AF100-1CN ,+/-18 V, 900 mW, universal active filterFeatures
I Military or commercial specifications
I Independent a, frequency, gain adjustments ..
AF151-1CJ ,DUAL UNIVERSAL ACTIVE FILTERFeatures
I Independent Q, frequency and gain adjustment
I Very low sensitivity to external co ..
AF216M245001-T , CHIP ANTENNA
AF216M245001-T , CHIP ANTENNA
AF2302N , 20V N-Channel Enhancement Mode MOSFET
AF2302NWLA , 20V N-Channel Enhancement Mode MOSFET
AM2965DC , Octal Dynamic Memory Drivers with Three-State Outputs
AM2965DC , Octal Dynamic Memory Drivers with Three-State Outputs
AM2965JC , Octal Dynamic Memory Drivers with Three-State Outputs
AM29853APC , PARITY BUS TRANSCEIVERS
AM29862DC , High Performance Bus Transceivers
AM29864DC , High Performance Bus Transceivers
AF100-1CN
+/-18 V, 900 mW, universal active filter
_ National
, Semiconductor
AF100 Universe! Active Filte
General Description
The AF1OO state variable active filter is a general second
order lumped RC network. Orgy four extemat resistors pro-
gram the AF100 for spaciiic second order functions. Low-
pass, highpass, and bandpass functions are available simul-
taneously at separate outputs. Notch and allpass functions
are available by summing the outputs in the uncommitted
output summing amplifier. Higher order systems are realized
by cascading AF100 active filters with appropriate program-
ming resistors.
Any of the classical filter configurations, such as Butter-
worth, Bessel, Cauer, and Chebyshev can be formed.
Features
a Military or commercial speWicatlons
D Independent o, frequency. gain adjustments
I: Low sensitivity to external component variation
u Separate lowpass, highpass, bandpass outputs
" Inputs may be diftertmtial, inverting, or non-inverting
u Allpass and notch outputs may be formed using uncom-
mitted amplifier
n Operates to 10 kHz
n a range to 500
a Power supply range
I: Frequency accuracy
I: Q frequency product $50,000
iSV to i18V
i 1% unadjusted
Connection Diagrams
Ceramic DttttlArt-Llrte Package
no no moms AMP AMP
Pm PIN m1 outrut -v 0mm -mpur Gtl0
Its l,, " " 12 ll 10 9
"-ll-o
1000pF
-ctit- -<)i
w. 1000p?
ylo? "
, l 3 I4 5 s 7 la
NPUT um mums " LOWPASS "P mt: uo
OUTPUT OUIPUI omrut Pm
TL/K110111-1
Top Vlew
Order Number AF100-1CJ or AF100-20J
See NS Package Number HY13A
Metal Can Package
TL/KM01t1-3
Plastic Dual-ln-Llne Package
W185 MASS
INTI oumn oumrr ' . . mm INPUT
" " " l,, l,, In 10 '
H, vv-
Ewoopr j
---it? took"
- k-ai;;
ll 2 3 4 5 Is 1 s
-v AMP AM? can AMP " mu LOW'PASS
mm -INPUT ou‘mn tl0WO1
TUK/10111-2
mot... Internally connected. Do not use.
Top Vlew
Order Number AF80th1CN or AF100-2CN
See NS Package Number N16A
Order Number AF1DO-1CJ, AF100-1G, AFtoo-ZCG or
AF1oo-28
See NS Package Number H123
Absolute Maximum Ratings
If Mllltary/Aerospace speclfled devlces are required,
please contact the National Semiconductor Sales
ofmtttfDistributttra for avallablllty and spetMeatlona.
Supply Voltage * 18V
Power Dissipation 900 mW/Package
(500 mW/Amp)
Differe n1ial Input Voltage * 36V
Output Short Circuit Duration (Note 1) Infinite
Lead Temperature (Soldering, 10 sec.) 300°C
Operating Temperature
AF1oo-1CJ, AF100-20J.
AF100-1CG, AF100-2CG,
AF100-ICN, AF100-2CN
AF100-1G, AF100-2G
Storage Temperature
AF100-1 G, AF100-26
AF100-ICG, AF1 00-2CG.
AF100-1CJ. AF100-20J,
AF100-1CN. AF100-2CN
Electrical Characteristics (Complete Active Filter) (Note 2)
- 25°C to + 85°C
- 55°C to +125°C
-65°C to + 125''C
- 25"C to + 100°C
Parameter Conditions Min Typ Max Unlts
Frequency Range to M Q g 50,000 10k Hz
Q Range tc x Q tg 50,000 500 Hz/Hz
to Accuracy
AF100-1, AF100-IC tc x Q 3 10,000, TA = 25''C 12.5 %
AF100-2, AF100-2C fc x Q s 10,000, TA = 25°C 1 1.0
fo Temperature Coefficient i 50 * 150 ppmf'C
Q Accuracy 10 M Q s 10,000 TA = 25''C 17.5 %
Q Temperature Coefficient i 300 i 750 ppmf'C
Power Supply Current vs = 115v 2.5 4.5 ' mA
Electrical Characteristics (Internal Op Amp) (Note 3)
Parameter Conditions Min Typ Max Units
Input Offset Voltage Rs S 10 kn 1.0 6.0 mV
Input Offset Current 4 50 nA
Input Bias Current 30 200 nA
Input Resistance 2.5 Mn
Large Signal Voltage Gain 53:12: d: my 25 160 V lmV
Output Voltage Swing RL = 10 kn i 12 i 14 V
BL = 2 kn i 10 l 13
Input Voltage Range , 12 V
Common Mode Rejection Ratio Rs s; 10 kn 70 90 dB
Supply Voltage Rejection Ratio Rs s; 10 kn 77 96 dB
Output Short Circuit Current 25 mA
Slew Rate (Unity Gain) 0.6 Nlps
Small Signal Bandwidth 1 MHz
Phase Margin 60 Degrees
Note t: Any of the amplitiers can be shorted to ground indefinitely, however more than one should not be tgrttultamrously shorted as the maximum junction
temperature will be exceeded.
Note 2: Specifications apply for Vs = t151t, ova! -25T to + 65'C for the AF100-1C and AF100-ZC and over -5tPC to +125'C for the AF100-1 and AF100-2,
unless otherwise smrdfie0.
Note 3: Spstyraatiorts apply for Vs = i15V, TA = 25'C.
Application Information
HIGHPASS BANDPASS LWASS AMP IN-
9 o o o ['.
'-.--1-°b---- o--. ------------ ----------. "''"-
- mp0",
'- --------- .
TL/k/lol'
FIGURE I, AF100 Schematlc
CIRCUIT DESCRIPTION AND OPERATION If the output is taken from the output of A3, numerator coef-
Aschematic of the AF100 is shown in Figure f. Amplifier A1 ticients aa and att equal zero and the transfer function be"
is a summing amplifier with inputs from integrator A2 to the comes:
non-inverting input and integrator M to the inverting input. T - a1
Amplifier A4 is an uncommitted amplifier. (s) - (Iowpass)
By adding external resistors the circuit can be used to gen- 82 + Tf s + od?
erate the second order tsystem Using proper input and output connections the circuit can
T(s) = !tsi.t..'.r+aat_s'a1 also he used to generate the transter functions tor a notch
s2 + bas + b1 and allpass filter. .
The denominator coefficients determine the complex pole In the transfer function for a notch function att becomes
pair location and the quality of the poles where zero, a1 equals 1, and a3 equals (022. The transfer function
me --- Jrii Tat the radian centerfrequency ttttttttttttts:
CDO - s2 + (922
Q = - = the quality of the complex pole pair Tts) - (notch)
b2 52 + S?. s + (no?
If the output is taken from the output ot A1, numerator coef- Q
ficients a1 and a2 equal zero, and the transfer function be- In the allpass transfer function tll = l, a2 = --oo/Q and
comes: 83 = woe. The transfer function becomes:
T(s)= tlas s2--f-l?s+ama
(hi h ass)
s2 + PPs + of g p T(s) = -.----- (allpass)
. $2 + -- s + c002
It the output l8 taken from the output of A2, numerator ooet- Q
ticients a1 and M equal zero and the transfer function be-
comes: COMMON CONFIGURATIONS
The specific transfer functions for some of the most useful
circuit configurations using the AF100 are illustrated in Fir.
ures 2 through 8. Also included are the gain equations for
each transfer function in the frequency band of interest, the
Q equation, center frequency equation and the Q determin-
ing resistor equation.
T(s) - 0,0 (bandpass)
$2 + Ti" + of
1000 pF RF P
= H?OHPASS BANDPASS Ltwehss
TL/K/10111-5
‘Externat components
FIGURE 2. Non-lnvertlng Input (Q > them, see tt Tuning Section)
Applications Information (Continued)
a) Non-inverting input (Figure a transfer equations are: b) Non-inverting input (Figure 3) transfer equations are:
st! -.t.i.,., 1.1 + le.
E + Em s2 LLL.R2
105 R R
3 = ..,l..L1_0sL..RN (highpass) 1 + 'n-IN
m A tr.t-..l.-,.i1.il.,s=l (Nghpass)
S (1) 1.1 BIN h g p
- 1 -----..._
BIN BIN 104
I+-H+-_-hr-" 1.1+-_-:
th, 105 HQ 1 HQ
- = ---_---r_-.--- (bandpass) -s an ----
elN A 1 + %
1.1 eb 105
--_r-.._ - = __.-.---..-..- (bandpass)
1 + !hy, + E StN h
105 RO ‘104
35 == w m -....---..---- (Iowpass) 1.1 + To
6IN 1 2 A WW2 T-ic,
ttt _ L03 - L03 tt 1 + FI-',
RH tttit Rm 4 = -"-'"-r-'''""""- (iowpass)
where 1 1 w - YZ _ 1_09
=2+ _-ui-..- +o. I-ii '"rt
A s [ E+1_°5]"" “W” where F1 F2
RQ Rm ttH
8t - 11 1.1 f EB
AN s-ro (1+!r1tt-,+'-lig) A=82+Sab1 -'ttyr" +0.1w1w2
105 R0 1 + -
fl =__1__ W
em s-. co Rm Rm) 1.1 + -
+ - + - R
(1 105 R0 Si = r)-_-'i',-S-
(1+105+105) iN s-+o 0.1 (1+'l-7)
61, RQ Hm
ai =__1_?_ 11+104
IN w = 00 + _IN + 'jg) . iCo
(1 105 no :3 = L"---,',),-?,
(00 =J0.1c)1w2 IN - 6° 1 + 'il)
105 105
l + iiT, + iiii 1 + 1e
Q = -..r.1ly_'1Y. 0.1 E st, Rm
1.1 an -- = - --"h7,
105 9'" ttt = ttro 1 + 1lt.1.
RQ = ''r'Cilrr7-Ttrs 105
. _ 1 - Tir, 000 == JWGi%
1/o.1 se tN 105
tot 1 + -
100k t2 - 0 -
"PP.- 1 1 + fA tot
w lit 511° . 1000pt arr 1000pt
l vvv vvv IF- _ 104
RO-----
'1. :tis 1 +1t2s V0193
o 1rt Rm -y_%.. - 1.1
o... i., oo.
HIG-IPASS EANDPASS LOWPASS
TLlK/10111-6
‘Enemal components
FIGURE 3. Non-Invertlng Input
(0 < Gum. see a Tuning Sectlon)
Applications Information (Continued)
Iooopr IOOOpF
bt, .521: I " I-.
'In O-NVV"
1 W." 'TI"
0'» " 0'I
= amass mums Lawns:
TrJKM0Mt-7
"Extamal components
FIGURE 4. Invortlng Input
c) Inverting input (Figure 4) transfer function equations are:
9h IN .
- = - h h
GIN h 1 19 pass)
Sat 104
- = ----. d
GIN A (ban pass)
to w 104
_ 1 2...
- = --......_ I
am h (lowpass)
- m - .1t21
1 RF RF2
1 1 + c,
A=52+Sw1 10!: +0Atottts2
St 105
- _ - -..- (lowpass)
6m s-ro Rm
an 104 .
- - -.--. thi hpass)
MN s» so Rm g
m (1 E)
em a) = we 1 1 + 12
(.00 = J01 0102
1 + It.Ls.
Q = -"T-itT4' t'"tr,"
1.1 + -
R0 = Q 10
at 1 1 + E - 1
0.1 'h'?. . Rm
woopr twopr
10k " " arz-
"d.", "W'. j F-- .
RN 2 .
‘n n" t . M L
PA.- .
100k = =
it 'ttf
d 0'11 oh, 0':
TL"" Hmnss moms Lowms
TLfKf10111-8
'Extemal components
FIGURE ti. Dlfhtrqtrttlal Input
d) Differential input iFigum 5) transfer function equations
Bh IN2 .
- == - h h
em A ( 19 pass)
Sttt 104
- I..,--
Bb Rme
- = - b d
am A ( an pass)
ttt a) 104
_ 1 il"...-
Bg Ree
- = - l
em h (lowpass)
109 109
1 = - = -
RF1 RF2
1 1 + -
A=s2+sa, RM +011“:
l 105 105 l 2
Ra RIM
mo = JO.1 anwg
1 m 1.0. 5
Q - Q MI 0.1&
104 001
R0 = o 10
1.1 + 104 105
(1)2 - - - -..-
0.1-e Ree RIM
Applications Information (Continued)
‘Extema! components
TLn010M1-9
FIGURE 6. Output Notch Using All Four Amplmers
e) Output notch (Figure 6) transfer function equations are:
(52+w22) g
I+1-trr!l-y RT,
&_ 105 R0
em 1.1
tot E 1_05 +0.1w1w2
109 109
I--,.,- ttta = - coo =J0.1w1w2
RF1 RF2
a, ---o m
& =_J1_k
MN s-oo ( RIN Rwy?!
1 +-''c+ -....
105 R0
'h - 1.1 Rg
eIN tr--.',
(1+m+M)Rh
105 RO
‘Extemal components
FIGURE 7. Input Notch Uslng Three Ampllflers
TL/K/10111-10
f) Input notch (Figure 7) transfer function equations are:
Cz f 1
'h - ltr-il $2 coz
eIN 2 ( 1.1 no 1
+ - ' 2
s tttol 105 + no too
a, - L09. u, - Itll
1 Rm 2 “Fa
Ft'? M flF9
wz = 00 - (no = 5.1m1w2
21 = - Irie
9m w a 0 92
i - -.f.i.iL
6|N a, - on 10-9
g) Allpass (Figure 8) transfer function equations are:
82 - S m + of
2 + Lett.!
Sr, - R0
em s2 + S on + omit
2 + lu
o = no 0.12g
1.1 an
- 109 w _ 109
1 _ - - -
RF1 2 RH
mo = 40.1 (01(02
Time delay at m = 14 seconds
Applications Information (Continued)
'Exiarnal components
FREQUENCY TUNING
FIGURE 8. Allpass
To tune the AF100 two resistors are required for frequen-
cies between 200 Hz and 10 kHz, For lower frequencies "T"
tuning or addition of external capacitors is required. Using
external capacitors allows the user to go as low in frequen-
cy as he desires. "T" tuning and external capacitors can be
used together.
Two resistor tuning for 200 Hz to 10 kHz
.33 X 106
R, = §9__Q
l; I14
FIGURE 9. Resistive Tuning
GRAPH A. Resistive Tuning
TL2l0t0111-12
100 1k 1% 1M
fc-FREOUENCY (Hz)
TL/K/10t11-13
TL/K/10111-11
"T" resistive tuning for to < 200 Hz
Rte RF
R = - R < -
, Rt - ah t 2
3 14 13 7
RT RT ttt RT
TL/Kl10111-14
FIGURE 10. T Tuning
GRAPH B. "T" Tunlng
Rs-RESISTANCE (n)
1 to 100 lk
FREQUENCY (H2)
TL/Kl10111-15
Applications Information (Continued)
RC tuning for fo < 200 Hz
- 0.05033
- fo(C +1x10-9)
TL/Kl10111-16
FIGURE 11. Low Frequency RC Tuning
0 TUNING
To tune the Q of an AF100 requires one resistor from pins 1
or 2 to ground. The value of the Q tuning resistor depends
on ma input connection and input resistance as well as the
value of the Q. The Q of the unit is inversely proportional to
resistance to ground at pin 1 and directly proportional to
resistance to ground from pin 2.
6 GRAPH c. thmo Non-lnvertlng Input
0.1 1.0 10 100
TL/K/10111-17
For 0 > thm in non-inverting mode:
Rt2 - a .80 - 1 - E
l . A7100
TL/K/lO111-1B
FIGURE 12. a Tunlng for o > ttum,
NortAmmrtlrtg Input
GRAPH D. G > tham,
Non-Invertlng Input
RN =1HEG
Rm = 10k
0.1 1.0 10 100
TLdKMtMtt-19
For a < QMIN in non-inverting mode:
3° - ( 105)
1 + "ii7d
0.3162-_"'-" -1.1
R111 1
o-MN-' '
TLIK/10111-20
FIGURE 13. 0 Tuning for 0 < them,
Non-inverting Input
GRAPH E. Q < 0m",
Non-lnvertlng Input
Ml 0.1 1.0 10
TL/K/10111-21
Applications Information (Continued)
For any ta in inverting mode
R0 = T""""1-/'""-'_'
3.160 (1.1 + F,',,',) - 1
o-MN---
TL/KM011t-22
FIGURE M. Q Tuning Inverting Input
GRAPH F. Q Tuning
Inverting Input
0.1 M 10 III)
TLIK/10111-23
NOTCH TUNING
Two methods to generate notches are the RC input and
Iowpass/highpass summing. The RC input method requires
adding a capacitor and resistor connected to the two inte-
grator inputs. The capacitor connects to "Int I'' and the
resistor connects to "Int 2". The output summing requires
two resistors connected to the Iowpass and highpass out-
For input RC notch tuning:
R _ RF x1o-9(f_o_)2
Z 02 tz
io 01mm
TL/K/10111-24
FIGURE 15. Input RC Notch
GRAPH G. Input RC Notch
0.1 1D 10
fC/ 12
For output notch tuning:
RHP--'-- Ct) LP
to 1 0
FIGURE 16. Output Notch
GRAPH H. Output Notch
RHP/RLP
0.1 ID 10
TL/KI10111-25
OUTPUT
TL/Kl10111-28
TL/Kl10111-27
Applications Information (Continued)
TUNING TIPS
In applications where 2% to 3% accuracy is not sufficient to
provide the required filter response, the AF100 stages can
be tuned by adding trim pots or trim resistors in series or
parallel with one of the frequency determining resistors and
the Q determining resistor.
When tuning a filter section, no matter what output configu-
ration is to be used in the circuit, measurements are made
between the input and the bandpass (pin 13) output.
Before any tuning is attempted the lowpass (pin 7) output
should be checked to see that the output is not clipping. At
the center frequency of the section the lowpass output is
10 dB higher than the bandpass output and 20 dB higher
than the highpass. This should be kept in mind because if
clipping occurs the results obtained when tuning will be in-
correct.
Frequency Tuning
By adjusting the resistance between pins 7 and 13 the cen-
ter frequency of a section can be adiusted. if the input is
through pin 1 the phase shift at center frequency will be
180° and if the input is through pin 2 the phase shift at
center frequency will be tp. Adjusting center frequent by
phase is the most accurate but tuning for maximum gain is
aiso correct.
"tl'' Tuning
The "tT' is tuned by adjusting the resistance between pin 1
or 2 and ground. Low Q tuning resistors will be from pin 2 to
ground (Q < 0.6). High t2 tuning resistors will be from pin 1
to ground. To tune the Q correctly the signal source must
have an output impedance very much lower than the input
resistance of the filter since the input resistance affects the
a. The input must be driven through the same resistance
the circuit will see to obtain precise adjustment.
The lower 3 dB (45") frequency, fu, and the upper 3 dB (45°)
frequency, fH, can be calculated by the following equations:
tH--(21z+ E +1)X(fo)
where to = center frequency
(CT,? 1
fL=( E -r1--21-a)xito)
When adiusting the o, set the signal source to either tH or fL
and adjust for 45'' phase change or a 3 dB gain change.
Notch Tuning
If a circuit has a iw axis zero pair the notch can be tuned by
adjusting the ratio of the summing resistors (lowpass/high-
pass summing) or the input resistance (input RC).
In either case the signal is connected to the input and the
proper resistor is adjusted for a null at the output.
Special Cases
When using the input RC notch the unit cannot be tuned
through the normal input so an additional 100k resistor can
be added at pin 1 and the unit can be tuned normally. Then
the 100k input resistor should be grounded and the notch
tuned through the normal RC input.
An alternative way of tuning is to tune using the ta resistor
as the input. This requires the Q resistor be lifted from
ground and connecting the signal source to the normally
grounded and of the Q resistor. This has the problem that
when the Q resistor is grounded after tuning, its value is
decreased by the output impedance of the source. This
technique has the advantage of not requiring an additional
resistor.
TUNING PROCEDURE (See Figure 17)
Center Frequency Tuning
Sat oscillator to center frequency desired for, the filter sec-
tion, adjust amplitude and check that clipping does not oc-
cur at the lowpass output pin 5 (AF100J).
Adjust the resistance between pins 13 and 7 until the phase
shift between input and bandpass output is 180°.
0 Tuning
Set oscillator to upper or lower 45' frequency (see tuning
tips) and tune the Q resistor until the phase shift is 135'
(upper 45" frequency) or 225° (lower 45'' frequency).
Zero Tuning
Set the oscillator output to the zero frequency and tune the
zero resistorfor a null at the ouput of the summing amplifier.
Gain Adlust
Set the oscillator to any desired frequency and the gain can
be adjusted by measuring the output of the summing ampli-
fier and adjusting the feedback resistance.
OSCILLATOR
" " l' GAIN
10 A1 h
1 l A . I
13 7 Lr., AC VOL'NUIR
VREWENCT
PHASE NEVER
TL/K/tmtl-ae
FIGURE 17. Filter Tuning Setup
Applications Information (Continued)
m m " m m n
3 "r, I15 fi _ Is lulu l, I4 _
1:10011 2RO 5:101:11
c hs c Ret
o/ M, moo 5 o-l l moo ' _
a 1L ato at l
R0:, 1:10011 $10011 thtyF
11 10 ' tt I 12 l
-.- = "a-.
y PSEUDO ROUND -
/2( ) TL/Kl10111-30
TL/K/10111-29
FIGURE 19. Slnglo Power Supply
FIGURE te. Single Power Supply Connectlon Using Conn tt cu on U sin q Roalstlve Dlvldora
unctttttrttlttttd Antpllfltsr to Split Supply
13 12 "
50.87k
- _ V- - - w.
TL/KI10111-31
Pettotrttttntm
0.1 dB ripple passband
0.1 dB notch width == 100 Hz
40 dB notch width " th25 Hz
4th Order 1010 Hz Notch
' "s, "
STAGE 1 ~10 . / STAGE 2
PC = 1031.1 Hz Iii -20 Fe -- 989.8 Hz
Q = 2834 I a - 28.34
if -30
Fa ---. 1012.2 HI F; = 1007.8 Hz
$80 980 1000 1020 1040
FREQUENCY (Hz)
TL/KI1OI11-32
FIGURE 20. 1010 Hz Nottth-Tehphotut Holding Tone Heloct Filter
FILTER DESIGN found, it is transformed to obtain the transfer function for the
actual filter desired. Graph I shaws the Iowpass amplitude
Since most filter tables are in terms of a normalized lowpass .
response which can be defined by four quantities.
prototype, the filter to be designed is usually reduced to e
Iowpass prototype. After the Iowpass transfer function is
Applications Information (Continued)
GRAPH l. Lowpass Prototype Response
cm (as)
hm // /// // /
LOG FREQUENCY
mmm 1 1 ~33
AMAx = the maximum peak to peak ripple in the passband.
AMIN = the minimum attenuation in the stopband.
to = the passband cuttoff frequency.
fs = the stopband start frequency.
By defining these four quantities for the Iowpass prototype
the normalized pole and zero locations and the 0 (quality)
of the poles can be determined from tables or by computer
programs.
To obtain the lowpass prototype for the highpass filter
(Graph J} AMAX and AMIN are the same as for the Iowpass
case but fc = Iff2 and ts = 1/f1.
GRAPH J. Highpaas Response
TuKm0111-34
To obtain the iowpass prototype for a bandpass filter (Graph
K) AW and AMIN are the same as for the Iowpass case but
fc = 1 fs = ET}:
wherefa = Jfo- = Jah- i.e.. geometric symmetry
ts - " = AMiN bandwidth
f4 - f2 = Ripple bandwidth
GRAPH K. Bandpass Response
ft t2 fs ft ts
TL/K/10111-35
To obtain the Iowpass prototype for the notch filter (Graph
L) AMAx and AMIN are the same as for the lowpass case
f5 - "
f = 1 f = -
c s " - f2
wherefa = 31f = Ja7
GRAPH L. Notch Response
ft ft fs " fs
TLlK/10111-36
Normalized Lowpaee Transformed to
Un-Normallzed Lowpass
The normalized Iowpass filter has the passband edge nor-
malized to unity. The un-normalized lowpass filter instead
has the passband edge at to. The normalized and un-nor-
maiized iowpass filters are related by the transformation B
= smc. This transform the normalized passband edge s =
j to the un-normalized passband edge s = Itoty
Normalle Lewpeee Transformed to
Un-Normellzed nghpaee
The transformation that can be used for lowpass to high-
pass is S = toc/s. Since S is inversely proportional to s, the
tow frequency and high frequency responses are inter.
changed. The normalized lowpass1/(S2 + 8/0 + 1) trans-
forms to the un-normalized highpass
s2+-69s+wc2
Normalized Lowpase Transformed to Un-Normallzed
Bandpass
The transtormation that can be used for Iowpass to band-
pass is S --- (s2 + m02)/BWs where c902 is the center fre-
quency of the desired bandpass filter and BW is the ripple
bandwidth.
Normalized Lowpaes Trattttfttrtttttd to Un-Normallzed
Bandstep (or Notch)
The bandstop filter has a reciprocal response to a bandpass
filter. Therefore a bandstop filttar can be obtained by first
transforming the iowpass prototype to a highpass and then
performing the bandpass transformation.
SELECTION OF TRANSFER FUNCTION
The selection of a function which approximates the shape of
the response desired is a complicated process. Except in
the simplest cases it requires the use of tables or computer
programs. The form of the transfer function desired is in
terms of the pole and zero locations. The most common
approximations found in tables are Butterworth, Tscheby-
chaff. Elliptic, and Bessel. The decision as to which approxi-
mation to use is usually a function of the requirements and
Applications Information (Continued)
system objectives. Butterworth filters are the simplest but
have the disadvantage of requiring high order transfer func-
tions to obtain sharp toil-offs.
The Tschebycheft function is a min/max approximation in
the passband. This approximation has the property that it is
equirippie which means that the error oscillates between
maximums and minimums of equal amplitude in the pass-
band. the Tschebycheff approximation, because of its equi-
ripple nature, has a much steeper transition region than the
Butterworth approximation.
The elliptic filter, also known as Cauer or Zolotarev filters,
are equiripple in the passband and stopband and have a
steeper transition region than the Butterworth or the Tsche-
bycheff.
For a specific Iowpass filter three quantities can be used to
determine the degree of the transfer function: the maximum
passband ripple, the minimum stopband attenuation, and
the transition ratio (tr = ms/wc). Decreasing AMAX, in-
creasing AWN. or decreasing tr will increase the degree of
the transfer function. But for the same requirements the el-
liptic filter will require the lowest order transfer function. Ta-
bles and graphs are available in reference books such as
"Reference Data for Radio Engineers", Howard W. Sams 8.
Co., Inc., 5th Edition, 1970 and Erich Christian and Egon
Eisenmann, "Filter Design Tables and Graphs", John Wiley
and Sons, 1966.
For specific transfer functions and their pole locations such
text as Louis Weinberg, "Network Analysis and Synthesis",
McGraw Hill Book Company, 1962 and Richard W. Daniels,
"Approximation Methods for Electronic Filter Design",
McGraw-Hill Book Company, 1974, are available.
DESIGN OF CASCADED MULTISEGTION FILTERS
The first step in designing is to define the response required
and define the performance specifications:
1. Type of filter:
Lowpass, highpass, bandpass, notch. allpass
2. Attenuation and frequency response
3. Performance
Center frequency/comer frequency plus tolerance and
stability
Insertion loss/gain plus tolerance and stability
Source impedance
Load impedance
RIPPLE _dB (Am) -1
Maximum output noise
Power consumption
Power supply voltage
Dynamic range
Maximum output level
The second step is to find the pole and zero location for the
transfer function which meet the above requirements. This
can be done by using tables and graphs or network synthe-
sis. The form of the transfer function which is easiest to
convert to a cascaded filter is a product of first and second
order terms in these forms:
First Order Second Order
s + - (lowpass)
tOR s2 + E s + mo?
S - (highpass)
S + can ttro
sit + - s + c002
-..e.._lS.L......._...... (bandpass)
s2 + g s + am2
si? + -_'tr + 2
s2 - ff-f S + am2
(allpass)
s2+9's+arni!
Each of the second order functions is realizable by tuning
an AF100 stage. By cascading these stages the desired
transfer function is realized.
CASCADING SECOND ORDER STAGES
The primary concern in cascading second order stages is to
minimize the maximum difference in amplitude from input to
output over the frequencies of interest. A computer program
is probably required in very complicated cases but some
general rules that can be used that will usually give satisfac-
tory resuits are:
-3 dil AT_Hz
Asm-di? /'" l
fl-8t fs fs fo _Hz fa f4 ft .HI
TL/KM0111-37
GRAPH M. Generallzed Model Response
Applications Information (Continued)
1. The highest "Q" pole pair should be paired with the zero
pair closest in frequency.
2. If highpass and lowpass stages are cascaded the low-
pass sections should be the higher frequency and high-
pass sections the lower frequency.
3. In cascaded filters of more than two sections the first
section should be the section with "O'' closest to 0.707
and then additional stages should be added in order of
least difference between first stage Q and their Q.
RFI Rre 77.6k 405k 100k
48.3k 15.51: 54.91: 33.0k
" v 3 w
100k 100k
3.93k 7 13
= Rn Rn
48.3k = 54.9k -
TL/K/lol)
Lowpass Elllptlc Filter
Fc = 1
Fs = 1.3
AMAX = 0.1 dB
AMIN = 40 dB
tol = 1.0415 th = 7.88 121 = 1.329 tz/to = 1.28 tT, = 1.63
fog WP.: 0.9165 th = 1.79 122 = 1.664 fz/fo = 1.82 (fl) = 3.30
ta, = 0.649 th = 0.625 123 = 4.1285 tz/to = 6.36 Ct) == 40.5
(503.3) (503.3) (503.3)
R = - X 105 R = M 105 =
F1 tot M ft; F2 102 M 1c RPS foa X to
at 1000 Hz = it:
RF1 = 48.3k sz = 54,9k Hpa = 77.6k
8th Order Elltptlc Fllter
GAIN (dB)
FREQUENCY (kHz)
FIGURE 21. Lowpass Elliptic Ftlter Example
TLIKI10111-39
Applications Information (Continued)
T; In Isa
100k t
HptJTolM,
i s moo '-owvur
2m it F'
' s "l" 7 13
Ft; " 1000/500 Hz
a = 0.707 at a F ch Q
== M.tho". 25.17“; .; 25.171: q 25.17k
12m:; uaaet.
Gainatdc= +13dB O o
Gainat1 kH/500Hz =10dB
500/1000 Ha Switchable
Butterworth Lowpass Flltor
w: (as)
TidKM0111-40
FIGURE 22. Swltchable Filter Example: 500 Hzl1000 Hz Butterworth Lowpau
STAGE 1
Fc = 3.328 Hz
a = 3.34
F2 = 4.213 Hz
GAIN (d3)
10 mo lan
FREQUENCY (Hz)
TL/K/10111-4a
FIGURE 23. EEG Delta Filter-tt Hz Lowpass
1000 10.000
FREQUENCY (Hz)
Tumom-u
TUK/10111-‘2
STAGE 2
F0 = 2.975 Hz
a --- 0.693
F; = 8.865 Hz
AF 100
Applications Information (Continued)
Input Level 1V ms 0 dBV
FREQUENCY DC
COUNTER VOLTMETER
SINE WAVE
SIGNAL -d INPUT OSCILLOSCOPE
GENERATOR TEST FIXTURE
OUTPUT
PHASE MEIER
t 15V DC
SUPPLY AC VOtTHETER
FIGURE 25. Test Circuit Block Diagram
COMPUTER AIDED DESIGN EXAMPLE'
This design is an example of a 60 Hz notch filter. The re-
sponse is to have the following specifications:
Maximum passband ripple 0.1 dB
Minimum rejection 35 dB
0.1 dB bandwidth 15 Hz max
-35 dB bandwidth 1.5 Hz min
The steps in the design of this filter are:
TL/K/10111-44
I. Design a Iowpass "prototype" for the filter.
2. Transformation of the Iowpass prototype into a notch fil-
ter design.
3. Using the pole and zero locations found'in step two cal-
culate the value of the resistors required to build the filter.
4. Draw a schematic of filter using values obtained in step
three.
'Computer programs shown are user interactive. Bold copy is user input, light copy is computer response. and tine indications in parenthesis are included for easy
identification of data common to several programs.
PROGRAM NO. 1
THIS PROGRAM DESIGNS BUTTERWORTH CHEBYCHEFF OR ELLIPTIC NORMALIZED LOWPASS FILTERS
WHAT TYPE OF FILTER? B-C-E
ELLIPTIC
DO YOU KNOW THE ORDER OF THE FILTER? WN
INPUT FC,FS,AMAX,AMIN
PI, 10, .1, M
1 .000
IS THIS SATISFACTORY? Y/ N
'? YES
1.823 (Line 1.1)
14.124 (Line 1.3)
(ATTENUATION IN dB)
.775 (Line 1.2)
Applications Information (Continued)
PROGRAM NO. 2 ENTER FREQUENCY SCALING FACTOR
(DETERMINES UN-NORMALIZED POLE + 7ERO 2 1
LOCATIONS OF FIRST SECTION) ENTER THE * OF FILTERS TO BE DESIGNED
(DATA ENTERED FROM PROGRAM NO. 1) 2 1
RUN ENTER THE C.F. AND BW OF EACH FILTER
WHAT TYPE FILTER BANDPASS on NOTCH ? 60, "
Ira'", OF POLE PAIRS? 1 OUTPUT or PROGRAM NO. 2
. TRANSFORMED POLE/ZERO LOCATIONS
ENTER ' OF JW AXIS ZEROS? 1 FIRST SECTION
ENTER ' OF REAL POLES? tl POLE LOCATIONS
ENTER ' OF ZEROS AT ZERO? o CENTER FREQ. Q
ENTER ' OF COMPLEX ZEROS? o 56.93601 (From Lima2.3) 11.31813 (From Line 2.4)
ENTER f OF REAL ZEROS? o 63.228877 (From Line 2.5) 11.31813 (From Line 2.6)
ENTER F&Q OF EACH POLE PAIR JW A’F'S ZEROS
7 1.823, .775 (FROM LINE t. t AND LINE 1.2) 59.471339 (Fmm U(w k. U
ENTER VALUES OF JW AXIS ZEROS 60.533361 (From Line AP)
? 14.124 (FROM 1.3)
PROGRAM NO. 3
(CHECK OF FILTER RESPONSE USING
PROGRAM NO. 2 DATA BASE)
NUMERATOR {ZEROSI
A(I)S A 2 + R(I)S + 20) A 2
1 0 59.471339 (From Line 2. 1)
1 0 60.533361 (From Line 2.2)
REAL POLE
COMPLEX POLE PAIRS
1 56.93601 11.31613 (FromLinss 2.3and2.4)
2 63.228877 11.31813 (From Lines 2.5and2.6)
FREQ. "lg" PHASE DELAY NORDELAY FREQ. N035?“ PHASE DELAY NOR.DELAY
40.000 .032 347.69 .002275 5.847169 60.600 -47.102 169.17 .050801 108.232021
45.000 .060 342.20 .004107 8.749738 60.800 --33.850 165.48 .051677 110.096278
50.000 .100 330.70 .009983 21.268142 61.000 -27.577 161.72 .052809 112.508334
55.000 -.795 290.54 .046620 99.324027 61.200 -23.418 157.87 .054167 115.403169
56.000 --2.298 270.61 .063945 136.234562 61.400 -20.198 153.92 .055712 118.694436
57.000 --5.813 245.51 .072894 155.299278 61.600 -17.554 149.85 .057391 122.270086
58.000 -12.748 220.19 .065758 140.096912 61.800 -15.308 145.65 .059136 125.989157
58.200 -14.740 215.54 .063369 135.006390 62.000 -13.362 141.33 .060869 129.681062
58.400 -17.032 211.06 .060979 129.914831 63.000 -6.557 116.23 .065975 140.559984
58.600 -19.722 206.76 .058692 125.043324 64.000 -2.936 95.30 .059402 126.556312
58.800 -22.983 202.61 .056588 120.561087 85.000 -1.215 76.38 .045424 96.774832
59.000 -27.t72 198.60 .054724 116.589928 66.000 -.463 62.43 .032614 69.484716
59.200 -33.235 194.72 .053139 113.212012 67.000 -.138 52.44 .023498 50.062947
59.400 -46.300 190.94 .051856 110.478482 70.000 .091 35.43 .010452 22.267368
59.600 -42.909 7.24 .050688 108.417405 75.000 .085 23.44 .004250 9.054574
59.800 -36.897 3.60 .050242 107.040235 80.000 .060 17.80 .002310 4.921727
60.00 -35.567 360.00 .048916 106.346516 85.000 .043 14.50 .001460 3.110493
60.200 -36.887 356.41 .049907 106.326777 90.000 .032 12.31 .00t011 2.154297
60.400 -42.757 352.81 .050206 106.963750
Applications Information (Continued)
EH . RHP
INPUI'
4th Order 60 Ha Notch Filter
cm (dB)
40 so so TO so so
razouzncr (H1) ll, "__- t:
TL/K/10111-46
FIGURE 26. Implementations of a 60
Hz Notch from Computer R3+R5
Cttlttulatlotttt v3 i ('-1ji'iti,'-?
"Tuning Resistors
0.1 dB bandwidth 15 Hz
-35 dB bandwidth 1.5 Hz
Tt./KM0111-45
TL/KM011t-47
Fl [vos, +V063(R7R8+ Recn7+ a) l-Voss!
FIGURE 27. DC Output Voltage Due to Amplmer vos
DEFINITION OF TERMS
AMAx Maximum passband peak-to-peak ripple
AMIN Minimum stopband loss
12 Frequency of M axis pair
fo Frequency of complex pole pair
a Quality of pole
to Passband edge
fs Stopband edge
AHp Gain from input to highpass output
Asp Gain from input to bandpass output
Aup Gain from input to Iowpass output
AAMp Gain from input to output of amplifier
Rf Pole frequency determining resistance
R2 Zero frequency determining resistance
Ra Pole quality determining resistance
fH Frequency above center frequency at which the gain
decreases by 3 dB for a bandpass filter
ft. Frequency below center frequency at which the gain
decreases by 3 dB for a bandpass filter
BW The bandwidth of a bandpass filter
N Order of the denominator of a transfer function
BIBLIOGRAPHY
R.W. Daniels: "Approximation Methods for Electronic Filter
thssign", McGraw-Hill Book Co., New York, 1974
GS. Moschytz: "Linear Integrated Networks Design", Van
Norstrand Reinhold Co., New York, 1975
E. Christian and E. Eisenmann, "Filter Design Tables and
Graphs", John Wiley & Sons, New York, 1966
A.I. Zverev, "Handbook of Filter Synthesis", John Wiley &
Sons, New York, 1967
Burr-Brown Research Corp., "Handbook of Operational/Um
plifier Design and Applications", MtrGraw-Hill Book Co.,
New York, 1971
This datasheet has been :
www.ic-phoenix.com
Datasheets for electronic components.
National Semiconductor was acquired by Texas Instruments.
corp/docs/irwestor_relations/Pr_09_23_201 1_national_semiconductor.html
This file is the datasheet for the following electronic components:
AF100-1CG - product/af100-1cg?HQS=T|-nulI-nulI-dscatalog-df-pf-null-wwe
AF100-1CJ - product/af100-1cj?HQS=T|-nuIl-nu|I-dscatalog-df-pf-nuII-wwe
AF100-1CN - product/af100-1cn?HQS=T|—nuII-nulI-dscatalog-df—pf—nuII-wwe
AF100-1G - product/af100—1g?HQS=T|—nu||—nu|I-dscataIog-df-pf-null-wwe
AF100-2CG - product/af100-ZCg?HQS=T|-nulI-nulI-dscatalog-df-pf-null-wwe
AF100-2CJ - product/af100-20j?HQS=T|-nuIl-nu|I-dscatalog-df-pf-nuII-wwe
AF100-2CN - product/af100-2cn?HQS=T|—nuII-nulI-dscatalog-df—pf—nuII-wwe
AF100-2G - product/af100-Zg?HQS=T|—nu||—nu|I-dscataIog-df-pf-null-wwe
