(2C)]* 1/(R1R2)1/2
.
(12)
If we want perfect attenuation, namely Vout= 0, then we have to set Vdiv to this
value:
Vdiv = Vin/(2R1/R2 + 1)
.
(13)
Remember we can set Vdiv to any value we wish by simply adjusting the variable
potentiometer resistor Rb in relation to resistor Ra. Namely,
Vdiv = VinRb/(Ra + Rb)
.
(14)
According to Coughlin and Discoll, here are the design equations:
Choose the notch resonance frequency fr and calculate the equivalent angular
resonance frequency r = 2fr. Say fr = 400 Hz is the interfering frequency, then r =
2fr = 2512 radians/sec. Select a “Q” of say 10. Then the bandwidth B becomes:
B = r/ Q = 251.2 radians/sec .
(15)
Calculate R2 using C1 = C2 = C = 0.01 uF:
Calculate R1 using:
R2 = 2/(BC) = 796 k
.
(16)
R1 = R2/(4Q2) = 1990 
.
(17)
Choose a convenient value for Ra, say 1 k and use this expression for Rb:
Rb = 2Q2Ra = 200 k .
(18)
The Experiments
Build either the band pass or notch filter using the 741 op amp, resistors and
capacitors and printed circuit board and a DIP socket holder for the op amp. Avraham
will give you the components and help you. Remember to connect up both the plus
and negative power supplies to the op amp. Check the frequency response manually
to see if you get the “peak” or the “notch” at your design resonance frequency fr. If
successfully, try to program the function generator together with the DMM in its ac
voltage mode (using LabView or VEE) to obtain the computerized frequency
response curve of your circuit. You might also try to determine the magnitude of the
band width B and compare it to the theoretical value.