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Texas Instruments DC Controlled Low Pass Filter Application notes
Application Report
SLOA240 – March 2017
DC Controlled Low-Pass Filter
Sanjay Dixit and Leni Skariah
ABSTRACT
This application report describes a dc controlled low-pass filter circuit using LM3046. The cut off frequency
can be varied by varying the capacitance of the low-pass filter.
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Contents
Introduction ...................................................................................................................
Basic Theory .................................................................................................................
Schematic Diagram ..........................................................................................................
Schematic Description ......................................................................................................
Test Results ..................................................................................................................
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List of Figures
1
DC Controlled Low-Pass Filter ............................................................................................. 2
2
DC Controlled Low-Pass Filter Schematic ............................................................................... 3
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Plot of Cut Off Frequencies vs Control Voltage
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With Vcontrol = 6 V, Fc = 20.7 KHz ........................................................................................... 4
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With Vcontrol = 5 V, Fc = 12.7 KHz ........................................................................................... 4
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With Vcontrol = 4 V, Fc = 7.42 KHz ........................................................................................... 4
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With Vcontrol = 3 V, Fc = 5.88 KHz ........................................................................................... 4
8
With Vcontrol = 2 V, Fc = 4.6 KHz............................................................................................. 4
9
With Vcontrol = 1 V, Fc = 4.39 KHz ........................................................................................... 4
.........................................................................
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Trademarks
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Introduction
In medical ultrasound systems, in the CW Doppler mode the received echoes are passed through the CW
mixer of the receive AFEs to demodulate the Doppler frequencies and produce I and Q signals. Output of
all the AFEs are summed, filtered and amplified before digitizing. The filter requires variable cut off based
on the analog signal bandwidth. The filter cut off frequencies can be selected by using a DC controlled
variable capacitance circuit. By using this method continuously variable cut off frequencies can be
achieved over a large range of frequency and this circuit has large signal handling capability. This can
also be used as front end for precision ADCs as anti-aliasing filter and any general purpose low-pass filter.
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1
Basic Theory
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Basic Theory
K
Vin
C
Zin
Va
R
V to I
Iin
re
Figure 1. DC Controlled Low-Pass Filter
In a differentiator, output voltage leads the input voltage by 90° , so Va leads VIN by 90°. Therefore, IIN
leads VIN by 90° that is the known property of a capacitor. By varying the phase shifted current, it is
possible to vary the capacitance of the circuit. Current can be controlled by a DC control voltage (multiplier
K).
As shown in Figure 1, Va is the output voltage of the differentiator. The equation for Va is shown in
Equation 1.
Va
§
VIN u R / ¨ R
©
1 ·
SC ¸¹
(1)
For a high-pass filter, Xc >> R, R can be neglected in the denominator and then Equation 1 becomes the
following:
Va
VIN u S u C u R
(2)
In Figure 1, the current Iin is shown as follows:
IIN
K u Va / re
(3)
By substituting Va from Equation 2 into Equation 3,Equation 3 then becomes as follows:
IIN
VIN u SC u R u
K
re
(4)
In Figure 1, the impedence Zin is shown as follows:
ZIN
VIN / IIN
where
(5)
By substituting ZIN in Equation 4 becomes the following:
ZIN 1 / s C u R u K / re
(6)
Therefore, ZIN is a capacitor of the value C × R × K/re:
Ceff
CuR u
K
re
(7)
and the circuit is capacitive.
By substituting the information from Equation 7 in the equation of the cut off frequency (fc =
1/(2*3.14*R*C)), the equation becomes Equation 8.
fc
1
* 3.14 * R1* Ceff
2
(8)
For Ceff, re, C, R, R1, see Figure 2. By substituting Equation 7 into Equation 8, Equation 8 becomes as
follows:
fc
K·
§
1/ ¨ 2 u S u R1 u C u R u ¸
re ¹
©
(9)
Hence, because of the differences in the value of ‘K’, the cut off frequencies of the filter can be varied.
2
DC Controlled Low-Pass Filter
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Schematic Diagram
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3
Schematic Diagram
AC Coupled Input
R1
IC½ + IC2/2
Multiplier
Ic1/2
Ic2/2
DC Bias Insertion
& Buffer
C
Q1
Q2
Q3
Differentiator
Q4
Ic2
LM3046
R
VE
Current Source
re
C1
Ic1
Figure 2. DC Controlled Low-Pass Filter Schematic
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Schematic Description
The variable capacitance circuit is implemented using an analog multiplier that uses four transistors, which
are used to make the dc conditions stable. This circuit can be integrated into a single LM3046 IC as
shown in Figure 2. Differentiator output drives the current source and the multiplier factor, K is varied by
the dc control voltage.
4.1
DC Conditions
Ic1
Va
33k
3V
33K
0.1 mA
(10)
For dc, C1 is open, therefore,
Ic 2
V22K
Ve
24.3K
1.74 V
24.3K
0.07 mA
(11)
22K u IC1 / 2 IC 2 / 2
(12)
By substituting IC1 and IC2 in Equation 10 and Equation 11 into Equation 12, the equation becomes
Equation 13.
V22K
§ 0.1
22K u ¨
© 2
0.07 ·
mA
2 ¸¹
1.87 V
(13)
So, the dc operating voltage, Vdc = 8 V – 1.87 V = 6.13 V, 8 V is set by the DC bias insertion, see
Figure 2.
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Schematic Description
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As Vcontrol increases, the current through Q2 increases, therefore, the current through Q1 is reduced. As
current through Q1 is reduced, the current through Q3 increases. which in turn makes the dc operating
voltage constant at 6.13 V. By the four transistor configuration dc, the bias point is kept stable.
4.2
AC Conditions
For AC conditions, C1 is short and the emitter resistor is re . In ac conditions, Q3 and Q2 do not come into
play. As Vcontrol increases, Q2 becomes more conductive and the current through Q1 is reduced. This
reduces the Ceff value; finally, Q1 stops conducting and the capacitance value becomes zero. For more
information, see Figure 2 for Q1. Q1. Q2. Q3. Q4. Ic1, IC2.
4.3
Example
R = 800 Ω
C = 4. 7 nF, for K = 1
Ceff = (4.7 nF × 800 Ω ×1)/2.3K
= 1.63 nF
Provided f ≪ fcutoff_differentiator
And, R1 = 22K
fc
1
u 3.14 u R1 u Ceff
2
(14)
By substituting Ceff and R1 in Equation 14 becomes fc = 4.46 KHz for K = 1.
Fcutoff
_differentiator
= 1/2 × π × R × C = 1/2 × 3.14 × 800 × 4.7 nF = 42.5 KHz
The cut off frequency is higher than the range of the filter suggested. Therefore, by varying the dc control
voltage in this example from 1 V to 6 V, the fc can be varied from 4.4 KHz to 21 KHz.
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Test Results
The circuit is tested using 1 Vpp sine wave source and the results are as shown in Figure 3.
22
20
F Cutoff (KHz)
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12
10
8
6
4
1
2
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4
V Control (V)
5
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Figure 3. Plot of Cut Off Frequencies vs Control Voltage
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DC Controlled Low-Pass Filter
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Test Results
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Figure 4. With Vcontrol = 6 V, Fc = 20.7 KHz
Figure 5. With Vcontrol = 5 V, Fc = 12.7 KHz
Figure 6. With Vcontrol = 4 V, Fc = 7.42 KHz
Figure 7. With Vcontrol = 3 V, Fc = 5.88 KHz
Figure 8. With Vcontrol = 2 V, Fc = 4.6 KHz
Figure 9. With Vcontrol = 1 V, Fc = 4.39 KHz
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