廬
APPLICATION BULLETIN
DESIGNING ACTIVE FILTERS WITH
THE DIAMOND TRANSISTOR OPA660
Part 1
By Christian Henn and Klaus Lehman, Burr-Brown International GmbH
Mailing Address: PO Box 11400 鈥?Tucson, AZ 85734 鈥?Street Address: 6730 S. Tucson Blvd. 鈥?Tucson, AZ 85706
Tel: (602) 746-1111 鈥?Twx: 910-952-111 鈥?Telex: 066-6491 鈥?FAX (602) 889-1510 鈥?Immediate Product Info: (800) 548-6132
Signal frequency bandwidth limitation, fast pulse shaping,
separation between telecommunications signals, and sup-
pression of unwanted carrier and disturbance frequencies are
among the most important jobs of filter circuits. While
active filters with operational amplifiers and switched ca-
pacitor filters are used for lower frequency applications,
passive filter versions dominate the application spectrum at
frequencies above 5MHz. Now, however, a new active filter
design has been developed that makes use of the open loop
pole and delay time of an operational amplifier. The filter
circuits consist of OPA660s, which provide the necessary
bandwidth and allow access to the first open-loop pole and
internal amplifier delay time. After presenting an overview
of conventional filter circuits using 2nd, 3rd, and 5th order
active filters with Tschebyscheff approximation, this Appli-
cation Note will discuss the new filter structure in detail.
The filter circuits presented in Part One are optimized for the
minimum possible number of components, while the filter
circuits that will be analyzed in Part Two require more
components, and board space, but are optimized for easy
adjustment of the important filter parameters.
1.0
2ND ORDER LOW-PASS FILTER
USING OPERATIONAL AMPLIFIERS
1.1
2nd Order Low-Pass Filter
With An Ideal Op Amp
Figure 1 shows a classical example of an active 2nd order
low-pass filter designed using an op amp. In this example,
the op amp, IOPA, is assumed to be ideal.
Equation 1 can be derived from Figure 1 and describes the
filter transfer function. In the following analyses, all param-
eters are assumed to be normalized to the 鈥?dB frequency,
蠅
g
, at which the amplitude |A
I
| is reduced to 鈥?dB. When
normalized to the 鈥?dB frequency, Equation 1 becomes
Equation 2. Technical literature about passive filters com-
monly uses the coefficients a
I
and b
I
(or a
1
or b
1
). Equation
3 is the result of comparing these coefficients and shows
their relation to the circuit parameters
蟿
1
and
蟿
2
. The coeffi-
cients
蠅
0i
(or
蠅
01
) and Q
i
(or Q
1
) are easier to calculate and
explain using circuit elements. Equation 4 shows these
coefficients and those of a
I
and b
I
(or a
1
and b
1
).
A
I
=
1
+
j蠅 鈥?/div>
(
2蟿
1
)
+
(
j蠅
)
鈥?/div>
(
蟿
1
蟿
2
)
2
[
]
鈥?
(1)
錚?/div>
錚?/div>
錚?/div>
錚?/div>
鈥?
2
錚?/div>
錚?蠅錚?/div>
蠅
2
A
I
= 錚?/div>
1
+
j
鈥?2蟿
1
蠅
g
+ 錚?/div>
j
錚?/div>
鈥?/div>
蟿
1
蟿
2
蠅
g
錚?/div>
蠅
g
錚?蠅
g
錚?/div>
錚?/div>
(
)
(
)
(2)
2
錚?/div>
錚?/div>
錚?蠅錚?/div>
蠅
錚?/div>
A
I
= 錚?/div>
1
+
j
鈥?a
1
+ 錚?/div>
j
錚?/div>
鈥?b
1
錚?/div>
錚?/div>
蠅
g
錚?蠅
g
錚?/div>
錚?/div>
錚?/div>
鈥?
(3)
錚?/div>
錚?/div>
2
錚?/div>
(4)
錚?/div>
錚?/div>
鈥?
2
錚?/div>
錚?蠅錚?/div>
蠅
1
1
A
I
= 錚?/div>
1
+
j
鈥?/div>
+錚?/div>
j
錚?/div>
鈥?/div>
錚?/div>
蠅
g
Q
1
蠅
01
/
蠅
g
錚?蠅
g
錚?/div>
蠅
01
/
蠅
g
錚?/div>
錚?/div>
(
)
(
)
These equations can be rearranged, resulting in:
a
1
=
2蟿
1
蠅
g
=
Q
1
蠅
01
/
蠅
g
(
1
)
; b
1
= 蟿
1
蟿
2
蠅
g 2
=
(
蠅
1
01
(5)
/
蠅
g
)
2
Rearranging Equation 5 gives dimensioning rules for the
active filter circuit shown in Figure 1:
C
1
R
2
V
IN
IOPA
C
2
V
OUT
I
A
I
= V
OUT
/ V
IN
I
R
1
蟿
1
=
2Q
1
蠅
01
/
蠅
g
蠅
g
(
1
)
;
蟿
2
=
(
蠅
2Q
1
01
/
蠅
g
蠅
g
)
(6)
The values for Q
i
and
蠅
01
/蠅
g
= f
01
/f
g
can be found in Tables
I to V for the various passband ripple specs and for filter
orders from 1 to 4.
FIGURE 1. 2nd Order Low-Pass Filter Using an Ideal Op
Amp.
漏
1994 Burr-Brown Corporation
AB-190
Printed in U.S.A.February, 1994
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