Mini Tutorial
MT-208
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Digitally Programmed State
Variable Filter
CMOS multiplying DACs. Note that R5 is implemented as the
feedback resistor implemented in the DAC. The schematic of
this circuit is shown in Figure 2.
by Hank Zumbahlen,
Analog Devices, Inc.
This example uses the AD7528 and the AD825. The AD7528 is
an 8-bit dual multiplying digital-to-analog converter (MDAC).
The AD825 is a high speed FET input op amp. Using these
components, the frequency range can be varied from around
550 Hz to around 150 kHz (see Figure 3). The Q can be varied
from approximately 0.5 to over 12.5 (see Figure 4). The gain of
circuit can be varied from 0 dB to –48 dB (see Figure 5).
IN THIS TUTORIAL
The parameters of digitally programmed state variable
filters can be adjusted individually. These filters are one of a
set of discrete circuits described in a series of mini tutorials.
The operation of the DACs in controlling the parameters can be
best thought of as the DACs changing the effective resistance of
the resistors. This relationship is
One of the attractive features of the state variable filter is that
the parameters (gain, cutoff frequency, and Q) can be individually adjusted. This attribute can be exploited to allow digital
control of these parameters.
DAC Equivalent Resistance
256 × DAC
Resistance
This, in effect, varies the resistance from 11 kΩ to 2.8 MΩ for
the AD7528.
To start, the state variable filter is reconfigured slightly. The
resistor divider that determines Q is changed to an inverting
configuration. The new filter schematic is shown in Figure 1.
Then the resistors R1, R2, R3 & R4 (of Figure 1) are replaced by
R7
R1
R8
R5
R3
C1
R4
C2
R6
AD825
LP OUT
AD825
AD825
AD825
BP OUT
R2
Figure 1. Redrawn State Variable Filter
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10411-001
IN
(1)
MT-208
Mini Tutorial
IN
R1
R2
LP OUT
R3
VIN RREF
HP OUT
CS
WR AD7528
IOUT
D0 … D7
AD825
AD825
...
LEVEL CONTROL
DAC A
R5
1kΩ
R6
1kΩ
C2
Q CONTROL
...
C1
DAC A
D0 … D7
DAC A
WR AD7528
IOUT
VIN RREF
CS
CS
AD7528
DAC A
VIN RREF
WR AD7528
IOUT
IOUT
CS
D0 … D7
VIN RREF
D0 . . .D7
AD825
AD825
...
...
FREQUENCY CONTROL
BP OUT
10411-002
WR
Figure 2. Digitally Controlled State Variable Filter
10
0
0
AMPLITUDE (dB)
AMPLITUDE (dB)
–20
–40
–10
–20
–40
–60
–80
0.1
0.3
1.0
3.0
10.0
30.0
FREQUENCY (kHz)
100.0
–80
0.1
1000.0
300.0
50
40
20
10
0
10411-004
AMPLITUDE (dB)
30
–20
0.1
0.3
1.0
FREQUENCY (kHz)
3.0
0.3
1.0
FREQUENCY (kHz)
3.0
10.0
Figure 5. Gain Variation vs. DAC Control Word
Figure 3. Frequency Response vs. DAC Control Word
–10
10411-005
10411-003
–60
One limitation of this design is that the frequency is dependent
on the ladder resistance of the DAC. This particular parameter
is not controlled. DACs are trimmed so that the ratios of the
resistors, not their absolute values, are controlled. In the case of
the AD7528, the typical value is 11 kΩ. It is specified as 8 kΩ
minimum and 15 kΩ maximum. A simple modification of the
circuit can eliminate this issue. The cost is two more op amps
(see Figure 6). In this case, the effective resistor value is set by
the fixed resistors rather than the DAC's resistance. Since there
are two integrators, the extra inversions caused by the added op
amps cancel.
10.0
Figure 4. Q Variation vs. DAC Control Word
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Mini Tutorial
MT-208
IN
R
C
OUT
VIN RREF
CS
REFERENCES
WR AD7528-4 IOUT
D0 … D7
AD825
Zumbahlen, Hank. Linear Circuit Design Handbook. Elsevier.
2008. ISBN: 978-7506-8703-4.
AD825
10411-006
...
CONTROL BUS
DAC A
used a digital pot in place of the MDACs. The difference is that
instead of increasing the effective resistance, the value of the pot
would be the maximum resistance.
Figure 6. Improved Digitally Variable Integrator
Note that multiplying DACs could be replaced by analog
multipliers. In this case, the control would obviously be an
analog rather than a digital signal. One could just as easily have
REVISION HISTORY
4/12—Revision 0: Initial Version
©2012 Analog Devices, Inc. All rights reserved. Trademarks and
registered trademarks are the property of their respective owners.
MT10411-0-4/12(0)
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