Microelectro Circuit Lab
Microelectro Circuit Lab ECE 3042
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This 0 page Class Notes was uploaded by Cassidy Effertz on Monday November 2, 2015. The Class Notes belongs to ECE 3042 at Georgia Institute of Technology - Main Campus taught by Staff in Fall. Since its upload, it has received 10 views. For similar materials see /class/233921/ece-3042-georgia-institute-of-technology-main-campus in ELECTRICAL AND COMPUTER ENGINEERING at Georgia Institute of Technology - Main Campus.
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Date Created: 11/02/15
PseudoRandom Sequences A truly random sequence of binary symbols ones and zeros for simplic ity would be one for which a knowledge of the complete past history of the sequence would be of no assistance in predicting the next symbol ie the probability that the next symbol would be a one or zero would still be one half even if the complete sequence of previous output were available Such a se quence would have to be produced by passing an analog noise source through a comparator sampled at regular clock intervals or some other scheme such as tossing a fair coin Such a sequence is sometime referred to as digital noise gt Uutput Figure 1 Pseudo Random Sequence Generator A pseudo random sequence is one that appears to be perfectly random for K output symbols but then repeats ie it is periodic with a cycle time of K symbols lf K can be made large enough this is not a great limitation any interval up to K symbols will appear to be perfectly random Such a sequence can be constructed using shift registers and EXCLUSIVE OR gates Shown in Fig 1 is an N stage shift register Each time a clock pulse is applied the state of the shift register shifts one stage to the right the state of the nal stage N is lost and the input to the rst stage 1 is obtained by EXCLUSIVE ORing a set of the stages of the shift register Typically stage N provides one of the EXCLUSIVE OR inputs while the other input is drawn from stage M other possibilities involve the EXCLUSIVE OR of the nal and a number of lower stages The output sequence is usually constructed by taking the consecutive values of any one stage stage N is most commonly used These circuits or machines are known as feedback shift registers or pseudo noise generators If the feedback taps stages chosen as inputs to the EXCLUSIVE OR gate are properly chosen a maximal length shift register sequence can be obtained For an N stage shift register K 2N 7 l for a maximal length shift register sequence Such a circuit goes by a number of names pseudo random sequence generator or maximal length shift register sequence gener ator pseudo random bit sequence generator pseudo randon noise generator or a pseudo noise generator Not all settings produce a maximal length se quence viz they have cycle periods less than K The selection of the proper taps to produce a maximal length pseudo random sequence for an N stage shift register is an arcane topic in higher mathematics Assuming that the taps have been selected to produce a maximal length pseudo random sequence the state machine or circuit shown in Fig 1 would produce an output sequence having one more 1 than zerwall the N bit binary numbers from 1 to N ones would be present in the N bit shift register for different clock pulses all zeros is excluded because it would cause the shift register to latch up in the all zero state If the EXCLUSIVE OR gate is followed by an inverter the complement of the previous output sequence will be obtained which will have one more zero than one The state of the shift register for various clock cycles assumes all of the N bit binary numbers with the exception of the all zeroes state Because K depends exponentially on N this makes it possible to have very long pseudo random sequences For instance with a 33 bit stage reg ister clocked at 1 MHZ the cycle time would be over 2 hours and with a 100 bit register clocked at 10 MHZ the cycle time would be around 27000 times the estimated age of the universe which is 15 billion years Thus even at relatively high clock rates it is possible to produce pseudo random se quences that would take centuries to repeat They can be used as random binary sequences for any time interval less than the cycle time Pseudo random sequences have numerous applications in electrical and computer engineeringiespecially telecommunications A pseudo random ana log noise source can be obtained by low pass ltering the output of the pseudo random sequence where the cutoff frequency of the lter should be much less than the clock frequency of the sequence generator Such a se quence may be used to scramble data for security reasons EXCLUSIVE ORing the data stream with the pseudo random sequence at the trans mitter and then reversing the procedure at the receiver with the identical pseudo random sequence which is known only to the valid users Digital pseudo random sequences are used extensively in error correcting and de tecting codes Because they have very peaked autocorrelation properties they are widely used radar ranging and GPS systems The almost random but repeatable nature of pseudo random sequences are widely used in spread spectrum communications systems such as digital cell phones that use CDMA technology to among other things give each digital cell phone a unique code Procedure The only dc power supply buses that will be used in this experiment are 5 V and ground The le are TTL digital le which would be incinerated by other voltages The 100 Ohm resistor and 100 MF capacitor should be used on the 5 V bus Each ECE 3042 Parts kit has 2 74LS74 D ip ops The 7418164 eight bit shift register and 741886 EXCLUSIVE OR will be supplied Return them to the lab instructor when no longer needed Using either the 74LS74 ip op lC or the 7418164 shift register lC assemble several shift registers having lengths from 2 to 8 and exper imentally determine the feedback taps that produced maximal length PN sequences Plot the time domain and frequency domain displays and use either Benchlink or lntulink to make plots for inclusion in the report If necessary use the LM 311 comparator to clean up the output se quence Listen to the sound produced by the connecting a small speaker to the output of the sequence Experiment with making the sound more melodious by inserting a lter between the output of the sequence and the speaker DISCHARGE q 7 L L THRESHOLD d 5 1 CONTROL 3 5 L lt lt lt TRIGGER Zq OUTPUT Z L T Lr1 GND T r F L SROO SRoo RVST L L SAME L L L H LHLH LHSAME Q L HLHL HLFOREID a H HHFORBIDHH L IAtrLALj7 gq1 a W 0quot on M W UA M yVW LaLwcAL Mawmud 13 TAN11MGLJj m m 1313 Mmm NR5 E I39ll RWwRQKLI LI i xg Va 3921 vpu T4 v lat 9 V0 21 I V47r 0 T W 4P7 WW WW m I t TL RICQMZ THltRP1CpxIZ To TL T H g TD 0 1 1 5 1 RIRL g Rszc ma R 2Ra 3 NI 5 1 maSFETi c D 7007 007 3 paw MaSFE a V14 CI 5007 T V ECE 3042 Experiment 6 Active Filter Design 1 Design a 3rd order Butterworth lowpass filters having a dc gain of unity and a cutoff frequency fc of 1028 kHz fc 1028103 K 1 The transferfunction is given on page 9 j F TBf K 1 This is the product of a 1st order LPF amp 2nd order 10 15 I 1 01 ITBlt0 ITBlt0 1 001 i 1103 1104 0 5 I 1103 1104 1105 1106 5000 1104 f f IO implement tnis Witn a circuit cascade tne circuit on page l Witn tnat on page 3913 For each the dc gain is unity K which means that RF is zero a wire and the resistor from the inverting input to ground is infinity nothing there Start by picking two of the capacitors to be 001pF For the Buttervvorth filter 030 amp 030 are the same So for the circuit on page 17 c 001107 6 R1 1 R1 1548 X 103 This is a 1st order LPF 7 2nfcC Forthe circuit shown on page 19 the 2nd order LPF pick c1 001107 6 C2 01C1 then Eq 678 applies with Q1 and m0m0 Q R 1 030 21tfc 1 C2 1 C2 111 1 174Q2 112 17 174Q2 2QmOC2 C1 2QmOC2 c1 R11374gtlt104 R21745gtlt103 Cl1x10 8 021x10 9 Now that all ofthe component values have been determined it39s time to simulate it with SPICE Butte rworth Fi Iter 3 n1 0 mm mum m m5 m Frequency HZ The HE A step S EI heaem the Tab and we the mums Use 7415 LF3515 LF3475 The yesmysvey yuuvuse ave The caps ave 2n Tvym he 3 caps yeasehamy eTese mhe dESTgn vaTues 2 Design a 3rd order unity dc gain Chebyshev LPF with a 3 frequency of 1028 kHz and 05 db ripple in the pass band db 7 05 f3 7 1028103 K1 11 3 t3x 7 4x3 7 3x j 7 J db 7 1010 1 Eq 647 must be solved to obtain the relationship between 630 amp m3 8 39T T which requires that Eq 646 be solved which is a cubic polynomial gx gx 4x3 7 3x 7 1 Since t300 To solve this form the vector v 8 71 This is done with the Insert Matrix selection from the toolbar 8 I The roots are now obtained with the polyroots function 3 With MathCad the index on arrays in a matrix begin with 0 v 7 0 1 Since this is a cubic polynomial it will have at least one real root and its the one required 4 J 70584 7 052m u polyrootsv u 70584 05221 X u2 0 X 1167 L 1167 f fc 3 fc 8805 X 103 The transfer function is Eq 656 which X requires h a2 a1 b1 h 7 t lasinh 1 s 7 0349 h 7 0531 01 11 n 5 3 2 h a2 1 2 a 7 6 1 1 1 2 mi 1 1 1 7 h 2 2 htan61 a2 0626 a1 1069 b1 1706 The transferfunction then becomes 1 1 Ted 7 J f 1 1112 1 jf a2fc 1 a1ch b1 a1fc For a check of the solution the magnitude of the transfer function in db will be plotted vsf yf 7 20logTCf 1 05 2 ya 0 o5 1 3 4 14103 1104 1105 100 1 1o 1 10 f f NOIe that It IS thIrIppIe DOX 3 db box 3 dB down at 1028 kHz Now the circuit must be designed This requires a 1st order Ipf cascaded with a 3rd order Ipf This can be done by cascading the circuit shown in Fig 66a page 17 with Fig 68 page 19 For the 1st orderfilter since the dc gain is unity K1 pick RF0 a wire and R1 infinity Pick cl 00110 6 1 R1 21ta2fcC1 R1 2885 x103 For the 2nd orderfilter K1 pick RF0 amp R3 open ckt f0 fCal moi 27Efo Q39 b1 Pick cl 0110 6 02 00101 1 R1 1 R19614gtlt103 C11gtlt107 2Qm0C2 1 R2 1 2QmOC2 R2 297455 C2 1gtlt107 9 m V 2885K o 1 0 mm L AC Phasez J7 u Chebyshev Gam m Frequency Gain Chebyshev 104 Frequency Second Order Infitite Gain Multiple Feedback BPF page 24 Exp 6 f01028kHz Q K1 030 21tf0 Iil 1 f J Q f0 Tf 7K f 12 1 f 1 1 1 f0 Q f 80393IgT0 Tlt0 01 n 001 3 4 5 110 110 110 C1 001HF R2 2409 R3 20kQ Given R3C1 R1C1 C2 1 m0 R1R2R3C1C2 R1 R2 R3C1C2 R1 R2 RIR2 Q C1 C2 7741 X 103 FindR1R2R3 15798 lg 1548x104 Gam Infinite Gain Multiple Feedback BPF m Frequency Page 23 Fig 611 Second Order Sallen Key BPF 10 146an 5 1 Q 5 f0 fc 171 M K 100 180argTltt W 0 n 100 1103 1104 1105 f R4 3kQ R5 3kQ C1 10nF C2 IOUF m0 21 f0 R5 R118k 2 R218k 2 R318k 2 K0 1 R Given R2 KoR3C2 K R1 R2 R1R2 C C RC 1 K039R1 m391 2 3 2 m 1 m 0 R1R2 R3C1C2 R1 R2 R1R2 R C C R1 R2 3 1 2 Q R1R2 Ko39Rl C1 C2 R3C2 17 R1 R2 R1 R2 Gam 5 2 x m FmRR2Rz ll78xl 3 0 2mm V W 1548K Phas Sallen Key BPF m Frequency Quick Start Guide for Tektronix 30 12B Two Channel DPO Oscilloscope Basics 0 ONOFF Turn on the scope The ONOFF switch is located at the lower left Push it in and wait 30 seconds for it to boot and clear the display Vertical Settings This is a 2 channel scope with the channels being called CH 1 and CH2 A channel is rst selected by pressing the CH 1 button yellow to right of display or CH 2 blue to right of display The volts per division may be changed by rotating the SCALE button To change the coupling press the MENU brown button in the Vertical section of the displays Always leave the input impedance set on 1M and the Probe Setup on 1X To turn a channel off press the channel button and then the OFF button located under the Vertical menu Autoset The AUTOSET black button is on middle right and is used to automatically set the controls on the scope to produce a suitable display under most circumstances It is under the Acquire menu Time Setting The timedivision is controlled by the knob under the Horizontal Menu Trigger The trigger menu allows the selection of either CH 1 CH2 or EXT TRIG as the trigger source The level and slope can also be set If AUTOSET is pressed these settings will be discarded Measurements Select the channel on which a measurement is desired Press MEASURE button near top right Press Select Measurement for CH 1 or CH2 Scroll through the soft menu choices for the desired measurement To remove a measurement press Remove Measurement Cursors Turn on the CURSOR button top center Press the channel the cursors are to be placed on Select horizontal or vertical bars Rotate the knob next to the cursor button to move a cursor Press SELECT to switch to the other cursor Spectra o Press the MATH button red button to right of display Press FFT soft button Use the HORIZONTAL SCALE button and position controls to obtain the desired spectra Monitor the itty bitty line at the top of the display to see which direction to rotate the knobs 0 To turn the spectra off press MATH button and then the OFF button Print Screens The software used to print the screen of Tektronix oscilloscopes to pcs is Wavestar If the user accounts can remember pro les some of the rigmarole may have to be done only once 0 START PROGRAMS Wavestar for Oscilloscopes Wavestar for Occilloscopes Left Click If a screen appears asking Select the Instrument select Tek TDS 3000 series Click next Always select GPIBOlINSTR The address ofthe scope is l The other two GPIB addresses are for the function generator and digital multimeter The ASRLl and ASRL10 are specters Click Next Give a name to the scope such as scope or oscope Click next Click next Click Finish Minimize the Instrument Manager On the Window Called Wavestar click new in the upper left hand corner On the New Datasheet menu Double Click Note Sheet and then expand the window Double Click Local in the upper left of the Wavestar window Double Click the Name Given to the scope Double Click Data 0 Click Screen Color the second one hold the left button down on the pointer Mouse or Trackball drag into the Notesheets and release Print Print Datasheet which is the printer icon on the left Leave the Wavestar Window Open if additional screen prints are to be made Frequency Response Programs Either VEE or LabVIEW may be used to obtain plots of the magnitude in decibels and phase in degrees of the complex transfer function versus frequency in Hertz The instruments that are used are the function generator and the scope the dmm isn t used but leave it turned on For either program connect the output of the function generator to both CH 1 of the scope and the input to the circuit Connect CH 2 of the scope to the output of the circuit VEE Open VEE Click IO and Find Instruments Click yes to send ID to instruments for each of the three instruments Double Click the instrument tetds 3012b and change the name in the dialog box from newinstrument to oscope Double Click the instrument ag3220a and change the name in the dialog box from newinstrument to funcgen Click Advanced Click Plug and Play Driver on the drop down menu click the down arrow and select AG33250A Big Brother or Big Sister to the AG33220A Click ok Click ok 0 Double Click the hp34401a Change the name from newinstrument to dmm Click ok Click Save Second Order All Pass Filter J71 f0 1028kHz Q 3 f 2 1 f J 7 1 o o 180 M 7 Mltfgt 20logTltfgtI ltfgt argltTltfgtgt 2 1E f 1 f J 1 fa Q f0 N71 fstop N 2000 1 0N7 1 fstm lkHz fstop 100kHz fi fsta f stat 1 I Mfi 0 L fi 0 1 1103 1 104 1105 1 103 1104 1 105 TWO Op Amp Second Order Notch AVAVAV R C v I I 0 AAA AAA I I AAA AAA vvv vvv I I vvv vvv 20R R c R R 3 V m 2 20R I ltgt z 2 1 j J71 fO 1028103 Q 3 Tf 1 1 11311 1 f Q f0 fstm 10 fstop 10 N 2000 1 0N71 1 N71 T f fstopW Mf 201ogTf f 180M f f 1 staIt f 1 start 0 I 100 20 L MU WI 0 40 l 60 100 1103 1 104 1 105 1103 1 104 1 105 ECE 3042 Experiment 6 Active Filter Design 1 Design a 3rd order Butterworth lowpass filters having a dc gain of unity and a cutoff frequency fc of 1028 kHz fc 1028103 K 1 The transferfunction is given on page 72 j F TBf K 1 This is the product of a 1st order LPF amp 2nd order 10 15 I 1 01 ITBlt0 ITBlt0 1 001 i 1103 1104 0 5 I 1103 1104 1105 1106 5000 1104 f f IO implement tnis Witn a circuit cascade tne circuit on page csz Witn tnat on page csa For each the dc gain is unity K which means that RF is zero a wire and the resistor from the inverting input to ground is infinity nothing there Start by picking two of the capacitors to be 001pF For the Buttervvorth filter 030 amp 030 are the same So for the circuit on page 82 c 001107 6 R1 1 R1 1548 X 103 This is a 1st order LPF 7 2nfcC Forthe circuit shown on page 83 the 2nd order LPF pick c1 001107 6 C2 01C1 then Eq 684 applies with Q1 and m0m0 Q R 1 030 21tfc 1 C2 1 C2 111 1 174Q2 112 17 174Q2 2QmOC2 C1 2QmOC2 c1 R11374gtlt104 R21745gtlt103 Cl1x10 8 021x10 9 Now that all ofthe component values have been determined it39s time to simulate it with SPICE w V 154 L 1 u Butte rworth Fi Iter m m Frequency HZ T ext stEp mm mm m 3 and mm m mums Use 7415 LF3515 LF3475 The veswsmvsmvyuuvu ave Thecaps aveZEI wmwa capsyeasunamy c use mm desng va ues 2 Desng aam uvdev um y a gem Chebyshev LPF MW e 73 Emmy umuza kHz and u 5 db pr e m me pass band 14 3m22m3 W 45 db 10 1 Eq 647 must be solved to obtain the relationship between 630 amp m T T which requires that Eq 646 be solved which is a cubic polynomial gx gx 4x3 7 3x 7 1 Since t300 To solve this form the vector v 8 This is done with the Insert Matrix selection from the toolbar 1 N j I The roots are now obtained with the polyroots function v 73 0 With MathCad the index on arrays in a matrix begin 4 j with 0 Since this is a cubic polynomial it will have at least one real root and its the one required 70584 7 052m u polyrootsv u 70584 05221 X u2 0 X 1167 L 1167 f fc 3 fc 8805 X 103 The transfer function is Eq 656 which requires h a2 a1 b1 h t lasinh 1 s 0349 h 0531 91 11 11 5 3 2 h a2 1 2 a 7 5111 6 1 1 1 2 lt 1 1 1 7 h 2 2 htan61 a2 0626 a1 1069 b1 1706 The transferfunction then becomes 1 yf 20logTCf 1 Tcf L1 jf 2 jf 1 azfc a1ch b1a1fc For a check of the solution the magnitude of the transfer function in db will be plotted vsf 1 0 05 2 ya 0 E 3905 1 4 3 4 5 100 1103 1104 110 llfO 110 f NOIe that It IS thIrIppIe DOX 3 db box 3 dB down at 1028 kHz Now the circuit must be designed This requires a 1st order pf cascaded with a 3rd order pf 83 This can be done by cascading the circuit shown in Fig 69a page 83 with Fig 611 page For the 1st orderfiter since the dc gain is unity K1 pick RF0 a wire and R1 infinity Pick c1 00110 6 1 R1 21ta2fcC1 R1 2885 x103 For the 2nd orderfiter K1 pick RF0 amp R3 open ckt fO fca1 m0 21tfO Q b1 Pick cl 0110 6 02 00101 1 R1 1 R19614gtlt103 C11gtlt107 2Qm0C2 1 79 R2 1 R2 297455 02 1gtlt10 2QmOC2 Chebyshev Gam m Frequency Chebyshev Gain 1000 104 Frequency Page 86 Fig 614 Second Order Sallen Key BPF f0 f0 j F fc1028kHz K1 Q 5 M K 100 N 180aIgTf 0 m R43m R5zmcmnp CzlEnF fur R5 R 18k0 R218k0 R318k0 1an 4 cm R2 KoR302 R R R R R 2 cc2R3c2 K R R2 R R2 R R 2 R30102 R R2 m R R2 R R R cc2R3c2 17 K 3 R R2 R R2 4 xm mRR2Rz 1 172 x m3 9 2mm V W W 1 n 1548K mm 01 J7 Phase n u AC1 3K R4 dEaLOPAMP Sallen Key BPF 01 Gain 001 H 104 Frequency Second Order Infitite Gain Multiple Feedback BPF page 87 Exp 6 f01028kHz Q5 K1 m02nf0 ya 1 f J Q fo Tf7K f2 f J J 1 f0 Q f 180aIgTD C EEIIJF 020 R1nm R22400 R32Uk0 Gwm R 2c K R1Cx02 R1R2R30102 mm Rgc cz mm R1 R2 7 cc 7 m x mZV FmdR R2R3 z 157 92 m 1542 x m 157 98 Pnasem J7 n lt
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