CN-0217: High Accuracy Impedance Measurements Using 12-Bit Impedance Converters PDF

Circuit Note
CN-0217
Devices Connected/Referenced
Circuits from the Lab™ reference circuits are engineered and
tested for quick and easy system integration to help solve today’s
analog, mixed-signal, and RF design challenges. For more
information and/or support, visit www.analog.com/CN0217.
AD5933
1 MSPS, 12-Bit Impedance Converter,
Network Analyzer
AD5934
250 kSPS, 12-Bit Impedance Converter,
Network Analyzer
AD8606
Precision, Low Noise, Dual CMOS Op Amp
High Accuracy Impedance Measurements Using 12-Bit Impedance Converters
EVALUATION AND DESIGN SUPPORT
CIRCUIT FUNCTION AND BENEFITS
Circuit Evaluation Boards
AD5933 Evaluation Board (EVAL-AD5933EBZ)
Design and Integration Files
Schematics, Layout Files, Bill of Materials
The AD5933 and AD5934 are high precision impedance converter
system solutions that combine an on-chip programmable frequency
generator with a 12-bit, 1 MSPS (AD5933) or 250 kSPS (AD5934)
analog-to-digital converter (ADC). The tunable frequency generator
allows an external complex impedance to be excited with a known
frequency.
The circuit shown in Figure 1 yields accurate impedance
measurements extending from the low ohm range to several
hundred kΩ, and it also optimizes the overall accuracy of the
AD5933/AD5934.
1.98V p-p
1.98V p-p
VDD
MCLK
AVDD
VDD
1.48V
VDD/2
DVDD
VDD
VDD
DDS
CORE
(27 BITS)
OSCILLATOR
DAC
VOUT
ROUT
SCL
SDA
I2C
INTERFACE
−
50kΩ
A1
+
47nF
50kΩ
TRANSMIT SIDE
OUTPUT AMPLIFIER
TEMPERATURE
SENSOR
ZUNKNOWN
A1, A2 ARE
½ AD8606
REAL
REGISTER
AD5933/AD5934
IMAGINARY
REGISTER
RFB
RFB
1024-POINT DFT
20kΩ
VIN
GAIN
I-V
VDD
LPF
VDD/2
AGND
−
A2
+
DGND
50kΩ
50kΩ
09915-001
ADC
(12 BITS)
20kΩ
Figure 1. Optimized Signal Chain for Impedance Measurement Accuracy (Simplified Schematic, All Connections and Decoupling Not Shown)
Rev. A
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CN-0217
Circuit Note
CIRCUIT DESCRIPTION
Matching the DC Bias of Transmit Stage to Receive Stage
The AD5933 and AD5934 have four programmable output voltage
ranges; each range has an output impedance associated with it.
For example, the output impedance for a 1.98 V p-p output voltage
is typically 200 Ω (see Table 1).
The four programmable output voltage ranges in the AD5933/
AD5934 have four associated bias voltages (see Table 2). For
example, the 1.98 V p-p excitation voltage has a bias of 1.48 V.
However, the current-to-voltage (I-V) receive stage of the AD5933/
AD5934 is set to a fixed bias of VDD/2 as shown in Figure 1.
Therefore, for a 3.3 V supply, the transmit bias voltage is 1.48 V, and
the receive bias voltage is 3.3 V/2 = 1.65 V. This potential difference
polarizes the impedance under test and can cause inaccuracies in
the impedance measurement.
Table 1. Output Series Resistance (ROUT) vs. Excitation Range
for VDD = 3.3 V Supply Voltage
Range
Range 1
Range 2
Range 3
Range 4
Output Excitation
Amplitude (V p-p)
1.98
0.97
0.383
0.198
Output Resistance (ROUT)
200 Ω typical
2.4 kΩ typical
1.0 kΩ typical
600 Ω typical
One solution is to add a simple high-pass filter with a corner
frequency in the low Hz range. Removing the dc bias from the
transmit stage and rebiasing the ac signal to VDD/2 keeps the dc
level constant throughout the signal chain.
The output impedance affects the impedance measurement
accuracy, particularly in the low kΩ range, and must be taken
into account when calculating the gain factor. Refer to the
AD5933 or AD5934 data sheets for more details on the gain
factor calculation.
Table 2. Output Levels and Respective DC Bias for VDD = 3.3 V
Supply Voltage
A simple buffer in the signal chain prevents the output impedance
from affecting the unknown impedance measurement. Select a
low output impedance amplifier with sufficient bandwidth to
accommodate the AD5933/AD5934 excitation frequency. An
example of the low output impedance achievable is shown in
Figure 2 for the AD8605/AD8606/AD8608 family of CMOS op
amps. The output impedance for this amplifier for an AV of 1 is
less than 1 Ω up to 100 kHz, which is the maximum operating
range of the AD5933/AD5934.
100
VS = 2.7V
90
70
AV = 100
60
50
AV = 10
AV = 1
20
10
0
1k
10k
100k
1M
FREQUENCY (Hz)
Output DC
Bias Level (V)
1.48
0.76
0.31
0.173
Selecting an Optimized I-V Buffer for the Receive Stage
The I-V amplifier stage of the AD5933/AD5934 can also add
minor inaccuracies to the signal chain. The I-V conversion
stage is sensitive to the amplifier's bias current, offset voltage,
and common-mode rejection ratio (CMRR). By selecting the
proper external discrete amplifier to perform the I-V conversion,
the user can choose an amplifier with lower bias current and
offset voltage specifications along with excellent CMRR, making
the I-V conversion more accurate. The internal amplifier can
then be configured as a simple inverting gain stage.
Optimized Signal Chain for High Accuracy Impedance
Measurements
40
30
Output Excitation
Amplitude (V p-p)
1.98
0.97
0.383
0.198
Selection of the RFB resistor still depends on the gain through
the system as described in the AD5933/AD5934 data sheets.
09915-002
OUTPUT IMPEDANCE (Ω)
80
Range
1
2
3
4
10M
Figure 2. Output Impedance of AD8605/AD8606/AD8608
100M
Figure 1 shows a proposed configuration for measuring low
impedance sensors. The ac signal is high-pass filtered and rebiased
before buffering with a very low output impedance amplifier. The
I-V conversion is completed externally before the signal returns
to the AD5933/AD5934 receive stage. Key specifications that
determine the required buffer are very low output impedance,
the single-supply capability, low bias current, low offset voltage,
and excellent CMRR performance. Some suggested parts are the
ADA4528-1, AD8628, AD8629, AD8605, and AD8606. Depending
on board layout, use a single-channel or dual-channel amplifier.
Use precision 0.1% resistors for both the biasing resistors (50 kΩ)
and gain resistors (20 kΩ and RFB) to reduce inaccuracies.
Rev. A | Page 2 of 6
Circuit Note
CN-0217
CIRCUIT EVALUATION AND TEST
35
25
20
15
1µF
0
29.95
30.00
30.05
30.10
30.15
FREQUENCY (kHz)
30.20
30.25
09915-003
5
Table 3. Low Impedance Range Setup for VDD = 3.3 V Supply
Voltage
Value
1.98 V (Range 1)
15
16 MHz
20.1 Ω
20.0 Ω
30 kHz to 30.2 kHz
R1 = 10.3 Ω, R2 = 30.0 Ω,
C3 = 1 µF (ZC = 5.3 Ω at
30 kHz)
10.3Ω
10
Example 1: Low Impedance Range
Figure 3. Measured Low Impedance Magnitude Results
20
10.3Ω, 30Ω
0
–20
PHASE (Degrees)
–40
–60
The results of the low impedance measurements are shown in
Figure 3, Figure 4, and Figure 5. Figure 5 is for the 10.3 Ω
measurement and is shown on an expanded vertical scale.
In addition, note that to achieve a wider range of measurements
a 200 mV p-p range was used. If the unknown Z is a small range, a
larger output voltage range can be used to optimize the ADC
dynamic range.
–100
29.95
30.00
30.05
30.10
30.15
FREQUENCY (kHz)
30.20
30.25
09915-004
1µF
Figure 4. Measured Low Impedance Phase Results
10.22
10.20
10.18
MAGNITUDE (Ω)
The accuracy achieved is very much dependent on how large the
unknown impedance range is relative to the calibration resistor,
RCAL. Therefore, in this example, the unknown impedance of
10.3 Ω measured 10.13 Ω, an approximate 2% error. Choosing
an RCAL closer to the unknown impedance achieves a more accurate
measurement; that is, the smaller the unknown impedance range is
centered on RCAL is the more accurate the measurement.
Consequently, for large unknown impedance ranges, it is possible
to switch in various RCAL resistors to break up the unknown
impedance range using external switches. The RON error of the
switch is removed by calibration during the RCAL gain factor
calculation. Using a switch to select various RFB values can
optimize the dynamic range of the signal seen by the ADC.
–80
10.16
10.14
10.12
10.10
10.08
10.06
10.04
29.50
30.00
30.05
30.10
30.15
FREQUENCY (kHz)
30.20
30.25
Figure 5. Measured 10.3 Ω Magnitude Results (Expanded Scale)
Rev. A | Page 3 of 6
09915-005
Parameter
Voltage Peak-to-Peak (V p-p)
Number of Settling Time Cycles
MCLK
RCAL
RFB
Excitation Frequency Range
Unknown Impedances
30Ω
30
MAGNITUDE (Ω)
The schematic in Figure 1 was developed to improve impedance
measurement accuracy, and some example measurements were
taken. The AD8606 dual-channel amplifier buffers the signal on
the transmit path and converts the receive signal from current to
voltage. For the three examples shown, the gain factor is calculated
for each frequency increment to remove frequency dependent
errors. A complete design package including schematics, bill of
materials, layout, and Gerber files is available for this solution at
www.analog.com/CN0217-DesignSupport. The software used is
the same software that is available with evaluation boards and is
accessible from the AD5933 and AD5934 product pages.
CN-0217
Circuit Note
Example 2: kΩ Impedance Range
–89.3
Using an RCAL of 99.85 kΩ, a wide range of unknown impedances
were measured according to the setup conditions listed in Table 4.
Figure 6 to Figure 10 document accuracy results. To improve
the overall accuracy, select an RCAL value closer to the unknown
impedance. For example, in Figure 9, an RCAL closer to the ZC
value of 217.5 kΩ is required. If the unknown impedance range
is large, use more than one RCAL resistor.
–89.4
–89.8
–89.9
–90.0
–90.1
Value
0.198 V (Range 4)
15
16 MHz
99.85 kΩ
100 kΩ
30 kHz to 50 kHz
R0 = 99.85 kΩ, R1 = 29.88 kΩ,
R2 = 14.95 kΩ, R3 = 8.21 kΩ,
R4 = 217.25 kΩ, C5 = 150 pF,
(ZC = 26.5 kΩ at 40 kHz),
C6 = 47 pF (ZC = 84.6 kΩ at
40 kHz)
–90.3
30
35
40
FREQUENCY (kHz)
45
50
09915-007
–90.2
Figure 7. Phase Result for ZC = 47 pF, RCAL = 99.85 kΩ
8280
R3
8260
120
110
8240
8220
8200
IDEAL
100
8160
30
IDEAL
35
90
40
FREQUENCY (kHz)
45
50
09915-008
8180
Figure 8. ZC = 8.21 kΩ, RCAL = 99.85 kΩ
218.5
80
MEASURED
70
35
40
FREQUENCY (kHz)
45
Figure 6. Magnitude Result for ZC = 47 pF, RCAL = 99.85 kΩ
50
IDEAL
217.5
217.0
216.5
216.0
R4
215.5
21.50
214.5
214.0
213.5
30
35
40
FREQUENCY (kHz)
45
Figure 9. ZC = 217.25 kΩ, RCAL = 99.85 kΩ
Rev. A | Page 4 of 6
50
09915-009
60
30
IMPEDANCE MAGNITUDE (kΩ)
218.0
09915-006
IMPEDANCE MAGNITUDE (kΩ)
–89.7
IMPEDANCE MAGNITUDE (Ω)
Parameter
Voltage Peak-to-Peak (V p-p)
Number of Settling Time Cycles
MCLK
RCAL
RFB
Excitation Frequency Range
Unknown Impedances
–89.6
PHASE (Degrees)
Table 4. kΩ Impedance Range Setup for VDD = 3.3 V Supply
Voltage
–89.5
Circuit Note
CN-0217
120
–60
R0
–65
–70
PHASE (Degrees)
80
C6
60
40
–80
IDEAL
MEASURED
–85
R1
C5
20
–90
R2
–95
32
34
36
38
40
42
44
46
48
50
FREQUENCY (kHz)
Figure 10. Magnitude Results for Example 2: R1, R2, R3, C5, C6
24
4
44
64
84
104
FREQUENCY (kHz)
Figure 12. Phase Results for ZC = 10 kΩ||10 nF, RCAL = 1 kΩ
Setup and Test
Example 3: Parallel R-C (R||C) Measurement
An R||C type measurement was also made using the configuration,
using an RCAL of 1 kΩ, an R of 10 kΩ, and a C of 10 nF, measured
across a frequency range of 4 kHz to 100 kHz. The magnitude
and phase results vs. ideal are plotted in Figure 11 and Figure 12.
Table 5. R||C Impedance Range Setup for VDD = 3.3 V Supply
Voltage
Parameter
Voltage Peak-to-Peak (V p-p)
Number of Settling Time Cycles
MCLK
RCAL
RFB
Excitation Frequency Range
Unknown Impedance R||C
09915-010
R3
0
30
Value
0.383 V (Range 3)
15
16 MHz
1 kΩ
1 kΩ
4 kHz to 100 kHz
R = 10 kΩ, C = 10 nF
The evaluation board software is the software used on the
EVAL-AD5933EBZ. Refer to the technical note available on the
CD provided with the evaluation board for details on the board
setup. Note that there are alterations to the schematic. Link
connections on the EVAL-AD5933EBZ board are listed in Table 4.
In addition, note that the location for RFB is located at R3 on the
evaluation board, and the location for ZUNKNOWN is C4.
Table 6. Link Connections for EVAL-AD5933EBZ
Link Number
LK1
LK2
LK3
LK4
LK5
LK6
4000
Default Position
Open
Open
Insert
Open
Insert
A
3500
Complete setup and operation for the hardware and software
for the evaluation board can be found in User Guide UG-364.
3000
COMMON VARIATIONS
2500
Other op amps can be used in the circuit, such as the ADA4528-1,
AD8628, AD8629, AD8605, and AD8608.
2000
Switching Options for System Applications
IDEAL
MEASURED
1500
1000
500
0
4
24
44
64
84
FREQUENCY (kHz)
Figure 11. Magnitude Results for ZC = 10 kΩ||10 nF, RCAL = 1 kΩ
104
09915-011
IMPEDANCE MAGNITUDE (Ω)
–75
09915–012
IMPEDANCE MAGNITUDE (kΩ)
100
For this particular circuit, the ZUNKNOWN and RCAL were interchanged
manually. However, in production, use a low on-resistance switch.
The choice of the switch depends on how large the unknown
impedance range is and how accurate the measurement result
needs to be. The examples in this circuit note use just one
calibration resistor, and so a low on-resistance switch, such as
the ADG849, can be used as shown in Figure 13. Multichannel
switch solutions, such as the quad ADG812, can also be used.
The errors caused by the switch resistance on the ZUNKNOWN are
removed during calibration, but by choosing a very low RON
switch, the effects can be further minimized.
Rev. A | Page 5 of 6
CN-0217
Circuit Note
LEARN MORE
CN-0217 Design Support Package:
http://www.analog.com/CN0217-DesignSupport
A1
MT-085 Tutorial, "Fundamentals of Direct Digital Synthesis
(DDS)," Analog Devices.
D
ADG849
Buchanan, David, "Choosing DACs for Direct Digital
Synthesis," AN-237 Application Note, Analog Devices.
IN
Riordan, Liam, "AD5933 Evaluation Board Example
Measurement," AN-1053 Application Note, Analog Devices.
S1
UG-364 User Guide for AD5933 Evaluation Board
S2
ADIsimDDS Design and Evaluation Tool
RFB
ZUNKNOWN
RCAL
AD5933/AD5934 Demonstration and Design Tool
Data Sheets and Evaluation Boards
A2
AD5933 Data Sheet
VDD
AD5933 Evaluation Board
50kΩ
09915–013
50kΩ
AD5934 Data Sheet
Figure 13. Switching Between RCAL and Unknown Z Using the ADG849
Ultralow RON SPDT Switch (Simplified Schematic, All Connections and
Decoupling Not Shown)
AD5934 Evaluation Board
AD8606 Data Sheet
ADG849 Data Sheet
ADG812 Data Sheet
REVISION HISTORY
3/13—Rev. 0 to Rev. A
Updated Table Numbers; Renumbered Sequentially....................3
Changes to Evaluation and Design Support Section ....................1
Changes to Setup and Test Section and Table 6 ............................5
Changes to Learn More Section ......................................................6
6/11—Revision 0: Initial Version
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CN09915-0-3/13(A)
Rev. A | Page 6 of 6
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