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VCA824IDGST

VCA824IDGST

  • 厂商:

    BURR-BROWN(德州仪器)

  • 封装:

    VSSOP10_3X3MM

  • 描述:

    宽带 420MHz,>40dB 增益调节范围,线性 V/V 可变增益放大器

  • 数据手册
  • 价格&库存
VCA824IDGST 数据手册
Order Now Product Folder Tools & Software Technical Documents Support & Community VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 VCA824 Ultra-Wideband, > 40-dB Gain Adjust Range, Linear in V/V Variable Gain Amplifier 1 Features • • • • • • • 1 710-MHz Small-Signal Bandwidth (G = 2 V/V) 320 MHz, 4-VPP Bandwidth (G = 10 V/V) 0.1-dB Gain Flatness to 135 MHz 2500-V/µs Slew Rate > 40-dB Gain Adjust Range High Gain Accuracy: 20-dB ±0.3-dB High Output Current: ±90 mA 2 Applications • • • • • Differential Line Receivers Differential Equalizers Pulse Amplitude Compensation Variable Attenuators Voltage-Tunable Active Filters The VCA824 internal architecture consists of two input buffers and an output current feedback amplifier stage integrated with a multiplier core to provide a complete variable gain amplifier (VGA) system that does not require external buffering. The maximum gain is set externally with two resistors, providing flexibility in designs. The maximum gain is intended to be set between 2 V/V and 40 V/V. Operating from ±5-V supplies, the gain control voltage for the VCA824 adjusts the gain linearly in V/V as the control voltage varies from 1 V to –1 V. For example, set for a maximum gain of 10 V/V, the VCA824 provides 10 V/V, at 1-V input, to 0.1 V/V at –1-V input of gain control range. The VCA824 offers excellent gain linearity. For a 20-dB maximum gain, and a gaincontrol input voltage varying between 0 V and 1 V, the gain does not deviate by more than ±0.3-dB (maximum at 25°C). Device Information(1) 3 Description PART NUMBER The VCA824 is a DC-coupled, wideband, linear-in V/V, continuously variable, voltage-controlled gain amplifier. The device provides a differential input to single-ended conversion with a high-impedance gain control input used to vary the gain down 40 dB from the nominal maximum gain set by the gain resistor (RG) and feedback resistor (RF). VCA824 PACKAGE BODY SIZE (NOM) SOIC (14) 8.65 mm × 3.91 mm VSSOP (10) 3.00 mm × 3.00 mm (1) For all available packages, see the orderable addendum at the end of the data sheet. SPACE Differential Equalization of an RC Load Differential Equalizer VIN1 9 +VIN 0 FB RG Gain (dB) R1 VCA824 C1 -VIN Initial Frequency Response of the VCA824 with RC Load -3 -6 -9 -12 RGVIN2 3 RG+ RS Equalized Frequency Response 6 RF 20W -15 -18 RS -21 -24 1M 10M 100M 1G Frequency (Hz) 1 An IMPORTANT NOTICE at the end of this data sheet addresses availability, warranty, changes, use in safety-critical applications, intellectual property matters and other important disclaimers. PRODUCTION DATA. VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 www.ti.com Table of Contents 1 2 3 4 5 6 7 Features .................................................................. Applications ........................................................... Description ............................................................. Revision History..................................................... Device Comparison Table..................................... Pin Configuration and Functions ......................... Specifications......................................................... 1 1 1 2 3 3 4 7.1 7.2 7.3 7.4 7.5 7.6 7.7 Absolute Maximum Ratings ...................................... 4 ESD Ratings.............................................................. 4 Recommended Operating Conditions....................... 4 Thermal Information .................................................. 4 Electrical Characteristics: VS = ±5 V......................... 5 Typical Characteristics: VS = ±5 V, AVMAX = 2 V/V... 7 Typical Characteristics: VS = ±5 V, AVMAX = 10 V/V ........................................................................... 11 7.8 Typical Characteristics: VS = ±5 V, AVMAX = 40 V/V ........................................................................... 15 8 Detailed Description ............................................ 19 8.1 Overview ................................................................. 19 8.2 Functional Block Diagram ....................................... 19 8.3 Feature Description................................................. 19 8.4 Device Functional Modes........................................ 19 9 Application and Implementation ........................ 22 9.1 Application Information............................................ 22 9.2 Typical Application .................................................. 28 10 Power Supply Recommendations ..................... 30 11 Layout................................................................... 30 11.1 Layout Guidelines ................................................ 30 11.2 Layout Example .................................................... 31 12 Device and Documentation Support ................. 32 12.1 12.2 12.3 12.4 12.5 12.6 Device Support...................................................... Receiving Notification of Documentation Updates Community Resources.......................................... Trademarks ........................................................... Electrostatic Discharge Caution ............................ Glossary ................................................................ 32 32 32 32 32 32 13 Mechanical, Packaging, and Orderable Information ........................................................... 32 4 Revision History Changes from Revision D (January 2016) to Revision E Page • Changed Output Voltage Swing parameter RL = 100 Ω specifications ................................................................................. 6 • Changed Output Current parameter specifications ................................................................................................................ 6 Changes from Revision C (December 2008) to Revision D Page • Added Pin Configuration and Functions section, ESD Ratings table, Feature Description section, Device Functional Modes, Application and Implementation section, Power Supply Recommendations section, Layout section, Device and Documentation Support section, and Mechanical, Packaging, and Orderable Information section ............................... 1 • Deleted Thermal Characteristics rows from Electrical Characteristics .................................................................................. 5 Changes from Revision B (August 2008) to Revision C • Revised second paragraph in the Wideband Variable Gain Amplifier Operation section describing pin 9.......................... 28 Changes from Revision A (December 2007) to Revision B • Page Page Changed storage temperature range rating in Absolute Maximum Ratings table from – 40 ° C to 125 ° C to – 65 ° C to 125 ° C .............................................................................................................................................................................. 4 Changes from Original (November 2007) to Revision A Page • Added typical value for output impedance ............................................................................................................................. 6 • Changed wording of explanation for X2Y capacitor usage at end of paragraph.................................................................. 28 2 Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 VCA824 www.ti.com SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 5 Device Comparison Table SINGLES DUALS GAIN ADJUST RANGE (dB) INPUT NOISE (nV/√Hz) SIGNAL BANDWIDTH (MHz) VCA810 — 80 2.4 35 — VCA2612 45 1.25 80 — VCA2613 45 1 80 — VCA2615 52 0.8 50 — VCA2617 48 4.1 50 VCA820 — 40 8.2 150 VCA821 — 40 6.0 420 VCA822 — 40 8.2 150 VCA824 — 40 6.0 420 6 Pin Configuration and Functions D Package 14-Pin SOIC Top View DGS Package 10-Pin VSSOP Top View +VCC 1 14 +VCC VG 2 +VIN FB 1 10 GND 13 NC +VCC 2 9 VOUT 3 12 FB VG 3 8 -VCC +RG 4 11 GND +VIN 4 7 -VIN -RG 5 10 VOUT +RG 5 6 -RG -VIN 6 9 VREF -VCC 7 8 -VCC NC = No Connection Pin Functions PIN I/O DESCRIPTION NAME SOIC VSSOP VCC 1,14 2 P Positive supply voltage VG 2 3 I Gain control voltage +VIN 3 4 I noninverting input +RG 4 5 I Gain set resistor noninverting input –RG 5 6 I Gain set resistor inverting input –VIN 6 7 I Inverting input –VCC 7,8 8 P Negative supply voltage VREF 9 — I Output reference voltage (Non- Inverting input of output buffer) VOUT 10 9 O Output voltage GND 11 10 P Ground FB 12 1 I Feedback resistor (inverting input of output buffer) NC 13 — — Not connected Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 3 VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 www.ti.com 7 Specifications 7.1 Absolute Maximum Ratings over operating free-air temperature range (unless otherwise noted) (1) MIN Power supply Internal power dissipation MAX UNIT ±6.5 V See Thermal Information Input voltage ±VS V Junction temperature (TJ) 260 °C 140 °C 125 °C Junction temperature (TJ), continuous operation Storage temperature (1) –65 Stresses beyond those listed under Absolute Maximum Ratings may cause permanent damage to the device. These are stress ratings only, which do not imply functional operation of the device at these or any other conditions beyond those indicated under Recommended Operating Conditions. Exposure to absolute-maximum-rated conditions for extended periods may affect device reliability. 7.2 ESD Ratings VALUE V(ESD) (1) (2) Electrostatic discharge Human body model (HBM), per ANSI/ESDA/JEDEC JS-001 (1) ±2000 Charged device model (CDM), per JEDEC specification JESD22C101 (2) ±500 Machine model (MM) ±200 UNIT V JEDEC document JEP155 states that 500-V HBM allows safe manufacturing with a standard ESD control process. JEDEC document JEP157 states that 250-V CDM allows safe manufacturing with a standard ESD control process. 7.3 Recommended Operating Conditions over operating free-air temperature range (unless otherwise noted) Operating voltage Operating temperature MIN NOM MAX 7 10 12 UNIT V –40 25 85 °C 7.4 Thermal Information VCA824 THERMAL METRIC (1) D (SOIC) DGS (VSSOP) 14 PINS 10 PINS UNIT RθJA Junction-to-ambient thermal resistance 90.3 173.1 °C/W RθJC(top) Junction-to-case (top) thermal resistance 49.8 46.6 °C/W RθJB Junction-to-board thermal resistance 44.9 94.3 °C/W ψJT Junction-to-top characterization parameter 13.8 2.2 °C/W ψJB Junction-to-board characterization parameter 44.6 92.7 °C/W RθJC(bot) Junction-to-case (bottom) thermal resistance n/a n/a °C/W (1) 4 For more information about traditional and new thermal metrics, see the Semiconductor and IC Package Thermal Metrics application report. Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 VCA824 www.ti.com SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 7.5 Electrical Characteristics: VS = ±5 V At AVMAX = 10 V/V, VG = 1V, RF = 402 Ω, RG = 80 Ω, and RL = 100 Ω, unless otherwise noted. PARAMETER TEST CONDITIONS TEST LEVEL (1) MIN TYP MAX UNIT AC PERFORMANCE AVMAX = 2 V/V, VG = 1 V , VO = 500 mVPP Small-Signal Bandwidth AVMAX = 10 V/V, VG = 1 V, VO = 500 mVPP 710 C 420 AVMAX = 40 V/V, VG = 1 V, VO = 500 mVPP Large-Signal Bandwidth AVMAX = 10 V/V, VG = 1 V, VO = 4 VPP C TA= 25°C Gain Control Bandwidth VO = 200 mVPP, TA= 25°C TA = 0°C to 70°C AVMAX = 10 V/V, VG = 1 V, VO = 2 VPP B AVMAX = 10 V/V, VG = 1 V, VO = 4 V Step TA= 0°C to 70° 235 C B TA = 0°C to 70°C V/μs 1700 1.5 B AVMAX = 10 V/V, VG = 1 V, VO = 4 V Step 2nd-Harmonic VO = 2 VPP, f = 20 MHz TA = 0°C to 70°C C B TA = 0°C to 70°C ns -66 –64 dBc –64 TA = 25°C VO = 2 VPP, f = 20 MHz 11 –64 TA = –40°C to 85°C 3rd-Harmonic ns 1.9 TA = 25°C Harmonic Distortion 1.8 1.9 TA = –40°C to 85°C Settling Time to 0.01% MHz 2500 1700 TA = 25°C AVMAX = 10 V/V, VG = 1 V, VO = 4 V Step MHz 135 1800 TA = –40°C to 85°C Rise-and-Fall Time MHz 330 235 TA= 25°C Slew Rate 320 240 TA = –40°C to 85°C Bandwidth for 0.1-dB Flatness MHz 170 –61 B TA = –40°C to 85°C –63 –61 dBc –61 Input Voltage Noise f > 100 kHz C 6 nV/√Hz Input Current Noise f > 100 kHz C 2.6 pA/√Hz GAIN CONTROL TA = 25°C Gain Error AVMAX = 10 V/V, VG = 1 V TA = 0°C to 70°C ±0.1 A ±0.5 TA = –40°C to 85°C AVMAX = 10 V/V, 0 < VG < 1 TA = 0°C to 70°C ±0.05 A TA = 0°C to 70°C ±1.06 A TA = 0°C to 70°C –26 A 22 A TA = 0°C to 70°C Gain Control Input Impedance TA = 25°C 30 35 TA = –40°C to 85°C Average Gain Control Bias Current Drift dB –23 TA = 25°C TA = 0°C to 70°C –24 –24 TA = –40°C to 85°C Gain Control Bias Current dB ±2.2 TA = 25°C Relative to max gain ±1.9 ±2.1 TA = –40°C to 85°C Gain at VG = –0.9V dB ±0.37 TA = 25°C AVMAX = 10 V/V, -0.8 < VG < 1 ±0.3 ±0.34 TA = –40°C to 85°C Gain Deviation dB ±0.6 TA = 25°C Gain Deviation ±0.4 μA 37 ±100 B nA/°C TA = –40°C to 85°C ±100 C 1.5 || 0.6 MΩ || pF DC PERFORMANCE TA = 25°C Input Offset Voltage AVMAX = 10 V/V, VCM = 0 V, VG = 1 V TA = 0°C to 70° ±4 A TA = –40°C to 85°C Average Input Offset Voltage Drift AVMAX = 10 V/V, VCM = 0 V, VG = 1 V TA = 0°C to 70°C AVMAX = 10 V/V, VCM = 0V, VG = 1 V ±30 B ±30 19 A TA = –40°C to 85°C (1) μV/°C TA = –40°C to 85°C TA = 0°C to 70°C mV ±19 TA = 25°C Input Bias Current ±17 ±17.8 25 29 μA 31 Test levels: (A) 100% tested at 25°C. Over temperature limits set by characterization and simulation. (B) Limits set by characterization and simulation. (C) Typical value only for information. Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 5 VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 www.ti.com Electrical Characteristics: VS = ±5 V (continued) At AVMAX = 10 V/V, VG = 1V, RF = 402 Ω, RG = 80 Ω, and RL = 100 Ω, unless otherwise noted. PARAMETER Average Input Bias Current Drift TEST CONDITIONS AVMAX = 10 V/V, VCM = 0 V, VG = 1 V TA = 0°C to 70°C TEST LEVEL (1) MIN B ±90 ±0.5 A AVMAX = 10 V/V, VCM = 0 V, VG = 1 V TA = 0°C to 70°C ±16 B nA/°C TA = –40°C to 85°C ±16 ±2.6 TA = 0°C to 70°C μA ±3.5 TA = 25°C Max Current Through Gain Resistance ±2.5 ±3.2 TA = –40°C to 85°C Average Input Offset Current Drift UNIT nA/°C TA = –40°C to 85° TA = 0°C to 70°C MAX ±90 TA = 25°C AVMAX = 10 V/V, VCM = 0 V, VG = 1 V Input Offset Current TYP B ±2.55 ±2.55 TA = –40°C to 85°C mA ±2.5 INPUT TA = 25°C Most Positive Common-Mode Input Voltage RL = 100 Ω TA = 0°C to 70°C 1.6 A TA = –40°C to 85°C RL = 100 Ω TA = 0°C to 70°C V 1.6 TA = 25°C Most Negative Common-Mode Input Voltage 1.6 1.6 –2.1 A –2.1 TA = –40°C to 85°C VCM = ±0.5 V TA = 0°C to 70°C V –2.1 TA = 25°C Common-Mode Rejection Ratio –2.1 80 A 65 60 TA = –40°C to 85°C dB 60 Differential C 1 || 1 MΩ || pF Common-Mode C 1 || 2 MΩ || pF Input Impedance OUTPUT TA = 25°C RL = 1 kΩ TA = 0°C to 70°C ±3.6 A TA = –40°C to 85°C 3.5 TA = 25°C Output Current VO = 0V, RL = 10 Ω 3.6 –3.3 –3.2 A V TA = 0°C to 70°C 3.3 TA = –40°C to 85°C 3.2 Source, TA = 25°C 60 Sink, TA = 25°C AVMAX = 10 V/V, f > 100 kHz –3 –2.9 90 –55 –50 A TA = 0°C to 70°C mA 50 TA = –40°C to 85°C Output Impedance V ±3.3 Output Voltage Swing RL = 100 Ω ±3.9 ±3.4 –42 45 C –38 0.01 Ω ±5 V POWER SUPPLY Specified Operating Voltage C TA = 25°C Minimum Operating Voltage ±4 TA = 0°C to 70°C B TA = –40°C to 85°C ±4 V ±4 TA = 25°C Maximum Operating Voltage ±6 TA = 0°C to 70°C A ±6 TA = –40°C to 85°C TA = 25°C Maximum Quiescent Current VG = 0 V TA = 0°C to 70°C 36.5 A TA = 0°C to 70°C 36.5 A TA = 0°C to 70°C –61 A TA = –40°C to 85°C 6 mA 34 TA = 25°C VG = 1 V 35 34.5 TA = –40°C to 85°C Power-Supply Rejection Ratio (-PSRR) mA 38.5 TA = 25°C VG = 0 V 37.5 38 TA = –40°C to 85°C Minimum Quiescent Current V ±6 Submit Documentation Feedback –59 -68 dB –58 Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 VCA824 www.ti.com SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 7.6 Typical Characteristics: VS = ±5 V, AVMAX = 2 V/V At TA = 25°C, RL = 100 Ω, RF = 453 Ω, RG = 453 Ω, VG = 1 V, VIN = single-ended input on +VIN with –VIN at ground, and 14Pin SOIC package, unless otherwise noted. 3 3 VO = 0.5VPP VG = 0V 0 Normalized Gain (dB) Normalized Gain (dB) 0 -3 VG = +1V -6 -9 -12 AVMAX = +2V/V VIN = 1VPP RL = 100W -15 -18 -3 VO = 1VPP -6 VO = 2VPP -9 VO = 4VPP -12 VO = 5VPP -15 -18 1M 10M 100M 1G 1M 10M Frequency (Hz) Figure 1. Small-Signal Frequency Response VIN = 250mVPP f = 20MHz VIN = 2VPP f = 20MHz 3 200 Output Voltage (V) Output Voltage (mV) 300 100 0 -100 2 1 0 -1 -2 -200 -3 -300 Time (10ns/div) Time (10ns/div) Figure 3. Small-Signal Pulse Response Figure 4. Large-Signal Pulse Response 0 0 -0.020 -dP, VG = 0V -0.025 -0.5 -0.6 -0.030 -dP, VG = +1V -0.7 -0.8 -0.035 -0.040 -dG, VG = +1V -0.045 -0.9 2 3 4 Magnitude (dB) Differential Gain (%) -0.015 -0.3 Differential Phase (°) -0.010 0.15 Left Scale -0.005 -dG, VG = 0V -0.2 0.2 0.1 0.10 0 0.05 0 -0.1 Right Scale -0.2 -0.05 -0.3 -0.10 -0.4 -0.15 AVMAX = +2V/V VG = +1V -0.5 0 50 Deviation from Linear Phase (°) -0.1 1 1G Figure 2. Large-Signal Frequency Response 4 400 -0.4 100M Frequency (Hz) -0.20 100 150 200 Frequency (MHz) Number of Video Loads Figure 5. Composite Video dG/dP Figure 6. Gain Flatness, Deviation From Linear Phase Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 7 VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 www.ti.com Typical Characteristics: VS = ±5 V, AVMAX = 2 V/V (continued) -60 -60 -65 -65 -70 3rd-Harmonic -75 -80 AVMAX = +2V/V VG = +1V VO = 2VPP RL = 100W 2nd-Harmonic -85 -90 0.1 1 10 Harmonic Distortion (dBc) Harmonic Distortion (dBc) At TA = 25°C, RL = 100 Ω, RF = 453 Ω, RG = 453 Ω, VG = 1 V, VIN = single-ended input on +VIN with –VIN at ground, and 14Pin SOIC package, unless otherwise noted. AVMAX = +2V/V VG = +1V VO = 2VPP f = 20MHz -70 2nd-Harmonic -75 -80 3rd-Harmonic -85 -90 100 100 1k Frequency (MHz) Resistance (W) Figure 7. Harmoneic Distortion vs Frequency AVMAX = +2V/V VG = +1V RL = 100W f = 20MHz Harmonic Distortion (dBc) -35 -40 -45 Figure 8. Harmonic Distortion vs Load Resistance -10 Maximum Current Through RG Limited -50 -55 -60 -65 2nd-Harmonic -70 -75 3rd-Harmonic -80 1 Maximum Current Through RG Limited -40 -50 3rd-Harmonic -60 -70 2nd-Harmonic -90 -0.6 10 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 Output Voltage Swing (VPP) Gain Control Voltage (V) Figure 9. Harmonic Distortion vs Output Voltage Figure 10. Harmonic Distortion vs Gain Control Voltage 38 40 36 35 Intercept Point (+dBm) Intercept Point (+dBm) -30 -80 -85 0.1 AVMAX = +2V/V VO = 2VPP RL = 100W f = 20MHz -20 Harmonic Distortion (dBc) -30 34 32 30 28 f = 20MHz At 50W Matched Load Constant Input Voltage Constant Output Voltage 30 25 20 15 26 At 50W Matched Load 24 0 8 10 20 30 40 50 60 70 80 90 100 10 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 Frequency (MHz) Gain Control Voltage (V) Figure 11. Two-Tone, 3rd-Order Intermodulation Intercept Figure 12. Two-Tone, 3rd-Order Intermodulation Intercept vs Gain Control Voltage Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 VCA824 www.ti.com SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 Typical Characteristics: VS = ±5 V, AVMAX = 2 V/V (continued) At TA = 25°C, RL = 100 Ω, RF = 453 Ω, RG = 453 Ω, VG = 1 V, VIN = single-ended input on +VIN with –VIN at ground, and 14Pin SOIC package, unless otherwise noted. 2.2 2.0 1.8 1.6 3 VG = 0VDC + 10mVPP VIN = 0.5VDC Normalized Gain (dB) 0 Gain (V/V) 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0 -3 -6 -9 -0.2 -1.2 -0.8 0 -0.4 0.4 0.8 -12 1.2 1M 10M Gain Control Voltage (V) Figure 13. Gain vs Gain Control Voltage 1G Figure 14. Gain Control Frequency Response 2 1 0 1.5 -1 1.0 10 0 VG = +1V -10 -20 Gain (dB) 3 Output Voltage (V) 4 VIN = 1VDC Input Voltage (V) 100M Frequency (Hz) -30 -40 -50 VG = -1V -60 0.5 -70 0 -80 VG = 2VPP -90 -0.5 -100 1M -1.0 10M Time (10ns/div) Figure 15. Gain Control Pulse Response Figure 16. Fully-Attenuated Response 1.4 10MHz 1.4 Group Delay (ns) Group Delay (ns) 1.6 1.2 1.0 0.8 1G 1.6 2.0 1.8 100M Frequency (Hz) 1MHz 20MHz 0.6 1.2 1.0 0.8 0.6 0.4 0.4 VG = +1V VO = 1VPP 0.2 0.2 0 -1.0 -0.8 -0.6 -0.4 -0.2 0 0 0.2 0.4 0.6 0.8 1.0 0 20 40 60 80 Gain Control Voltage (V) Frequency (MHz) Figure 17. Group Delay vs Gain Control Voltage Figure 18. Group Delay vs Frequency Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 100 9 VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 www.ti.com Typical Characteristics: VS = ±5 V, AVMAX = 2 V/V (continued) At TA = 25°C, RL = 100 Ω, RF = 453 Ω, RG = 453 Ω, VG = 1 V, VIN = single-ended input on +VIN with –VIN at ground, and 14Pin SOIC package, unless otherwise noted. 9 100 VO = 0.5VPP CL = 10pF 6 CL = 22pF CL = 100pF RS (W) RS (W) 3 10 CL = 47pF 0 RF -3 VIN + RS VCA824 -6 0.1dB Flatness Targeted 1 NOTE: (1) 1kW is optional. 10 100 1 1k 10 100 1k Capacitive Load (pF) Capacitive Load (pF) Figure 20. Frequency Response vs Capacitive Load Figure 19. Recommended RSvs Capacitive Load 200 10 Input Voltage Noise Density (pA/ÖHz) Output Voltage Noise Density (nV/ÖHz) (1) 1kW -9 1 VG = 0V 100 VG = +1V VG = -1V 10 1 100 10 VOUT CL - 1k 10k 100k 1M 10M 100 1k 10k 100k 1M Frequency (Hz) Frequency (Hz) Figure 21. Output Voltage Density Figure 22. Input Current Noise Density Submit Documentation Feedback 10M Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 VCA824 www.ti.com SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 7.7 Typical Characteristics: VS = ±5 V, AVMAX = 10 V/V At TA = 25°C, RL = 100 Ω, RF = 402 Ω, RG = 80 Ω, VG = 1 V, and VIN = single-ended input on +VIN with –VIN at ground, unless otherwise noted. 3 3 VG = 0V 0 Normalized Gain (dB) Normalized Gain (dB) 0 -3 -6 VG = +1V -9 -12 AVMAX = +10V/V VIN = 200mVPP RG = 100W -15 -18 VO = 1VPP -3 VO = 0.5VPP -6 -9 -12 VO = 4VPP -15 VO = 2VPP -18 1M 10M 100M 1G 0 200M Frequency (Hz) Figure 23. Small-Signal Frequency Response VIN = 50mVPP f = 20MHz Output Voltage (V) Output Voltage (mV) 0 -100 VIN = 400mVPP f = 20MHz 1 0 -1 -2 -200 -3 -300 Time (10ns/div) Time (10ns/div) Figure 26. Large-Signal Pulse Response 0.20 0.1 Left Scale -0.1 0.10 -0.2 0.05 0 -0.3 Right Scale -0.05 -0.4 -0.10 AVMAX = +10V/V VG = +1V 50 -0.15 100 150 200 Deviation from Linear Phase (°) 0.15 0 Output Voltage Noise Density (nV/ÖHz) Figure 25. Small-Signal Pulse Response Magnitude (dB) 1G 2 100 0 800M Figure 24. Large-Signal Frequency Response 3 200 -0.6 600M Frequency (Hz) 300 -0.5 400M 200 VG = +1V 100 VG = -1V VG = 0V 10 100 1k 10k 100k 1M 10M Frequency (Hz) Frequency (MHz) Figure 27. Gain Flatness, Deviation from Linear Phase Figure 28. Output Voltage Noise Density Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 11 VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 www.ti.com Typical Characteristics: VS = ±5 V, AVMAX = 10 V/V (continued) -50 -66 -55 -68 Harmonic Distortion (dBc) Harmonic Distortion (dBc) At TA = 25°C, RL = 100 Ω, RF = 402 Ω, RG = 80 Ω, VG = 1 V, and VIN = single-ended input on +VIN with –VIN at ground, unless otherwise noted. -60 3rd-Harmonic -65 -70 -75 AVMAX = +10V/V VG = +1V VO = 2VPP RL = 100W 2nd-Harmonic -80 -85 0.1 1 10 -70 AVMAX = +10V/V VG = +1V VO = 1VPP f = 20MHz -72 3rd-Harmonic -74 -76 -78 2nd-Harmonic -80 100 100 1k Frequency (MHz) Resistance (W) Figure 29. Harmonic Distortion vs Frequency AVMAX = +10V/V VG = +1V RL = 100W f = 20MHz Harmonic Distortion (dBc) -30 -40 Figure 30. Harmonic Distortion vs Load Resistance -10 Maximum Current Through RG Limited Harmonic Distortion (dBc) -20 -50 -60 2nd-Harmonic -70 3rd-Harmonic -80 AVMAX = +10V/V VO = 2VPP RL = 100W f = 20MHz -20 -30 Maximum Current Through RG Limited -40 3rd-Harmonic -50 -60 2nd-Harmonic -90 0.1 1 -70 -0.6 10 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 Output Voltage Swing (VPP) Gain Control Voltage (V) Figure 31. Harmonic Distortion vs Output Voltage Figure 32. Harmonic Distortion vs Gain Control Voltage 34 35 32 30 Intercept Point (+dBm) Intercept Point (+dBm) Constant Input Voltage 30 28 Constant Output Voltage 25 20 15 26 f = 20MHz At 50W Matched Load At 50W Matched Load 24 0 12 10 20 30 40 50 60 70 80 90 100 10 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 Frequency (MHz) Gain Control Voltage (V) Figure 33. Two-Tone, 3rd-Order Intermodulation Intercept Figure 34. Two-Tone, 3rd-Order Intermodulation Intercept vs Gain Control Voltage Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 VCA824 www.ti.com SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 Typical Characteristics: VS = ±5 V, AVMAX = 10 V/V (continued) At TA = 25°C, RL = 100 Ω, RF = 402 Ω, RG = 80 Ω, VG = 1 V, and VIN = single-ended input on +VIN with –VIN at ground, unless otherwise noted. 3 0 Normalized Gain (dB) Gain (V/V) 11 10 9 8 7 6 5 4 3 2 1 0 VG = 0VDC + 10mVPP VIN = 0.1VDC -3 -6 -9 -12 -1 -1.2 -15 -0.8 0 -0.4 0.4 0.8 1.2 1M 10M Gain Control Voltage (V) Figure 35. Gain vs Gain Control Voltage 1 0 1.5 -1 4 3 Output Voltage (V) 2 5 Output Voltage (V) VIN = 0.2VDC 1.0 0.5 1W Internal Power Dissipation 100W Load 2 1 50W Load 0 25W Load -1 -2 1W Internal Power Dissipation -3 0 -4 -0.5 -5 -150 -1.0 Time (10ns/div) -50 0 50 100 150 Figure 38. Output Voltage and Current Limitations 0.4 0.3 Input Voltage (V) VG = +1V VG = -1V AVMAX = +10V/V VG = -0.3V Input Voltage Left Scale 2.0 1.5 0.2 1.0 0.1 0.5 0 -0.1 0 Output Voltage Right Scale -0.5 -0.2 -1.0 -0.3 -1.5 Output Voltage (V) Gain (dB) -100 Output Current (mA) Figure 37. Gain Control Pulse Response 30 20 10 0 -10 -20 -30 -40 -50 -60 -70 -80 -90 -100 1G Figure 36. Gain Control Frequency Response 3 Input Voltage (V) 100M Frequency (Hz) Input Referred VO = 2VPP 1M 10M 100M 1G -0.4 Frequency (Hz) Figure 39. Fully-Attenuated Response -2.0 Time (40ns/div) Figure 40. IRG Limited Overdrive Recovery Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 13 VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 www.ti.com Typical Characteristics: VS = ±5 V, AVMAX = 10 V/V (continued) At TA = 25°C, RL = 100 Ω, RF = 402 Ω, RG = 80 Ω, VG = 1 V, and VIN = single-ended input on +VIN with –VIN at ground, unless otherwise noted. Output Voltage Right Scale 6 1.65 4 1.60 10MHz 0.2 2 0 0 -0.2 -0.4 -2 Input Voltage Left Scale Output Voltage (V) Input Voltage (V) 0.4 AVMAX = +10V/V VG = +1V Group Delay (ns) 0.6 1MHz 1.50 20MHz 1.45 -4 -0.6 1.55 1.40 -1.0 -0.8 -0.6 -0.4 -0.2 -6 0 0.2 0.4 0.6 0.8 1.0 Gain Control Voltage (V) Time (40ns/div) Figure 42. Group Delay vs Gain Control Voltage Figure 41. Output Limited Overdrive Recovery 1.8 1.6 Group Delay (ns) 1.4 1.2 1.0 0.8 0.6 0.4 VG = +1V VO = 1VPP 0.2 0 0 20 40 60 80 100 Frequency (MHz) Figure 43. Group Delay vs Frequency 14 Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 VCA824 www.ti.com SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 7.8 Typical Characteristics: VS = ±5 V, AVMAX = 40 V/V At TA = 25°C, RL = 100 Ω, RF = 402 Ω, RG = 18 Ω, VG = 1 V, VIN = single-ended input on +VIN with –VIN at ground, and SO-14 package, unless otherwise noted. 3 3 0 VG = 0V -3 Normalized Gain (dB) Normalized Gain (dB) 0 -6 VG = +1V -9 -12 -3 -18 VO = 1VPP -9 -12 VO = 2VPP AVMAX = +40V/V VIN = 50mVPP RL = 100W -15 VO = 0.5VPP VO = 4VPP -6 -15 -18 1M 10M 100M 1G 0 100 Frequency (Hz) 200 200 400 500 600 Frequency (MHz) Figure 44. Small-Signal Frequency Response Figure 45. Large-Signal Frequency Response 400 2.5 VIN = 12.5mVPP f = 20MHz 300 VIN = 100mVPP f = 20MHz 2.0 Output Voltage (V) Output Voltage (mV) 1.5 200 100 0 -100 1.0 0.5 0 -0.5 -1.0 -1.5 -200 -2.0 -2.5 -300 Time (10ns/div) Time (10ns/div) 0.15 0.2 0.10 0.05 0 0 -0.1 -0.2 -0.05 -0.3 -0.10 -0.4 -0.15 -0.20 -0.5 0 20 40 60 200 Deviation from Linear Phase (°) AVMAX = +40V/V VG = +1V 0.1 Magnitude (dB) Figure 47. Large-Signal Pulse Response Output Voltage Noise Density (nV/ÖHz) Figure 46. Small-Signal Pulse Response 1000 VG = +1V VG = 0V 100 VG = -1V 10 100 1k 10k 100k 1M 10M Frequency (Hz) Frequency (MHz) Figure 48. Gain Flatness, Deviation from Linear Phase Figure 49. Output Voltage Noise Density Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 15 VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 www.ti.com Typical Characteristics: VS = ±5 V, AVMAX = 40 V/V (continued) At TA = 25°C, RL = 100 Ω, RF = 402 Ω, RG = 18 Ω, VG = 1 V, VIN = single-ended input on +VIN with –VIN at ground, and SO-14 package, unless otherwise noted. -35 -45 -55 Harmonic Distortion (dBc) -40 Harmonic Distortion (dBc) -50 AVMAX = +40V/V VG = +1V VO = 2VPP RL = 100W -50 -55 -60 2nd-Harmonic -65 -60 -70 -75 -80 3rd-Harmonic -70 -85 0.1 1 10 3rd-Harmonic -65 100 AVMAX = +40V/V VG = +1V VO = 1VPP f = 20MHz 100 1k Frequency (MHz) Resistance (W) Figure 50. Harmonic Distortion vs Frequency AVMAX = +40V/V VG = +1V RL = 100W f = 20MHz Harmonic Distortion (dBc) -20 -30 Figure 51. Harmonic Distortion vs Load Resistance -10 Maximum Current Through RG Limited -40 -50 2nd-Harmonic -60 3rd-Harmonic -70 -20 -25 -30 -35 -40 3rd-Harmonic 2nd-Harmonic -45 -50 -80 0.1 1 -55 -0.6 10 -0.4 -0.2 0 0.2 0.6 0.8 1.0 Gain Control Voltage (V) Figure 52. Harmonic Distortion vs Output Voltage Figure 53. Harmonic Distortion vs Gain Control Voltage 35 Intercept Point (+dBm) 32 30 28 26 30 Constant Input Voltage 25 Constant Output Voltage 20 15 24 f = 20MHz At 50W Matched Load At 50W Matched Load 22 0 16 0.4 Output Voltage Swing (VPP) 34 Intercept Point (+dBm) AVMAX = +40V/V VO = 2VPP RL = 100W f = 20MHz Maximum Current Through RG Limited -15 Harmonic Distortion (dBc) -10 2nd-Harmonic 10 20 30 40 50 60 70 80 90 100 10 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 Frequency (MHz) Gain Control Voltage (V) Figure 54. Two-Tone, 3rd-Order Intermodulation Intercept Figure 55. Two-Tone, 3rd-Order Intermodulation Intercept vs Gain Control Voltage Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 VCA824 www.ti.com SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 Typical Characteristics: VS = ±5 V, AVMAX = 40 V/V (continued) At TA = 25°C, RL = 100 Ω, RF = 402 Ω, RG = 18 Ω, VG = 1 V, VIN = single-ended input on +VIN with –VIN at ground, and SO-14 package, unless otherwise noted. 45 3 0 35 Normalized Gain (dB) Intercept Point (+dBm) 40 30 25 20 15 10 -3 -6 -9 -12 5 -15 0 -5 -1.2 VG = 0VDC + 10mVPP VIN = 10mVDC -18 -0.8 -0.4 0 0.4 0.8 1.2 1M 10M Gain Control Voltage (V) Figure 56. Gain vs Gain Control Voltage -1 40 30 VG = +1V 20 10 0 Gain (dB) 0 Output Voltage (V) 2 1 1.5 Input Voltage (V) 1G Figure 57. Gain Control Frequency Response 3 VIN = 50mVDC 1.0 -10 -20 -30 -40 0.5 -50 0 -60 VG = -1V Input Referred VO = 2VPP -70 -0.5 -80 1M -1.0 Time (10ns/div) 0.4 AVMAX = +40V/V VG = -0.3V 1.2 0.1 0.4 0 0 -0.1 -0.4 -0.2 -0.8 Output Voltage Right Scale Output Voltage Right Scale 2 0 0 -0.1 -2 Input Voltage Left Scale -0.2 -1.6 4 0.1 -1.2 -0.4 AVMAX = +40V/V VG = +1V -0.3 Output Voltage (V) 0.8 6 0.2 Output Voltage (V) 0.2 -0.3 1G Figure 59. Fully Attenuated Response Input Voltage (V) 0.3 100M 0.3 1.6 Input Voltage Left Scale 10M Frequency (Hz) Figure 58. Gain Control Pulse Response Input Voltage (V) 100M Frequency (Hz) -4 -6 Time (40ns/div) Time (40ns/div) Figure 60. IRG Limited Overdrive Recovery Figure 61. Output Limited Overdrive Recovery Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 17 VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 www.ti.com Typical Characteristics: VS = ±5 V, AVMAX = 40 V/V (continued) At TA = 25°C, RL = 100 Ω, RF = 402 Ω, RG = 18 Ω, VG = 1 V, VIN = single-ended input on +VIN with –VIN at ground, and SO-14 package, unless otherwise noted. 2.5 2.15 10MHz 2.10 2.0 Group Delay (ns) Group Delay (ns) 20MHz 2.05 2.00 1MHz 1.95 1.90 1.5 1.0 0.5 1.85 1.80 -1.0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 Gain Control Voltage (V) VG = +1V VO = 1VPP 0 0 40 60 80 100 Frequency (MHz) Figure 62. Group Delay vs Gain Control Voltage 18 20 Submit Documentation Feedback Figure 63. Group Delay vs Frequency Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 VCA824 www.ti.com SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 8 Detailed Description 8.1 Overview The VCA824 is a voltage controlled variable gain amplifier with differential inputs and a single ended output. The maximum gain is set by external resistors while the gain range is controlled by an external analog voltage. The maximum gain is designed for gains of 2 V/V up to 100 V/V and the analog control allows a gain range of over 40 dB. The VCA824 Input consists of two buffers, which together create a fully symmetrical, high impedance differential input with a typical common mode rejection of 80 dB. The gain set resistor is connected between the two input buffer output pins, so that the input impedance is independent of the gain settings. The bipolar inputs have a input voltage range of 1.6 and –2.1 V on ±5 V supplies. The amplifier maximum gain is set by external resistors, but the internal gain control circuit is controlled by a continuously variable, analog voltage. The gain control is a multiplier stage which is linear in V/V. The gain control input pin operates over a voltage range of –1 V to 1 V. The VCA824 contains a high-speed, high-current output buffer. The output stage can typically swing ±3.9 V and source/sink ±90 mA. The VCA824 can be operated over a voltage range of ±3.5 V to ±6 V. 8.2 Functional Block Diagram +VIN VIN R1 50W Source RF RG+ 50W RG VOUT RGR3 R2 50W Load -VIN 50W VG 8.3 Feature Description The VCA824 can be operated with both single ended or differential input signals. The inputs present consistently high impedance across all gain configurations. By using an analog control signal the amplifier gain is continuously variable for smooth, glitch free gain changes. With a large signal bandwidth of 320 Mhz and a slew rate of 2500 V/us the VCA824 offers linear performance over a wide range of signal amplitudes and gain settings. The low impedance/high current output buffer can drive loads ranging from low impedance transmission lines to high-impedance, switched-capacitor analog-to-digital converters. By using closely matched internal components, the VCA824 offers gain accuracy of ±0.3 dB. 8.4 Device Functional Modes The VCA824 functions as a differential input, single maximum gain of operation-ended output variable gain amplifier. This functional mode is enabled by applying power to the amplifier supply pins and is disabled by turning the power off. The gain is continuously variable through the analog gain control input. While the gain range is fixed, the maximum gain is set by two external components, Rf and Rg, as shown in the Functional Block Diagram. The maximum gain is equal to 2x (Rf / Rg). This gain is achieved with a 1-V voltage on the gain adjust pin VG. As the voltage decreases on the VG pin, the gain decreases in a linear in dB fashion with over 40 dB of gain range from 1-V to –1-V control voltage. As with most other differential input amplifiers, inputs can be applied to either one or both of the amplifier inputs. The amplifier gain is controlled through the gain control pin. 8.4.1 Maximum Gain Of Operation This section describes the use of the VCA824 in a fixed-gain application in which the VG control pin is set at VG = 1 V. The tradeoffs described here are with bandwidth, gain, and output voltage range. Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 19 VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 www.ti.com Device Functional Modes (continued) In the case of an application that does not make use of the VGAIN, but requires some other characteristic of the VCA824, the RG resistor must be set such that the maximum current flowing through the resistance IRG is less than ±2.6 mA typical, or 5.2 mAPP as defined in Electrical Characteristics: VS = ±5 V, and must follow Equation 1. VOUT IRG = AVMAX ´ RG (1) As Equation 1 illustrates, once the output dynamic range and maximum gain are defined, the gain resistor is set. This gain setting in turn affects the bandwidth, because in order to achieve the gain (and with a set gain element), the feedback element of the output stage amplifier is set as well. Keeping in mind that the output amplifier of the VCA824 is a current-feedback amplifier, the larger the feedback element, the lower the bandwidth because the feedback resistor is the compensation element. Limiting the discussion to the input voltage only and ignoring the output voltage and gain, Equation 2 illustrates the tradeoff between the input voltage and the current flowing through the gain resistor. 8.4.2 Output Current And Voltage The VCA824 provides output voltage and current capabilities that are unsurpassed in a low-cost monolithic VCA. Under no-load conditions at 25°C, the output voltage typically swings closer than 1 V to either supply rails; the 25°C swing limit is within 1.2 V of either rails. Into a 15-Ω load (the minimum tested load), the VCA824 device is tested to deliver more than ±160 mA. The specifications described above, though familiar in the industry, consider voltage and current limits separately. In many applications, it is the voltage × current, or V-I product, that is more relevant to circuit operation (See Figure 38). The X- and Y-axes of this graph show the zero-voltage output current limit and the zero-current output voltage limit, respectively. The four quadrants give a more detailed view of the VCA824 output drive capabilities, noting that the graph is bounded by a Safe Operating Area of 1-W maximum internal power dissipation. Superimposing resistor load lines onto the plot shows that the VCA824 can drive ±2.5 V into 25-Ω or ±3.5 V into 50-Ω without exceeding the output capabilities or the 1-W dissipation limit. A 100-Ω load line (the standard test circuit load) shows the full ±3.9-V output swing capability, as shown in Typical Characteristics. The minimum specified output voltage and current overtemperature are set by worst-case simulations at the cold temperature extreme. Only at cold startup do the output current and voltage decrease to the numbers shown in Electrical Characteristic. As the output transistors deliver power, the respective junction temperatures increase, thereby increasing the available output voltage swing and output current. In steady-state operation, the available output voltage and current are always greater than the temperature shown in the overtemperature specifications because the output stage junction temperatures are higher than the specified operating ambient. 8.4.3 Input Voltage Dynamic Range The VCA824 has a input dynamic range limited to 1.6 V and –2.1 V. Increasing the input voltage dynamic range can be done by using an attenuator network on the input. If the VCA824 is trying to regulate the amplitude at the output, such as in an AGC application, the input voltage dynamic range is directly proportional to Equation 2. VIN(PP) = RG ´ IRG(PP) (2) As such, for unity-gain or under-attenuated conditions, the input voltage must be limited to the CMIR of ±1.6 V (3.2 VPP) and the current (IRQ) must flow through the gain resistor, ±2.6 mA (5.2 mAPP). This configuration sets a minimum value for RE such that the gain resistor must be greater than Equation 3. 3.2VPP RGMIN = = 615.4W 5.2mAPP (3) Values lower than 615.4 Ω are gain elements that result in reduced input range, as the dynamic input range is limited by the current flowing through the gain resistor RG (IRG). If the IRG current limits the performance of the circuit, the input stage of the VCA824 goes into overdrive, resulting in limited output voltage range. Such IRGlimited overdrive conditions are shown in Figure 40 for the gain of 10V/V and Figure 60 for the gain of 40 V/V. 20 Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 VCA824 www.ti.com SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 Device Functional Modes (continued) 8.4.4 Output Voltage Dynamic Range With its large output current capability and its wide output voltage swing of ±3.9 V typical on 100-Ω load, it is easy to forget other types of limitations that the VCA824 can encounter. For these limitations, careful analysis must be done to avoid input stage limitation: either voltage or IRG current. Note that if control pin VG varies, the gain limitation may affect other aspects of the circuit. 8.4.5 Bandwidth The output stage of the VCA824 is a wideband current-feedback amplifier. As such, the feedback resistance is the compensation of the last stage. Reducing the feedback element and maintaining the gain constant limits the useful range of IRG, and therefore, reduces the gain adjust range. For a given gain, reducing the gain element limits the maximum achievable output voltage swing. 8.4.6 Offset Adjustment As a result of the internal architecture used on the VCA824, the output offset voltage originates from the output stage and from the input stage and multiplier core. Figure 67 shows how to compensate both sources of the output offset voltage. Use this procedure to compensate the output offset voltage: starting with the output stage compensation, set VG = –1 V to eliminate all offset contribution of the input stage and multiplier core. Adjust the output stage offset compensation potentiometer. Finally, set VG = 1 V to the maximum gain and adjust the input stage and multiplier core potentiometer. This procedure effectively eliminates all offset contribution at the maximum gain. Because adjusting the gain modifies the contribution of the input stage and the multiplier core, some residual output offset voltage remains. 8.4.7 Noise The VCA824 offers 6 nV/√Hz input-referred voltage noise density at a gain of 10 V/V and 2.6-pA/√Hz inputreferred current noise density. The input-referred voltage noise density considers that all noise terms (except the input current noise but including the thermal noise of both the feedback resistor and the gain resistor) are expressed as one term. This model is formulated in Equation 4 and Figure 68. eO = AVMAX ´ 2 ´ (RS ´ in)2 + en2 + 2 ´ 4kTRS (4) A more complete model is shown in Figure 69. For additional information on this model and the actual modeled noise terms, please contact the High-Speed Product Application Support team at www.ti.com. 8.4.8 Input and ESD Protection The VCA824 is built using a very high-speed complementary bipolar process. The internal junction breakdown voltages are relatively low for these very small geometry devices. These breakdowns are reflected in the Absolute Maximum Ratings. All pins on the VCA824 are internally protected from ESD by means of a pair of back-to-back reverse-biased diodes to either power supply, as shown in Figure 64. These diodes begin to conduct when the pin voltage exceeds either power supply by about 0.7 V. This situation can occur with loss of the amplifier power supplies while a signal source is still present. The diodes can typically withstand a continuous current of 30 mA without destruction. To ensure long-term reliability, however, diode current should be externally limited to 10 mA whenever possible. +VS ESD protection diodes internally connected to all pins. External Pin Internal Circuitry -VS Figure 64. Internal ESD Protection Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 21 VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 www.ti.com 9 Application and Implementation NOTE Information in the following applications sections is not part of the TI component specification, and TI does not warrant its accuracy or completeness. TI’s customers are responsible for determining suitability of components for their purposes. Customers should validate and test their design implementation to confirm system functionality. 9.1 Application Information 9.1.1 Difference Amplifier Because both inputs of the VCA824 are high-impedance, a difference amplifier can be implemented without any major problem. Figure 65 shows this implementation. This circuit provides excellent common-mode rejection ratio (CMRR) as long as the input is within the CMRR range of –2.1 V to 1.6 V. Note that this circuit does not make use of the gain control pin, VG. Also, it is recommended to choose RS such that the pole formed by RS and the parasitic input capacitance does not limit the bandwidth of the circuit. Figure 66 shows the common-mode rejection ratio for this circuit implemented in a gain of 10 V/V for VG = 1 V. Note that because the gain control voltage is fixed and is normally set to 1V, the feedback element can be reduced in order to increase the bandwidth. When reducing the feedback element, make sure that the VCA824 is not limited by common-mode input voltage, the current flowing through RG, or any other limitation described in this data sheet. RF VIN+ +VIN RG+ RS RG FB VCA824 RG-VIN VIN- 20W RS Figure 65. Difference Amplifier Common-Mode Rejection Ratio (dB) 85 80 Input Referred 75 70 65 60 55 50 45 40 10k 100k 1M 10M 100M Frequency (Hz) Figure 66. Common-Mode Rejection Ratio 22 Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 VCA824 www.ti.com SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 Application Information (continued) +5V Output Stage Offset Compensation Circuit 10kW 0.1mF 4kW -5V RF VIN +VIN RG+ 50W RG FB VOUT VCA824 RG-VIN +5V 50W 1kW 10kW 0.1mF Input Stage and Multiplexer Core Offset Compensation Circuit -5V Figure 67. Adjusting the Input and Output Voltage Sources RF in RS +VIN RG+ eO RG FB VCA824 eO RG-VIN * 4kTRS in RS * 4kTRS NOTE: RF and RG are noiseless. Figure 68. Simple Noise Model Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 23 VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 www.ti.com Application Information (continued) VG inINPUT VG +VIN V+ RS1 * * enINPUT 4kTRS1 FB x1 RF +RG * inINPUT VOUT RG (Noiseless) ICORE eO iinOUTPUT -RG VREF x1 RF enOUTPUT -VIN V- 4kTRF * * RS2 enINPUT iniOUTPUT * 4kTRF inINPUT GND * 4kTRS2 Figure 69. Full Noise Model 24 Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 VCA824 www.ti.com SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 Application Information (continued) 9.1.2 Differential Equalizer If the application requires frequency shaping (the transition from one gain to another), the VCA824 can be used advantageously because its architecture allows the application to isolate the input from the gain setting elements. Figure 70 shows an implementation of such a configuration. The transfer function is shown in Equation 5. RF 1 + sRGC1 ´ G=2´ RG 1 + sR1C1 (5) VIN1 RF +VIN RG+ RS R1 FB RG VCA824 C1 RGVIN2 -VIN 20W RS Figure 70. Differential Equalizer This transfer function has one pole, P1 (located at RGC1), and one zero, Z1 (located at R1C1). When equalizing an RC load, RL and CL, compensate the pole added by the load located at RLCL with the zero Z1. Knowing RL, CL, and RG allows the user to select C1 as a first step and then calculate R1. Using RL = 75-Ω, CL = 100pF and wanting the VCA824 to operate at a gain of 2 V/V, which gives RF = RG = 453-kΩ, allows the user to select C1 = 15.5 pF to ensure a positive value for the resistor R1. With all these values known, to achieve greater than 300 MHz bandwidth, R1 can be calculated to be 20-Ω. Figure 71 shows the frequency response for both the initial, unequalized frequency response and the resulting equalized frequency response. 9 Equalized Frequency Response 6 3 Gain (dB) 0 Initial Frequency Response of the VCA824 with RC Load -3 -6 -9 -12 -15 -18 -21 -24 1M 10M 100M 1G Frequency (Hz) Figure 71. Differential Equalization of an RC Load 9.1.3 Differential Cable Equalizer A differential cable equalizer can easily be implemented using the VCA824. An example of a cable equalization for 100 feet of Belden Cable 1694F is illustrated in Figure 73, with Figure 72 showing the result for this implementation. This implementation has a maximum error of 0.2 dB from DC to 70 MHz. Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 25 VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 www.ti.com Application Information (continued) 1694F Cable Attenuation (dB) Equalizer Gain (dB) 2.0 1.5 1.0 Cable Attenuation 0.5 VCA824 Equalization 0 -0.5 -1.0 1 10 100 Frequency (MHz) Figure 72. Cable Attenuation vs Equalizer Gain Note that this implementation shows the cable attenuation side-by-side with the equalization in the same plot. For a given frequency, the equalization function realized with the VCA824 matches the cable attenuation. The circuit in Figure 73 is a driver circuit. To implement a receiver circuit, the signal is received differentially between the +VIN and –VIN inputs. VIN R2 453W +VIN R8 50W RG+ R18 13.6kW R17 6kW R21 3kW R9 432W RG-VIN C6 320mF FB VREF VCA824 C7 300mF GND VG R1 20W VOUT R10 75W VOUT 75W Load R5 50W C5 4pF VG = +1VDC C9 10mF Figure 73. Differential Cable Equalizer 9.1.4 Voltage-Controlled Lowpass Filter [application sub] In the circuit of Figure 74, the VCA824 serves as the variable-gain element of a voltage-controlled low-pass filter. This section discusses how this implementation expands the circuit voltage swing capability over that normally achieved with the equivalent multiplier implementation. The circuit control voltage, VG, is calculated as according to the simplified relationship described in Equation 6. VOUT R2 1 =´ R 2C VIN R1 1+s G 26 (6) Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 VCA824 www.ti.com SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 Application Information (continued) R2 332W 24pF C R1 332W RF 1kW VIN 24pF +VIN RG+ OPA690 RG 200W FB VCA824 Out RG-VIN 50W VOUT 20W VG Figure 74. Voltage-Control Low-Pass Filter The response control results from amplification of the feedback voltage applied to R2. First, consider the case where the VCA824 produces G = 1V/V. Then this circuit performs as if the amplifier were replaced by a short circuit. Visually replacing the amplifier by a short leaves a simple voltage-feedback amplifier with a feedback resistor bypassed by a capacitor. Replacing this gain with a variable gain, G, the pole can be written as shown in Equation 7. G f8 = 2pR2C (7) Because the VCA824 is most linear in the midrange, the median of the adjustable pole should be set at VG = 0V (see Figure 13, Figure 33, Figure 54, and Equation 8). Selecting R1 = R2 = 332Ω, and targeting a median frequency of 10MHz, the capacitance (C) is 24pF. Because the OPA690 was selected for the circuit of Figure 74, and in order to limit peaking in the OPA690 frequency response, a capacitor equal to C was added on the inverting mode to ground. This architecture has the effect of setting the high-frequency noise gain of the OPA690 to 2V/V, ensuring stability and providing flat frequency response. -0.8V £ VG £ 0.8V (8) Once the median frequency is set, the maximum and minimum frequencies can be determined by using VG = –0.8 V and VG = 0.8 V in the gain equation of Equation 9. Note that this is a first-order analysis and does not take into consideration the open-loop gain limitation of the OPA690. RF VG + 1 G=2´ ´ RG 2 (9) With the components shown, the circuit provides a linear variation of the low-pass cutoff from 2MHz to 20MHz, using –1V ≤ VG ≤ 1V. 9.1.5 Wideband Variable Gain Amplifier Operation The VCA824 provides an exceptional combination of high output power capability with a wideband, greater than 40dB gain adjust range, linear in V/V variable gain amplifier. The VCA824 input stage places the transconductance element between two input buffers, using the output currents as the forward signal. As the differential input voltage rises, a signal current is generated through the gain element. This current is then mirrored and gained by a factor of two before reaching the multiplier. The other input of the multiplier is the voltage gain control pin, VG. Depending on the voltage present on VG, up to two times the gain current is provided to the transimpedance output stage. The transimpedance output stage is a current-feedback amplifier providing high output current capability and high slew rate, 2500 V/μs. This exceptional full-power performance comes at the price of relatively high quiescent current (36.5 mA), but low input voltage noise for this type of architecture (6 nV/√Hz). Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 27 VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 www.ti.com Application Information (continued) Figure 75 shows the dc-coupled, gain of 10 V/V, dual power-supply circuit used as the basis of Electrical Characteristics- Vs = ± 5 V Electrical Characteristics: VS = ±5 V and Typical Characteristics. For test purposes, the input impedance is set to 50-Ω with a resistor to ground and the output impedance is set to 50-Ω with a series output resistor. Voltage swings reported in Electrical Characteristics- VS = ± 5 V are taken directly at the input and output pins, while output power (dBm) is at the matched 50-Ω load. For the circuit in Figure 75, the total effective load is 100-Ω ∥ 1-kΩ. Note that for the 14-pin, SOIC package, there is a voltage reference pin, VREF (pin 9). For the 14-pin SOIC package, this pin must be connected to ground through a 20-Ω resistor to avoid possible oscillations of the output stage. In the 10-pin, MSOP package, this pin is internally connected and does not require such precaution. An X2Y® capacitor has been used for power-supply bypassing. The combination of low inductance, high resonance frequency, and integration of three capacitors in one package (two capacitors to ground and one across the supplies) enables the VCA824 to achieve the low second-harmonic distortion reported in Electrical Characteristics- VS = ± 5 V. ® 0.1mF +5V X2Y Capacitor Detail X2Yâ Capacitor (see detail) +VS -5V A G1 + 2.2mF VG B -VS +VIN VIN 20W x1 FB IRG RG+ RG 200W G2 + 2.2mF RF 1kW x2 RG- VOUT VOUT x1 20W VREF -VIN SO-14 VCA824 20W Figure 75. DC-Coupled, AVMAX = 10 V/V, Bipolar Supply Specification and Test Circuit 9.2 Typical Application A four-quadrant multiplier can easily be implemented using the VCA824. By placing a resistor between FB and VIN, the transfer function depends upon both VIN and VG, as shown in Equation 10. VOUT = RF RG ´ VG ´ VIN + RF RF RG - R1 ´ VIN (10) Setting R1 to equal RG, the term that depends only on VIN drops out of the equation, leaving only the term that depends on both VG and VIN. VOUT then follows Equation 11. RF VOUT = ´ VIN ´ VG RG (11) 28 Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 VCA824 www.ti.com SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 Typical Application (continued) R1 VG RF VIN +VIN RG+ FB VCA824 R2 RS Source Impedance RG RG-VIN 20W R3 Figure 76. Four-Quadrant Multiplier Circuit Figure 77 illustrates the behavior of this circuit. Keeping the input amplitude of a 1-MHz signal constant and varying the VG voltage (100 kHz, 2 VPP) gives the modulated output voltage shown in Figure 77. 9.2.1 Design Requirements A multiplier requires two inputs, one for the X input and one for the Y input. The output of the multiplier circuit is in the form of Vout = aVin1 × bVin2 : where a and b are real numbers and should not be negative. For four quadrant operation both positive and negative inputs must be supported on the X and Y inputs. A four-quadrant multiplier can easily be implemented using the VCA824. By placing a resistor between FB and VIN, the transfer function depends upon both VIN and VG, as shown in Equation 10 9.2.2 Detailed Design Procedure Setting R1 to equal RG, the term that depends only on VIN drops out of the equation, leaving only the term that depends on both VG and VIN. VOUT then follows Equation 11. The behavior of this circuit is illustrated in Figure 77. Keeping the input amplitude of a 1MHz signal constant and varying the VG voltage (100 kHz, 2 VPP) gives the modulated output voltage shown in Figure 77. 9.2.3 Application Curve 1.5 fIN = 1MHz fVG = 0.1MHz Amplitude (V) 1.0 0.5 0 -0.5 VIN VOUT -1.0 VG -1.5 0 1 2 3 4 5 6 7 8 9 10 Time (ms) Figure 77. Modulated Output Signal of the 4-Quadrant Multiplexer Circuit Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 29 VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 www.ti.com 10 Power Supply Recommendations High-speed amplifiers require low inductance power supply traces and low ESR bypass capacitors. When possible both power and ground planes should be used in the printed circuit board design and the power plane should be adjacent to the ground plane in the board stack-up. The power supply voltage should be centered on the desired amplifier output voltage, so for ground referenced output signals, split supplies are required. The power supply voltage should be from 7-V to 12-V. 11 Layout 11.1 Layout Guidelines Achieving optimum performance with a high-frequency amplifier such as the VCA824 requires careful attention to printed circuit board (PCB) layout parasitics and external component types. Recommendations to optimize performance include: a. Minimize parasitic capacitance to any AC ground for all of the signal I/O pins. This recommendation includes the ground pin (pin 2). Parasitic capacitance on the output can cause instability: on both the inverting input and the noninverting input, it can react with the source impedance to cause unintentional band limiting. To reduce unwanted capacitance, a window around the signal I/O pins should be opened in all of the ground and power planes around those pins. Otherwise, ground and power planes should be unbroken elsewhere on the board. Place a small series resistance (greater than 25-Ω) with the input pin connected to ground to help decouple package parasitics. b. Minimize the distance (less than 0.25”) from the power-supply pins to high-frequency 0.1-μF decoupling capacitors. At the device pins, the ground and power plane layout should not be in close proximity to the signal I/O pins. Avoid narrow power and ground traces to minimize inductance between the pins and the decoupling capacitors. The power-supply connections should always be decoupled with these capacitors. Larger (2.2-μF to 6.8-μF) decoupling capacitors, effective at lower frequencies, should also be used on the main supply pins. These capacitors may be placed somewhat farther from the device and may be shared among several devices in the same area of the PCB. c. Careful selection and placement of external components preserve the high-frequency performance of the VCA824. Resistors should be a very low reactance type. Surface-mount resistors work best and allow a tighter overall layout. Metal-film and carbon composition, axially-leaded resistors can also provide good highfrequency performance. Again, keep the leads and PCB trace length as short as possible. Never use wirewound type resistors in a high-frequency application. Because the output pin is the most sensitive to parasitic capacitance, always position the series output resistor, if any, as close as possible to the output pin. Other network components, such as inverting or noninverting input termination resistors, should also be placed close to the package. d. Connections to other wideband devices on the board may be made with short direct traces or through onboard transmission lines. For short connections, consider the trace and the input to the next device as a lumped capacitive load. Relatively wide traces (50 mils to 100 mils, or 1.27 mm to 2.54 mm) should be used, preferably with ground and power planes opened up around them. e. Socketing a high-speed part like the VCA824 device is not recommended. The additional lead length and pin-to-pin capacitance introduced by the socket can create an extremely troublesome parasitic network, which can make it almost impossible to achieve a smooth, stable frequency response. Best results are obtained by soldering the VCA824 device onto the board. 11.1.1 Thermal Considerations The VCA824 does not require heatsinking or airflow in most applications. The maximum desired junction temperature sets the maximum allowed internal power dissipation as described in this section. In no case should the maximum junction temperature be allowed to exceed 150°C. Operating junction temperature (TJ) is given by Equation 12: TJ = TA + PD ´ qJA 30 Submit Documentation Feedback (12) Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 VCA824 www.ti.com SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 Layout Guidelines (continued) The total internal power dissipation (PD) is the sum of quiescent power (PDQ) and additional power dissipated in the output stage (PDL) to deliver load power. Quiescent power is simply the specified no-load supply current times the total supply voltage across the part. PDL depends on the required output signal and load; for a grounded resistive load, however, it is at a maximum when the output is fixed at a voltage equal to one-half of either supply voltage (for equal bipolar supplies). Under this worst-case condition, PDL = VS 2/(4 × RL), where RL is the resistive load. Note that it is the power in the output stage and not in the load that determines internal power dissipation. As a worst-case example, compute the maximum TJ using a VCA824ID (SO-14 package) in the circuit of Figure 75 operating at maximum gain and at the maximum specified ambient temperature of 85°C. 2 PD = 10V(38.5mA) + 5 /(4 ´ 100W) = 447.5mW (13) Maximum TJ = +85°C + (0.449W ´ 80°C/W) = 120.8°C (14) This maximum operating junction temperature is well below most system level targets. Most applications should be lower because an absolute worst-case output stage power was assumed in this calculation of VCC/2, which is beyond the output voltage range for the VCA824. 11.2 Layout Example Figure 78. Layout Recommendation Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 31 VCA824 SBOS394E – NOVEMBER 2007 – REVISED JULY 2019 www.ti.com 12 Device and Documentation Support 12.1 Device Support 12.1.1 Development Support 12.1.1.1 Demonstration Boards Two printed circuit boards (PCBs) are available to assist in the initial evaluation of circuit performance using the VCA824 in its two package options. Both of these are offered free of charge as unpopulated PCBs, delivered with a user's guide. The summary information for these fixtures is shown in Table 1. Table 1. EVM Ordering Information PRODUCT PACKAGE BOARD PART NUMBER LITERATURE REQUEST NUMBER VCA824ID SO-14 DEM-VCA-SO-1B SBOU050 VCA824IDGS MSOP-10 DEM-VCA-MSOP-1A SBOU051 The demonstration fixtures can be requested at the Texas Instruments web site (www.ti.com) through the VCA824 product folder. 12.2 Receiving Notification of Documentation Updates To receive notification of documentation updates, navigate to the device product folder on ti.com. In the upper right corner, click on Alert me to register and receive a weekly digest of any product information that has changed. For change details, review the revision history included in any revised document. 12.3 Community Resources The following links connect to TI community resources. Linked contents are provided "AS IS" by the respective contributors. They do not constitute TI specifications and do not necessarily reflect TI's views; see TI's Terms of Use. TI E2E™ Online Community TI's Engineer-to-Engineer (E2E) Community. Created to foster collaboration among engineers. At e2e.ti.com, you can ask questions, share knowledge, explore ideas and help solve problems with fellow engineers. Design Support TI's Design Support Quickly find helpful E2E forums along with design support tools and contact information for technical support. 12.4 Trademarks E2E is a trademark of Texas Instruments. X2Y is a registered trademark of X2Y Attenuators LLC. All other trademarks are the property of their respective owners. 12.5 Electrostatic Discharge Caution This integrated circuit can be damaged by ESD. Texas Instruments recommends that all integrated circuits be handled with appropriate precautions. Failure to observe proper handling and installation procedures can cause damage. ESD damage can range from subtle performance degradation to complete device failure. Precision integrated circuits may be more susceptible to damage because very small parametric changes could cause the device not to meet its published specifications. 12.6 Glossary SLYZ022 — TI Glossary. This glossary lists and explains terms, acronyms, and definitions. 13 Mechanical, Packaging, and Orderable Information The following pages include mechanical, packaging, and orderable information. This information is the most current data available for the designated devices. This data is subject to change without notice and revision of this document. For browser-based versions of this data sheet, refer to the left-hand navigation. 32 Submit Documentation Feedback Copyright © 2007–2019, Texas Instruments Incorporated Product Folder Links: VCA824 PACKAGE OPTION ADDENDUM www.ti.com 22-Jul-2019 PACKAGING INFORMATION Orderable Device Status (1) Package Type Package Pins Package Drawing Qty Eco Plan Lead/Ball Finish MSL Peak Temp (2) (6) (3) Op Temp (°C) Device Marking (4/5) VCA824ID ACTIVE SOIC D 14 50 Green (RoHS & no Sb/Br) CU NIPDAU Level-2-260C-1 YEAR -40 to 85 VCA824ID VCA824IDGST ACTIVE VSSOP DGS 10 250 Green (RoHS & no Sb/Br) CU NIPDAUAG Level-2-260C-1 YEAR -40 to 85 BOT (1) The marketing status values are defined as follows: ACTIVE: Product device recommended for new designs. LIFEBUY: TI has announced that the device will be discontinued, and a lifetime-buy period is in effect. NRND: Not recommended for new designs. Device is in production to support existing customers, but TI does not recommend using this part in a new design. PREVIEW: Device has been announced but is not in production. Samples may or may not be available. OBSOLETE: TI has discontinued the production of the device. (2) RoHS: TI defines "RoHS" to mean semiconductor products that are compliant with the current EU RoHS requirements for all 10 RoHS substances, including the requirement that RoHS substance do not exceed 0.1% by weight in homogeneous materials. Where designed to be soldered at high temperatures, "RoHS" products are suitable for use in specified lead-free processes. TI may reference these types of products as "Pb-Free". RoHS Exempt: TI defines "RoHS Exempt" to mean products that contain lead but are compliant with EU RoHS pursuant to a specific EU RoHS exemption. Green: TI defines "Green" to mean the content of Chlorine (Cl) and Bromine (Br) based flame retardants meet JS709B low halogen requirements of
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