3ĆV Accelerometer Featuring TLV2772
`
`Application Report
`
`1998
`
`Advanced Analog Products
`
`SLVA040
`
`APPLE 1040
`
`1
`
`

`

`IMPORTANT NOTICE
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`Copyright  1998, Texas Instruments Incorporated
`
`2
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`2
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`3-V Accelerometer Featuring TLV2772
`
`Application Report
`
`Jim Karki
`Advanced Analog Products
`Advanced Analog Applications Group
`Abstract
`This paper describes a complete solution for digital measurement of acceleration. An AMP accelerometer
`sensor is used for the conversion between mechanical acceleration and electrical analog. This electrical signal
`is then conditioned using Texas Instruments’ TLV2772 op amp (on the Universal Op Amp EVM), digitized using
`the TLV1544 ADC EVM, and processed with the TMS320C5X EVM. This provides the user with a quick and easy
`way to evaluate a complete 3-axis accelerometer solution.
`
`Contents
`
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`1 Introduction
`5
`2 System Description
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`6
`2.1 Sensor
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`7
`2.2 Signal Conditioning
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`7
`2.3 ADC
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`7
`2.4 Processor, Memory, and Display
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`7
`3 System Specification Requirements
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`7
`3.1 G-Force Measurement Requirements
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`7
`3.2 Power Requirements
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`7
`4 Sensor and Signal Conditioning Design
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8
`4.1 Hand Analysis
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8
`4.2 Spice Simulation
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`11
`5 Circuit Realization
`14
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5.1 Test of Signal Conditioning Circuit
`17
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5.2 Test of Shock Sensor and Signal Conditioning Circuit
`17
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5.3 TLV1544 EVM
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`18
`5.4 Interfacing the TLV1544 EVM to the TMS320C5C EVM
`19
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5.5 The TMS320C5X EVM
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`19
`6 Error and Noise Analysis
`20
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`6.1 System Gain Error Analysis
`20
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`6.2 System Noise Analysis
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`21
`7 System Test and Evaluation
`23
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8 Calibration Data/Analysis
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`24
`8.1 Calibration
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`24
`9 References
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`27
`Appendix A. Source Code Listings
`28
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
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`3
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`3
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`3-V Accelerometer Featuring TLV2772
`
`Figures
`
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`1–1 Typical Analog Data Collection System
`5
`2–1 Accelerometer System Diagram
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`6
`4–1 1-Axis Accelerometer Sensor and Signal Conditioning Circuit
`. . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8
`4–2 DC Circuit Model
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8
`4–3 AC Circuit Model
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`9
`4–4 Bode Plot H1(s) = Vp/Vi
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`10
`4–5 Bode Plot of H2(s) = Vo/Vp
`10
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`4–6 Bode Plot of H3(s) = Vadc/Vo
`11
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`4–7 Bode Plot of H(s) = Vadc/Vi
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`11
`4–8 TLV2772 Sub-Circuit Model
`12
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`4–9 SPICE Simulation Schematic
`13
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`4–10 SPICE Simulation Results
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`13
`5–1 Signal Conditioning Schematic using Two Universal Operational Amplifier EVM Boards
`16
`. . .
`5–2 Network Analyzer Display
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`17
`5–3 Spring Test Fixture
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`17
`5–4 Output Displayed on Oscilloscope
`18
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5–5 Schematic – Signal Conditioning to TLV1544 ADC
`19
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5–6 Interface Between TLV1544 EVM and TMS320C5X EVM
`19
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`6–1 Sampling Input Model
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`21
`7–1 X-Axis Acceleration Graphed in Excel
`23
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8–1 X-Axis Output Vs. Input
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`24
`8–2 X-Axis % Error
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`25
`8–3 Y-Axis Output vs. Input
`25
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8–4 Y-Axis % Error
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`26
`8–5 Z-Axis Output vs. Input
`26
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8–6 Z-Axis % Error
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`27
`8–7 Average Output vs. Input Over Frequency for Each Axis
`27
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`Tables
`
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5–1 Board 1 – Universal Operational Amplifier EVM Area 100
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5–2 Board 2 – Universal Operational Amplifier EVM Area 100
`5–3 Board 1 – Universal Operational Amplifier EVM Area 100 ACH-04-08-05 Connections
`. . . . . .
`5–4 Interface Between Signal Conditiioning Circuit and TLV1544 EVM
`. . . . . . . . . . . . . . . . . . . . . . . .
`8–1 X-Axis Output Vs. Input Using X-Axis Mean Sensitivity = 1.16 mV/g
`. . . . . . . . . . . . . . . . . . . . . .
`8–2 X-Axis % Error
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8–3 Y-Axis Output Vs. Input Using Y-Axis Mean Sensitivity = 1.35 mV/g
`. . . . . . . . . . . . . . . . . . . . . . .
`8–4 Y-Axis % Error
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`8–5 Z-Axis Output Vs. Input Using Z-Axis Mean Sensitivity = 1.01 mV/g
`. . . . . . . . . . . . . . . . . . . . . . .
`8–6 Z-Axis % Error
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`14
`14
`16
`18
`24
`25
`25
`26
`26
`27
`
`4
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`4
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`

`

`3-V Accelerometer Featuring TLV2772
`
`1 Introduction
`
`Accelerometers are used in aerospace, defense,
`automotive, household appliances, instrumentation,
`audio, transport, material handling, etc. This application
`report develops a data collection system for
`acceleration in 3 axis.
`
`Figure 1 shows a block diagram of a typical analog
`data collection system. This application presents
`information about the sensor, signal conditioning, ADC,
`processor, display, and memory.
`
`Power
`Supply
`
`Distribution
`
`Display
`
`Memory
`
`Sensor
`
`ADC
`
`Processor
`
`DAC
`
`Signal
`Conditioning
`
`Analog
`Output
`
`Signal
`Conditioning
`
`Figure 1–1. Typical Analog Data Collection System
`
`
`
`5
`
`5
`
`

`

`3-V Accelerometer Featuring TLV2772
`
`Figure 2.1 shows the accelerometer system diagram
`
`2 System Description
`
`0.1mF
`
`AVDD
`
`DVDD
`
`FB
`
`FB
`
`NC
`
`87 6 5
`
`OUT
`OUT
`SENSE
`PG
`
`IN
`IN
`EN
`GND
`
`12 3 4
`
`0.1mF
`
`10mF
`
`4 V 10 V
`
`Supply Range
`
`TPS7133
`
`AVDD
`
`Platform
`
`PC
`
`ISA
`
`INT3
`
`FSR
`
`FSX
`
`DR
`
`DX
`
`XF
`
`CLKX
`CLKR
`
`TMS320C50PQ
`
`DPS
`
`40
`124
`
`104
`
`43
`
`106
`
`109
`
`124
`
`46
`
`6
`3 1
`
`3
`2 1 1
`
`I/O Interface
`
`FS
`
`4
`
`EOC
`
`DATA OUT
`
`14
`GNDREF–
`
`11
`
`A3
`
`DATA IN
`
`CS
`
`TLV1544D
`
`Z-axis
`
`1 kW
`
`9
`
`A2
`
`8
`
`A1
`
`7
`
`X-axis
`
`I/O CLK
`VCCREF+INVCLKCSTART
`10
`
`12
`
`15
`
`A0
`
`6
`
`5
`
`20 kW
`
`20 kW
`
`AVDD2.4 V
`
`DVDD
`
`Y-axis
`
`22mF
`
`Reference
`
`Signal Condition
`
`Computer
`Personal
`
`(TMS320C5XEVM)
`
`Data Processor
`
`(TLV1544ADCEVM)
`
`Data Converter
`
`10mF
`
`0.1mF
`
`R
`
`C A
`
`TLV431
`
`V+
`
`2.2 kW
`
`1.23 V
`
`100 kW
`
`0.22mF
`
`TLV2772
`
`1
`
`8
`
`4
`
`– +
`
`32
`
`V+
`
`100 kW
`
`2.2 nF
`
`0.22mF
`
`TLV2772
`
`1 kW
`
`7
`
`– +
`
`56
`
`100 kW
`
`2.2 nF
`
`0.22mF
`
`TLV2772
`
`1 kW
`
`1
`
`8
`
`4
`
`– +
`
`32
`
`V+
`
`100 kW
`
`1 kW
`
`1.23 V
`
`2.2 nF
`
`0.22 mF
`1 Meg
`
`7.5 kW
`
`100 kW
`
`0.22 mF
`1 Meg
`
`10 kW
`
`100 kW
`
`0.22 mF
`1 Meg
`
`10 kW
`
`,9,13
`
`4 8 3
`
`CTG
`
`GND
`
`SGND
`
`10
`
`RGND-Z
`
`Z-axis
`
`12
`
`D/S2-Z
`
`4
`1 2 1
`
`1
`5 6 7 1
`
`D/S1-Z
`
`RGND-X
`
`X-axis
`
`D/S2-X
`
`D/S1-X
`
`RGND-Y
`
`Y-axis
`
`D/S2-Y
`
`D/S1-Y
`
`1.23 V
`
`V+
`
`ACH-04-08-05
`
`Signal Conditioning
`
`Sensor and
`
`Figure 2–1. Accelerometer System Diagram
`
`6
`
`
`
`6
`
`

`

`3-V Accelerometer Featuring TLV2772
`
`2.1 Sensor
`An AMP ACH04-08-05 shock sensor converts
`mechanical acceleration into electrical signals. The
`shock sensor contains three piezoelectric sensing
`elements oriented to simultaneously measure
`acceleration in three orthogonal linear axes. The
`sensor responds from 0.5 Hz to above 5 kHz. An
`internal JFET buffers the output. Typical output voltage
`for x and y axis is 1.80 mV/g. Typical output voltage for
`the z axis is 1.35 mV/g. Refer to AMP’s web site at
`http://www.amp.com/sensors for in-depth information
`about this sensor, piezo materials in general, and other
`related products.
`
`2.2 Signal Conditioning
`Circuitry using the Texas Instruments TLV2772
`operational amplifier provides amplification and
`frequency shaping of the shock sensor output. Due to
`its high slew rate and bandwidth, rail-to-rail output
`swing, high input impedance, high output drive and
`excellent dc precision the TLV2772 is ideal for this
`application. The device provides 10.5 V/m s slew rate
`and 5.1 MHz gain bandwidth product while consuming
`only 1 mA of supply current per amplifier. The
`rail-to-rail output swing and high output drive make this
`device ideal for driving the analog input to the TLV1544
`analog-to-digital converter. The amplifier typically has
`360 m V input offset voltage, 17 nV/vHz input noise
`voltage, and 2 pA input bias current. Refer to Texas
`Instruments’ web site at http://www.ti.com and search
`on TLV2772 to download a TLV2772 data sheet,
`literature #SLOS209.
`
`The Universal Operational Amplifier EVM is used to
`construct the ACH04-08-05 shock sensor and TLV2772
`operational amplifier circuitry. The Universal
`Operational Amplifier EVM facilitates construction of
`surface mount operational amplifier circuits for
`engineering evaluation. Refer to Texas Instruments’
`web site at http://www.ti.com to download the Universal
`Operational Amplifier EVM User’s Manual, literature
`#SLVU006.
`
`2.3 ADC
`The TLV1544 EVM provides analog-to-digital
`conversion. The TLV1544 is a low-voltage (2.7 V to 5.5
`V dc single supply), 10-bit analog-to-digital converter
`(ADC) with serial control, 4 analog inputs, conversion
`time = 10 m s, and programmable 1 m A power down
`mode. Refer to Texas Instruments’ web site at
`http://www.ti.com to download a TLV1544 data sheet,
`literature #SLAS139B, TLV1544 EVM User’s Manual,
`literature #SLAU014, and related information.
`
`2.4 Processor, Memory, and Display
`The TMS320C5x EVM controls and collects data
`samples from the TLV1544. Refer to Texas
`Instruments’ web site at http://www.ti.com to download
`the TMS320C5x EVM Technical Reference, literature
`#SPRU087, and related information .
`The TMS320C5x EVM installs into a PC platform. The
`PC provides programming and control of the
`TMS320C5x EVM , and provides resources for file
`storage or other processing of the collected data.
`
`3 System Specification Requirements
`
`The following system specification requirements were
`derived to guide the design.
`
`3.1 G-Force Measurement Requirements
`±50g
`Range:
`Noise:
`0.05g pk-pk (equivalent input noise
`measured in g)
`Resolution: 0.1g
`Frequency Response: 1 Hz to 500 Hz (min 3 dB BW)
`
`3.2 Power Requirements
`Input Voltage: 3 V ±10%, Noise = 30 mV pk-pk
`(20 MHz BW)
`Input Current: 5 mA (max) (power requirements for
`sensor and signal conditioning
`circuitry)
`
`
`
`7
`
`7
`
`

`

`3-V Accelerometer Featuring TLV2772
`
`4 Sensor and Signal Conditioning Design
`
`Circuit design is a 3-step process:
`1. Hand analysis
`2. SPICE simulation
`3. Circuit breadboard and lab testing
`The signal from the sensor must be amplified and
`frequency shaped to provide a signal that the ADC can
`properly convert into a digital number.
`The schematic in Figure 4–1 shows the topology used
`in this application for 1 axis of the sensor and signal
`conditioning circuit.
`
`Input power is 3 V and ground. The TLV431 precision
`voltage regulator, when configured as shown, produces
`a nominal 1.23-V reference voltage. This voltage
`provides the signal reference for the signal conditioning
`circuitry and the bias voltage for the internal JFETs in
`the shock sensor.
`The transfer function of the signal conditioning circuit is
`derived by several means, the easiest of which may be
`by using super position. Perform a dc analysis, perform
`an ac analysis, and superimpose the results.
`
`VDD
`
`VREF
`
`R6
`
`R
`
`C
`
`A
`
`TLV431
`
`Voltage Referance
`
`Output
`to ADC
`
`C3
`
`C2
`
`R4
`
`VDD
`
`8
`
`– +
`
`1/2
`TLV2772
`
`1
`
`R5
`
`4
`
`Signal
`Conditioning
`
`VREF
`
`R3
`
`VDD
`
`1 Axis ACH–04–08–05
`
`R2
`
`2 3
`
`Input From Sensor
`
`VREF
`
`C1
`
`R1
`
`Shock Sensor
`
`Figure 4–1. 1-Axis Accelerometer Sensor and Signal Conditioning Circuit
`
`4.1 Hand Analysis
`In hand analysis, simplifying assumptions make
`solutions easier to derive. If the circuit does not
`function as anticipated, these assumption must be
`reevaluated.
`
`DC Analysis
`4.1.1
`To perform a dc analysis, assume all inductors are
`short circuits and all capacitors are open circuits.
`Assume that the resistance of R2 is insignificant
`compared to the input impedance of the op amp.
`Therefore, Vref will appear at the positive input to the
`op amp.
`Assuming the ADC input does not impose a significant
`load on the circuit, the voltage divider formed between
`the ADC input and R5 can be disregarded.
`
`R4
`
`VDD
`
`8
`
`– +
`
`1/2
`TLV2772
`
`VREF
`
`R3
`
`2 3
`
`Vn
`
`Vp
`
`1
`
`Vdc
`
`4
`
`Signal
`Conditioning
`
`Figure 4–2. DC Circuit Model
`
`8
`
`
`
`8
`
`

`

`3-V Accelerometer Featuring TLV2772
`
`Vp+ Vi
`
`H1(s) +
`
`or
`
`R2
`R2 ) 1ńsC1
`Vp
`R2
`Vi +
`R2 ) 1ńsC1
`
`4.1.2.2 H2(s) = Vo / Vp
`The amplifier gain is found by solving for H2(s) =
`Vo/Vp. The solution is a non-inverting amplifier with:
`Vo
`Vp+ ǒ1 )
`3Ǔ
`
`H2(s) +
`
`ZR
`
`Where:
`R4
`Z+
`1 ) sC2R4
`substituting
`
`H2(s) +
`
`Vo
`Vp+ 1 )
`
`R4
`R3ǒ
`
`1
`
`1 ) sC2R4Ǔ
`4.1.2.3 H3(s) = Vadc / Vo
`Assuming that the input impedance to the TLV1544
`ADC is very high in comparison to the impedance of
`C3 and R5, C3 and R5 form a passive low-pass filter
`where:
`1
`Vadc+ Vo
`1 ) sC3R5
`Vadc
`1
`Vo +
`1 ) sC3R5
`
`or
`
`H3(s) +
`
`4.1.2.4 H(s) = Vadc / Vi
`Superimposing the results from above gives the overall
`transfer function:
`Vadc
`
`R2
`
`Vi + ǒR2 ) 1ńsC1Ǔ
`
`H(s) +
`R4
`ǒ1 )
`1 ) sC2R4ǓǓ ǒ
`R3ǒ
`1 ) sC3R5Ǔ
`
`1
`
`1
`
`To find the complete response, add the ac and dc
`components so that:
`
`Vadc = Vi H(s) + Vref
`
`4.1.3 Gain Calculation
`Since the TLV2772 is capable of rail-to-rail output, with
`a 3 V supply, Vout min = 0 V and Vout max = 3 V. With
`no signal from the sensor, Vout nom = reference
`voltage = 1.23 V. Therefore, the maximum negative
`swing from nominal is 0 V – 1.23 V = –1.23 V, and the
`maximum positive swing is 3 V – 1.23 V = 1.77 V.
`Model the shock sensor as a low impedance voltage
`source with output of 2.25 mV/g max in the x and y axis
`and 1.70 mV/g max in the z axis, and calculate the
`required amplification of the signal conditioning circuit
`as follows:
`Gain = Output Swing ÷ (Sensor Sensitivity ⋅ Acceleration)
`
`
`
`9
`
`The dc model shown in Figure 4–2 is based on the
`assumptions made above.
`The gain of the amplifier with reference to the negative
`input, Vn, is:
`Vdc
`Vref+ –R4
`R3
`The gain of the amplifier with reference to the
`positive input, Vp is:
`
`or Vdc + –Vref R4
`R3
`
`Vdc
`R4
`R4
`R3Ǔ
`R3Ǔ or Vdc + Vref ǒ1 )
`Vref+ ǒ1 )
`Superimposing the positive and negative dc gains of
`the amplifier results in:
`
`Vdc = Vref
`
`The output of the amplifier is referenced to Vref. The ac
`response is superimposed upon this dc level.
`
`4.1.2 AC Analysis
`For ac analysis break the circuit into 3 parts and
`determine the transfer functions;
`• H1(s) = Vp / Vi
`• H2(s) = Vo / Vp
`• H3(s) = Vadc / Vo
`Combine the results to obtain the overall transfer
`function:
`• H(s) = Vadc / Vi
`Where Vi is the input signal from the shock sensor and
`Vadc is the output signal to the analog-to-digital
`converter. Figure 4–3 shows the ac model with the dc
`sources shorted.
`
`C2
`
`R4
`
`VDD
`
`8
`
`1/2
`TLV2772
`
`– +
`
`1
`
`vO
`
`R5
`
`Vadc
`Output
`to ADC
`
`4
`
`C3
`
`Signal
`Conditioning
`
`R3
`
`Input
`Form
`Sensor
`
`vI
`
`vn
`
`C1
`
`vp
`
`2
`
`3
`
`R2
`
`Figure 4–3. AC Circuit Model
`
`4.1.2.1 H1(s)=Vp /Vi
`Capacitor C1 and resistor R2 form a passive high-pass
`filter from the sensor input to the high impedance
`positive input to the TLV2772 where:
`
`9
`
`

`

`3-V Accelerometer Featuring TLV2772
`
`4.1.4.2 Component Values for H2(s) = Vo/Vp
`To minimize phase shift in the feedback loop caused by
`the input capacitance of the TLV2772, it is best to
`minimize the value of feedback resistor R4. Also, to
`reduce the required capacitance in the feedback loop,
`a large-value resistor is required for R4. A compromise
`value of 100 kW
` is used for R4. To set the upper cutoff
`frequency, the required capacitor value for C2 is:
`C2 = 1 ÷ (2p × upper cutoff frequency (Hz) × R4 (W
`C2 = 1 ÷ (6.28 × 500 Hz × 100 kW
`) = 3.18 nF
`A more common 2.2 nF capacitor is used for C2. This
`changes the upper cutoff frequency to 724 Hz.
`
`))
`
`Phase – deg
`
`180
`
`90
`
`0
`
`–90
`
`–180
`
`Gain
`
`Phase
`
`40
`
`20
`
`0
`
`–20
`
`–40
`
`Gain – dB
`
`0.1
`
`1
`
`100
`1k
`10
`f – Frequency – Hz
`
`10k
`
`100k
`
`Figure 4–5. Bode Plot of H2(s) = Vo/Vp
`
`Using the amplifier gain calculated above, Figure 4–5
`shows the bode plot approximation to the transfer
`function H2(s) = Vo/Vp for the x and y channels. The z
`channel is the same except the gain is slightly higher in
`the pass band.
`
`4.1.4.3 Component Values for H3(s) = Vadc/Vo
`Resistor R5 and capacitor C3 cause the signal
`response to roll-off further. To set the frequency for this
`roll off to begin at the upper cutoff frequency, select
`1÷(2p
`⋅C3(F) × R4(W
`)) = upper cutoff frequency(Hz).
`With R5 = 1 kW
` and C3 = 0.22 m F, the roll-off frequency
`= 1 ÷ (6.28 × 0.22 m F × 1 kW
`) = 724 Hz.
`Figure 4–6 shows the bode plot approximation to the
`transfer function H3(s) = Vadc/Vo.
`
`To avoid saturating the op amp, base the gain
`calculations on the maximum negative swing of
`–1.23 V and the maximum sensor output of 2.25 mV/g
`for the x and y axis, and 1.70 mV/g for the z axis.
`Therefore:
`Gain(x,y) = –1.23 V ÷ ( 2.25 mV/g × (–50g)) = 10.9 and
`Gain(z) = –1.23 V ÷ ( 1.70 mV/g × (–50g)) = 14.5
`Choosing R3 = 10 kW
` and R4 = 100 kW
`, gives a gain of
`11 in the x and y channels. Choosing R3 = 7.5 kW
` and
`R4 = 100 kW
`, gives a gain of 14.3 in the z channel.
`
`4.1.4 Bandwidth Calculations
`To calculate the component values for the frequency
`shaping characteristics of the signal conditioning
`circuit, use 1 Hz and 500 Hz as the minimum required
`3-dB bandwidth from the specifications requirements.
`
`4.1.4.1 Component Values for H1(s) = Vp / Vi
`To minimize the value of the input capacitor required to
`set the lower cutoff frequency, a large value resistor is
`required for R2. A 1 MW
` resistor is used here. To set
`the lower cutoff frequency, the value for capacitor C1
`must be:
`C1 = 1 ÷ (2p × lower cutoff frequency (Hz) × R2 (W
`C1 = 1 ÷ (6.28 × 1 Hz × 1 MW
`) = 0.159 m F
`A more common 0.22-m F capacitor is used for C1. This
`moves the lower cutoff frequency to 0.724 Hz.
`Figure 4–4 shows the bode plot approximation to
`the input transfer function, H1(s) = Vp/Vi.
`
`))
`
`Phase – deg
`
`180
`
`90
`
`0
`
`–90
`
`–180
`
`Phase
`
`Gain
`
`40
`
`20
`
`0
`
`–20
`
`–40
`
`Gain – dB
`
`0.1
`
`1
`
`1k
`100
`10
`f – Frequency – Hz
`
`10k
`
`100k
`
`Figure 4–4. Bode Plot H1(s) = Vp/Vi
`
`10
`
`
`
`10
`
`

`

`3-V Accelerometer Featuring TLV2772
`
`4.2 Spice Simulation
`Spice simulation verifies the results of hand analysis
`and provides a more accurate result than what is
`practical by hand.
`The proper models must be used to perform SPICE
`simulation of the shock sensor and signal conditioning
`circuit.
`The data sheet for the ACH-04-05-08 shock sensor
`states that the internal JFET used to drive the output is
`similar to the industry standard 2N4117. To model the
`sensor, a signal source is used to drive the gate of a
`2N4117 JFET and proper bias is applied.
`Modeling the signal conditioning circuit is straight
`forward except that most available SPICE versions do
`not have a library model for the TLV2772. This is easily
`remedied. Place a similar part on the schematic and
`modify its model with the model editor to match that of
`the TLV2772. Figure 4–8 below shows the TLV2772
`sub-circuit model (as printed in the TLV2772 data
`sheet).
`
`Phase – deg
`
`180
`
`90
`
`0
`
`–90
`
`Gain
`
`Phase
`
`Phase
`
`Gain
`
`–180
`
`40
`
`20
`
`0
`
`–20
`
`–40
`
`Gain – dB
`
`0.1
`
`1
`
`100
`1k
`10
`f – Frequency – Hz
`
`10k
`
`100k
`
`Figure 4–6. Bode Plot of H3(s) = Vadc/Vo
`
`4.1.4.4 Transfer Function H(s) = Vadc / Vi
`Superimposing the previous bode plot approximations
`results in the bode plot approximation for the overall
`transfer function to be expected from the signal
`conditioning circuit as shown in Figure 4–7.
`
`Phase – deg
`
`180
`
`90
`
`0
`
`–90
`
`–180
`
`Gain
`
`Phase
`
`40
`
`20
`
`0
`
`–20
`
`–40
`
`Gain – dB
`
`0.1
`
`1
`
`100
`1k
`10
`f – Frequency – Hz
`
`10k
`
`100k
`
`Figure 4–7. Bode Plot of H(s) = Vadc/Vi
`
`
`
`11
`
`11
`
`

`

`3-V Accelerometer Featuring TLV2772
`
`.SUBCKT TLV2772-X 1 2 3 4 5
`C1
`11
`12 2.3094E-12
`C2
`6
`7
`8.0000E-12
`CSS 10
`99 2.1042E-12
`DC
`5
`53 DY
`DE
`54
`5
`DY
`DLP
`90
`91 DX
`DLN 92
`90 DX
`DP
`4
`3
`DX
`EGND 99
`0
`POLY(2) (3,0) (4,0) 0 .5 .5
`FB
`7
`99 POLY(5) VB VC VE VLP VLN 0 19.391E6 – 1E3 1E3 19E6 – 19E6
`GA 6 0
`11 12
`150.80E-6
`GCM 0 6
`10 99
`7.5576E-9
`ISS
`3
`10 DC 116.40E-6
`HLIM 90
`0
`VLIM IK
`J1
`11
`2
`10
`JX1
`J2
`12
`1
`10
`JX2
`R2
`6
`9
`100.0E3
`RD1
`4
`11 6.6315E3
`RD2
`4
`12 6.6315E3
`RO1
`8
`5
`17.140
`RO2
`7
`99 17.140
`RP
`3
`4
`4.5455E3
`RSS 10
`99 1.7182E6
`VB
`9
`0
`DC 0
`VC
`3
`53 DC .1
`VE
`54
`4
`DC .1
`VLIM 7
`8
`DC 0
`VLP
`91
`0
`DC 47
`VLN 0
`92 DC 47
`.MODEL DX D(IS=800.0E-18)
`.MODEL DY D(IS=800.0E-18 Rs=1m Cjo=10p)
`.MODEL JX1 PJF(IS=2.250E-12 BETA=195.36E-6 VTO=–1)
`.MODEL JX2 PJF(IS=1.750E-12 BETA=195.36E-6 VTO=–1)
`.ENDS
`
`Figure 4–8. TLV2772 Sub-Circuit Model
`
`Figure 4–9 shows the schematic used for SPICE
`simulation. Figures 4–10 show the simulation results.
`
`12
`
`
`
`12
`
`

`

`3-V Accelerometer Featuring TLV2772
`
`1
`
`R5
`
`1 kW
`
`Vadc
`
`C3
`0.22 m F
`
`0
`
`VDD
`U1A
`
`8
`
`+
`
`TLV2772
`
`–
`
`4
`
`0
`
`R4
`
`100 kW
`
`C2
`
`2.2 nF
`
`3 2
`
`VREF
`
`VDD
`
`ACH–04–05–08 Model
`
`VDD
`
`1.23 V
`
`3 V
`
`0
`
`0
`
`FN4117A
`
`Vs
`
`10 Meg
`
`VREF
`
`R1
`100 kW
`
`C1
`
`0.22 m F
`R2
`1 Meg
`
`R3
`
`10 kW
`VREF
`
`Figure 4–9. SPICE Simulation Schematic
`
`The SPICE simulations show agreement with the hand
`calculations and the bode plot approximations.
`The analyses above do not consider the frequency
`response of the shock sensor, which falls off below
`0.5 Hz and above 5 kHz. The data sheet for the
`
`ACH-04-08-05 does not specify the role-off
`characteristics of the shock sensor’s frequency
`response, but in general it is expected that there will be
`more attenuation in the signal below 0.5 Hz and above
`5 kHz.
`
`Figure 4–10. SPICE Simulation Results
`
`
`
`13
`
`13
`
`

`

`3-V Accelerometer Featuring TLV2772
`
`5 Circuit Realization
`
`The shock sensor and signal conditioning circuits are
`built on area 100 of two Universal Operational Amplifier
`EVM boards (SLOP 120–1). One EVM board holds a
`TLV2772, an ACH-04-05-08, a TLV431, and required
`ancillary devices. The other board has only a TLV2772
`and required ancillary devices. The signal conditioning
`circuit is constructed by installing required components
`and wiring. The two boards share signals and sources
`
`through board-to-board connectors. Standoffs and
`screws secure the two boards together. Figure 5–1
`shows the schematic diagram with reference
`designators for using area 100 on two Universal
`Operational Amplifier EVM boards.
`Tables 5–1 and 5–2 summarize reference designator
`part descriptions to construct the shock sensor and
`signal conditioning circuits.
`
`Table 5–1. Board 1 – Universal Operational Amplifier EVM Area 100
`
`REFERENCE
`DESIGNATOR
`R101
`R102
`R103
`R104
`R105
`R106
`R107
`R108
`R109
`R110
`R111
`R112
`R113
`R114
`R115
`R116
`R117
`R118
`A1OUT
`A101–
`A102–
`A103+
`A104+
`
`REFERENCE
`DESIGNATOR
`R101
`R102
`R103
`R104
`R105
`
`DESCRIPTION
`1 MW
` 1% SMT
`10 kW
` 1% SMT
`Not used
`100 kW
` 1% SMT
`100 kW
` 1% SMT
`Not used
`10 kW
` 1% SMT
`1 MW
` 1% SMT
`Use 0.22 m F 10% X7R SMT Capacitor
`Use 0.22 m F 10% X7R SMT Capacitor
`0 W
` or Jumper
`Not used
`Not used
`2.2 kW
` 5% SMT
`0 W
` or Jumper
`Not used
`Not used
`Not used
`X Axis output
`Not used
`Jump to VREF1
`Jump to VREF1
`X Axis input from ACH-04-05-08 pin 6
`
`REFERENCE
`DESIGNATOR
`C101
`C102
`C103
`C104
`C105
`C106
`C107
`C108
`C109
`C110
`C111
`C112
`U101
`U102
`V1+
`VREF1
`GND1
`R119
`B104+
`B103+
`B102–
`B101–
`B1OUT
`
`DESCRIPTION
`
`Not used
`2200 pF 5% NPO SMT
`2.2 m F 20% Y5V SMT
`0.1 m F 10% X7R SMT
`2200 pF 5% NPO SMT
`Not used
`Not used
`Not used
`0 W or Jumper
`Not used
`Not used
`Not used
`TLV2772CD
`TLV431ACDBV5
`3 V power input
`Signal conditioning reference
`Signal and power ground
`0 W or Jumper
`Y Axis input form ACH-04-05-08 pin 2
`Jump to VREF1
`Jump VREF1
`Not used
`Y Axis output
`
`Table 5–2. Board 2 – Universal Operational Amplifier EVM Area 100
`
`DESCRIPTION
`
`Not used
`Not used
`Not used
`0 W
` or Jumper
`100 kW
` 1% SMT
`
`REFERENCE
`DESIGNATOR
`C101
`C102
`C103
`C104
`C105
`
`DESCRIPTION
`
`Not used
`Not used
`Not used
`0.1 m F 10% X7R SMT
`2200 pF 5% NPO SMT
`
`14
`
`
`
`14
`
`

`

`3-V Accelerometer Featuring TLV2772
`
`REFERENCE
`DESIGNATOR
`R106
`R107
`R108
`R109
`R110
`R111
`R112
`R113
`R114
`R115
`R116
`R117
`R118
`A1OUT
`A101–
`A102–
`A103+
`A104+
`
`DESCRIPTION
`
`Not used
`7.5 kW
` 1% SMT
`1 MW
` 1% SMT
`Use 0.22 m F 10% X7R SMT Capacitor
`Not used
`Not used
`Not used
`0 W
` or Jumper
`Not used
`Not used
`Not used
`Not used
`Not used
`Z Axis output
`Not used
`Jump to VREF1
`Jump to VREF1
`Z Axis input from ACH-04-05-08 pin 12
`
`Table 5–2. Board 2 – Universal Operational Amplifier EVM Area 100
`REFERENCE
`DESIGNATOR
`C106
`C107
`C108
`C109
`C110
`C111
`C112
`U101
`U102
`V1+
`VREF1
`GND1
`R119
`B104+
`B103+
`B102–
`B101–
`B1OUT
`
`DESCRIPTION
`
`Not used
`Not used
`Not used
`0 W or Jumper
`Not used
`Not used
`Not used
`TLV2772CD
`Not used
`3 V from Board 1
`Signal conditioning reference from Board 1
`Circuit common connect to board 1 GND1
`0 W or Jumper
`Not used
`Not used
`Not used
`Not used
`Not used
`
`Board-to-board connectors provide required
`connections between board 1 and board 2. The
`required board-to-board connections are GND1, V1+,
`and VREF. Also, pin 12 of the ACH-04-08–05 must be
`connected to A104+ on board 2. This is accomplished
`by using board-to-board connectors in the breadboard
`area and connecting the appropriate nodes thereto.
`Figure 5–1 is the schematic of the 3-axis realization of
`the 1-axis circuit shown in Figure 4–1, except for output
`filter components R5 and C3. To ease component
`placement, the output filters for each channel are
`placed on the TLV1544 EVM. For standalone testing of
`the signal conditioning circuit without the TLV1544
`EVM, temporarily place the filter components on board
`1 and board 2. Remove them for final integration.
`
`The ACH-04-08-05 shock sensor mounts in the
`breadboard area on board 1. Table 5–3 summarizes
`the con