LTC2238IUH

LTC2238/LTC2237/LTC2236 10-Bit, 65/40/25Msps Low Noise 3V ADCs DESCRIPTIO The LTC®2238/LTC2237/LTC2236 are 10-bit 65Msps/ 40Msps/25Msps, low power 3V A/D converters designed for digitizing high frequency, wide dynamic range signals. The LTC2238/LTC2237/LTC2236 are perfect for demanding imaging and communications applications with AC performance that includes 61.8dB SNR and 85dB SFDR for signals at the Nyquist frequency. DC specs include ±0.1LSB INL (typ), ±0.05LSB DNL (typ) and ±0.5LSB INL, ±0.5LSB DNL over temperature. The transition noise is a low 0.07LSBRMS. A single 3V supply allows low power operation. A separate output supply allows the outputs to drive 0.5V to 3.6V logic. A single-ended CLK input controls converter operation. An optional clock duty cycle stabilizer allows high performance at full speed for a wide range of clock duty cycles. , LTC and LT are registered trademarks of Linear Technology Corporation. All other trademarks are the property of their respective owners. FEATURES ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ Sample Rate: 65Msps/40Msps/25Msps Single 3V Supply (2.7V to 3.4V) Low Power: 205mW/120mW/75mW 61.8dB SNR 85dB SFDR No Missing Codes Flexible Input: 1VP-P to 2VP-P Range 575MHz Full Power Bandwidth S/H Clock Duty Cycle Stabilizer Shutdown and Nap Modes Pin Compatible Family: 125Msps: LTC2251 (10-Bit), LTC2253 (12-Bit) 105Msps: LTC2250 (10-Bit), LTC2252 (12-Bit) 80Msps: LTC2239 (10-Bit), LTC2229 (12-Bit) 65Msps: LTC2238 (10-Bit), LTC2228 (12-Bit) 40Msps: LTC2237 (10-Bit), LTC2227 (12-Bit) 25Msps: LTC2236 (10-Bit), LTC2226 (12-Bit) 32-Pin (5mm × 5mm) QFN Package APPLICATIO S ■ ■ ■ ■ ■ Wireless and Wired Broadband Communication Imaging Systems Ultrasound Spectral Analysis Portable Instrumentation TYPICAL APPLICATIO REFH REFL FLEXIBLE REFERENCE OVDD + ANALOG INPUT INPUT S/H CORRECTION LOGIC SNR (dBFS) – 10-BIT PIPELINED ADC CORE OUTPUT DRIVERS D9 • • • D0 OGND CLOCK/DUTY CYCLE CONTROL 223876 TA01 CLK U U U LTC2238: SNR vs Input Frequency, –1dB, 2V Range, 65Msps 62.5 61.5 60.5 59.5 58.5 57.5 0 100 50 150 INPUT FREQUENCY (MHz) 200 223876 G09 223876fa 1 LTC2238/LTC2237/LTC2236 ABSOLUTE AXI U RATI GS PACKAGE/ORDER I FOR ATIO TOP VIEW SENSE MODE VCM VDD D9 D8 D7 OF OVDD = VDD (Notes 1, 2) UH PACKAGE 32-LEAD (5mm × 5mm) PLASTIC QFN TJMAX = 125°C, θJA = 34°C/W EXPOSED PAD (PIN 33) IS GND MUST BE SOLDERED TO PCB SHDN Supply Voltage (VDD) ................................................. 4V Digital Output Ground Voltage (OGND) ....... –0.3V to 1V Analog Input Voltage (Note 3) ..... –0.3V to (VDD + 0.3V) Digital Input Voltage .................... –0.3V to (VDD + 0.3V) Digital Output Voltage ................ –0.3V to (OVDD + 0.3V) Power Dissipation ............................................ 1500mW Operating Temperature Range LTC2238C, LTC2237C, LTC2236C ........... 0°C to 70°C LTC2238I, LTC2237I, LTC2236I ..........–40°C to 85°C Storage Temperature Range ..................–65°C to 125°C 32 31 30 29 28 27 26 25 AIN+ 1 AIN– 2 REFH 3 REFH 4 REFL 5 REFL 6 VDD 7 GND 8 9 10 11 12 13 14 15 16 OE NC NC NC NC CLK D0 24 D6 23 D5 22 D4 33 21 OVDD 20 OGND 19 D3 18 D2 17 D1 ORDER PART NUMBER LTC2238CUH LTC2238IUH LTC2237CUH LTC2237IUH LTC2236CUH LTC2236IUH QFN PART MARKING* 2238 2238 2237 2237 2236 2236 Order Options Tape and Reel: Add #TR Lead Free: Add #PBF Lead Free Tape and Reel: Add #TRPBF Lead Free Part Marking: http://www.linear.com/leadfree/ Consult LTC Marketing for parts specified with wider operating temperature ranges. *The temperature grade is identified by a label on the shipping container. CO VERTER CHARACTERISTICS PARAMETER Resolution (No Missing Codes) Integral Linearity Error Differential Linearity Error Offset Error Gain Error Offset Drift Full-Scale Drift Transition Noise Internal Reference External Reference SENSE = 1V Differential Analog Input (Note 5) Differential Analog Input (Note 6) External Reference CONDITIONS ● ● ● ● ● The ● denotes the specifications which apply over the full operating temperature range, otherwise specifications are at TA = 25°C. (Note 4) MIN 10 –0.5 –0.5 –12 –2.5 ±0.1 ± 0.05 ±2 ±0.5 ±10 ±30 ±5 0.07 0.5 0.5 12 2.5 LTC2238 TYP MAX MIN 10 –0.5 –0.5 –12 –2.5 ±0.1 ± 0.05 ±2 ±0.5 ±10 ±30 ±5 0.07 0.5 0.5 12 2.5 LTC2237 TYP MAX MIN 10 –0.5 –0.5 –12 –2.5 ±0.1 ± 0.05 ±2 ±0.5 ±10 ±30 ±5 0.07 0.5 0.5 12 2.5 LTC2236 TYP MAX UNITS Bits LSB LSB mV %FS µV/°C ppm/°C ppm/°C LSBRMS 223876fa 2 U W U U WW W U LTC2238/LTC2237/LTC2236 A ALOG I PUT SYMBOL VIN VIN,CM IIN ISENSE IMODE tAP tJITTER CMRR PARAMETER The ● denotes the specifications which apply over the full operating temperature range, otherwise specifications are at TA = 25°C. (Note 4) CONDITIONS +– Analog Input Range (AIN Analog Input Common Mode (AIN+ + AIN–)/2 Analog Input Leakage Current SENSE Input Leakage MODE Pin Leakage Sample-and-Hold Acquisition Delay Time Sample-and-Hold Acquisition Delay Time Jitter Analog Input Common Mode Rejection Ratio Full Power Bandwidth DY A IC ACCURACY SYMBOL SNR PARAMETER Signal-to-Noise Ratio The ● denotes the specifications which apply over the full operating temperature range, otherwise specifications are at TA = 25°C. AIN = –1dBFS. (Note 4) CONDITIONS 5MHz Input 12.5MHz Input 20MHz Input 30MHz Input 70MHz Input 140MHz Input SFDR Spurious Free Dynamic Range 2nd or 3rd Harmonic 5MHz Input 12.5MHz Input 20MHz Input 30MHz Input 70MHz Input 140MHz Input Spurious Free Dynamic Range 4th Harmonic or Higher 5MHz Input 12.5MHz Input 20MHz Input 30MHz Input 70MHz Input 140MHz Input S/(N+D) Signal-to-Noise Plus Distortion Ratio 5MHz Input 12.5MHz Input 20MHz Input 30MHz Input 70MHz Input 140MHz Input IMD Intermodulation Distortion fIN1 = 28.2MHz, fIN2 = 26.8MHz ● ● ● ● ● ● ● ● ● ● ● ● U WU U MIN ● ● ● ● ● ● TYP 1.5 1.5 MAX 1.9 2 1 3 3 UNITS V V V µA µA µA ns psRMS dB MHz AIN –) 2.7V < VDD < 3.4V (Note 7) Differential Input (Note 7) Single Ended Input (Note 7) 0V < AIN+, AIN– < VDD 0V < SENSE < 1V ±0.5V to ±1V 1 0.5 –1 –3 –3 0 0.2 80 Figure 8 Test Circuit 575 MIN LTC2238 TYP MAX 61.8 MIN LTC2237 TYP MAX 61.8 MIN 60 LTC2236 TYP MAX 61.8 61.8 UNITS dB dB dB dB 60 60 61.8 61.7 61.6 85 69 69 85 85 80 85 75 74 85 85 85 61.8 60 60 61.8 61.7 61.6 80 61.8 61.7 61.6 85 69 85 85 80 85 75 85 85 85 61.8 60 61.6 61.6 61.6 80 61.6 61.5 80 85 85 61.8 61.8 85 80 85 85 61.6 61.6 85 85 dB dB dB dB dB dB dB dB dB dB dB dB dB dB dB dB dB dB dB dB dB 223876fa 3 LTC2238/LTC2237/LTC2236 I TER AL REFERE CE CHARACTERISTICS PARAMETER VCM Output Voltage VCM Output Tempco VCM Line Regulation VCM Output Resistance CONDITIONS IOUT = 0 DIGITAL I PUTS A D DIGITAL OUTPUTS SYMBOL VIH VIL IIN CIN LOGIC OUTPUTS OVDD = 3V COZ ISOURCE ISINK VOH VOL OVDD = 2.5V VOH VOL OVDD = 1.8V VOH VOL High Level Output Voltage Low Level Output Voltage IO = –200µA IO = 1.6mA High Level Output Voltage Low Level Output Voltage IO = –200µA IO = 1.6mA Hi-Z Output Capacitance Output Source Current Output Sink Current High Level Output Voltage Low Level Output Voltage PARAMETER High Level Input Voltage Low Level Input Voltage Input Current Input Capacitance CONDITIONS VDD = 3V VDD = 3V LOGIC INPUTS (CLK, OE, SHDN) The ● denotes the specifications which apply over the full operating temperature range, otherwise specifications are at TA = 25°C. (Note 4) MIN ● ● ● 4 U U U U U (Note 4) MIN 1.475 TYP 1.500 ±25 3 4 MAX 1.525 UNITS V ppm/°C mV/V Ω 2.7V < VDD < 3.4V –1mA < IOUT < 1mA TYP MAX UNITS V 2 0.8 –10 3 10 V µA pF VIN = 0V to VDD (Note 7) OE = High (Note 7) VOUT = 0V VOUT = 3V IO = –10µA IO = –200µA IO = 10µA IO = 1.6mA ● ● 3 50 50 2.7 2.995 2.99 0.005 0.09 2.49 0.09 1.79 0.09 0.4 pF mA mA V V V V V V V V 223876fa LTC2238/LTC2237/LTC2236 POWER REQUIRE E TS SYMBOL VDD OVDD IVDD PDISS PSHDN PNAP PARAMETER Analog Supply Voltage Output Supply Voltage Supply Current Power Dissipation Shutdown Power Nap Mode Power SHDN = H, OE = H, No CLK SHDN = H, OE = L, No CLK CONDITIONS (Note 9) (Note 9) The ● denotes the specifications which apply over the full operating temperature range, otherwise specifications are at TA = 25°C. (Note 8) MIN ● ● ● ● The ● denotes the specifications which apply over the full operating temperature range, otherwise specifications are at TA = 25°C. (Note 4) SYMBOL fs tL PARAMETER CLK Low Time CONDITIONS ● ● ● ● ● TI I G CHARACTERISTICS Sampling Frequency (Note 9) Duty Cycle Stabilizer Off Duty Cycle Stabilizer On (Note 7) Duty Cycle Stabilizer Off Duty Cycle Stabilizer On (Note 7) tH CLK High Time tAP tD Sample-and-Hold Aperture Delay CLK to DATA Delay Data Access Time After OE↓ CL = 5pF (Note 7) CL = 5pF (Note 7) ● ● ● BUS Relinquish Time (Note 7) Pipeline Latency Note 1: Stresses beyond those listed under Absolute Maximum Ratings may cause permanent damage to the device. Exposure to any Absolute Maximum Rating condition for extended periods may affect device reliability and lifetime. Note 2: All voltage values are with respect to ground with GND and OGND wired together (unless otherwise noted). Note 3: When these pin voltages are taken below GND or above VDD, they will be clamped by internal diodes. This product can handle input currents of greater than 100mA below GND or above VDD without latchup. Note 4: VDD = 3V, fSAMPLE = 65MHz (LTC2238), 40MHz (LTC2237), or 25MHz (LTC2236), input range = 2VP-P with differential drive, unless otherwise noted. UW LTC2238 TYP MAX 3 3 68.3 205 2 15 3.4 3.6 80 240 MIN 2.7 0.5 LTC2237 TYP MAX 3 3 40 120 2 15 3.4 3.6 48 144 MIN 2.7 0.5 LTC2236 TYP MAX 3 3 25 75 2 15 3.4 3.6 30 90 UNITS V V mA mW mW mW 2.7 0.5 UW MIN 1 7.3 5 7.3 5 LTC2238 TYP MAX 65 7.7 7.7 7.7 7.7 0 500 500 500 500 MIN 1 11.8 5 11.8 5 LTC2237 TYP MAX 40 12.5 12.5 12.5 12.5 0 500 500 500 500 MIN 1 18.9 5 18.9 5 LTC2236 TYP MAX 25 20 20 20 20 0 500 500 500 500 UNITS MHz ns ns ns ns ns 1.4 2.7 4.3 3.3 5 5.4 10 8.5 1.4 2.7 4.3 3.3 5 5.4 10 8.5 1.4 2.7 4.3 3.3 5 5.4 10 8.5 ns ns ns Cycles Note 5: Integral nonlinearity is defined as the deviation of a code from a straight line passing through the actual endpoints of the transfer curve. The deviation is measured from the center of the quantization band. Note 6: Offset error is the offset voltage measured from –0.5 LSB when the output code flickers between 00 0000 0000 and 11 1111 1111. Note 7: Guaranteed by design, not subject to test. Note 8: VDD = 3V, fSAMPLE = 65MHz (LTC2238), 40MHz (LTC2237), or 25MHz (LTC2236), input range = 1VP-P with differential drive. Note 9: Recommended operating conditions. 223876fa 5 LTC2238/LTC2237/LTC2236 TYPICAL PERFOR A CE CHARACTERISTICS LTC2238: Typical INL, 2V Range, 65Msps 1.00 0.75 0.50 DNL ERROR (LSB) INL ERROR (LSB) 0.25 0 –0.25 –0.50 –0.75 –1.00 0 256 512 CODE 223876 G01 0.25 0 –0.25 –0.50 –0.75 –1.00 AMPLITUDE (dB) 768 LTC2238: 8192 Point FFT, fIN = 30MHz, –1dB, 2V Range, 65Msps 0 –10 –20 –30 0 –10 –20 –30 AMPLITUDE (dB) AMPLITUDE (dB) –50 –60 –70 –80 –90 –50 –60 –70 –80 –90 AMPLITUDE (dB) –40 –100 –110 –120 0 5 20 15 10 25 FREQUENCY (MHz) 30 223876 G04 LTC2238: 8192 Point 2-Tone FFT, fIN = 28.2MHz and 26.8MHz, –1dB, 2V Range, 65Msps 0 –10 –20 –30 AMPLITUDE (dB) –40 –60 –70 –80 –90 COUNT –50 SNR (dBFS) –100 –110 –120 0 5 20 15 10 25 FREQUENCY (MHz) 30 223876 G07 6 UW LTC2238: Typical DNL, 2V Range, 65Msps 1.00 0.75 0.50 0 –10 –20 –30 –40 –50 –60 –70 –80 –90 –100 –110 –120 LTC2238: 8192 Point FFT, fIN = 5MHz, –1dB, 2V Range, 65Msps 1024 0 256 512 CODE 768 1024 223876 G02 0 5 20 15 10 25 FREQUENCY (MHz) 30 223876 G03 LTC2238: 8192 Point FFT, fIN = 70MHz, –1dB, 2V Range, 65Msps 0 –10 –20 –30 –40 –50 –60 –70 –80 –90 –100 –110 –120 0 5 20 15 10 25 FREQUENCY (MHz) 30 223876 G05 LTC2238: 8192 Point FFT, fIN = 140MHz, –1dB, 2V Range, 65Msps –40 –100 –110 –120 0 5 20 15 10 25 FREQUENCY (MHz) 30 223876 G06 LTC2238: Grounded Input Histogram, 65Msps 70000 60000 65520 LTC2238: SNR vs Input Frequency, –1dB, 2V Range, 65Msps 62.5 61.5 50000 40000 30000 20000 60.5 59.5 58.5 10000 0 0 511 512 CODE 0 513 223876 G08 57.5 0 100 50 150 INPUT FREQUENCY (MHz) 200 223876 G09 223876fa LTC2238/LTC2237/LTC2236 TYPICAL PERFOR A CE CHARACTERISTICS LTC2238: SFDR vs Input Frequency, –1dB, 2V Range, 65Msps 100 95 90 100 SFDR SNR AND SFDR (dBFS) SNR (dBc AND dBFS) 90 SFDR (dBFS) 85 80 75 70 65 0 50 150 INPUT FREQUENCY (MHz) 100 200 223876 G10 LTC2238: SFDR vs Input Level, fIN = 30MHz, 2V Range, 65Msps 120 110 100 SFDR (dBc AND dBFS) 90 80 70 60 50 40 30 20 10 0 –60 dBc dBFS IVDD (mA) 2V RANGE 65 1V RANGE 60 55 50 IOVDD (mA) 80dBc SFDR REFERENCE LINE –50 –40 –30 –20 INPUT LEVEL (dBFS) LTC2237: Typical INL, 2V Range, 40Msps 1.00 0.75 0.50 DNL ERROR (LSB) INL ERROR (LSB) 0.25 0 –0.25 –0.50 –0.75 –1.00 0 256 512 CODE 223876 G16 0.25 0 –0.25 –0.50 –0.75 AMPLITUDE (dB) 768 UW –10 223876 G13 LTC2238: SNR and SFDR vs Sample Rate, 2V Range, fIN = 5MHz, –1dB 80 70 60 50 40 30 20 10 50 0 10 20 30 40 50 60 70 80 90 100 110 SAMPLE RATE (Msps) 223876 G11 LTC2238: SNR vs Input Level, fIN = 30MHz, 2V Range, 65Msps dBFS 80 dBc 70 SNR 60 0 –60 –50 –40 –20 –30 INPUT LEVEL (dBFS) –10 0 223876 G12 LTC2238: IVDD vs Sample Rate, 5MHz Sine Wave Input, –1dB 80 75 70 6 5 4 3 2 1 0 0 10 20 30 40 50 60 SAMPLE RATE (Msps) 70 80 LTC2238: IOVDD vs Sample Rate, 5MHz Sine Wave Input, –1dB, OVDD = 1.8V 0 0 10 20 30 40 50 60 SAMPLE RATE (Msps) 70 80 223876 G14 223876 G15 LTC2237: Typical DNL, 2V Range, 40Msps 1.00 0.75 0.50 0 –10 –20 –30 –40 –50 –60 –70 –80 –90 –100 –110 0 256 512 CODE 223876 G17 LTC2237: 8192 Point FFT, fIN = 5MHz, –1dB, 2V Range, 40Msps 1024 –1.00 768 1024 –120 0 5 10 FREQUENCY (MHz) 15 20 223876 G18 223876fa 7 LTC2238/LTC2237/LTC2236 TYPICAL PERFOR A CE CHARACTERISTICS LTC2237: 8192 Point FFT, fIN = 30MHz, –1dB, 2V Range, 40Msps 0 –10 –20 AMPLITUDE (dB) AMPLITUDE (dB) –50 –60 –70 –80 –90 –100 –110 –120 0 5 10 FREQUENCY (MHz) 223876 G19 –50 –60 –70 –80 –90 –100 –110 –120 AMPLITUDE (dB) –30 –40 15 LTC2237: 8192 Point 2-Tone FFT, fIN = 21.6MHz and 23.6MHz, –1dB, 2V Range, 40Msps 0 –10 –20 AMPLITUDE (dB) –30 –40 –60 –70 –80 –90 –100 –110 –120 SNR (dBFS) COUNT –50 0 5 10 FREQUENCY (MHz) 15 LTC2237: SFDR vs Input Frequency, –1dB, 2V Range, 40Msps 100 95 90 100 SNR (dBc AND dBFS) 90 SFDR (dBFS) SNR AND SFDR (dBFS) 85 80 75 70 65 0 50 150 INPUT FREQUENCY (MHz) 100 200 223876 G25 8 UW 223876 G22 LTC2237: 8192 Point FFT, fIN = 70MHz, –1dB, 2V Range, 40Msps 0 –10 –20 –30 –40 0 –10 –20 –30 –40 –50 –60 –70 –80 –90 –100 –110 –120 LTC2237: 8192 Point FFT, fIN = 140MHz, –1dB, 2V Range, 40Msps 20 0 5 10 FREQUENCY (MHz) 15 20 223876 G20 0 5 10 FREQUENCY (MHz) 15 20 223876 G21 LTC2237: Grounded Input Histogram, 40Msps 70000 60000 61.5 50000 40000 30000 20000 58.5 10000 0 0 510 511 CODE 0 512 223876 G23 LTC2237: SNR vs Input Frequency, –1dB, 2V Range, 40Msps 62.5 65520 60.5 59.5 20 57.5 0 100 50 150 INPUT FREQUENCY (MHz) 200 223876 G24 LTC2237: SNR and SFDR vs Sample Rate, 2V Range, fIN = 5MHz, –1dB 80 SFDR 70 LTC2237: SNR vs Input Level, fIN = 5MHz, 2V Range, 40Msps dBFS 60 50 40 30 20 10 dBc 80 70 SNR 60 50 0 10 20 30 40 50 60 SAMPLE RATE (Msps) 70 80 0 –60 –50 –20 –40 –30 INPUT LEVEL (dBFS) –10 0 223876 G26 223876 G27 223876fa LTC2238/LTC2237/LTC2236 TYPICAL PERFOR A CE CHARACTERISTICS LTC2237: SFDR vs Input Level, fIN = 5MHz, 2V Range, 40Msps 120 110 100 SFDR (dBc AND dBFS) 90 80 70 60 50 40 30 20 10 0 –60 dBFS dBc 80dBc SFDR REFERENCE LINE IOVDD (mA) IVDD (mA) –50 –20 –40 –30 INPUT LEVEL (dBFS) LTC2236: Typical INL, 2V Range, 25Msps 1.00 0.75 0.50 DNL ERROR (LSB) INL ERROR (LSB) 0.25 0 –0.25 –0.50 –0.75 –1.00 0 256 512 CODE 223876 G31 0.25 0 –0.25 –0.50 –0.75 –1.00 AMPLITUDE (dB) 768 LTC2236: 8192 Point FFT, fIN = 30MHz, –1dB, 2V Range, 25Msps 0 –10 –20 –30 AMPLITUDE (dB) AMPLITUDE (dB) –50 –60 –70 –80 –90 –50 –60 –70 –80 –90 AMPLITUDE (dB) –40 –100 –110 –120 0 2 8 6 4 10 FREQUENCY (MHz) 12 223876 G34 UW –10 LTC2237: IVDD vs Sample Rate, 5MHz Sine Wave Input, –1dB 50 4 LTC2237: IOVDD vs Sample Rate, 5MHz Sine Wave Input, –1dB, OVDD = 1.8V 45 2V RANGE 40 1V RANGE 35 3 2 1 30 0 0 10 30 40 20 SAMPLE RATE (Msps) 50 223876 G29 0 0 10 30 40 20 SAMPLE RATE (Msps) 50 223876 G30 223876 G28 LTC2236: Typical DNL, 2V Range, 25Msps 1.00 0.75 0.50 LTC2236: 8192 Point FFT, fIN = 5MHz, –1dB, 2V Range, 25Msps 0 –10 –20 –30 –40 –50 –60 –70 –80 –90 –100 –110 –120 1024 0 256 512 CODE 768 1024 223876 G32 0 2 8 6 4 10 FREQUENCY (MHz) 12 223876 G33 LTC2236: 8192 Point FFT, fIN = 70MHz, –1dB, 2V Range, 25Msps 0 –10 –20 –30 –40 0 –10 –20 –30 –40 –50 –60 –70 –80 –90 –100 –110 –120 0 2 8 6 4 10 FREQUENCY (MHz) 12 223876 G35 LTC2236: 8192 Point FFT, fIN = 140MHz, –1dB, 2V Range, 25Msps –100 –110 –120 0 2 8 6 4 10 FREQUENCY (MHz) 12 223876 G36 223876fa 9 LTC2238/LTC2237/LTC2236 TYPICAL PERFOR A CE CHARACTERISTICS LTC2236: 8192 Point 2-Tone FFT, fIN = 10.9MHz and 13.8MHz, –1dB, 2V Range, 25Msps 0 –10 –20 –30 AMPLITUDE (dB) –40 –60 –70 –80 –90 SNR (dBFS) COUNT –50 –100 –110 –120 0 2 8 6 4 10 FREQUENCY (MHz) 12 223876 G37 LTC2236: SFDR vs Input Frequency, –1dB, 2V Range, 25Msps 100 95 SNR (dBc AND dBFS) 90 SNR AND SFDR (dBFS) SFDR (dBFS) 85 80 75 70 65 0 50 150 INPUT FREQUENCY (MHz) 100 200 223876 G40 LTC2236: SFDR vs Input Level, fIN = 5MHz, 2V Range, 25Msps 120 110 100 SFDR (dBc AND dBFS) 90 80 70 60 50 40 30 20 10 0 –60 15 –50 –40 –30 –20 INPUT LEVEL (dBFS) –10 0 dBc 80dBc SFDR REFERENCE LINE dBFS 30 35 25 1V RANGE 20 IOVDD (mA) IVDD (mA) 10 UW 223876 G43 LTC2236: Grounded Input Histogram, 25Msps 70000 60000 61.5 50000 40000 30000 20000 58.5 10000 0 0 511 512 CODE 0 513 223876 G38 LTC2236: SNR vs Input Frequency, –1dB, 2V Range, 25Msps 62.5 65520 60.5 59.5 57.5 0 100 50 150 INPUT FREQUENCY (MHz) 200 223876 G39 LTC2236: SNR and SFDR vs Sample Rate, 2V Range, fIN = 5MHz, –1dB 100 SFDR 90 LTC2236: SNR vs Input Level, fIN = 5MHz, 2V Range, 25Msps 80 70 60 50 40 30 20 10 dBc dBFS 80 70 SNR 60 50 0 5 10 15 20 25 30 35 40 45 50 SAMPLE RATE (Msps) 223876 G41 0 –60 –50 –40 –20 –30 INPUT LEVEL (dBFS) –10 0 223876 G42 LTC2236: IVDD vs Sample Rate, 5MHz Sine Wave Input, –1dB 3 LTC2236: IOVDD vs Sample Rate, 5MHz Sine Wave Input, –1dB, OVDD = 1.8V 2V RANGE 2 1 0 5 25 10 15 20 SAMPLE RATE (Msps) 30 35 0 0 5 25 10 15 20 SAMPLE RATE (Msps) 30 35 223876 G44 223876 G45 223876fa LTC2238/LTC2237/LTC2236 PI FU CTIO S AIN+ (Pin 1): Positive Differential Analog Input. AIN- (Pin 2): Negative Differential Analog Input. REFH (Pins 3, 4): ADC High Reference. Short together and bypass to pins 5, 6 with a 0.1µF ceramic chip capacitor as close to the pin as possible. Also bypass to pins 5, 6 with an additional 2.2µF ceramic chip capacitor and to ground with a 1µF ceramic chip capacitor. REFL (Pins 5, 6): ADC Low Reference. Short together and bypass to pins 3, 4 with a 0.1µF ceramic chip capacitor as close to the pin as possible. Also bypass to pins 3, 4 with an additional 2.2µF ceramic chip capacitor and to ground with a 1µF ceramic chip capacitor. VDD (Pins 7, 32): 3V Supply. Bypass to GND with 0.1µF ceramic chip capacitors. GND (Pin 8): ADC Power Ground. CLK (Pin 9): Clock Input. The input sample starts on the positive edge. SHDN (Pin 10): Shutdown Mode Selection Pin. Connecting SHDN to GND and OE to GND results in normal operation with the outputs enabled. Connecting SHDN to GND and OE to VDD results in normal operation with the outputs at high impedance. Connecting SHDN to VDD and OE to GND results in nap mode with the outputs at high impedance. Connecting SHDN to VDD and OE to VDD results in sleep mode with the outputs at high impedance. OE (Pin 11): Output Enable Pin. Refer to SHDN pin function. NC (Pins 12, 13, 14, 15): Do Not Connect These Pins. D0-D9 (Pins 16, 17, 18, 19, 22, 23, 24, 25, 26, 27): Digital Outputs. D9 is the MSB. OGND (Pin 20): Output Driver Ground. OVDD (Pin 21): Positive Supply for the Output Drivers. Bypass to ground with 0.1µF ceramic chip capacitor. OF (Pin 28): Over/Under Flow Output. High when an over or under flow has occurred. MODE (Pin 29): Output Format and Clock Duty Cycle Stabilizer Selection Pin. Connecting MODE to GND selects offset binary output format and turns the clock duty cycle stabilizer off. 1/3 VDD selects offset binary output format and turns the clock duty cycle stabilizer on. 2/3 VDD selects 2’s complement output format and turns the clock duty cycle stabilizer on. VDD selects 2’s complement output format and turns the clock duty cycle stabilizer off. SENSE (Pin 30): Reference Programming Pin. Connecting SENSE to VCM selects the internal reference and a ±0.5V input range. VDD selects the internal reference and a ±1V input range. An external reference greater than 0.5V and less than 1V applied to SENSE selects an input range of ±VSENSE. ±1V is the largest valid input range. VCM (Pin 31): 1.5V Output and Input Common Mode Bias. Bypass to ground with 2.2µF ceramic chip capacitor. GND (Exposed Pad) (Pin 33): ADC Power Ground. The exposed pad on the bottom of the package needs to be soldered to ground. U U U 223876fa 11 LTC2238/LTC2237/LTC2236 FUNCTIONAL BLOCK DIAGRA AIN+ INPUT S/H FIRST PIPELINED ADC STAGE SECOND PIPELINED ADC STAGE THIRD PIPELINED ADC STAGE FOURTH PIPELINED ADC STAGE FIFTH PIPELINED ADC STAGE SIXTH PIPELINED ADC STAGE AIN– VCM 2.2µF 1.5V REFERENCE RANGE SELECT REFH SENSE REF BUF DIFF REF AMP REFH 1µF Figure 1. Functional Block Diagram 12 W SHIFT REGISTER AND CORRECTION REFL INTERNAL CLOCK SIGNALS OVDD OF CLOCK/DUTY CYCLE CONTROL D9 CONTROL LOGIC OUTPUT DRIVERS • • • D0 0.1µF 2.2µF 1µF REFL CLK MODE SHDN OE 223876 F01 U U OGND 223876fa LTC2238/LTC2237/LTC2236 TI I G DIAGRA ANALOG INPUT CLK tD D0-D9, OF N–5 N–4 N–3 N–2 N–1 N 223876 TD01 W tAP N tH tL N+1 N+2 N+3 N+4 N+5 223876fa UW 13 LTC2238/LTC2237/LTC2236 APPLICATIO S I FOR ATIO DYNAMIC PERFORMANCE Signal-to-Noise Plus Distortion Ratio The signal-to-noise plus distortion ratio [S/(N + D)] is the ratio between the RMS amplitude of the fundamental input frequency and the RMS amplitude of all other frequency components at the ADC output. The output is band limited to frequencies above DC to below half the sampling frequency. Signal-to-Noise Ratio The signal-to-noise ratio (SNR) is the ratio between the RMS amplitude of the fundamental input frequency and the RMS amplitude of all other frequency components except the first five harmonics and DC. Total Harmonic Distortion Total harmonic distortion is the ratio of the RMS sum of all harmonics of the input signal to the fundamental itself. The out-of-band harmonics alias into the frequency band between DC and half the sampling frequency. THD is expressed as: THD = 20Log (√(V22 + V32 + V42 + . . . Vn2)/V1) where V1 is the RMS amplitude of the fundamental frequency and V2 through Vn are the amplitudes of the second through nth harmonics. The THD calculated in this data sheet uses all the harmonics up to the fifth. Intermodulation Distortion If the ADC input signal consists of more than one spectral component, the ADC transfer function nonlinearity can produce intermodulation distortion (IMD) in addition to THD. IMD is the change in one sinusoidal input caused by the presence of another sinusoidal input at a different frequency. 14 U If two pure sine waves of frequencies fa and fb are applied to the ADC input, nonlinearities in the ADC transfer function can create distortion products at the sum and difference frequencies of mfa ± nfb, where m and n = 0, 1, 2, 3, etc. The 3rd order intermodulation products are 2fa + fb, 2fb + fa, 2fa – fb and 2fb – fa. The intermodulation distortion is defined as the ratio of the RMS value of either input tone to the RMS value of the largest 3rd order intermodulation product. Spurious Free Dynamic Range (SFDR) Spurious free dynamic range is the peak harmonic or spurious noise that is the largest spectral component excluding the input signal and DC. This value is expressed in decibels relative to the RMS value of a full scale input signal. Input Bandwidth The input bandwidth is that input frequency at which the amplitude of the reconstructed fundamental is reduced by 3dB for a full scale input signal. Aperture Delay Time The time from when CLK reaches mid-supply to the instant that the input signal is held by the sample and hold circuit. Aperture Delay Jitter The variation in the aperture delay time from conversion to conversion. This random variation will result in noise when sampling an AC input. The signal to noise ratio due to the jitter alone will be: SNRJITTER = –20log (2π • fIN • tJITTER) 223876fa W UU LTC2238/LTC2237/LTC2236 APPLICATIO S I FOR ATIO CONVERTER OPERATION As shown in Figure 1, the LTC2238/LTC2237/LTC2236 is a CMOS pipelined multistep converter. The converter has six pipelined ADC stages; a sampled analog input will result in a digitized value five cycles later (see the Timing Diagram section). For optimal AC performance the analog inputs should be driven differentially. For cost sensitive applications, the analog inputs can be driven single-ended with slightly worse harmonic distortion. The CLK input is single-ended. The LTC2238/LTC2237/LTC2236 has two phases of operation, determined by the state of the CLK input pin. Each pipelined stage shown in Figure 1 contains an ADC, a reconstruction DAC and an interstage residue amplifier. In operation, the ADC quantizes the input to the stage and the quantized value is subtracted from the input by the DAC to produce a residue. The residue is amplified and output by the residue amplifier. Successive stages operate out of phase so that when the odd stages are outputting their residue, the even stages are acquiring that residue and vice versa. When CLK is low, the analog input is sampled differentially directly onto the input sample-and-hold capacitors, inside the “Input S/H” shown in the block diagram. At the instant that CLK transitions from low to high, the sampled input is held. While CLK is high, the held input voltage is buffered by the S/H amplifier which drives the first pipelined ADC stage. The first stage acquires the output of the S/H during this high phase of CLK. When CLK goes back low, the first stage produces its residue which is acquired by the second stage. At the same time, the input S/H goes back to acquiring the analog input. When CLK goes back high, the second stage produces its residue which is acquired by the third stage. An identical process is repeated for the third, fourth and fifth stages, resulting in a fifth stage residue that is sent to the sixth stage ADC for final evaluation. Each ADC stage following the first has additional range to accommodate flash and amplifier offset errors. Results from all of the ADC stages are digitally synchronized such that the results can be properly combined in the correction logic before being sent to the output buffer. U SAMPLE/HOLD OPERATION AND INPUT DRIVE Sample/Hold Operation Figure 2 shows an equivalent circuit for the LTC2238/ LTC2237/LTC2236 CMOS differential sample-and-hold. The analog inputs are connected to the sampling capacitors (CSAMPLE) through NMOS transistors. The capacitors shown attached to each input (CPARASITIC) are the summation of all other capacitance associated with each input. During the sample phase when CLK is low, the transistors connect the analog inputs to the sampling capacitors and they charge to and track the differential input voltage. When CLK transitions from low to high, the sampled input voltage is held on the sampling capacitors. During the hold phase when CLK is high, the sampling capacitors are disconnected from the input and the held voltage is passed to the ADC core for processing. As CLK transitions from high to low, the inputs are reconnected to the sampling capacitors to acquire a new sample. Since the sampling capacitors still hold the previous sample, a charging glitch proportional to the change in voltage between samples will be seen at this time. If the change between the last sample and the new sample is small, the charging glitch seen at the input will be small. If the input change is large, such as the change seen with input frequencies near Nyquist, then a larger charging glitch will be seen. LTC2238/LTC2237/LTC2236 VDD 15Ω CPARASITIC 1pF CSAMPLE 4pF CPARASITIC 1pF VDD CLK CSAMPLE 4pF AIN+ VDD 15Ω AIN– 223876 F02 W U U Figure 2. Equivalent Input Circuit 223876fa 15 LTC2238/LTC2237/LTC2236 APPLICATIO S I FOR ATIO Single-Ended Input For cost sensitive applications, the analog inputs can be driven single-ended. With a single-ended input the harmonic distortion and INL will degrade, but the SNR and DNL will remain unchanged. For a single-ended input, AIN+ should be driven with the input signal and AIN– should be connected to 1.5V or VCM. Common Mode Bias For optimal performance the analog inputs should be driven differentially. Each input should swing ±0.5V for the 2V range or ±0.25V for the 1V range, around a common mode voltage of 1.5V. The VCM output pin (Pin 31) may be used to provide the common mode bias level. VCM can be tied directly to the center tap of a transformer to set the DC input level or as a reference level to an op amp differential driver circuit. The VCM pin must be bypassed to ground close to the ADC with a 2.2µF or greater capacitor. Input Drive Impedance As with all high performance, high speed ADCs, the dynamic performance of the LTC2238/LTC2237/LTC2236 can be influenced by the input drive circuitry, particularly the second and third harmonics. Source impedance and reactance can influence SFDR. At the falling edge of CLK, the sample-and-hold circuit will connect the 4pF sampling capacitor to the input pin and start the sampling period. The sampling period ends when CLK rises, holding the sampled input on the sampling capacitor. Ideally the input circuitry should be fast enough to fully charge the sampling capacitor during the sampling period 0.1µF ANALOG INPUT T1 1:1 25Ω 25Ω T1 = MA/COM ETC1-1T 25Ω RESISTORS, CAPACITORS ARE 0402 PACKAGE SIZE Figure 3. Single-Ended to Differential Conversion Using a Transformer 16 U 1/(2FENCODE); however, this is not always possible and the incomplete settling may degrade the SFDR. The sampling glitch has been designed to be as linear as possible to minimize the effects of incomplete settling. For the best performance, it is recommended to have a source impedance of 100Ω or less for each input. The source impedance should be matched for the differential inputs. Poor matching will result in higher even order harmonics, especially the second. Input Drive Circuits Figure 3 shows the LTC2238/LTC2237/LTC2236 being driven by an RF transformer with a center tapped secondary. The secondary center tap is DC biased with VCM, setting the ADC input signal at its optimum DC level. Terminating on the transformer secondary is desirable, as this provides a common mode path for charging glitches caused by the sample and hold. Figure 3 shows a 1:1 turns ratio transformer. Other turns ratios can be used if the source impedance seen by the ADC does not exceed 100Ω for each ADC input. A disadvantage of using a transformer is the loss of low frequency response. Most small RF transformers have poor performance at frequencies below 1MHz. Figure 4 demonstrates the use of a differential amplifier to convert a single ended input signal into a differential input signal. The advantage of this method is that it provides low frequency input response; however, the limited gain bandwidth of most op amps will limit the SFDR at high input frequencies. VCM 2.2µF 25Ω 0.1µF 12pF AIN– 223876 F03 W UU AIN+ LTC2238 LTC2237 LTC2236 223876fa LTC2238/LTC2237/LTC2236 APPLICATIO S I FOR ATIO VCM HIGH SPEED DIFFERENTIAL 25Ω AMPLIFIER ANALOG INPUT 2.2µF AIN+ 0.1µF LTC2238 LTC2237 LTC2236 ANALOG INPUT T1 0.1µF 25Ω 12Ω 25Ω 12Ω 0.1µF 8pF AIN– 223876 F06 + CM + 12pF – – 25Ω AIN– 223876 F04 Figure 4. Differential Drive with an Amplifier Figure 5 shows a single-ended input circuit. The impedance seen by the analog inputs should be matched. This circuit is not recommended if low distortion is required. The 25Ω resistors and 12pF capacitor on the analog inputs serve two purposes: isolating the drive circuitry from the sample-and-hold charging glitches and limiting the wideband noise at the converter input. VCM 1k 1k 25Ω 2.2µF AIN+ LTC2238 LTC2237 LTC2236 0.1µF ANALOG INPUT 12pF 25Ω 0.1µF AIN– 223876 F05 Figure 5. Single-Ended Drive For input frequencies above 70MHz, the input circuits of Figure 6, 7 and 8 are recommended. The balun transformer gives better high frequency response than a flux coupled center tapped transformer. The coupling capacitors allow the analog inputs to be DC biased at 1.5V. In Figure 8, the series inductors are impedance matching elements that maximize the ADC bandwidth. U VCM 2.2µF AIN+ LTC2238 LTC2237 LTC2236 T1 = MA/COM, ETC 1-1-13 RESISTORS, CAPACITORS ARE 0402 PACKAGE SIZE W UU Figure 6. Recommended Front End Circuit for Input Frequencies Between 70MHz and 170MHz VCM 2.2µF 0.1µF ANALOG INPUT T1 0.1µF 25Ω T1 = MA/COM, ETC 1-1-13 RESISTORS, CAPACITORS ARE 0402 PACKAGE SIZE AIN– 223876 F07 AIN+ 25Ω 0.1µF LTC2238 LTC2237 LTC2236 Figure 7. Recommended Front End Circuit for Input Frequencies Between 170MHz and 300MHz VCM 2.2µF 0.1µF ANALOG INPUT T1 0.1µF 25Ω 6.8nH AIN– 223876 F08 6.8nH 25Ω 0.1µF AIN+ LTC2238 LTC2237 LTC2236 T1 = MA/COM, ETC 1-1-13 RESISTORS, CAPACITORS, INDUCTORS ARE 0402 PACKAGE SIZE Figure 8. Recommended Front End Circuit for Input Frequencies Above 300MHz 223876fa 17 LTC2238/LTC2237/LTC2236 APPLICATIO S I FOR ATIO Reference Operation Figure 9 shows the LTC2238/LTC2237/LTC2236 reference circuitry consisting of a 1.5V bandgap reference, a difference amplifier and switching and control circuit. The internal voltage reference can be configured for two pin selectable input ranges of 2V (±1V differential) or 1V (±0.5V differential). Tying the SENSE pin to VDD selects the 2V range; tying the SENSE pin to VCM selects the 1V range. The 1.5V bandgap reference serves two functions: its output provides a DC bias point for setting the common mode voltage of any external input circuitry; additionally, the reference is used with a difference amplifier to generate the differential reference levels needed by the internal ADC circuitry. An external bypass capacitor is required for the 1.5V reference output, VCM. This provides a high frequency low impedance path to ground for internal and external circuitry. The difference amplifier generates the high and low reference for the ADC. High speed switching circuits are connected to these outputs and they must be externally bypassed. Each output has two pins. The multiple output pins are needed to reduce package inductance. Bypass capacitors must be connected as shown in Figure 9. Other voltage ranges in-between the pin selectable ranges can be programmed with two external resistors as shown in Figure 10. An external reference can be used by applying its output directly or through a resistor divider to SENSE. It is not recommended to drive the SENSE pin with a logic device. The SENSE pin should be tied to the appropriate level as close to the converter as possible. If the SENSE pin is driven externally, it should be bypassed to ground as close to the device as possible with a 1µF ceramic capacitor. 18 U LTC2238/LTC2237/LTC2236 1.5V VCM 2.2µF 4Ω 1.5V BANDGAP REFERENCE 1V RANGE DETECT AND CONTROL SENSE BUFFER INTERNAL ADC HIGH REFERENCE 0.5V TIE TO VDD FOR 2V RANGE; TIE TO VCM FOR 1V RANGE; RANGE = 2 • VSENSE FOR 0.5V < VSENSE < 1V 1µ F REFH 2.2µF 1µ F REFL INTERNAL ADC LOW REFERENCE 223876 F09 W UU 0.1µF DIFF AMP Figure 9. Equivalent Reference Circuit 1.5V VCM 2.2µF SENSE 1µF LTC2238 LTC2237 LTC2236 12k 0.75V 12k 223876 F10 Figure 10. 1.5V Range ADC 223876fa LTC2238/LTC2237/LTC2236 APPLICATIO S I FOR ATIO Input Range The input range can be set based on the application. The 2V input range will provide the best signal-to-noise performance while maintaining excellent SFDR. The 1V input range will have better SFDR performance, but the SNR will degrade by 0.6dB. See the Typical Performance Characteristics section. Driving the Clock Input The CLK input can be driven directly with a CMOS or TTL level signal. A sinusoidal clock can also be used along with a low-jitter squaring circuit before the CLK pin (see Figure 11). The noise performance of the LTC2238/LTC2237/LTC2236 can depend on the clock signal quality as much as on the analog input. Any noise present on the clock signal will result in additional aperture jitter that will be RMS summed with the inherent ADC aperture jitter. In applications where jitter is critical, such as when digitizing high input frequencies, use as large an amplitude as possible. Also, if the ADC is clocked with a sinusoidal signal, filter the CLK signal to reduce wideband noise and distortion products generated by the source. Figures 12 and 13 show alternatives for converting a differential clock to the single-ended CLK input. The use of a transformer provides no incremental contribution to phase noise. The LVDS or PECL to CMOS translators provide little degradation below 70MHz, but at 140MHz will degrade the SNR compared to the transformer solution. The nature of the received signals also has a large 4.7µF FERRITE BEAD 0.1µF SINUSOIDAL CLOCK INPUT 0.1µF 1k CLK 50Ω 1k NC7SVU04 LTC2238 LTC2237 LTC2236 CLEAN SUPPLY 100Ω 223876 F11 Figure 11. Sinusoidal Single-Ended CLK Drive U bearing on how much SNR degradation will be experienced. For high crest factor signals such as WCDMA or OFDM, where the nominal power level must be at least 6dB to 8dB below full scale, the use of these translators will have a lesser impact. The transformer shown in the example may be terminated with the appropriate termination for the signaling in use. The use of a transformer with a 1:4 impedance ratio may be desirable in cases where lower voltage differential signals are considered. The center tap may be bypassed to ground through a capacitor close to the ADC if the differential signals originate on a different plane. The use of a capacitor at the input may result in peaking, and depending on transmission line length may require a 10Ω to 20Ω ohm series resistor to act as both a low pass filter for high frequency noise that may be induced into the clock line by neighboring digital signals, as well as a damping mechanism for reflections. CLEAN SUPPLY FERRITE BEAD 0.1µF LTC2238/ LTC2237/ LTC2236 4.7µF CLK 223876 F12 W UU IF LVDS USE FIN1002 OR FIN1018. FOR PECL, USE AZ1000ELT21 OR SIMILAR Figure 12. CLK Drive Using an LVDS or PECL to CMOS Converter ETC1-1T 5pF-30pF DIFFERENTIAL CLOCK INPUT CLK LTC2238/ LTC2237/ LTC2236 223876 F13 0.1µF FERRITE BEAD VCM Figure 13. LVDS or PECL CLK Drive Using a Transformer 223876fa 19 LTC2238/LTC2237/LTC2236 APPLICATIO S I FOR ATIO Maximum and Minimum Conversion Rates The maximum conversion rate for the LTC2238/LTC2237/ LTC2236 is 65Msps (LTC2238), 40Msps (LTC2237), and 25Msps (LTC2236). For the ADC to operate properly, the CLK signal should have a 50% (±5%) duty cycle. Each half cycle must have at least 7.3ns (LTC2238), 11.8ns (LTC2237), and 18.9ns (LTC2236) for the ADC internal circuitry to have enough settling time for proper operation. An optional clock duty cycle stabilizer circuit can be used if the input clock has a non 50% duty cycle. This circuit uses the rising edge of the CLK pin to sample the analog input. The falling edge of CLK is ignored and the internal falling edge is generated by a phase-locked loop. The input clock duty cycle can vary from 40% to 60% and the clock duty cycle stabilizer will maintain a constant 50% internal duty cycle. If the clock is turned off for a long period of time, the duty cycle stabilizer circuit will require a hundred clock cycles for the PLL to lock onto the input clock. To use the clock duty cycle stabilizer, the MODE pin should be connected to 1/3VDD or 2/3VDD using external resistors. The lower limit of the LTC2238/LTC2237/LTC2236 sample rate is determined by droop of the sample-and-hold circuits. The pipelined architecture of this ADC relies on storing analog signals on small valued capacitors. Junction leakage will discharge the capacitors. The specified minimum operating frequency for the LTC2238/LTC2237/ LTC2236 is 1Msps. LTC2228/27/26 OVDD VDD VDD 0.5V TO 3.6V 0.1µF OVDD DATA FROM LATCH OE OGND PREDRIVER LOGIC 43Ω TYPICAL DATA OUTPUT 222876 F14 Figure 14. Digital Output Buffer 20 U DIGITAL OUTPUTS Table 1 shows the relationship between the analog input voltage, the digital data bits, and the overflow bit. Table 1. Output Codes vs Input Voltage AIN+ – AIN– (2V Range) >+1.000000V +0.998047V +0.996094V +0.001953V 0.000000V –0.001953V –0.003906V –0.998047V –1.000000V