Analog Devices AN584 Application Notes

AN-584
a
APPLICATION NOTE
One Technology Way • P.O. Box 9106 • Norwood, MA 02062-9106 • Tel: 781/329-4700 • Fax: 781/326-8703 • www.analog.com
Using the AD813x
THEORY OF OPERATION
, controls the output common-
OGM
mode voltage. The additional output is the analog complement of the single output of a conventional op amp. For its operation, the AD813x makes use of two feedback loops as compared to the single loop of con­ventional op amps. While this provides significant freedom to create various novel circuits, basic op amp theory can still be used to analyze the operation.
One of the feedback loops controls the output common­mode voltage, V
. Its input is V
OUT,cm
(Pin 2) and the
OCM
output is the common-mode, or average voltage, of the two differential outputs (+OUT and –OUT). The gain of this circuit is internally set to unity. When the AD813x is operating in its linear region, this establishes one of the operational constraints: V
OUT,cm
= V
OCM
.
The second feedback loop controls the differential opera­tion.
Similar to an op amp, the gain and gain-shaping of the transfer function is controllable by adding passive feedback networks. However, only one feedback net­work is constrain the desired, two possible as a
required to “close the loop” and fully
operation. But depending on the function feedback networks can be used. This is result of having two outputs that are each
inverted with respect to the differential inputs.
DEFINITION OF TERMS
C
F
R
F
R
G
+D
IN
V
OCM
–D
IN
+IN
–IN
R
G
AD813x
R
F
C
F
–OUT
+OUT
R
V
,dm
L
OUT
,dm
Figure 1. Circuit Definitions
Differential voltage refers to the difference between two node voltages. For example, the output differential volt­age (or equivalently output differential-mode voltage) is defined as:
VVV
V
+OUT
=+(–)
OUT,dm OUT OUT
and
V
refer to the voltages at the +OUT and –OUT
–OUT
(1)
terminals with respect to a common reference.
Common-mode voltage refers to the average of two node voltages. The output common-mode voltage is defined as:
VVV
=+(+)/2
OUT,cm OUT OUT
(2)
PIN FUNCTION DESCRIPTIONS
Pin No. Mnemonic Function
1 –IN Negative Input 2V
OCM
Voltage applied to this pin sets the common-mode output voltage with a ratio of 1:1. For example, 1 V
dc on VOCM will set the dc bias level on +OUT and –OUT to 1 V.
3 V+ Positive Supply Voltage 4 +OUT Positive Output. Note: The voltage
is inverted at +OUT.
at –D
5 –OUT
IN
Negative Output. Note: The voltage at +DIN is inverted at –OUT.
6 V– Negative Supply Voltage 7 NC No Connect 8 +IN Positive Input
GENERAL USAGE OF THE AD813x
Several assumptions are made here for a first-order analysis, which are the typical assumptions used for the analysis of op amps:
• The input impedances are arbitrarily large and their loading effect can be ignored.
• The input bias currents are sufficiently small so they can be neglected.
• The output impedances are arbitrarily low.
• The open-loop gain is arbitrarily large, which drives the amplifier to a state where the input differential voltage is effectively zero.
• Offset voltages are assumed to be zero.
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© Analog Devices, Inc., 2002
AN-584
While it is possible to operate the AD813x with a purely differential input, many of its applications call for a circuit that has a single-ended input with a differential output.
For a single-ended-to-differential circuit, the RG of the undriven input will be tied to a reference voltage. For now this is ground. Other conditions will be discussed later. Also, the voltage at V
, and hence V
OCM
OUT,cm
will be assumed to be ground for now. Figure 2 shows a gener­alized schematic of such a circuit using an AD813x with two feedback paths.
R
F1
R
G1
+
R
G2
R
F2
Figure 2. Typical Four-Resistor Feedback Circuit
For each feedback network, a feedback factor can be defined, which is the fraction of the output signal that is fed back to the opposite-sign input. These terms are:
β1/( )
=+RRR
111
GGF
β2/( )
=+RRR
222
GGF
(3)
(4)
The feedback factor ␤1 is for the side that is driven, while the feedback factor 2 is for the side that is tied to a ref­erence voltage (ground for now). Note also that each feedback factor can vary anywhere between 0 and 1.
A single-ended-to-differential gain equation can be derived that is true for all values of 1 and 2:
G 2 (1 1) / ( 1 2) +
βββ
(5)
This expression is not very intuitive. One observation that can be made right away is that a tolerance error in 1 does not have the same effect on gain as the same tolerance error in 2.
For RF1/RG1 = RF2/RG2 the gain equation simplifies to G = RF/RG.
BASIC CIRCUIT OPERATION
One of the more useful and easy to understand ways to use the AD813x is to provide two equal-ratio feedback networks. To match the effect of parasitics, these net­works should actually be comprised of two equal-value feedback resistors, R tors, R
. This circuit is diagrammed in Figure 1.
G
and two equal-value gain resis-
F
Like a conventional op amp, the AD813x has two dif
ferential inputs that can be driven with both a differen­tial-mode input voltage, V voltage, V
. Another input, V
IN,cm
conventional op amps, but provides another consider on the AD813x. It is totally separate above inputs. There are also two complementary
, and a common-mode input
IN,dm
OCM
, is not
present on
input to
from the
outputs whose response can be defined by a differential-mode output, V
and a common-mode output, V
OUT,dm
OUT,cm
.
Table I indicates the gain from any type of input to either type of output.
Table I. Differential and Common-Mode Gains
Input V
V
IN,dm
V
IN,cm
V
OCM
OUT,dm
RF/R 0 0 (By Design) 0 1 (By Design)
The differential output (V tial input voltage (V
) times RF/RG. In this case, it does
IN,dm
G
OUT,dm
V
OUT,cm
0 (By Design)
) is equal to the differen-
not matter if both differential inputs are driven, or only one output is driven and the other is tied to a reference voltage, like ground. As can be seen from the two zero entries in the first column, neither of the common-mode inputs has any effect on this gain.
The gain from V
IN,dm
to V
is 0 and to first-order does
OUT,cm
not depend on the ratio matching of the feedback net­works. The common-mode feedback loop within the AD813x provides a corrective action to keep this gain term minimized. The term “balance error” describes the degree to which this gain term differs from zero.
The gain from V
IN,cm
to V
does directly depend on
OUT,dm
the matching of the feedback networks. The analogous term for this transfer function, which is used in conven­tional op amps, is “common-mode rejection ratio” or CMRR. Thus, if it is desirable to have a high CMRR, the feedback ratios must be well matched.
The gain from V
IN,cm
to V
is also ideally 0, and is
OUT,cm
first-order independent of the feedback ratio matching. As in the case of V
IN,dm
to V
, the common-mode
OUT,cm
feedback loop keeps this term minimized.
The gain from V
OCM
to V
is ideally 0 only when the
OUT,dm
feedback ratios are matched. The amount of differential output signal that will be created by varying V
OCM
is
related to the degree of mismatch in the feedback networks.
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V
controls the output common-mode voltage V
OCM
OUT,cm
with a unity-gain transfer function. With equal-ratio feedback networks (as assumed above), its effect on each output will be the same, which is another way to say that the gain from V
OCM
to V
is zero. If not
OUT,dm
driven, the output common-mode will be at mid-supplies. It is recommended that a 0.1 µF bypass resistor be con­nected to V
OCM
.
When unequal feedback ratios are used, the two gains associated with V
become nonzero. This signifi-
OUT,dm
cantly complicates the mathematical analysis along with any intuitive understanding of how the part oper­ates. Some of these configurations will be in another section.
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In the case of a single-ended input signal (for example if –D
is grounded and the input signal is applied to +DIN),
IN
the input impedance becomes:
R
IN,dm
 
=
 
R
G
1
R
2
RR
×+
()
GF
The circuit’s input impedance is effectively higher than it would be for a conventional op amp connected as an inverter because a fraction of the differential output voltage appears at the inputs as a common-mode signal, partially bootstrapping the voltage across the input resistor R
 
 
F
 
(8)
G
.
ESTIMATING THE OUTPUT NOISE VOLTAGE
Similar to the case of a conventional op amp, the differ­ential output errors (noise and offset voltages) can be estimated by multiplying the input referred terms, at +IN and –IN, by the circuit noise gain. The noise gain is defined as:
R
F
1
R
G
(6)
G
=+
N
To compute the total output referred noise for the circuit of Figure 1, consideration must also be given to the contribution of the resistors
R
and
F
R
. Refer to Table II
G
for estimated output noise voltage densities at various closed-loop gains.
Table II. Recommended Resistor Values and Noise Performance for Specific Gains
Output Output
R
GRF
Gain ()(⍀) –3 dB AD813x
Bandwidth Noise Noise
AD813x + RG, R
F
1 499 499 360 MHz 16 nV/Hz 17 nV/Hz 2 499 1.0 k 160 MHz 24.1 nV/Hz 26.1 nV/Hz 5 499 2.49 k 65 MHz 48.4 nV/Hz 53.3 nV/Hz 10 499 4.99 k 20 MHz 88.9 nV/Hz 98.6 nV/Hz
CALCULATING AN APPLICATION CIRCUIT’S INPUT IMPEDANCE
The effective input impedance of a circuit such as that in Figure 1, at +D
and –DIN, will depend on whether the
IN
amplifier is being driven by a single-ended or differen­tial signal source. For balanced differential input signals, the input impedance (R
) between the inputs (+D
IN,dm
IN
and –DIN) is simply:
R2R
IN,dm G
(7)
INPUT COMMON-MODE VOLTAGE RANGE IN SINGLE­SUPPLY APPLICATIONS
The AD813x is optimized for level-shifting “ground”
ref­erenced input signals. For a single-ended input this would imply, for example, that the voltage at –DIN in Figure 1 would be zero volts when the amplifier’s negative power supply voltage (at V–) was also set to zero volts.
SETTING THE OUTPUT COMMON-MODE VOLTAGE
The AD813x’s V
pin is internally biased at a voltage
OCM
approximately equal to the mid-supply point (average value of the voltages on V+ and V–). Relying on this internal bias will result in an output common-mode voltage that is within about 100 mV of the expected value. In cases where more accurate control of the output common mode level is required, it is recommended that an external source, or resistor divider (with R
< 10 k), be used.
SOURCE
APPLICATION NOTES FOR THE AD813x DIFFERENTIAL AMPS ADC DRIVING High-Performance ADC Driving
The circuit in Figure 3 shows a simplified front-end con
nection for an AD813x driving an AD9224, a 12-bit, 40 MSPS A/D converter. The A/D works best when driven differentially, which minimizes its distortion as described in its data sheet. The AD813x eliminates the need for a transformer to drive the ADC and performs single-ended-to-differential conversion, common-mode level-shifting, and buffering of the driving signal.
The positive and negative outputs of the AD813x are connected to the respective differential inputs of the AD9224 via a pair of 49.9 resistors to minimize the effects of the switched-capacitor front-end of the AD9224. For best distortion performance it is run from supplies of ±5 V.
-
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The AD813x can also be configured with unity gain for a single-ended input-to-differential output. The additional 23 , 522 total, at the input to –IN is to balance the parallel impedance of the 50 Ω source and its 50 termi- nation that drives the noninverting input.
The signal generator has a ground-referenced, bipolar output, i.e., it drives symmetrically above and below ground. Connecting V
to the CML pin of the AD9224
OCM
sets the output common-mode of the AD813x at 2.5 V, which is the mid-supply level for the AD9224. This volt­age is bypassed by a 0.1 µF capacitor.
The full-scale analog input range of the AD9224 is set to 4 V p-p, by shorting the SENSE terminal to AVSS. This has been determined to be the scaling to provide mini­mum harmonic distortion.
For the AD813x to swing a 4 V p-p, each output swings 2 V p-p, while providing signals that are 180 degrees out of phase. With a common-mode voltage at the output of
2.5 V, this means that each AD813x output will swing between 1.5 V and 3.5 V.
A ground-referenced 4 V p-p, 5 MHz signal at D
+ was
IN
used to test the circuit in Figure 3. When the combined­device circuit was run with a sampling rate of 20 MHz MSPS, the SFDR (spurious free dynamic range) was measured at –85 dBc.
SINGLE 3 V SUPPLY DIFFERENTIAL A-TO-D DRIVER
Many newer A-to-D converters can run from a single 3 V supply, which can save significant system power. In order to increase the dynamic range at the analog input, have differential inputs, which doubles the
they
dynamic range with respect to a single-ended input. An added benefit of using a differential input is that the distortion can be improved.
The low distortion and ability to run from a single 3 V supply make the AD813x suitable as an A-to-D driver for some 10-bit, single-supply applications. Figure 4 shows a schematic of a circuit for an AD813x driving an AD9203, 10-bit, 40 MSPS A-to-D converter.
1V p-p
348
49.9
348
24.9
3V
10k
10k
0.1␮F
348
348
3V
AD813x
+
0.1␮F 10␮F
60.4
60.4
20pF
20pF
+5V
499
50
SOURCE
499 49.9
49.9
0.1pF
VINB
VINA
523
+5V
0.1pF 0.1pF
AVSS DRVSS
+
AD813x
–5V
DRVDDAVDD
AD9224
SENSE CML
V
OCM
49.9
499
Figure 3. AD813x Driving an AD9224, a 12-Bit, 40 MSPS
A/D Converter
3V
0.1␮F
AVDD DRVDD
AINN
AD9203
AINP
AVSS DRVSS
0.1␮F
DIGITAL OUTPUTS
Figure 4. AD813x Driving AD9203, a 10-Bit 40 MSPS A/D
Converter
The common-mode of the AD813x output is set at mid­supply by the voltage divider connected to V
OCM
, and ac
bypassed with a 0.1 µF capacitor. This provides for maximum dynamic range between the supplies at the output of the AD813x. The 110 Ω resistors at the AD813x output, along with the shunt capacitors form a one-pole, low-pass filter for lowering noise and antialiasing.
Figure 5 shows an FFT plot that was taken from the com­bined devices at an analog input frequency of 2.5 MHz
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and a 40 MSPS sampling rate. The performance of the AD813x compares very favorably with a center-tapped transformer drive, which has typically been the best way to drive this A-to-D converter. The AD813x has the advantage of maintaining dc performance, which a transformer solution cannot provide.
10
10
20
30
40
50
60
70
OUTPUT dBc
80
90
100
110
120
FUND
0
2ND
3RD
0
2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0
INPUT FREQUENCY – MHz
5TH
4TH
fS = 40MHz
= 2.5MHz
f
IN
6TH
9TH
7TH
8TH
Figure 5. FFT Response for AD813x Driving AD9203
BALANCED LINE DRIVING TWISTED-PAIR LINE DRIVER
When driving a twisted-pair cable, it is desirable to drive only a pure differential signal onto the line. If the signal is purely differential (i.e., fully balanced), and the trans­mission line is twisted and balanced, there will be a minimum radiation of any signal.
The complementary electrical fields will mostly be con­fined to the space between the two twisted conductors and will not significantly radiate out from the cable. The current in the cable will create magnetic fields that will radiate to some degree. However, with each twist, the two adjacent twists will have an opposite polarity mag­netic field. If the twist pitch is tight enough, these small magnetic field loops will contain most of the magnetic flux, and the magnetic far-field strength will be negligible.
Any imbalance in the differential drive signal will appear as a common-mode signal on the cable. This is the equivalent of a single wire that is driven with the com­mon-mode signal. In this case, the wire will act as an antenna and radiate. Thus, in order to minimize radia­tion when driving differential twisted-pair cables, the differential drive signal should be very well balanced.
The common-mode feedback loop in the AD813x helps to minimize the amount of common-mode voltage at the output, and therefore can be used to create a well-balanced differential line driver.
Figure 6 shows a circuit of an AD813x driving a twisted­pair line, like a Category 3 or Category 5 (Cat3 or Cat5), already installed in many buildings for telephony and data communications. The characteristic impedance of such transmission lines is usually about 100 Ω. The out- standing balance of the AD813x output will minimize the common-mode signal and therefore the amount of EMI generated by driving the twisted pair.
+5V
+
10␮F
0.1␮F
49.9
3
8
5
24.9
2
AD813x
1
6
–5V
4
49.9
0.1␮F
+
10␮F
100
AD8129/ AD8130
RECEIVER
49.9
Figure 6. Single-Ended-to-Differential 100 Ω Line Driver
The two resistors in series with each output terminate the line at the transmit end. Since the impedances of the outputs of the AD813x are very low, they can be thought of as a short circuit, and the two terminating resistors form a 100 termination at the transmit end of the transmission line. The receive end is directly terminated by a 100 resistor across the line.
This back-termination of the transmission line divides the output signal by two. The fixed gain-of-two of the AD813x will create a net unity gain for the system from end to end.
In this case, the input signal is provided by a signal generator with an output impedance of 50 . This is ter­minated with a 49.9 resistor near +D
of the AD813x.
IN
The effective parallel resistance of the source and termi­nation is 25 . The 24.9 resistor from –D matches the +D
source impedance and minimizes any
IN
to ground
IN
dc and gain errors.
If +D
is driven by a low-impedance source over a short
IN
distance, such as the output of an op amp, no termina­tion resistor is required at +D
. In this case, the –DIN can
IN
be directly tied to ground.
TRANSMIT EQUALIZER
Any length of transmission line will attenuate the signals it carries. This effect is worse at higher frequencies than at low frequencies. One way to compensate for this is to provide an equalizer circuit that boosts the higher quencies in the transmitter circuit, so that at the
fre-
receive
end of the cable the attenuation effects are diminished.
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By lowering the impedance of the RG component of the feedback network at higher frequency, the gain can be increased at high frequency. Figure 7 shows a gain of a two line driver that has its RGs shunted by 10 pF resis­tors. The effect of this is shown in the frequency response plot of Figure 8.
499
10pF
V
IN
24.9
49.9
249 249
10pF
499
49.9
49.9
100
V
OUT
Figure 7. Frequency Boost Circuit
20
10
0
10
20
– dB
IN
–30
/V
OUT
–40
V
50
60
70
80
1
10 100
FREQUENCY – MHz
1000
Figure 8. Frequency Response for Transmit Boost Circuit
MISCELLANEOUS APPLICATIONS Balanced Transformer Driver
Transformers are among the oldest devices that have been used to perform a single-ended-to-differential con­version (and vice versa). Transformers also can perform the additional functions of galvanic isolation, step-up or step-down of voltages, and impedance transformation. For these reasons, transformers will always find uses in certain applications.
However, when driving a transformer single-endedly and then looking at its output, there is a fundamental imbalance due to the parasitics inherent in the trans­former. The primary (or driven) side of the transformer has one side at dc potential (usually ground), while the other side is driven. This can cause problems in systems that require good balance of the transformer’s differen­tial output signals.
If the interwinding capacitance (C
) is assumed to be
STRAY
uniformly distributed, a signal from the driving source will couple to the secondary output terminal that is closest to the primary’s driven side. On the other hand, no sig­nal will be coupled to the opposite terminal of the secondary, because its nearest primary terminal is not driven (see Figure 9). The exact amount of this imbalance will depend on the particular parasitics of the trans­former, but will mostly be a problem at higher frequencies.
SIGNAL WILL BE COUPLED ON THIS SIDE VIA C
PRIMARY
52.3
NO SIGNAL IS COUPLED ON THIS SIDE
C
STRAY
C
STRAY
V
UNBAL
STRAY
500
0.005% 500
0.005%
SECONDARY V
DIFF
Figure 9. Transformer Single-Ended-to-Differential Converter Is Inherently Imbalanced
The balance of a differential circuit can be measured by connecting an equal-valued resistive voltage divider across the differential outputs and then measuring the center point of the circuit with respect ground. Since the two differential outputs are supposed to be of equal amplitude, but 180 degrees opposite phase, there should be no signal present for perfectly balanced outputs.
The circuit in Figure 9 shows a Minicircuits T1-6T trans­former connected with its primary driven single-endedly and the secondary connected with a precision voltage divider across its terminals. The voltage divider is made up of two 500 , 0.005% precision resistors. The voltage V
, which is also equal to the ac common-mode volt-
UNBAL
age, is a measure of how closely the outputs are balanced.
The plots in Figure 10 show a comparison between the where the transformer is driven single-endedly by generator and driven differentially using The top signal trace of Figure 10 shows the single-ended configuration, while the the differentially driven balance response.
an AD813x. the balance of bottom shows
The 100 MHz
case
a signal
balance is 35 dB better when using the AD813x.
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0
–20
V
, FOR TRANSFORMER
40
60
80
OUTPUT BALANCE ERROR dB
100
0.3 500
UNBAL
WITH SINGLE-ENDED DRIVE
V
, DIFFERENTIAL DRIVE
UNBAL
1 10 100
FREQUENCY – MHz
Figure 10. Output Balance Error for Circuits of Figure 9 and Figure 11
The well-balanced outputs of the AD813x will provide a drive signal to each of the transformer’s primary inputs that are of equal amplitude and 180 degrees out of phase. Thus, depending on how the polarity of the sec­ondary is connected, the signals that conduct across the interwinding capacitance will either both assist the transformer’s secondary signal equally, or both buck the secondary signals. In either case, the parasitic effect will be symmetrical and provide a well-balanced trans­former output. (See Figure 11.)
499
C
STRAY
C
STRAY
V
UNBAL
500
0.005%
500
0.005%
V
DIFF
499
499
+IN
–IN
499
49.9
OUT–
AD813x
OUT+
49.9
Figure 11. AD813x Forms a Balanced Transformer Driver
Full-Wave Rectifier
Figure 12 shows the configuration of such a circuit. Each of the AD813x outputs drives the anode of an HP2835 Schottky diode. These Schottky diodes were chosen for their high-speed operation. At lower frequencies (approxi­mately
lower than 10 MHz), a silicon signal diode such as
a 1N4148 can be used. The cathodes of the two diodes are connected together and this output node is con­nected to ground by a 100 resistor.
+5V
R
F1
–5V
348
R
348
HP2835
F2
R
L
100
V
OUT
R
G1
R
24.9
T2
10k
348
R
G2
348
5V
CR1
V
IN
R
T1
49.9
Figure 12. Full-Wave Rectifier
The diodes should be operated such that they are slightly forward-biased when the differential output voltage is zero. For the Schottky diodes, this is about 400 mV.
The forward biasing can be conveniently adjusted by CR1, which, in this circuit, raises and lowers V
OUT,cm
without
creating a differential output voltage.
One advantage of this circuit is that the feedback loop is never momentarily opened while the diodes reverse their polarity within the loop. This is the scheme that is sometimes used for full-wave rectifiers that use conven­tional op amps. These conventional circuits do not work well at frequencies above about 1 MHz.
If there is not enough forward bias (V
too low), the
OUT,cm
lower sharp cusps of the full-wave rectified output waveform will be rounded off. Also, as the frequency increases, there tends to be some rounding of the lower cusps. The forward bias can be increased to yield sharper cusps at higher frequencies.
There is not a reliable, entirely quantifiable, means to measure the performance of a full-wave rectifier. Since the ideal waveform has periodic sharp discontinuities, it should have (primarily even) harmonics that have no upper bound on the frequency. However, for a practical circuit, as the frequency increases, the higher harmonics become attenuated and the sharp cusps that are present at low frequencies become significantly rounded.
The circuit was run at a frequency up to 300 MHz and, while it was still functional, the major harmonic that remained in the output was the second. This made it look like a sine wave at 600 MHz. Figure 13 is an oscillo­scope plot of the output when driven by a 100 MHz,
2.5 V p-p input.
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Sometimes a second harmonic generator is actually useful, such as creating a clock to oversample a DAC by a
factor of two. If the output of this circuit is run
through
a low-pass filter, it can be used as a second har-
monic generator.
1V
100mV 2ns
Figure 13. Full-Wave Rectifier Response with 100 MHz Input
Differential Filtering Applications
Similar to an op amp, various types of active filters can be created with the AD813x. These can have single­ended inputs and differential outputs, which can provide an antialias function when driving a differential A/D converter.
Figure 14 is a schematic of a low-pass, multiple feedback filter. The active section contains two poles, and an additional pole is added at the output. The filter was designed to have a –3 dB frequency of 1 MHz. The actual –3 dB frequency was measured to be 1.12 MHz as shown in Figure 15.
2.15k
549
2k
V
IN
24.9
49.9
100pF
100pF
2k
953
953
2.15k
33pF
33pF
549
200pF
200pF
V
OUT
Figure 14. 1 MHz, 3-Pole Differential Output Low-Pass Multiple Feedback Filter
10
0
10
20
30
– dB
IN
–40
/V
OUT
–50
V
60
70
80
90
10k
100k 1M 10M 100M
FREQUENCY – Hz
Figure 15. Frequency Response of 1 MHz Low-Pass Filter
E02656–0–2/02(0)
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PRINTED IN U.S.A.
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