Using op amps, resistors, and capacitors, design a circuit that

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1 EE 30 Homework 7 Spring 010 Note: This homework assignment has a mixture of some problems that are quite straightforward and some that are quite challenging. Target solving at least 75% of the problems. Anything over 75% should be viewed as Extra Credit. Problem 1 Using op amps, resistors, and capacitors, design a circuit that 1 ' a) solves the differential equation V o = Vo + Vi + V 4 s + 5 b) has a transfer function of T () s = s + 6s + 1 Problem Assume all that you have a single 1nF capacitor, any number of op amps, and any number of resistors. Design a circuit that has a port impedance of 1uF. Problem 3 Determine the maximum frequency of the input that can be applied to the following circuit if there is to be no SR distortion in the output. Assume the Op Amp is ideal except for a SR of 5V/uS and V IN =sin(πft). ' i R1 = K R = 10K Problem 4 In the following circuit, the input is a sinusoid given by V IN =V M sin(ωt). Assume the Op Amp has a frequency-dependent gain that can be modeled with the gainbandwidth product parameter GB. Since the gain of the circuit decreases with frequency, the SR limitations become relaxed and for some value of V M, the op amp will never go into slew, even at high frequencies. Determine the maximum value of V M, in terms of the SR, GB, and K 0, that can be applied without ever causing the output of the circuit to slew at any frequency. R K= 0 1+ R 1

2 Problem 5 Obtain an expression that relates the input voltage and the output voltage (designated as V X ) in the following circuit. I = e X Vx Problem 6 Obtain an expression for and plot V OUT vs V IN for the following circuits. Assume the op amps are ideal. R 1 =1K R =47K V OUT R 1 =1K V IN R =5K V OUT V IN V Problem 7 The transfer characteristics of a nonlinear device are shown. a) Give a mathematical expression for the transfer characteristics b) If R =4K and R 1 =1K, determine the output of the following circuit if V IN =1V. c) Obtain an expression for and plot the transfer characteristics of the circuit shown for -10V<V IN <10V. Assume R =4K and R 1 =1K.

3 Problem 8 (weighted as two homework problems) The data sheet for the Vishay family of thermistors is shown. a) Locate the R 5 =1000Ω resistor and note the B 5/85 value for this device b) Obtain an expression for and plot the resistance of the R 5 =1000 thermistor versus temperature for 0 o C <T< 100 o C c) Design a circuit that will provide a High output if T>50 o C and a low output if T<50 o C using the R5=1000Ω thermistor as a temperature sensor Note: There is an error in equation (1) of the datasheet. It should read 3 ( A+B/T+C/T +D/T ) = R e ( ) ref Problem 9 Design a comparator that has an output that is high when V IN >V and low when V IN <V Problem 10 a) Determine V OUT1 and V OUT is S 1 is open if V IN is a 1Hz triangular waveform with peak maximum and minimum values of +V and -V respectively. Assume the op amps are biased with ± 10V supplies and that the positive and negative saturation voltages of the op amp are ± 10V as well. b) Repeat if S 1 is closed c) Repeat part a) for the following circuit

4 Problem 11 Repeat part b) for the previous problem if S 1 is closed. Problem 1 Design a square wave generator that will provide a 4KHz square wave with a positive peak value of +10V and a negative peak value of -10V. You may use any number of op amps, resistors, and capacitors in this design. Problem 13 (weighted as two HW problems) a) Determine and plot the poles of the amplifier shown if the Op Amp has a GB of 1MHz. Is the amplifier stable? b) Repeat part a) if the + and terminals of the first op amp are interchanged. c) Repart part a) if the + and terminals of both op amps are interchanged. Assume the op amps are ideal except for a frequency dependent gain that can be modeled by A(s)=GB/s. Problem 14 The simple circuit shown below was presented in class as one circuit that will shift the two-level Boolean signals of +15V and -15V to the more standard two-level Boolean signals of 0V and 5V. One disadvantage of this circuit is the extra dc voltage source. The second circuit shown below uses only the +15V bias that is likely already as a biasing voltage of the op amp. Determine, if possible, the resistors R 1, R and R 3 needed to make this a (-15, 15) to (0,5) level shifter. 15V VIN 5K 1K V OUT VIN R3 VOUT 3V R1 R

5 FEATURES Accuracy over a wide temperature range High stability over a long life Excellent price/performance ratio UL recognized, file E Old part number was /4/6... Component in accordance to RoHS 00/95/EC and WEEE 00/96/EC QUICK REFERENCE DATA PARAMETER VALUE Resistance value at 5 C 3.3 Ω to 470 kω Tolerance on R 5 - value ± %; ± 3 %; ± 5 % B 5/85 - value 880K to 4570K Tolerance on B 5/85 - value ± 0.5 % to ± 3 % Maximum dissipation 500 mw Dissipation factor δ (for information only) 7mW/K 8.5 mw/k (for R 5 value 680 Ω) 1. s Response time Thermal time constant τ (for information only) 15 s Operating temperature range: at zero dissipation; continuously - 40 C to + 15 C at zero dissipation; for short periods 150 C at maximum dissipation 0 C to 55 C Climatic category acc. IEC /15/56 Weight 0.3 g APPLICATIONS Temperature measurement, sensing and control, temperature compensation in industrial and consumer electronics DESCRIPTION These thermistors have a negative temperature coefficient. The device consists of a chip with two solid copper tin plated leads. It is grey lacquered and color coded, but not insulated. PACKAGING The thermistors are packed in bulk or tape on reel; see code numbers and relevant packaging quantities. DESIGN-IN SUPPORT For complete Curve Computation, visit: MARKING The thermistors are marked with colored bands; see dimensions drawing and Electrical data and ordering information. MOUNTING By soldering in any position. Not intended for potted applications. ELECTRICAL DATA AND ORDERING INFORMATION UL R 5 B 5/85 - VALUE APPROVED 1NC ORDERING CODE SAP MATERIAL NO. COLOR CODE (3) (1) NTCLE100E3... () [K] [± %] [Y/N] I II III N * *B0 Orange Orange Gold N * *B0 Yellow Violet Gold N * *B0 Blue Grey Gold N * *B0 Brown Black Black N * *B0 Brown Green Black N *9 9*B0 Red Red Black Y * *B0 Orange Orange Black Y * *B0 Yellow Violet Black Y * *B0 Blue Grey Black N * *B0 Brown Black Brown N * *B0 Brown Green Brown N *1 1*B0 Red Red Brown N * *B0 Orange Orange Brown N * *B0 Yellow Violet Brown Document Number: 9049 For technical questions, contact: nlr@vishay.com Revision: 05-May-09 75

6 ELECTRICAL DATA AND ORDERING INFORMATION R 5 B 5/85 - VALUE UL APPROVED [K] [± %] [Y/N] I II III N * *B0 Blue Grey Brown N *10 10*B0 Brown Black Red N *15 15*B0 Brown Green Red N *0 0*B0 Red Black Red Y * *B0 Red Red Red Y *7 7*B0 Red violet Red Y *33 33*B0 Orange Orange Red Y *47 47*B0 Yellow Violet Red Y *50 50*B0 Green Black Red Y *68 68*B0 Blue Grey Red Y * *B0 Brown Black Orange Y *13 13*B0 Brown Red Orange Y * *B0 Brown Green Orange Y *3 3*B0 Red Red Orange N * *B0 Orange Orange Orange N * *B0 Yellow Violet Orange N * *B0 Green Black Orange N * *B0 Blue Grey Orange N * *B0 Brown Black Yellow Y * *B0 Brown Green Yellow Y *4 4*B0 Red Red Yellow N * *B0 Orange Orange Yellow N * *B0 Yellow Violet Yellow Notes (1) Replace * in 1NC by 3 for 5 %, 6 for 3 %, 4 for % () Replace * in SAP by J for 5 %, H for 3 %, G for % (3) For R 5 ± % band IV is red, ± 3 % band IV is orange, ± 5 % band IV is gold 1NC ORDERING CODE SAP MATERIAL NO. COLOR CODE (3) (1) NTCLE100E3... () DIMENSIONS in millimeters DERATING AND TEMPERATURE TOLERANCES B T IV III II I H P (%) 100 Power derating curve H 1 L d P to T amb ( C) PHYSICAL DIMENSIONS FOR RELEVANT TYPE (all dimensions in millimeters) CODE NUMBER H 1 B max. d Min. Max. H max. L P T max to ± ± to ± ± ± For technical questions, contact: nlr@vishay.com Document Number: Revision: 05-May-09

7 TEMPERATURE DEVIATION AS A FUNCTION OF THE AMBIENT TEMPERATURE TEMPERATURE DEVIATION AS A FUNCTION OF THE AMBIENT TEMPERATURE 3.0 ΔT (K) Curves valid for. to 10 kω Curve 1: ΔR 5/R 5 = 5 % Curve : ΔR 5/R 5 = 3 % Curve 3: ΔR 5/R 5 = % Curve 4: ΔR 5/R 5 = 1 % (for series only) ΔT (K) Curves valid for 1 to kω Curve 1: ΔR 5/R 5 = 5 % Curve : ΔR 5/R 5 = 3 % Curve 3: ΔR 5/R 5 = % T ( C) T ( C) TEMPERATURE DEVIATION AS A FUNCTION OF THE AMBIENT TEMPERATURE TEMPERATURE DEVIATION AS A FUNCTION OF THE AMBIENT TEMPERATURE ΔT (K) Curves valid for 33 to 47 kω Curve 1: ΔR 5/R 5 = 5 % Curve : ΔR 5/R 5 = 3 % Curve 3: ΔR 5/R 5 = % Curve 4: ΔR 5/R 5 = 1 % (for series only) ΔT (K) Curves valid for 68 to 100 kω Curve 1: ΔR 5/R 5 = 5 % Curve : ΔR 5/R 5 = 3 % Curve 3: ΔR 5/R 5 = % Curve 4: ΔR 5/R 5 = 1 % (for series only) T ( C) T ( C) TEMPERATURE DEVIATION AS A FUNCTION OF THE AMBIENT TEMPERATURE TEMPERATURE DEVIATION AS A FUNCTION OF THE AMBIENT TEMPERATURE ΔT (K) Curves valid for 150 to 0 kω Curve 1: ΔR 5/R 5 = 5 % Curve : ΔR 5/R 5 = 3 % Curve 3: ΔR 5/R 5 = % ΔT (K) Curves valid for 330 to 470 kω Curve 1: ΔR 5/R 5 = 5 % Curve : ΔR 5/R 5 = 3 % Curve 3: ΔR 5/R 5 = % T ( C) T ( C) Document Number: 9049 For technical questions, contact: nlr@vishay.com Revision: 05-May-09 77

8 VALUE AND TOLERANCE These thermistors have a narrow tolerance on the B-value, the result of which provides a very small tolerance on the nominal resistance value over a wide temperature range. For this reason the usual graphs of R = f(t) are replaced by Resistance Values at Intermediate Temperatures Tables, together with a formula to calculate the characteristics with a high precision. FORMULAE TO DETERMINE NOMINAL RESISTANCE VALUES The resistance values at intermediate temperatures, or the operating temperature values, can be calculated using the following interpolation laws (extended Steinhart and Hart ): R(T) R ref e A + B T + B T + C T ( 3 ) (1) T (R) = R A 1 + B 1 ln C R 1 ln R + D ref R 1 ln R 1 ref R ref () where: A, B, C, D, A 1, B 1, C 1 and D 1 are constant values depending on the material concerned; see table below. R ref is the resistance value at a reference temperature (in this event 5 C). T is the temperature in K. Formulae numbered and are interchangeable with an error of max C in the range 5 C to 15 C and max C in the range - 40 C to + 5 C. PARAMETER FOR DETERMINING NOMINAL RESISTANCE VALUES NUMBER B 5/85 (K) NAME TOL. B VALUE % A B (K) C (K ) DETERMINATION OF THE RESISTANCE/TEMPERATURE DEVIATION FROM NOMINAL VALUE The total resistance deviation is obtained by combining the R 5 -tolerance and the resistance deviation due to B-tolerance. When: X=R 5 -tolerance Y = resistance deviation due to B-tolerance Z = complete resistance deviation, then: Z X Y = % or Z X+Y When: TCR = temperature coefficient ΔT = temperature deviation, Z then: ΔT = TCR The temperature tolerances are plotted in the graphs on the previous page. Example: at 0 C, assume X = 5 %, Y = 0.89 % and TCR = 5.08 %/K (see Table ), then: 5 Z = % = { } 100% = % ( 5.93% ) Z 5.93 ΔT = = = C ( 1.17 C) TCR 5.08 A NTC with a R 5 - value of 10 kω has a value of 3.56 kω between and C Mat O. with Bn = 880K E E E E E Mat P. with Bn = 3990K E E E E E Mat Q. with Bn = 3041K E E E E E Mat R. with Bn = 3136K E E E E E Mat S. with Bn = 3390K E E E E E (1) Mat I. with E E E E E () Bn = 358K E E E E E Mat H. with Bn = 3560K E E E E E Mat B. with Bn = 3740K E E E E E Mat A. with Bn =3977K E E E E E Mat C. with Bn = 4090K E E E E E Mat D. with Bn = 4190K E E E E E Mat E. with Bn = 4370K E E E E E Mat F. with Bn = 4570K E E E E E-07 Notes (1) Temperature < 5 C () Temperature 5 C For technical questions, contact: nlr@vishay.com Document Number: Revision: 05-May-09 D (K 3 ) A 1 B 1 (K -1 ) C 1 (K - ) D 1 (K -3 )

9 For complete Curve Computation, visit: RESISTANCE VALUES AT INTERMEDIATE TEMPERATURES WITH R 5 AT 3.3, 4.7 AND 6.8 Ω T oper [ C] **338 NTCLE100E3338*** **478 NTCLE100E3478*** **688 NTCLE100E3688*** TCR [%/K] ΔR/R DUE TO B tol Document Number: 9049 For technical questions, contact: nlr@vishay.com Revision: 05-May-09 79

10 For complete Curve Computation, visit: RESISTANCE VALUES AT INTERMEDIATE TEMPERATURES WITH R 5 AT 10, 15 AND Ω T oper [ C] **109 NTCLE100E3109*** TCR [%/K] ΔR/R DUE TO B tol **159 NTCLE100E3159*** TCR [%/K] ΔR/R DUE TO B tol **9 NTCLE100E39*** TCR [%/K] ΔR/R DUE TO B tol For technical questions, contact: nlr@vishay.com Document Number: Revision: 05-May-09

11 For complete Curve Computation, visit: RESISTANCE VALUES AT INTERMEDIATE TEMPERATURES WITH R 5 AT 33, 47 AND 68 Ω T oper [ C] **339 NTCLE100E3339*** **479 NTCLE100E3479*** **689 NTCLE100E3689*** TCR [%/K] ΔR/R DUE TO B tol Document Number: 9049 For technical questions, contact: nlr@vishay.com Revision: 05-May-09 81

12 For complete Curve Computation, visit: RESISTANCE VALUES AT INTERMEDIATE TEMPERATURES WITH R 5 AT 100, 150, 0, 330, 470 AND 680 Ω T oper [ C] **101 NTCLE100E3101*** **151 NTCLE100E3151*** **1 NTCLE100E31*** **331 NTCLE100E3331*** **471 NTCLE100E3471*** **681 NTCLE100E3681*** TCR [%/K] ΔR/R DUE TO B tol. For technical questions, contact: nlr@vishay.com Document Number: Revision: 05-May-09

13 For complete Curve Computation, visit: RESISTANCE VALUES AT INTERMEDIATE TEMPERATURES WITH R 5 AT 1, 1.5 AND kω T oper [ C] **10 NTCLE100E310*** **15 NTCLE100E315*** **0 NTCLE100E30*** TCR [%/K] ΔR/R DUE TO B tol Document Number: 9049 For technical questions, contact: nlr@vishay.com Revision: 05-May-09 83

14 For complete Curve Computation, visit: RESISTANCE VALUES AT INTERMEDIATE TEMPERATURES WITH R 5 AT.,.7, 3.3, 4.7, 5.0, 6.8 AND 10 kω T oper [ C] ** NTCLE100E3*** **7 NTCLE100E37*** **33 NTCLE100E333*** **47 NTCLE100E347*** **50 NTCLE100E350*** **68 NTCLE100E368*** **103 NTCLE100E3103*** TCR [%/K] ΔR/R DUE TO B tol. For technical questions, contact: nlr@vishay.com Document Number: Revision: 05-May-09

15 For complete Curve Computation, visit: RESISTANCE VALUES AT INTERMEDIATE TEMPERATURES WITH R 5 AT 1, 15 AND kω T oper [ C] **13 NTCLE100E313*** **153 NTCLE100E3153*** **3 NTCLE100E33*** TCR [%/K] ΔR/R DUE TO B tol Document Number: 9049 For technical questions, contact: nlr@vishay.com Revision: 05-May-09 85

16 For complete Curve Computation, visit: RESISTANCE VALUES AT INTERMEDIATE TEMPERATURES WITH R 5 AT 33, 47, 50, 68 AND 100 kω T oper [ C] ** *** ** *** TCR [%/K] ΔR/R DUE TO B tol NTCLE100E3 ** *** ** *** ** *** TCR [%/K] ΔR/R DUE TO B tol For technical questions, contact: nlr@vishay.com Document Number: Revision: 05-May-09

17 For complete Curve Computation, visit: RESISTANCE VALUES AT INTERMEDIATE TEMPERATURES WITH R 5 AT 150, 0, 330 AND 470 kω T oper [ C] ** *** **4 4*** TCR [%/K] NTCLE100E3 ΔR/R DUE TO B tol. ** *** ** *** TCR [%/K] ΔR/R DUE TO B tol Document Number: 9049 For technical questions, contact: nlr@vishay.com Revision: 05-May-09 87

18 PACKAGING TAPE SPECIFICATIONS Thermistors on tape D P ΔP ΔH T H H 3 d L D 0 H H 1 W 0 W 1 A W W P 0 P 1 F 1E pitch /NTCLE100E3...T1 DIMENSIONS in millimeters DETAILS SYMBOL DIMENSIONS NOMINAL TOLERANCE REMARKS Body diameter D 3.3 ± max. for to 4.1 Lead diameter Feed hole diameter d D ± 10 % ± 0. Lead to lead distance F.54 ± 0.3 Guaranteed between component and tape Distance component to tape centre Component height Component alignment Distance top/bottom of components Length of lacquer under the comp. bottom H H 1 Δh H H ± 1.0 max. ±.0 max. ± 1 1 to 4 max. for to 4.1 Length of snipped lead L 11.0 max. Pitch between thermistors Feed hole pitch Feed hole center to lead center Component alignment Total thickness Total tape thickness Tape width Hold down tape width Hole position Hold down tape position Inspection level: mechanical: S3 Direction of unreeling P P 0 P 1 Δp T t W W 0 W 1 W detail A t ± 1.0 ± 0.3 ± 0.7 ± 1.3 max. max. ± ± 0.3 ± 0.5 ± 1 Taped according to IEC (cover tape may differ from shown) Cumulative pitch error ± 1 mm/0 pitches guaranteed between component and tape 4 max. for to 4.1 with cardboard tape 0.5 ± 0.1 None of the hold down tapes may cover the holes For technical questions, contact: nlr@vishay.com Document Number: Revision: 05-May-09

19 Thermistors on tape P T D Δp H H 1 H 3 D 0 H d H 0 L W 1 W W 0 P 0 P 1 F W t Taped according to IEC (cover tape may differ from shown) E pitch DIMENSIONS in millimeters DETAILS SYMBOL DIMENSIONS NOMINAL TOLERANCE REMARKS Body diameter Lead diameter Feed hole diameter D d D ± 0.5 ± 10 % ± 0. 5 max. for to 3.1 Lead to lead distance F 5.0 Distance component to tape centre Component height Compinent top to seating plane Component alignment Distance top - bottom lead clinch H H 0 H 1 Δh not defined ± ± 0.5 max. ±.0 Length of snipped lead L 11.0 max. Pitch between thermistors Feed hole pitch Feed hole center to lead center Component alignment Total thickness Total tape thickness Tape width Hold down tape width Hole position Hold down tape position Inspection level: mechanical: S3 P P 0 P 1 Δp T t W W 0 W 1 W ± 1.0 ± 0.3 ± 0.7 ± 1.3 max. max. ± ± 0.3 ± 0.5 ± 1.0 Guaranteed between component and tape 1 max. for to 3.1 Cumulative pitch error ± 1 mm/0 pitches guaranteed between component and tape 4 max. for to 3.1 with cardboard tape 0.5 ± 0.1 None of the hold down tapes may cover the holes Document Number: 9049 For technical questions, contact: nlr@vishay.com Revision: 05-May-09 89

20 REEL SPECIFICATIONS Dimensions of the reel 3 18 CODE NUMBERS AND RELEVANT PACKAGING QUANTITIES PARAMETER BULK / NTCLE100E3...B0 Quantity 500 Note (1) Taped according IEC TAPE AND REEL (1) 1E PITCH / NTCLE100E3...T per reel, reels per box TAPE AND REEL (1) E PITCH / NTCLE100E3...T 1500 per reel, reels per box max. CHARACTERISTICS OF TAPED PRODUCTS Minimum pull-out force of the component: 5 N Minimum peel-off force of adhesive tape: 6 N Minimum tearing force tape: 15 N Minimum pull-off force of tape-reel: 5 N STORAGE CONDITIONS Storage temperature range: - 5 C to + 40 C Maximum relative humidity: 80 %, non-condensing 4 ±1 56 max. TESTS AND REQUIREMENTS Essentially all tests are carried out in accordance with IEC publication ; Environmental testing, except where indicated. STABILITY TESTS CECC CLAUSE IEC TEST METHOD Notes (1) For R kω the drift requirement is ΔR/R < 5 % () For R 5 from. kω to 10 kω, requirement is ± % max. TEST PROCEDURE REQUIREMENTS D3; Endurance 5 C; 1000 h ΔR/R < 1 % 1 Endurance - 40 C; 1000 h ΔR/R < 1 % 539 Endurance 500 mw; 55 C; 1000 h ΔR/R < 3 % (1) Dry heat, (steady state) 15 C; 1000 h ΔR/R < 3 % D1; Damp heat (steady state) 56 days at 40 C; 90 to 95 % RH ΔR/R < 3 % C; Rapid change of temperature - 40 C to + 15 C; 50 cycles ΔR/R < % Other applicable tests Robustness of leads: 1 Tensile strength Loading force 10 N ΔR/R 1 % Bending Loading force 5 N 58 Soldering: Solderability 40 C max.; duration 4 s max. ΔR/R 1 % () Resistance to heat 65 C max.; duration 5 s max. 7 Impact Free fall; 1 m ΔR/R 1 % 9 Shock 490 m/s; half sinewave ΔR/R 1 % 45 Resistance to solvent (isopropanol) Ambient temp for 5 minutes; 5 N with hydrophylic cotton wool No traces of lacquer on cotton wool 6 Vibration 1.5 mm peak to peak: 10 Hz to 58 Hz 10 gp: 50 Hz to 500 Hz 1 octave/min. h in each direction in three orthogonal directions No visible damage ΔR/R < 1 % Inflammability 1980, needle flame test Non-flammable For technical questions, contact: nlr@vishay.com Document Number: Revision: 05-May-09

21 Legal Disclaimer Notice Vishay Disclaimer All product specifications and data are subject to change without notice. Vishay Intertechnology, Inc., its affiliates, agents, and employees, and all persons acting on its or their behalf (collectively, Vishay ), disclaim any and all liability for any errors, inaccuracies or incompleteness contained herein or in any other disclosure relating to any product. Vishay disclaims any and all liability arising out of the use or application of any product described herein or of any information provided herein to the maximum extent permitted by law. The product specifications do not expand or otherwise modify Vishay s terms and conditions of purchase, including but not limited to the warranty expressed therein, which apply to these products. No license, express or implied, by estoppel or otherwise, to any intellectual property rights is granted by this document or by any conduct of Vishay. The products shown herein are not designed for use in medical, life-saving, or life-sustaining applications unless otherwise expressly indicated. Customers using or selling Vishay products not expressly indicated for use in such applications do so entirely at their own risk and agree to fully indemnify Vishay for any damages arising or resulting from such use or sale. Please contact authorized Vishay personnel to obtain written terms and conditions regarding products designed for such applications. Product names and markings noted herein may be trademarks of their respective owners. Document Number: Revision: 18-Jul-08 1