(3) Bipolar Transistor Current Sources


 Tyler McGee
 1 years ago
 Views:
Transcription
1 B73 lectonics Analysis & Design (3) Bipola Tansisto Cuent Souces Leaning utcome Able to descibe and: Analyze and design a simple twotansisto BJT cuentsouce cicuit to poduce a given bias cuent. Analyze and design moe sophisticated BJT cuentsouce cicuits, such as the theetansisto cicuit, cascode cicuit, Wilson cicuit, and Widla cicuit. Analyze the output esistance of the vaious BJT cuentsouce cicuits. efeence: Neamen, Chapte 5 and Chapte 0 3.0) Biasing BJT Cicuits to Achieve Fowadactive Mode 3.0.) Single Base esisto Biasing 3.0) Biasing BJT Cicuits to Achieve Fowadactive Mode (Cont) 3.0.) oltage Divide Biasing Fig 5.5: Commonemitte cicuit with a single bias esisto in the base. Advantages: Simple. Disadvantages: No bias stabilization, i.e. Qpoint vaies with. equies lage esistos (M s), i.e. uses lage aea, which is an impotant issue in C design. Advantages: Smalle esistos equied (in k ange). has povided bias stabilization and negative feedback. Disadvantages: esisto size is still undesiable fo C design. Fig 5.54: Commonemitte cicuit with an emitte esisto and voltage divide bias cicuit in the base. 3.0) Biasing BJT Cicuits to Achieve Fowadactive Mode (Cont) 3.0.3) Positive and Negative oltage Biasing Figue 5.57: Simple tansisto cicuit biased with both positive and negative dc voltages. Advantages: Used fo diffeential amplifie biasing. Allows, in cetain apps, fo elimination of C C and allows use of dc input voltages as input signals. Disadvantages: esisto size is still undesiable fo C design. 3.0) Biasing BJT Cicuits to Achieve Fowadactive Mode (Cont) 3.0.4) The main issues equied fo biasing in C design Bias stabilization: biasing uses constant cuent souces. Avoid devices consuming lage aea, i.e. avoiding the use of modeate and lage esistos (which consume lage aea on C). Lectue: D Jamaludin Bin ma 3
2 B73 lectonics Analysis & Design 3.) ntegated Cicuit Biasing Can be a cuent souce that establishes the quiescent collecto cuent CQ as shown in Figue 0. 3.) ntegated Cicuit Biasing (Cont) Figue 0.: Bipola cicuit with cuentsouce biasing. Advantages: mitte cuent becomes independent of and B. Collecto cuent and C voltage ae independent of tansisto gain, fo easonable values. alue of B (hence in ) can be inceased without affecting bias stability. Biased using voltage. Figue 0.: Bipola cicuit with cuentsouce biasing. 3.) Bipola Tansisto Cuent Souces 3..) PoblemSolving Technique Sum cuents at the vaious nodes in the cicuit to find the elation between the efeence cuent and the bias cuent. To find the output esistance, place a test voltage at the output node and analyze the smallsignal equivalent cicuit. 3.) Bipola Tansisto Cuent Souces 3..) BJT Cuent Souces Will be studied: TwoTansisto Cuent Souce (T) Basic TheeTansisto Cuent Souce (3T) Cascode Cuent Souce (T on T) Wilson Cuent Souce (Modified 3T) Widla Cuent Souce (T with ) Multitansisto Cuent Mios (T) Keep in mind that the efeence cuent is constant, which may make some of the base voltage constant o at signal gound. 3.3) Twotansisto Cuent Souce Figue 0.: (a) Basic twotansisto cuent souce. (b) Twotansisto cuent souce with efeence esisto. Basic twotansisto cuent souces: (a) Using npn tansistos. (b) Using pnp tansistos. Lectue: D Jamaludin Bin ma 3
3 B73 lectonics Analysis & Design Analogy continues The wheel is now used to build a machine with wheels ( ) B B B B B B B B 3.3) Twotansisto Cuent Souce (Cont) C B B C B B B C B B B B Also called as a Cuent Mio, with two matched tansistos Q & Q B B B B B C C Q is diodeconnected. B B B efeence cuent established by Lectue: D Jamaludin Bin ma B (0.) 33
4 B73 lectonics Analysis & Design 3.3.) Cuent elationship Design ample 0. Sum cuents at collecto of Q C B C C and B C / utput cuent: C (0.) (0.4) bjective: Design a twotansisto cuent souce to meet a set of specifications. Specifications: The cicuit to be designed has the configuation shown in Figue 0.(b). Assume that matched tansistos ae available with paametes B (on) 0.6, 00, and A. The designed output is to be 00 µa. The bias voltages ae to be 5 and Design ample 0. (Cont) Design ample 0. (Cont) Solution: The efeence cuent can be witten as (00)( ) 04A 00 iginal Figue 0.(b) With specifications Fom quation (0.), the esisto is found to be B (on) kΩ 04 Net 3.3.) utput esistance, o (Cont) 3.3.) utput esistance, o n actual tansistos, the aly voltage ( A ) is finite. So, o is also finite. Then the collecto cuent is a function of the collectoemitte voltage. Thus, the stability of is affected by the bias conditions in the load cicuit. Figue 0. Figue 0.(b) Figue 0.3: The dc equivalent of simple amplifie biased with twotansisto cuent souce. Lectue: D Jamaludin Bin ma 34
5 B73 lectonics Analysis & Design 3.3.) utput esistance, o (Cont) efe to Figue 0.3. The voltage applied to base of Q 0 is a dc voltage. When is changed, C changes since B voltage of Q 0 is essentially a constant. A vaiation in C in tun changes the output cuent, because of the aly effect. 3.3.) utput esistance, o (Cont) Figue 0.4 shows vesus C chaacteistics at a constant B voltage. Figue 0.4: utput cuent vs collectoemitte voltage, showing the aly voltage. 3.3.) utput esistance, o (Cont) 3.3.) utput esistance, o (Cont) The atio of load cuent to efeence cuent, taking the aly effect* into account, is C C (0.5) *efe to quation 5.6 in Neaman whee A is the ealy voltage and facto ( /) accounts fo the finite gain. A A C B C B0 (0.6) The diffeential change in with espect to a change in C is d d C A B A (0.7) 3.3.) utput esistance, o (Cont) Assuming B << A, then 3.3.) utput esistance, o (Cont) ample 0. d d C A (0.8) bjective: Detemine the change in load cuent poduced by a change in collectoemitte voltage in a twotansisto cuent souce. whee o is the smallsignal output esistance looking into the collecto of Q Conside the cicuit shown in Figue 0.3. The cicuit paametes ae: 5,  5, and 9.3 k. Assume the tansisto paametes ae: 50, B (on) 0.7, and A 80. Detemine the change in as C changes fom 0.7 to 5. Lectue: D Jamaludin Bin ma 35
6 B73 lectonics Analysis & Design 3.3.) utput esistance, o (Cont) 3.3.) utput esistance, o (Cont) ample 0. (Cont) ample 0. (Cont) Solution: The efeence cuent is B (on) ( 5).0mA 9.3k Fo C 0.7, tansistos Q to Q ae identically biased. Fom quation (0.5),.0m 0.96mA / / 50 Fom quation (0.8), the small signal output esistance is A kΩ 0.96m 3.3.) utput esistance, o (Cont) 3.3.) utput esistance, o (Cont) ample 0. (Cont) ample 0. (Cont) The change in load cuent is detemined fom d d d C d d C 0.05mA (5 0.7) 83.k The pecent change in output cuent is theefoe d 0.05m % 0.96m 3.3) Twotansisto Cuent Souces (Cont) 3.3.3) Mismatched Tansistos 3.3.3) Mismatched Tansistos (Cont) n pactice, Q and Q may not be eactly identical. f >>, base cuents can be neglected. The cuentvoltage elationship, neglecting aly effect, is then Thus, any deviation in the bias cuent fom the ideal, as a function of mismatch between Q and Q, is diectly elated to the atio of the evesesatuation cuents S and S. and C C Theefoe, S (0.0) S B / T S e e B / T S S is a stong function of tempeatue. Theefoe, in most C fabication of cuent souces, Q and Q must be close to one anothe so that thei tempeatues will be the same in ode fo the cicuit to opeate popely. Also, paametes S and S ae functions of cosssectional aea of B junctions. Hence, quation (0.0) allows scaling of with espect to by having tansistos of diffeent sizes. Lectue: D Jamaludin Bin ma 36
7 B73 lectonics Analysis & Design 3.4) mpoved CuentSouce Cicuits Cuent souce cicuits that have impoved load cuent stability against changes in and changes in output tansisto collecto voltage ae: Basic TheeTansisto Cuent Souce: bette appoimation of Cascode Cuent Souce: highe output esistance by facto of Wilson Cuent Souce: highe output esistance by facto of / Widla Cuent Souce: highe output esistance by ( g m ) Net Analogy continues mpovements: ) Bette stability with 3 wheels ) Bette design with wheels 3.4.) Basic 3Tansisto Cuent Souce 3.4.) Basic 3Tansisto Cuent Souce (Cont) Twotansisto Theetansisto Figue 0.5: Basic theetansisto cuent souce. ( ) 3 B 3 B B 3 B B 3.4.) Basic 3Tansisto Cuent Souce (Cont) Shown in Figue 0.5 Assume that all tansistos ae identical. Theefoe: B B B B B C C B B Figue 0.5: Basic theetansisto cuent souce. Note: Cuent in Q 3 is substantially smalle than in eithe Q and Q, i.e. 3 < Lectue: D Jamaludin Bin ma 37
8 B73 lectonics Analysis & Design 3.4.) Basic 3Tansisto Cuent Souce (Cont) 3.4.) Basic 3Tansisto Cuent Souce (Cont) Sum cuents at collecto of Q C B3 C C and B C / B B, 3 B, 3 ( 3 ) B3 Theefoe, C C 3 C ( ) ( ) 3 C B C ( ) ( ) Then C ( ) (0.6) Advantages: Bette appoimation of to is less sensitive to vaiation in ) Basic 3Tansisto Cuent Souce (Cont) 3.4.) Basic 3Tansisto Cuent Souce (Cont) Assuming B3 B, then efeence Cuent is B3 B B (0.7) Figue 0.6: (a) Twotansisto cuent mio (b) Theetansisto cuent mio (c) aiation in bias cuents with a change in 3.4.) Basic 3Tansisto Cuent Souce (Cont) 3.4.) Basic 3Tansisto Cuent Souce (Cont) (Cont) The paametes fo the cicuit shown in Figue 0.5 ae: 3,  3, and 30 k. The tansisto paametes: Fo Q and Q ae B, (on) 0.7 and 0. Fo Q 3 ae B3 (on) 0.6 and 80. Assume A fo all tansistos. Detemine the value of each cuent shown in the figue. Lectue: D Jamaludin Bin ma 38
9 B73 lectonics Analysis & Design 3.4.) Basic 3Tansisto Cuent Souce (Cont) 3.4.) Cascode Cuent Souce utput esistance, The output esistance looking into the collecto of output tansisto Q of the basic 3 tansisto shown in Figue 0.5 is the same as that of the tansisto cuent souce, that is 4 d d C ; A (0.8) This means any mismatch between Q and Q poduces a deviation in the bias cuent fom the ideal, as given by quation (0.0). Figue 0.7: (a) Bipola cascode cuent mio (b) Smallsignal equivalent cicuit. 3.4.) Cascode Cuent Souce (Cont) 3.4.) Cascode Cuent Souce (Cont) Twotansisto Cascode Cascode CS is a cuentsouce cicuit with o much geate than that of the twotansisto cicuit. 4 Fo a constant, base voltages of Q and Q 4 ae constant, which implies these teminals ae at signal gound. 3.4.) Cascode Cuent Souce (Cont) 3.4.) Cascode Cuent Souce (Cont) Figue 0.7(b) can be eaanged as follows. Since g m be 0, then be4  ( o 4 ) Summing cuents at output node yields g g m4 be4 m4 ( ( ) o π 4 o4 be4 ) o ( ) o 4 π 4 Lectue: D Jamaludin Bin ma 39
10 B73 lectonics Analysis & Design 3.4.) Cascode Cuent Souce (Cont) 3.4.3) Wilson Cuent Souce Combining tems and assuming 4 << o : ( ) 4 o 4 π o4 (0.0) The output esistance has inceased by a facto of compaed to tansisto cuent souce, which inceases the stability of the cuent souce with changes in output voltage. Net Figue 0.8: Wilson cuent souce ) Wilson Cuent Souce (Cont) Theetansisto Wilson C3 ( ) B ( ) ( )( ) B ( )( ) B ( ) B B B B C ( 3) C3 ( ) B 3.4.3) Wilson Cuent Souce (Cont) 3.4.3) Wilson Cuent Souce (Cont) Anothe configuation of a 3tansisto cuent souce. Figue 0.8: Wilson cuent souce. Assume that all tansistos ae identical. Theefoe: B B B B B C C Cuent levels in all thee tansistos ae nealy the same, theefoe 3 Sum cuents at the collecto of Q C B3 (0.) At the emitte of Q 3 C B 3 C At the collecto of Q 3 C C3 (0.) (0.3) C3 Lectue: D Jamaludin Bin ma 30
11 B73 lectonics Analysis & Design 3.4.3) Wilson Cuent Souce (Cont) 3.4.3) Wilson Cuent Souce (Cont) eplacing C with C C B3 C3 C3 Solve fo the output cuent: C3 ( ) (0.4) (0.5) quation (0.5) is essentially the same as that of pevious 3tansisto cuent souce. The diffeence between the two 3 tansisto cuentsouce cicuits is the output esistance ) Wilson Cuent Souce (Cont) n Wilson cuent souce: the output esistance looking into the collecto of Q 3 is o3 / (/) o3 which is appoimately a facto / lage than that of eithe the tansisto souce o the basic 3tansisto souce. This means that, in the Wilson cuent souce, the change in bias cuent with a change in output collecto voltage is much smalle ) Widla Cuent Souce n all the pevious cuent souce cicuits, the load cuent and efeence cuents have been nealy equal. Fo the twotansisto cuent souce in Fig 0.(a): f a load cuent of 0 A is equied, fo 5 and  5, the esistance value needed is ( 5) 930kΩ B n Cs, esistos on the ode of M equie lage aeas and ae difficult to fabicate accuately. Theefoe, need to limit C esisto values to the low k ange. A Widla cuent souce, Figue 0.9, meets the objective of limiting C esisto values to the low k ange. Twotansisto Widla A voltage diffeence is poduced acoss esisto, so that the B voltage of Q is less than the B voltage of Q. Figue 0.9: Widla cuent souce. A smalle B voltage poduces a smalle collecto cuent, which in tun means that the load cuent is less than the efeence cuent. Lectue: D Jamaludin Bin ma 3
12 B73 lectonics Analysis & Design Cuent elationship f Q and Q ae identical and if >> fo both tansistos, then B C T B e ln B / T S S B C e T B / T S ln S B B B B T ln T ln and Thus, and B B C T C e T e B S ln ln B S S S / T / T Combining: Fom cicuit: Finally: B B B B T T ln ln (0.8) (0.9) (0.30) quation (0.30) gives the elationship between efeence and bias cuents. Design ample 0.4 bjective: Design a Widla cuent souce to achieve specified efeence and load cuents. Specifications: The cicuit to be designed has the configuation shown in Figue 0.9. Assume bias voltages of 5 and Assume B 0.7. Design the Widla cuent souce cicuit such that ma and µa. Design ample 0.4 (Cont) Solution: esistance is B ( 5) 9.3kΩ m esistance is, fom quation (0.30), T 0.06 m ln ln 9.58kΩ Design ample 0.4 (Cont) Fom quation (0.9) can detemine the diffeence between the two B voltages, as follows: B B ()(9.58k) 0.5 Lectue: D Jamaludin Bin ma 3
13 B73 lectonics Analysis & Design ample 0.5 ample 0.5 (Cont) bjective: To detemine the cuent in Widla cuent souce cicuit. Assume the Widla souce is biased at 5 and  5, and assume esisto values 7 k and 4 k. Also assume B 0.7. Solution: The efeence cuent is found to be B ( 5).33mA 7k The load cuent is found fom the elation T ln o 5.7 A Solving the tanscendental equation using gaph. ( 4k ) (0.06) ln(.33m/ ) A tanscendental equation cannot be solved diectly. A compute solution o a tial and eo solution yields Pevious Question utput esistance The output esistance looking into the collecto of Q in Figue 0.9 can be epessed as d dc (0.3) This output esistance can be detemined by using the smallsignal equivalent cicuit in the following figue. o Then, detemine output esistance at collecto of Q using simplified equivalent cicuits as follows. Fig 0.0(b): Simplified Noton equivalent cicuit fo detemining output esistance. Lectue: D Jamaludin Bin ma 33
14 B73 lectonics Analysis & Design o esistances and ae in paallel. Define ' Then π g g m π m π ' ( ( ' o ) o π ) ' o Collecting tems, poducing o o o o ' ( g ' ) m g m o Nomally, (/ o ) << g m ; theefoe (0.37) Hence, the output esistance ( o ) of the Widla cuent souce is a facto ( g m ) lage than that of the simple twotansisto cuent souce. ample 0.6 bjective: Detemine the change in load cuent with a change in collecto voltage in a Widla cuent souce. The stability of the load cuent, as a function of a change in output voltage, is impoved in the Widla cuent souce, compaed to the simple twotansisto cuent souce. Conside the cicuit in Figue 0.9. The paametes ae: 5,  5, 9.3 k, and 9.58 k. Let A 80 and 00. Detemine the change in as C changes by 4. ample 0.6 (Cont) ample 0.6 (Cont) Solution: Fom ample 0.4, µa. The smallsignal collecto esistance is A 80 A 6.67MΩ o o µ CQ We can detemine that gm µ gm 0.46mA/ gm 0.06 T and π T T (00)(0.06) 7kΩ µ π CQ T π CQ The output esistance of the cicuit is o [ gm( π )] [ (0.46m)( 9.58k 7k) ] 34.9MΩ (6.67M) Fom quation (0.3), the change in load cuent is d d d C (4) (34.9M) 0.5A % Net Lectue: D Jamaludin Bin ma 34
15 B73 lectonics Analysis & Design 3.5) Multitansisto Cuent Mios 3.5) Multitansisto Cuent Mios (Cont) Fig 0.: Multitansisto cuent mio. The B voltage of efeence tansisto Q can also be applied to multiple output tansistos to geneate multiple load cuents, as shown in Figue 0. The elationship between each load cuent and, assuming all tansistos ae matched and A, is... ( ) N N 3.5) Multitansisto Cuent Mios (Cont) 3.5) Multitansisto Cuent Mios (Cont) The collecto of multiple output tansistos can be connected togethe, changing the load cuent vesus cuent elationship. An eample of such a cicuit is shown in Figue 0.3 Fig 0.3: Multioutput tansisto cuent souce. Assume all tansistos ae matched. f is vey lage the base cuents can be neglected. Then, 3 3 Tansistos ae connected in paallel to incease the effective B aea of the device, hence inceasing the load cuent. Cicuit symbols as shown in Figue 0.4 can be used to indicate paallel output tansistos. Figue 0.4: quivalent cicuit symbols (a) two tansistos in paallel, (b) thee tansistos in paallel, and (c) N tansistos in paallel 3.5) Multitansisto Cuent Mios (Cont) Fig 0.5: Genealised cuent mio Genealized Cuent Mio As shown in Figue 0.5 btain seveal s as multiples of a single pnp to souce cuent npn to sink cuent f is vey lage, base cuent effects can be neglected. So:, 3, ) Multitansisto Cuent Mios (Cont) Genealized Cuent Mio (Cont) Tansistos Q and Q (connected as diodes) with established the efeence cuent which is given by B ( Q ) B ( Q) (0.39) ffect of finite : to be less than since supplies all base cuents. t becomes moe sevee as moe tansistos ae added. Lectue: D Jamaludin Bin ma 35
16 B73 lectonics Analysis & Design 3.5) Multitansisto Cuent Mios (Cont) Design ample 0.7 bjective: Design a genealized cuent mio to meet a set of specifications. Specifications: The cicuit to be designed has the configuation shown in Figue 0.5. The bias voltages ae 5, Neglect base cuents and assume B B 0.6. Design the cicuit such that 400 µa. Detemine the othe cuents and find the value fo. 3.5) Multitansisto Cuent Mios (Cont) Design ample 0.7 (Cont) Solution: Fo 400 µa, 3 00 µa and µa esisto is B ( Q ) B ( Q ) ( 5) 44kΩ ) Multitansisto Cuent Mios (Cont) 3.5) Multitansisto Cuent Mios (Cont) Pevious Question Pevious Question Answes: (i) 4mA ma B3 B kω ma A 00 (ii) 5k 4mA Ω C C (iii) C3 α 3 3 ( B B) 00 ma ma C3 9.85µ A ma ( ) B 0.0mA 00 (iv) The advantage :. Bette appoimation of to. less sensitive to vaiation in 3.6) utput oltage Swing The minimum output voltage, (min), of the cuent mio influences the maimum symmetical output voltage, UT, swing of the load cicuit being biased. 3.6) utput oltage Swing (Cont) Fo the cascode and Wilson cuent souces: (min) C _ B C (sat) The minimum output voltage fo the twotansisto cuent souce is: (min) C _ C (sat) whee C (sat) may be in the ode of 0. to 0.3. The value may be in the ode of 0.7 to 0.9. Note: ncease in (min) means educed maimum output voltage swing of the load cicuit, which is citical in the lowpowe applications. Lectue: D Jamaludin Bin ma 36
17 B73 lectonics Analysis & Design 3.7) BJT Active Load Cicuit Fig 0.8: Bipola commonemitte cicuit (with esistive load). n bipola amplifie, such as shown in Fig 0.8, the smallsignal voltage gain is diectly popotional to collecto esisto C. To incease the gain, need to incease the value of C, but thee is a pactical limitation. Assuming C C acts as a shot cicuit to the signal fequency, can be shown that the voltage gain of this cicuit is given by: A v  g m C whee g m CQ / T 3.7) BJT Active Load Cicuit (Cont) Assuming the Qpoint is in the cente of the load line, then CQ CC / C o C CC / CQ Theefoe A v CC / T Fo a easonable values of bias voltage, the maimum value of smallsignal voltage gain is essentially fied. 3.7) BJT Active Load Cicuit (Cont) To get aound this limitation need a load that will pass a given cuent at a given bias voltage, but which will incementally esist a change in cuent bette than fied C. This load device can be a tansisto, which will also occupy less aea in an C, anothe advantage of using tansistos in place of esistos. n addition, active loads poduce a much lage smallsignal voltage gain than discete esistos. 3.7.) DC Analysis: BJT Active Load Cicuit Fig 0.9: Simple BJT amp with active load, showing cuents and voltages., Q, and Q fom the active load. Q is efeed to as the active load device fo dive tansisto Q 0. The combination of, Q, and Q foms the pnp vesion of the tansisto cuent souce. Q 0 and Q emain biased in the fowadactive egion, and the output voltage must emain in the ange C0 (sat) < <  C (sat) 3.7.) DC Analysis: BJT Active Load Cicuit (Cont) Fig 0.30: oltage tansfe chaacteistics of bipola cicuit with active load. stablish Qpoint in the egion whee Q 0 and Q in fowadactive mode. nly small ange of input voltage is available. 3.7.) DC Analysis: BJT Active Load Cicuit (Cont) Fig 0.3: Dive tansisto chaacteistics and load cuve fo BJT cicuit with active load. Qpoint coesponds to Q As input changes between H and L the Qpoint moves up and down load cuve poducing a change in output voltage. When Q 0 is diven into satuation. When Q is diven into satuation. Lectue: D Jamaludin Bin ma 37
18 B73 lectonics Analysis & Design 3.8) Summay of BJT Cuent Souce Cicuits Simplest: Twotansisto cuent souce Need to impove appoimation of Need to impove stability of by having highe output esistance ( ) 3.8) Summay of BJT Cuent Souce Cicuits (Cont) 3.8.) Load Cuent and utput esistance mpoved cuent souce topologies Basic 3tansisto: bette appo of Cascode: highe by facto of Wilson: highe by facto of / Widla: highe by ( g m ) 3.8) Summay of BJT Cuent Souce Cicuits (Cont) 3.8.) Load Cuent and utput esistance (Cont) 3.8) Summay of BJT Cuent Souce Cicuits (Cont) 3.8.) Compaison of Cuent Souce Cicuits Twotansisto Widla 3.8) Summay of BJT Cuent Souce Cicuits (Cont) 3.8.) Compaison of Cuent Souce Cicuits (Cont) 3.8) Summay of BJT Cuent Souce Cicuits (Cont) 3.8.) Compaison of Cuent Souce Cicuits (Cont) Twotansisto Cascode Twotansisto Theetansisto Lectue: D Jamaludin Bin ma 38
19 B73 lectonics Analysis & Design 3.8) Summay of BJT Cuent Souce Cicuits (Cont) 3.8.) Compaison of Cuent Souce Cicuits (Cont) Theetansisto Wilson Lectue: D Jamaludin Bin ma 39
1.4 Phase Line and Bifurcation Diag
Dynamical Systems: Pat 2 2 Bifucation Theoy In pactical applications that involve diffeential equations it vey often happens that the diffeential equation contains paametes and the value of these paametes
More informationCIRCUITS LABORATORY EXPERIMENT 7
CIRCUITS LABORATORY EXPERIMENT 7 Design of a Single Tansisto Amplifie 7. OBJECTIVES The objectives of this laboatoy ae to: (a) Gain expeience in the analysis and design of an elementay, single tansisto
More informationFinancing Terms in the EOQ Model
Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad
More informationSemipartial (Part) and Partial Correlation
Semipatial (Pat) and Patial Coelation his discussion boows heavily fom Applied Multiple egession/coelation Analysis fo the Behavioal Sciences, by Jacob and Paticia Cohen (975 edition; thee is also an updated
More informationProblem Set # 9 Solutions
Poblem Set # 9 Solutions Chapte 12 #2 a. The invention of the new highspeed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease
More informationQuestions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing
M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow
More informationGauss Law. Physics 231 Lecture 21
Gauss Law Physics 31 Lectue 1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
More informationEpisode 401: Newton s law of universal gravitation
Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce
More informationIntroduction to Electric Potential
Univesiti Teknologi MARA Fakulti Sains Gunaan Intoduction to Electic Potential : A Physical Science Activity Name: HP: Lab # 3: The goal of today s activity is fo you to exploe and descibe the electic
More informationTutorial Problems: Bipolar Junction Transistor (Basic BJT Amplifiers)
Tutorial Problems: Bipolar Junction Transistor (Basic BJT Amplifiers) Part A. CommonEmitter Amplifier 1. For the circuit shown in Figure 1, the transistor parameters are β = 100 and V A =. Design the
More informationDetermining solar characteristics using planetary data
Detemining sola chaacteistics using planetay data Intoduction The Sun is a G type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this inestigation
More informationAn Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei iskewad chaacteistics? The Finance Development Cente 2002 1 Fom
More information2  ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1
 ELECTROSTATIC POTENTIAL AND CAPACITANCE Page. Line Integal of Electic Field If a unit positive chage is displaced by `given by dw E. dl dl in an electic field of intensity E, wok done is Line integation
More informationProblem Set 6: Solutions
UNIVESITY OF ALABAMA Depatment of Physics and Astonomy PH 164 / LeClai Fall 28 Poblem Set 6: Solutions 1. Seway 29.55 Potons having a kinetic enegy of 5. MeV ae moving in the positive x diection and ente
More informationNUCLEAR MAGNETIC RESONANCE
19 Jul 04 NMR.1 NUCLEAR MAGNETIC RESONANCE In this expeiment the phenomenon of nuclea magnetic esonance will be used as the basis fo a method to accuately measue magnetic field stength, and to study magnetic
More informationCHAPTER 10 Aggregate Demand I
CHAPTR 10 Aggegate Demand I Questions fo Review 1. The Keynesian coss tells us that fiscal policy has a multiplied effect on income. The eason is that accoding to the consumption function, highe income
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More information2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,
3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects
More informationThe Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = W/q 0 1V [Volt] =1 Nm/C
Geneal Physics  PH Winte 6 Bjoen Seipel The Electic Potential, Electic Potential Enegy and Enegy Consevation Electic Potential Enegy U is the enegy of a chaged object in an extenal electic field (Unit
More informationCoordinate Systems L. M. Kalnins, March 2009
Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean
More informationUNIVERSIDAD DE CANTABRIA TESIS DOCTORAL
UNIVERSIDAD DE CANABRIA Depatamento de Ingenieía de Comunicaciones ESIS DOCORAL Cyogenic echnology in the Micowave Engineeing: Application to MIC and MMIC Vey Low Noise Amplifie Design Juan Luis Cano de
More informationSTUDENT RESPONSE TO ANNUITY FORMULA DERIVATION
Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts
More informationJapan s trading losses reach JPY20 trillion
IEEJ: Mach 2014. All Rights Reseved. Japan s tading losses each JPY20 tillion Enegy accounts fo moe than half of the tading losses YANAGISAWA Akia Senio Economist Enegy Demand, Supply and Foecast Goup
More informationAN937 APPLICATION NOTE
APPLICATION NOTE One Technology Way P.O. Box 906 Norwood, MA 02062906, U.S.A. Tel: 78.329.4700 Fax: 78.46.33 www.analog.com Designing Amplifier Circuits: How to Avoid Common Problems by Charles Kitchin
More informationPower and Sample Size Calculations for the 2Sample ZStatistic
Powe and Sample Size Calculations fo the Sample ZStatistic James H. Steige ovembe 4, 004 Topics fo this Module. Reviewing Results fo the Sample Z (a) Powe and Sample Size in Tems of a oncentality Paamete.
More informationRevision Guide for Chapter 11
Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams
More informationSELFINDUCTANCE AND INDUCTORS
MISN0144 SELFINDUCTANCE AND INDUCTORS SELFINDUCTANCE AND INDUCTORS by Pete Signell Michigan State Univesity 1. Intoduction.............................................. 1 A 2. SelfInductance L.........................................
More informationManual ultrasonic inspection of thin metal welds
Manual ultasonic inspection of thin metal welds Capucine Capentie and John Rudlin TWI Cambidge CB1 6AL, UK Telephone 01223 899000 Fax 01223 890689 Email capucine.capentie@twi.co.uk Abstact BS EN ISO 17640
More informationExperiment 6: Centripetal Force
Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee
More informationCONDUCTION OBJECTIVES
CONDUCTION INTRODUCTION This package deals pimaily with the mechanisms by which electical excitation speads ove the membanes of excitable cells. Many physiological phenomena depend on the conduction of
More information4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first nonzero digit to
. Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate
More informationExcitation energies for molecules by TimeDependent. based on Effective Exact Exchange KohnSham potential
Excitation enegies fo molecules by TimeDependent DensityFunctional Theoy based on Effective Exact Exchange KohnSham potential Fabio Della Sala National Nanotechnology Laboatoies Lecce Italy A. Göling
More informationTransistors. NPN Bipolar Junction Transistor
Transistors They are unidirectional current carrying devices with capability to control the current flowing through them The switch current can be controlled by either current or voltage ipolar Junction
More informationOpen Economies. Chapter 32. A Macroeconomic Theory of the Open Economy. Basic Assumptions of a Macroeconomic Model of an Open Economy
Chapte 32. A Macoeconomic Theoy of the Open Economy Open Economies An open economy is one that inteacts feely with othe economies aound the wold. slide 0 slide 1 Key Macoeconomic Vaiables in an Open Economy
More informationProblems of the 2 nd International Physics Olympiads (Budapest, Hungary, 1968)
Poblems of the nd ntenational Physics Olympiads (Budapest Hungay 968) Péte Vankó nstitute of Physics Budapest Univesity of Technical Engineeing Budapest Hungay Abstact Afte a shot intoduction the poblems
More informationFXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.
Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing
More informationSupplementary Material for EpiDiff
Supplementay Mateial fo EpiDiff Supplementay Text S1. Pocessing of aw chomatin modification data In ode to obtain the chomatin modification levels in each of the egions submitted by the use QDCMR module
More informationUNIT CIRCLE TRIGONOMETRY
UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + =   
More informationSkills Needed for Success in Calculus 1
Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell
More informationOn Correlation Coefficient. The correlation coefficient indicates the degree of linear dependence of two random variables.
C.Candan EE3/53METU On Coelation Coefficient The coelation coefficient indicates the degee of linea dependence of two andom vaiables. It is defined as ( )( )} σ σ Popeties: 1. 1. (See appendi fo the poof
More informationCarterPenrose diagrams and black holes
CatePenose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
More informationConverting knowledge Into Practice
Conveting knowledge Into Pactice Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 2 0 1 0 C o p y i g h t s V l a d i m i R i b a k o v 1 Disclaime and Risk Wanings Tading
More informationAntiLock Braking System Training Program
COVERST.EPS ac T to $2.50 BS A AntiLock Baking System Taining Pogam Student Manual TP9738 Revised 399 Module 1 ABS Components and System Opeation Module 2 ABS Diagnosis and Repai Module 3 ATC Opeation,
More informationAN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM
AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,
More informationClass AB Output Stage
Class AB Output Stage Class AB amplifier Operation Multisim Simulations  Operation Class AB amplifier biasing Multisim Simulations  Biasing 1 Class AB Operation 2 Basic Class AB Amplifier Circuit Bias
More informationChapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
More informationThe LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.
Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the
More informationObservations: With transformers, we need to convert the voltage magnitudes, impedances, currents, etc. repeatedly.
1 ntductin t Pe Unit Calculatins (ECE 459 nte) Obsevatins: With tansfmes, we need t cnvet the vltage magnitudes, impedances, cuents, etc. epeatedly. Questins: Can we bypass these cmplicatins? Answe: By
More informationQuasi Resonant DC Link Converters
Quasi Resonant DC Link Convetes Analysis and Design fo a Battey Chage Application Pe Kalsson Lund 1999 Cove pictue Measuement of the esonant link voltage fo the quasi esonant DC link battey chage implemented.
More informationest using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.
9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,
More informationPAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII  SPETO  1995. pod patronatem. Summary
PCE SEMINIUM Z PODSTW ELEKTOTECHNIKI I TEOII OBWODÓW 8  TH SEMIN ON FUNDMENTLS OF ELECTOTECHNICS ND CICUIT THEOY ZDENĚK BIOLEK SPŠE OŽNO P.., CZECH EPUBLIC DLIBO BIOLEK MILITY CDEMY, BNO, CZECH EPUBLIC
More informationGravitational Mechanics of the MarsPhobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning
Gavitational Mechanics of the MasPhobos System: Compaing Methods of Obital Dynamics Modeling fo Exploatoy Mission Planning Alfedo C. Itualde The Pennsylvania State Univesity, Univesity Pak, PA, 6802 This
More informationVISCOSITY OF BIODIESEL FUELS
VISCOSITY OF BIODIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use
More informationLecture 16: Color and Intensity. and he made him a coat of many colours. Genesis 37:3
Lectue 16: Colo and Intensity and he made him a coat of many colous. Genesis 37:3 1. Intoduction To display a pictue using Compute Gaphics, we need to compute the colo and intensity of the light at each
More informationPHYSICS 111 HOMEWORK SOLUTION #5. March 3, 2013
PHYSICS 111 HOMEWORK SOLUTION #5 Mach 3, 2013 0.1 You 3.80kg physics book is placed next to you on the hoizontal seat of you ca. The coefficient of static fiction between the book and the seat is 0.650,
More information81 Newton s Law of Universal Gravitation
81 Newton s Law of Univesal Gavitation One of the most famous stoies of all time is the stoy of Isaac Newton sitting unde an apple tee and being hit on the head by a falling apple. It was this event,
More informationPhysics HSC Course Stage 6. Space. Part 1: Earth s gravitational field
Physics HSC Couse Stage 6 Space Pat 1: Eath s gavitational field Contents Intoduction... Weight... 4 The value of g... 7 Measuing g...8 Vaiations in g...11 Calculating g and W...13 You weight on othe
More informationDYNAMICS AND STRUCTURAL LOADING IN WIND TURBINES
DYNAMIS AND STRUTURAL LOADING IN WIND TURBINES M. Ragheb 12/30/2008 INTRODUTION The loading egimes to which wind tubines ae subject to ae extemely complex equiing special attention in thei design, opeation
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance the availability
More informationAn Infrastructure Cost Evaluation of Single and MultiAccess Networks with Heterogeneous Traffic Density
An Infastuctue Cost Evaluation of Single and MultiAccess Netwoks with Heteogeneous Taffic Density Andes Fuuskä and Magnus Almgen Wieless Access Netwoks Eicsson Reseach Kista, Sweden [andes.fuuska, magnus.almgen]@eicsson.com
More informationDatabase Management Systems
Contents Database Management Systems (COP 5725) D. Makus Schneide Depatment of Compute & Infomation Science & Engineeing (CISE) Database Systems Reseach & Development Cente Couse Syllabus 1 Sping 2012
More informationVoltage ( = Electric Potential )
V1 Voltage ( = Electic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage is
More informationThe Binomial Distribution
The Binomial Distibution A. It would be vey tedious if, evey time we had a slightly diffeent poblem, we had to detemine the pobability distibutions fom scatch. Luckily, thee ae enough similaities between
More informationINITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS
INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance
More information
Michal Szyper. "Inductance Measurement." Copyright 2000 CRC Press LLC. .
Michal Szype. "Inductance Measuement." Copyight 2000 CRC Pess LLC. . Inductance Measuement Michal Szype Univesity of Mining and Metallugy 50.1 Definitions of Inductance 50.2
More informationTowards Realizing a Low Cost and Highly Available Datacenter Power Infrastructure
Towads Realizing a Low Cost and Highly Available Datacente Powe Infastuctue Siam Govindan, Di Wang, Lydia Chen, Anand Sivasubamaniam, and Bhuvan Ugaonka The Pennsylvania State Univesity. IBM Reseach Zuich
More informationMechanics 1: Work, Power and Kinetic Energy
Mechanics 1: Wok, Powe and Kinetic Eneg We fist intoduce the ideas of wok and powe. The notion of wok can be viewed as the bidge between Newton s second law, and eneg (which we have et to define and discuss).
More informationForces & Magnetic Dipoles. r r τ = μ B r
Foces & Magnetic Dipoles x θ F θ F. = AI τ = U = Fist electic moto invented by Faaday, 1821 Wie with cuent flow (in cup of Hg) otates aound a a magnet Faaday s moto Wie with cuent otates aound a Pemanent
More informationThe Predictive Power of Dividend Yields for Stock Returns: Risk Pricing or Mispricing?
The Pedictive Powe of Dividend Yields fo Stock Retuns: Risk Picing o Mispicing? Glenn Boyle Depatment of Economics and Finance Univesity of Cantebuy Yanhui Li Depatment of Economics and Finance Univesity
More informationPerformance Analysis of an Inverse Notch Filter and Its Application to F 0 Estimation
Cicuits and Systems, 013, 4, 1171 http://dx.doi.og/10.436/cs.013.41017 Published Online Januay 013 (http://www.scip.og/jounal/cs) Pefomance Analysis of an Invese Notch Filte and Its Application to F 0
More informationAN2030 APPLICATION NOTE
AN2030 APPICATION NOTE BACK EMF DETECTION DURING PWM ON TIME BY ST7MC INTRODUCTION The diect back EMF sensing scheme used by ST72141 synchonously samples the moto back EMF duing PWM off time without the
More informationChapter 2. Electrostatics
Chapte. Electostatics.. The Electostatic Field To calculate the foce exeted by some electic chages,,, 3,... (the souce chages) on anothe chage Q (the test chage) we can use the pinciple of supeposition.
More informationDIFFERENT TYPES OF HUMAN HEAD SHAPES FOR CELLULAR PHONE EXPOSURE ON ELECTROMAGNETIC ABSORPTION
DIFFERENT TYPES OF HUMAN HEAD SHAPES FOR CELLULAR PHONE EXPOSURE ON ELECTROMAGNETIC ABSORPTION Mohammad Rashed Iqbal Fauque* #1, Mohammad Taiqul Islam* 2, Nobahiah Misan* #3 * Institute of Space Science
More informationAP Physics Electromagnetic Wrap Up
AP Physics Electomagnetic Wap Up Hee ae the gloious equations fo this wondeful section. F qsin This is the equation fo the magnetic foce acting on a moing chaged paticle in a magnetic field. The angle
More informationEfficient Redundancy Techniques for Latency Reduction in Cloud Systems
Efficient Redundancy Techniques fo Latency Reduction in Cloud Systems 1 Gaui Joshi, Emina Soljanin, and Gegoy Wonell Abstact In cloud computing systems, assigning a task to multiple seves and waiting fo
More informationExperiment MF Magnetic Force
Expeiment MF Magnetic Foce Intoduction The magnetic foce on a cuentcaying conducto is basic to evey electic moto  tuning the hands of electic watches and clocks, tanspoting tape in Walkmans, stating
More informationChris J. Skinner The probability of identification: applying ideas from forensic statistics to disclosure risk assessment
Chis J. Skinne The pobability of identification: applying ideas fom foensic statistics to disclosue isk assessment Aticle (Accepted vesion) (Refeeed) Oiginal citation: Skinne, Chis J. (2007) The pobability
More informationAdvanced Control of Active Filters. in a Battery Charger Application. Martin Bojrup
Advanced Contol of Active Filtes in a Battey Chage Application Matin Bojup Lund 999 ii Cove pictue Measuement on the dynamic esponse of the MRI hamonic filte contolle: load cuent (top), esulting line cuent
More informationThe impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011
The impact of migation on the povision of UK public sevices (SRG.10.039.4) Final Repot Decembe 2011 The obustness The obustness of the analysis of the is analysis the esponsibility is the esponsibility
More informationInstituto Superior Técnico Av. Rovisco Pais, 1 1049001 Lisboa Email: virginia.infante@ist.utl.pt
FATIGUE LIFE TIME PREDICTIO OF POAF EPSILO TB30 AIRCRAFT  PART I: IMPLEMETATIO OF DIFERET CYCLE COUTIG METHODS TO PREDICT THE ACCUMULATED DAMAGE B. A. S. Seano 1, V. I. M.. Infante 2, B. S. D. Maado
More informationThe force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges
The foce between electic chages Coulomb s Law Two chaged objects, of chage q and Q, sepaated by a distance, exet a foce on one anothe. The magnitude of this foce is given by: kqq Coulomb s Law: F whee
More informationNE/SA/SE555/SE555C PIN CONFIGURATIONS FEATURES APPLICATIONS ORDERING INFORMATION. D, N, FE Packages. F Package
DESCIPTION The monolithic timing circuit is a highly stable controller capable of producing accurate time delays, or oscillation. In the time delay mode of operation, the time is precisely controlled by
More informationAdaptive Queue Management with Restraint on NonResponsive Flows
Adaptive Queue Management wi Restaint on NonResponsive Flows Lan Li and Gyungho Lee Depatment of Electical and Compute Engineeing Univesity of Illinois at Chicago 85 S. Mogan Steet Chicago, IL 667 {lli,
More informationLINES AND TANGENTS IN POLAR COORDINATES
LINES AND TANGENTS IN POLAR COORDINATES ROGER ALEXANDER DEPARTMENT OF MATHEMATICS 1. Polacoodinate equations fo lines A pola coodinate system in the plane is detemined by a point P, called the pole, and
More informationDeflection of Electrons by Electric and Magnetic Fields
Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An
More informationGraphs of Equations. A coordinate system is a way to graphically show the relationship between 2 quantities.
Gaphs of Equations CHAT PeCalculus A coodinate sstem is a wa to gaphicall show the elationship between quantities. Definition: A solution of an equation in two vaiables and is an odeed pai (a, b) such
More informationControlling the Money Supply: Bond Purchases in the Open Market
Money Supply By the Bank of Canada and Inteest Rate Detemination Open Opeations and Monetay Tansmission Mechanism The Cental Bank conducts monetay policy Bank of Canada is Canada's cental bank supevises
More informationHour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and
Hou Exam No. Please attempt all of the following poblems befoe the due date. All poblems count the same even though some ae moe complex than othes. Assume that c units ae used thoughout. Poblem A photon
More informationExam #1 Review Answers
xam #1 Review Answes 1. Given the following pobability distibution, calculate the expected etun, vaiance and standad deviation fo Secuity J. State Pob (R) 1 0.2 10% 2 0.6 15 3 0.2 20 xpected etun = 0.2*10%
More informationAn Epidemic Model of Mobile Phone Virus
An Epidemic Model of Mobile Phone Vius Hui Zheng, Dong Li, Zhuo Gao 3 Netwok Reseach Cente, Tsinghua Univesity, P. R. China zh@tsinghua.edu.cn School of Compute Science and Technology, Huazhong Univesity
More informationChapter 4. Electric Potential
Chapte 4 Electic Potential 4.1 Potential and Potential Enegy... 43 4.2 Electic Potential in a Unifom Field... 47 4.3 Electic Potential due to Point Chages... 48 4.3.1 Potential Enegy in a System of
More informationReduced Pattern Training Based on Task Decomposition Using Pattern Distributor
> PNN05P762 < Reduced Patten Taining Based on Task Decomposition Using Patten Distibuto ShengUei Guan, Chunyu Bao, and TseNgee Neo Abstact Task Decomposition with Patten Distibuto (PD) is a new task
More informationStrength Analysis and Optimization Design about the key parts of the Robot
Intenational Jounal of Reseach in Engineeing and Science (IJRES) ISSN (Online): 23209364, ISSN (Pint): 23209356 www.ijes.og Volume 3 Issue 3 ǁ Mach 2015 ǁ PP.2529 Stength Analysis and Optimization Design
More informationYARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH
nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav
More informationChapter 30: Magnetic Fields Due to Currents
d Chapte 3: Magnetic Field Due to Cuent A moving electic chage ceate a magnetic field. One of the moe pactical way of geneating a lage magnetic field (.11 T) i to ue a lage cuent flowing though a wie.
More informationMagnetic Field and Magnetic Forces. Young and Freedman Chapter 27
Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew  electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field
More informationThe Role of Gravity in Orbital Motion
! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State
More informationFigure 2. So it is very likely that the Babylonians attributed 60 units to each side of the hexagon. Its resulting perimeter would then be 360!
1. What ae angles? Last time, we looked at how the Geeks intepeted measument of lengths. Howeve, as fascinated as they wee with geomety, thee was a shape that was much moe enticing than any othe : the
More informationDefinitions and terminology
I love the Case & Fai textbook but it is out of date with how monetay policy woks today. Please use this handout to supplement the chapte on monetay policy. The textbook assumes that the Fedeal Reseve
More information