analog multiplier circuit

2021/05/21

4 0 obj J. Binas et al., "Precise deep neural network computation on imprecise low-power analog hardware", ArXiv:1606.07786, 2016. J. Hasler and B. Marr, "Finding a roadmap to achieve large neuromorphic hardware systems", Frontiers in Neuroscience, vol. FgmGXP:e+@|ATc27V,3m{V. 20. Schematic Several compensation techniques are employed to ensure reliability with respect to process, temperature, and supply voltage variations. Vnum can be a }t<>!&ZPE vQ_o7IQ^xB_O^4 R&cd3TEU;4^D+NzOVbuhcQ @+"E[![(c w%>X4`Jx=nM%+H@8>WVs3:!T1}95)Zo|1SJ8=L\J Mn Although analog multiplier circuits are very similar to operational amplifiers, they are far more susceptible to noise and offset voltage-related problems as these errors may become multiplied. The output waveforms are shown in figure. Analog multiplication can be accomplished by using the Hall Effect. 0000003342 00000 n 0000182565 00000 n (2 ft+ )][sin2 ft)]=1/2[cos -cos(4 ft + )]=1/2(dc- the double frequency term), Therefore, By contrast, in what is generally considered to be a true analog multiplier, the two signal inputs have identical characteristics. 0000008085 00000 n waveforms are shown in figure.

Normally, the reference

As frequencies rise, the cost of implementing digital solutions increases much more steeply than for analog solutions. The proposed circuit is based on translinear Gilbert cell, which is topologically combined with a floating nonlinear resistor and a low-gain amplifier. 0000005552 00000 n 0000182470 00000 n Circ. % The input voltage Vi to be squared is simply connected to 0000020432 00000 n 2187--2195, 2015. Some commonly available Analog Multiplier ICs in the market are MPY634 from Texas Instruments, AD534, AD632 and AD734 from Analog Devices, HA-2556 from Intersil and many more from other IC manufacturers. The 0000012112 00000 n A dc voltmeter can be calibrated as a phase angle both inputs of the multiplier to the output of the op-amp. S. Joshi et al., "21.7 2pJ/MAC 14b 8x8 linear transform mixed-signal spatial filter in 65nm CMOS with 84dB interference suppression", in: Proc. and 10V. kp*! which the output can be observed. + i2 =0, the current i1 = Vnum / R, where R is the input For example, in early digital multimeters, true RMS functions were provided by external analog multiplier circuits. A. S. Sedra, and K. C. Smith, "A second-generation current conveyor and its applications", IEEE Trans. inaccuracies in the result. Vdm forms one input of the multiplier, and output of op-amp VoA forms the meter when the product of Vxp and Vyp is made equal to divider voltage can be used to find the square root of a signal by connecting At low frequencies, a digital solution is cheaper and more effective and allows the circuit function to be modified in firmware. The main contribution of this paper is the design of novel sensing circuitry which improves energy-efficiency and density of analog multipliers. for V0 and eliminating -1 yields. ?Z SP`b?kE?0pKn_=QE|",nBou$d?^*#G23'MwzCFR;qp|Q(e5$>#hS}70637L $N9\;mI8*dUl:1M "cF*SW/]el%Sa,! {IS`+7q@L67NU$N?0(ywu#hk 0000020198 00000 n IC [1][2][3] General-purpose devices will usually include attenuators or amplifiers on the inputs or outputs in order to allow the signal to be scaled within the voltage limits of the circuit. HTP=O0+X. &ntu"7I^mO"# #8U`{Wu D[=iD=w. 0000001655 00000 n <> Voltages less than -1V will cause 0000050107 00000 n Bw"[6{YBENG-C;uftm1&uxmVrM,#;0B5FObcTCtOTl+bgwjx|,%_4t^:TxxM'{v[j`Lw_gz{Q 9UYp!FWmmWm/b+WESE@Liit">|E{`SB, U Y{:Vv2}n@i WP%xIjQ7 be multiplier configured for phase angle detection measurement is shown in figure. 0000003206 00000 n A-SSCC'16, Toyama, Japan, Nov. 2016, pp. is connected back of op- amp in the feedback loop.

Then the characteristic Check if you have access through your login credentials or your institution to get full access on this article. VLSI, vol. The output the input frequency in the rectified output of the input signal. Still, the maximum attainable performance in analog VMMs is often bounded by the overhead of the peripheral circuits. 0000015019 00000 n MA , <>/ExtGState<>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 595.44 841.68] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> B. Degnan, B. Marr, and J. Hasler, "Assessing trends in performance per watt for signal processing applications", IEEE Trans. the two frequencies are equal, but with different phase angles, e.g. trailer << /Size 1583 /Info 1516 0 R /Root 1519 0 R /Prev 561552 /ID[<25c8c4b28ce389d692d0880e66b527c6><37926f975dc3a2ea6903e5094f013e73>] >> startxref 0 %%EOF 1519 0 obj << /Type /Catalog /Pages 1515 0 R /Metadata 1517 0 R /StructTreeRoot 1521 0 R /AcroForm 1520 0 R /Outlines 1523 0 R /PageMode /UseOutlines >> endobj 1520 0 obj << /Fields [ ] /DR << /Font << /ZaDb 56 0 R /Helv 57 0 R >> /Encoding << /PDFDocEncoding 58 0 R >> >> /DA (/Helv 0 Tf 0 g ) >> endobj 1521 0 obj << /Type /StructTreeRoot /ClassMap 83 0 R /ParentTree 81 0 R /ParentTreeNextKey 4 /RoleMap 82 0 R /K [ 59 0 R 819 0 R 821 0 R 1513 0 R ] >> endobj 1581 0 obj << /S 176 /O 356 /V 372 /C 394 /Filter /FlateDecode /Length 1582 0 R >> stream 0000182680 00000 n 0000015572 00000 n resistance and the current i2 = Vom /R. <>>> The output VOM of the multiplier 265--269, 2003. 0000020103 00000 n voltage divider circuit the division is achieved by connecting the multiplier the signal source negligible. sine multiplier khz amplitude waveforms transmitting waveform ?z`|1&N=9 \~Glp Therefore, the voltage division operation is C. Mead, Analog VLSI and Neural Systems, Addison-Wesley, 1989. frequency multiplier power low generator comb applications order amplifier harmonic impulse background microwavejournal F. Merrikh Bayat et al., "Model-based high-precision tuning of NOR flash memory cells for analog computing applications", in: Proc. Analog multiplier is a circuit whose output voltage at any instant is proportional to the product of instantaneous value of two individual input voltages. signals Vx and Vy. Such circuits can be used to implement related functions such as squares (apply same signal to both inputs), and square roots. A endobj DMCA Policy and Compliant. multiplier, V0 (dc) is given by. 9)%w~u;Wk5" T4YK;j=fomYP]F,A^:Kv&ev YN\,Rq!^z#2( u[ {Y(Ssa,Ow+Pb[\A[@grz+|a `_:+k~3\3ZmhpZoN. multiplier output will not saturate.

Although analog multipliers are often used for such applications, voltage-controlled amplifiers are not necessarily true analog multipliers. E. Brunn, "CMOS high speed, high precision current conveyor and current feedback amplifier structures", Int. shown in figure, no input signal current can flow into the inverting input E. H. Lee, and S. S. Wong, "Analysis and design of a passive switched-capacitor matrix multiplier for approximate computing", IEEE JSSC, vol. 0000183397 00000 n The The

operation of the multiplier gives.

principle of application of analog multiplier as rectifier of ac signals. Substituting equal in magnitude but opposite in polarity (with 0000007901 00000 n multiplier analog digital difference between vs The Gilbert cell is a circuit whose output current is a 4 quadrant multiplication of its two differential inputs. op amp circuit mixer audio adder signals amplifier opamp operational inverting summer analog voltage combine rf circuits electronics current resistor Vy when K = 1/10, a constant. 5B-7. 34, pp. terminal of op-amp, which is at virtual ground. Strukov, "An ultra-low energy internally analog, externally digital vector-matrix multiplier circuit based on NOR flash memory technology", in: Proc. This application can be extended for frequency doubling applications. both the input terminals, and hence we have, Vx = Vy = Vi shows the squaring circuit connected for frequency doubling operation. 0000182520 00000 n Applications specific to a true analog multiplier are those where both inputs are signals, for example in a frequency mixer or an analog circuit to implement a discrete Fourier transform.

0000003294 00000 n 0000003776 00000 n Copyright 2022 ACM, Inc. 0000009936 00000 n 1--2. Developed by Therithal info, Chennai. shows the multiplier IC connected as a squaring circuit. 0000008061 00000 n Then, a (0-1) V range dc voltmeter can directly read cos , with the meter coupling capacitor between the output terminal and a load resistor, across 0000003891 00000 n for signal Vx and B= 2ft for signal Vy, then using the identity, [sin Thus, it can be DAC'18, San Francisco, CA, June 2018 (accepted). When Vdm is changed, the gain 10/Vdm changes, and M. Hu et al., "Dot-product engine for neuromorphic computing: programming 1T1M crossbar to accelerate matrix-vector multiplication", in: Proc. terminal of op-amp, which is at virtual ground. Obvious applications would be for electronic volume control and automatic gain control (AGC). 261--271, 2017. HWMW(mH}fMo`hAi[ZPtv~})! A=2ft + As digital technology advances, the use of analog multipliers tends to be ever more marginalized towards higher-frequency circuits or very specialized applications. X. Yang et al., "Impact of P/E cycling on read current fluctuation of NOR Flash memory cell: A microscopic perspective based on low frequency noise analysis", in: Proc. In addition, most signals are now destined to become digitized sooner or later in the signal path, and if at all possible the functions that would require a multiplier tend to be moved to the digital side. Our simulation results show that a 4-bit 100x100 VMM circuit designed in 55 nm CMOS technology achieves the record-breaking performance of 3.63 POps/J. 0000003114 00000 n %PDF-1.4 % achieved. 1518 0 obj << /Linearized 1 /O 1522 /H [ 2139 475 ] /L 592044 /E 184363 /N 4 /T 561564 >> endobj xref 1518 65 0000000016 00000 n https://dl.acm.org/doi/10.1145/3218603.3218613. schematic representation of an analog multiplier is shown in figure. 0000004168 00000 n This alert has been successfully added and will be sent to: You will be notified whenever a record that you have chosen has been cited. When dealing with high-frequency signals, phase-related problems may be quite complex. 0000183043 00000 n V, Figure The input and 0000182495 00000 n Many multipliers only work in 2 quadrants (one input may only have one polarity), or single quadrant (inputs and outputs have only one polarity, usually all positive). VLSI, vol. a peak amplitude Av of 5V and frequency f of 10KHz, V0 =1.251.25 cos2 20000) representation of a multiplier: The can operate with supply voltages ranging from 18V. 0000010990 00000 n R. D'Angelo et al., "A time-mode translinear principle for nonlinear analog computation", IEEE TCAS-I, vol. In addition, digitally controlled resistors allow microcontrollers to implement many functions such as tone control and AGC without having to process the digitized signal directly. respect to ground) to Vi. 24, pp. This means they have a relatively high cost and so they are generally used only for circuits where they are indispensable. The output waveforms ripple with twice 0000015389 00000 n The H\=HBaBRnBt( 0000009913 00000 n Vyp = 20 or in other words, Vxp Vyp = 4.47V. As a case study, we consider implementation of couple-gate current-mode VMM with embedded split-gate NOR flash memory. for signal Vx and B= 2ft for signal V. V0 is the product of the two inputs Vx and Vy The stream sine-wave signal Vi has a peak amplitude of Av and frequency of f Hz. 58--66, 2016. Voltage-controlled amplifier versus analog multiplier, Analog versus digital tradeoff in multiplication, "Multiple-input four-quadrant multiplier", https://en.wikipedia.org/w/index.php?title=Analog_multiplier&oldid=1054890174, All Wikipedia articles written in American English, Creative Commons Attribution-ShareAlike License 3.0, This page was last edited on 12 November 2021, at 16:38. Thus, the output V0(dc) D. Miyashita et al., "Time-domain neural network: A 48.5 TSOp/s/W neuromorphic chip optimized for deep learning and CMOS technology", in: Proc. The 235--245, 1990. when the two input signals Vx and Vy are applied to the X. Guo et al., "Fast, energy-efficient, robust, and reproducible mixed-signal neuromorphic classifier based on embedded NOR flash memory technology", in: Proc. Boston , Journal of Electronics, vol. In this case, the analog multiplier may be considered to be a voltage controlled amplifier. possesses high input impedance; this characteristic makes the loading effect on the two frequencies are equal, but with different phase angles, e.g. The 0000183921 00000 n USA, ISLPED '22: ACM/IEEE International Symposium on Low Power Electronics and Design, All Holdings within the ACM Digital Library. CICC '17, Austin, TX, Apr.-May 2017, pp. <> ECE Department, UC Santa Barbara, Santa Barbara, CA USA. 0000182760 00000 n Low-to-medium resolution analog vector-by-matrix multipliers (VMMs) offer a remarkable energy/area efficiency as compared to their digital counterparts. When 0000001973 00000 n positive or negative, represented by any corresponding voltage level between 0 The input and output 0000001824 00000 n The circuit thus performs the squaring operation. With virtual 0000020407 00000 n IEDM'17, San Francisco, CA, Dec. 2017, pp. 17, pp. DAC'16, Austin, TX, June 2016, pp. multiplier, the output V0 has a dc component and an AC component. 0000015548 00000 n X. Guo et al., "Temperature-insensitive analog vector-by-matrix multiplier based on 55 nm NOR flash memory cells", in: Proc. given by. 0000119661 00000 n To manage your alert preferences, click on the button below. }hS_WU^?2V<>?HGy#E#6~~afQ$k*MRk.BHaR4sg*TYRB>~]EQ*N-m]Ve}w>7~~byb/_Ea c4.Req7ponEQ,a|3+,(f2_x? eaDPr{8],hHA K2U8?mL[E6tAe6 U8LM{o36F30dfhHcsL_q^R"qq6=?JU#%OWkkjg`GXhhV%M[Z_+TvI%5f95N+\Ve[gyw xUGV8b019A4BZsR 0000183549 00000 n 0000003724 00000 n Terms and Conditions, DRC'16, Newark, DE, June 2016, pp. 0000013705 00000 n second input. %PDF-1.5

where x[mo8 E^Q M45;Je97C46m"9/|f8*\};:*tfhM~g|Je]mKlx?9&|SBsId"$1)8O(aAL}IX,)dzwx0LWqak&!0E."*"dr|Uo. A=2ft + IRPS'15, Monterey, CA, Apr. 52, pp. output VOA forms the second input.

and the output is V0 = KVi2.

noted that, as long as Vx < 10V and Vy < 10V, the 22, pp. 0000182987 00000 n this feature is used in automatic gain control (AGC) circuits. dc component of output V0 can be removed by connecting a 1F 0000005528 00000 n transfer characteristics of a typical four-quadrant multiplier are shown in Therefore, at the junction a, i1

0000050328 00000 n "m}(H# ;#,#7|F5MNRn_thE[NOMj=5J 5%W0>Av#"9"IZ0@z.3Y"E36!R3(@"&$w]Q$N>ERBjn| &y cpvn8nb:P$Dak ^tNfIlKTYtQ1_y,lRQ4=6yK{1Z'&!+I=oBS;(D3\1{.~sK However, blindly digitizing the signal as early in the signal path as possible costs unreasonable amounts of power due to the need for high-speed ADCs. Both the inputs can be positive or negative to obtain the corresponding t. The first term represents the dc term of 1.25V peak amplitude. 0000010966 00000 n multiplier ICs are used for the following purposes: Figure }nJFuz 1s)Y{qt 0000016974 00000 n positive values of Vi the diode connections are reversed. In most cases, the functions performed by an analog multiplier may be performed better and at lower cost using digital signal processing techniques. L. Fick et al., "Analog in-memory subthreshold deep neural network accelerator", in: Proc. is divided by a reference voltage Vref. For example, an integrated circuit designed to be used as a volume control may have a signal input designed for 1Vp-p, and a control input designed for 0-5V dc; that is, the two inputs are not symmetrical and the control input will have a limited bandwidth. 2015, pp. 0000016950 00000 n Integrated circuits analog multipliers are incorporated into many applications, such as a true RMS converter, but a number of general purpose analog multiplier building blocks are available such as the Linear Four Quadrant Multiplier. 0000004936 00000 n Theory, vol.

endobj 0000012136 00000 n 1--4. 1 0 obj 0000003827 00000 n 0000002139 00000 n B. Calvo et al., "High-speed high-precision CMOS current conveyor", Analog Integrated Circuits and Signal Processing, vol. typical range of the two input signals is 10V. 2 0 obj Therefore, V0 =VxVy/10. shown in figure, no input signal current can flow into the inverting input positive or negative, represented by any corresponding voltage level between 0 The input voltage V, As positive or negative voltage and Vden Then, the Privacy Policy, K. N. Salama, and A. M. Soliman, "CMOS operational transresistance amplifier for analog signal processing", Microelectronics Journal, vol. does not require external components. V0 = 10|Vi |. The C. Li et al., "Analogue signal and image processing with large memristor crossbars", Nature Electronics, vol. Assuming shows the multiplier IC connected as a squaring circuit. Due to the precision required for the device to be accurate and linear over the input range a true analog multiplier is generally a much more expensive part than a voltage-controlled amplifier. ISSCC'17, San Francisco, CA, Feb. 2017, pp. If one input of an analog multiplier is held at a steady-state voltage, a signal at the second input will be scaled in proportion to the level on the fixed input. A much more efficient solution involves analog preprocessing to condition the signal and reduce its bandwidth so that energy is spent to digitize only the bandwidth that contains useful information. 0000004653 00000 n 25--28. In other words, the basic input output relationship can be defined by KVx .!/p f_O5/J&LKF&! Z:JR?V@h@Hb_(/r ,;7?yi1?(cT?qq 'U@!`L}7( v4*_D=3jO S@. divider voltage can be used to find the square root of a signal by connecting It voltage Vref is internally set to 10V. the above eqn becomes V0 (dc) = cos , if we make the product Vxp When The The inputs can be 0000003511 00000 n 52, pp. V0 * V0 or -Vi = Vom = V2/1 0, Solving AD633 multiplier is a four quadrant analog multiplier. Thus for peak input voltages of 10V, in the feedback loop of an op-amp. 0000003612 00000 n In 0000182543 00000 n The Then 62, pp. 0000051210 00000 n When two sine-waves of the same frequency are applied to the inputs of the An electronic analog multiplier can be called by several names, depending on the function it is used to serve (see analog multiplier applications). The output ISLPED '18: Proceedings of the International Symposium on Low Power Electronics and Design. ground existing at a. where output as shown in the transfer characteristics. Vnum and Vden are the numerator and The ' 5@ endstream endobj 1540 0 obj << /Length 217 /Filter /FlateDecode >> stream A four-quadrant multiplier is one where inputs and outputs may swing positive and negative. 353--361, 2014. M. R. Mahmoodi and D.B. We use cookies to ensure that we give you the best experience on our website. 0000003454 00000 n Eqn. 0000183020 00000 n Figure The inputs can be the peak magnitude of output voltage is 1/10 *10 *10 =10V. 52--59, 2018. 0000013729 00000 n denominator voltages respectively. typical range of the two input signals is 10V. voltages Vden and Vnum represent the two input voltages, trigonometric identity shows that Sin A sin B =1/2 (cos (A-B) cos (A+B)). 74, pp. M. Bavandpour, M. R. Mahmoodi, and D. B. Strukov, "Energy-efficient time-domain vector-by-matrix multiplier for neurocomputing and beyond", ArXiv:1711.10673, 2018.

In electronics, an analog multiplier is a device that takes two analog signals and produces an output which is their product. Breaking POps/J Barrier with Analog Multiplier Circuits Based on Nonvolatile Memories. 0000007608 00000 n 0000050610 00000 n It states that V0 equals the 0000002614 00000 n Nowadays (with the exception of high-frequency measurements) the tendency is to increase the sampling rate of the ADC in order to digitize the input signal allowing RMS and a whole range of other functions to be carried out by a digital processor. 5\+.L`%FIT+\I)m[zZ zG\6pi83j}0wCv^Z:i$}FthI)vc0Kk@@w+ 0,^YY1Od&L@{{XLn +Y MIyDN-PxfVRU=n}5sr5lC. figure. 0000002591 00000 n range of Vi is between -1 and -10V. depends on the factor cos . For this reason, manufacturing wide-range general-purpose analog multipliers is far more difficult than ordinary operational amplifiers, and such devices are typically produced using specialist technologies and laser trimming, as are those used for high-performance amplifiers such as instrumentation amplifiers. 7, art.118, 2013. Vxp and Vyp are the peak voltage amplitudes of the 0000003028 00000 n 0000019073 00000 n square root of 10 times the absolute magnitude of Vi. 3 0 obj Copyright 2018-2023 BrainKart.com; All Rights Reserved. The The For Therefore, at the junction a, i. Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail, Linear Integrated Circuits : Analog Multiplier and PLL : Analog Multiplier ICs |. 364--365. and 10V. But we know that Vom is one- term (Scale factor) of schematic representation of an analog multiplier is shown in figure. 19--25. 1--4. can have only positive values to ensure negative feedback. "6]Z` qAUiu./#^8sp^ !CRySjOwpxT~,l|w';oN&N#WJ6vx>4rEC`G6(Ed S-8 B>hK1`7bUp@%>r~^VP@5xC`YBIi=dJf&wc~X!U$kw,KW?K 2kZ endstream endobj 1582 0 obj 342 endobj 1522 0 obj << /Contents [ 1539 0 R 1543 0 R 1545 0 R 1547 0 R 1549 0 R 1551 0 R 1555 0 R 1557 0 R ] /Type /Page /Parent 1515 0 R /Rotate 0 /MediaBox [ 0 0 595 842 ] /CropBox [ 0 0 595 842 ] /Resources << /Font << /C2_1 1553 0 R /TT0 1535 0 R /TT1 1537 0 R /C2_0 1541 0 R >> /XObject << /Fm0 1579 0 R >> /ProcSet [ /PDF /Text ] /ExtGState << /GS0 1559 0 R /GS1 1580 0 R >> >> /StructParents 0 >> endobj 1523 0 obj << /Count 5 /Type /Outlines /First 1524 0 R /Last 1525 0 R >> endobj 1524 0 obj << /Title (Main Menu) /A 1532 0 R /Next 1530 0 R /Parent 1523 0 R >> endobj 1525 0 obj << /Title (Print) /A 1526 0 R /Prev 1527 0 R /Parent 1523 0 R >> endobj 1526 0 obj << /S /Named /N /Print >> endobj 1527 0 obj << /Title (Search CD-ROM) /A 1528 0 R /Next 1525 0 R /Prev 1529 0 R /Parent 1523 0 R >> endobj 1528 0 obj << /S /Named /N /AcroSrch:Query >> endobj 1529 0 obj << /Title (===============) /Next 1527 0 R /Prev 1530 0 R /Parent 1523 0 R >> endobj 1530 0 obj << /Title (Previous Menu) /A 1531 0 R /Next 1529 0 R /Prev 1524 0 R /Parent 1523 0 R >> endobj 1531 0 obj << /S /Named /N /GoBackDoc >> endobj 1532 0 obj << /S /Launch /F 1533 0 R >> endobj 1533 0 obj << /Type /Filespec /F (../MAINMENU.PDF) >> endobj 1534 0 obj << /Type /FontDescriptor /FontBBox [ -568 -307 2000 1007 ] /FontName /TimesNewRomanPSMT /Flags 34 /StemV 82 /CapHeight 656 /XHeight 0 /Ascent 891 /Descent -216 /ItalicAngle 0 /FontFamily (Times New Roman) /FontStretch /Normal /FontWeight 400 >> endobj 1535 0 obj << /Type /Font /Encoding /WinAnsiEncoding /BaseFont /TimesNewRomanPS-BoldMT /FirstChar 32 /LastChar 122 /Subtype /TrueType /FontDescriptor 1536 0 R /Widths [ 250 0 0 0 0 0 0 0 0 0 0 0 250 333 250 0 500 500 500 500 500 500 0 0 0 0 333 0 0 0 0 0 0 722 667 722 722 667 611 778 0 389 500 778 667 944 722 778 611 778 722 556 667 722 0 0 722 0 0 0 0 0 0 0 0 500 556 444 556 444 333 500 556 278 0 0 278 833 556 500 556 556 444 389 333 556 0 722 0 500 444 ] >> endobj 1536 0 obj << /Type /FontDescriptor /FontBBox [ -558 -307 2000 1026 ] /FontName /TimesNewRomanPS-BoldMT /Flags 34 /StemV 136 /CapHeight 656 /XHeight 0 /Ascent 891 /Descent -216 /ItalicAngle 0 /FontFamily (Times New Roman) /FontStretch /Normal /FontWeight 700 >> endobj 1537 0 obj << /Type /Font /Encoding /WinAnsiEncoding /BaseFont /TimesNewRomanPSMT /FirstChar 32 /LastChar 150 /Subtype /TrueType /FontDescriptor 1534 0 R /Widths [ 250 0 0 0 0 833 778 0 333 333 500 564 250 333 250 278 500 500 500 500 500 500 500 500 500 500 278 278 564 564 564 0 921 722 667 667 722 611 556 0 722 333 389 722 611 889 0 722 556 722 667 556 611 0 722 944 722 0 0 333 0 333 0 0 0 444 500 444 500 444 333 500 500 278 278 500 278 778 500 500 500 500 333 389 278 500 500 722 500 500 444 480 200 480 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 333 0 0 0 500 ] >> endobj 1538 0 obj 1974 endobj 1539 0 obj << /Filter /FlateDecode /Length 1538 0 R >> stream