Passive Filters. References: Barbow (pp ), Hayes & Horowitz (pp 32-60), Rizzoni (Chap. 6)

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Passive Filters. References: Barbow (pp 265-275), Hayes & Horowitz (pp 32-60), Rizzoni (Chap. 6)"

Transcription

1 Passve Flters eferences: Barbow (pp 6575), Hayes & Horowtz (pp 360), zzon (Chap. 6) Frequencyselectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called pass band). The ampltude of sgnals outsde ths range of frequences (called stop band) s reduced (deally reduced to zero). Typcally n these crcuts, the nput and output currents are kept to a small value and as such, the current transfer functon s not an mportant parameter. The man parameter s the voltage transfer functon n the frequency doman, H v (j) = o /. Subscrpt v of H v s frequently dropped. As H(j) s complex number, t has both a magntude and a phase, flters n general ntroduce a phase dfference between nput and output sgnals. LowPass Flters An deal lowpass flter s transfer functon s shown. The frequency between pass and stop bands s called the cutoff frequency ( c ). All of the sgnals wth frequences below c are transmtted and all other sgnals are stopped. H(j ) Pass Band Stop Band c In practcal flters, pass and stop bands are not clearly defned, H(j) vares contnuously from ts maxmum toward zero. The cutoff frequency s, therefore, defned as the frequency at whch H(j) s reduced to / = 0.7 of ts maxmum value. Ths corresponds to sgnal power beng reduced by / as P. Κ 0.7Κ H(j ) c Lowpass L flters L A seres L crcut as shown acts as a lowpass flter. For no load resstance (output s open crcut, L ), o can be found from the voltage dvder formula: o = jl H(j) = o = jl = j(l/) o To fnd the cutoff frequency, we note H(j) = (L/) ECE60L Lecture Notes, Sprng 004 7

2 H(j) s maxmum when denomnator s smallest,.e., 0 (alternatvely fnd d H(j) /d and set t equal to zero to fnd = 0). In ths case, H(j) max = H(j c ) = H(j) =c = H(j) max = ( c L/) = ( ) c L = c L = Therefore, c L and H(j) = j/ c Input Impedance: Usng the defnton of the nput mpedance, we have: Z = I = jl The value of the nput mpedance depends on the frequency. For good voltage couplng, we need to ensure that the nput mpedance of ths flter s much larger than the output mpedance of the prevous stage. Thus, the mnmum value of Z s an mportant number. Z s mnmum when the mpedance of the nductor s zero ( 0). Output Impedance: The output mpdenace can be found by kllng the source and fndng the equvalent mpdenace between output termnals: L Z o Z o = jl where the source resstance s gnored. Agan, the value of the output mpedance also depends on the frequency. For good voltage couplng, we need to ensure that the output mpedance of ths flter s much smaller than the nput mpedance of the next stage, the maxmum value of Z o s an mportant number. Z o s maxmum when the mpedance of the nductor s nfnty ( ). ECE60L Lecture Notes, Sprng 004 8

3 Lowpass C flters A seres C crcut as shown also acts as a lowpass flter. For no load resstance (output s open crcut, L ): o = H(j) = /(jc) /(jc) = jc j(c) C o To fnd c, we follow a procedure smlar to L flters above to fnd c = C and H(j) = j/ c smlar to the voltage transfer functon for lowpass L flters (only c s dfferent). Input and Output Impedances: Followng the same procedure as for L flters, we fnd: Z jc Z o jc and and Frstorder Lowpass flters L and C flters above are part of the famly of frstorder flters (they nclude only one capactor or nductor). In general, the voltage transfer functon of a frstorder lowpass flter s n the form: H(j) = K j/ c The maxmum value of H(j) = K s called the flter gan. For L and C flters, K =. K H(j) = (/ c ) H(j) = tan ( c ). 0.8 H 0.6 Phase f/f c f/f c For lowpass L flters: c L For lowpass C flters: c = C ECE60L Lecture Notes, Sprng 004 9

4 Bode Plots and Decbel The rato of output to nput power n a twoport network s usually expressed n Bell: ( ) Po Number of Bels = log 0 P or o Number of Bels = log 0 because P. Bel s a large unt and decbel (db) s usually used: o Number of decbels = 0 log 0 or o o = 0 log 0 db There are several reasons why decbel notaton s used: ) Hstorcally, the analog systems were developed frst for audo equpment. Human ear hears the sound n a logarthmc fashon. A sound whch appears to be twce as loud actually has 0 tmes power, etc. Decbel translates the output sgnal to what ear hears. ) If several twoport network are placed n a cascade (output of one s attached to the nput of the next), t s easy to show that the overall transfer functon, H, s equal to the product of all transfer functons: H(j) = H (j) H (j)... 0 log 0 H(j) = 0 log 0 H (j) 0 log 0 H (j)... H(j) db = H (j) db H (j) db... makng t easer to fnd the overall response of the system. 3) Plot of H(j) db versus frequency has specal propertes that agan make analyss smpler as s seen below. For example, usng db defnton, we see that, there s 3 db dfference between maxmum gan and gan at the cutoff frequency: 0 log H(j c ) 0 log H(j) max = 0 log [ H(jc ) H(j) max ] = 0 log ( ) 3 db Bode plots are plots of H(j) db (magntude) and H(j) (phase) versus frequency n a semlog format. Bode plots of frstorder lowpass flters (K = ) are shown below (W denotes c ). ECE60L Lecture Notes, Sprng 004 0

5 H(j) db H(j) At hgh frequences, / c, H(j) [ ] H(j) / db = 0 log = 0 log( c ) 0 log() c / c whch s a straght lne wth a slope of 0 db/decade n the Bode plot. It means that f s ncreased by a factor of 0 (a decade), H(j) db changes by 0 db. At low frequences, / c, H(j) whch s also a straght lne n the Bode plot. The ntersecton of these two asymptotc values s at = /(/ c ) or = c. Because of ths, the cutoff frequency s also called the corner frequency. The behavor of the phase of H(j) can be found by examnng H(j) = tan (/ c ). At low frequences, / c, H(j) 0 and at hgh frequences, / c, H(j) 90. At cutoff frequency, H(j) 45. ECE60L Lecture Notes, Sprng 004

6 Termnated L and C flters Termnated twoport networks are referred to those wth a fnte load resstance. For example, consder ths termnated lowpass C flter: oltage Transfer Functon: From the crcut, C o L H(j) = o = /(jc) L [/(jc) L ] / j( C) wth L Ths s smlar to the transfer functon for untermnated C flter but wth resstance beng replaced by. Therefore, c = C = ( L )C and H(j) / j/ c We see that the mpact of the load s to reduce the flter gan (K / < ) and to shft the cutoff frequency to a hgher frequency as L <. Input Impedance: Z jc L Output Impedance: Z o jc, Z o max As long as L Z o or L (our condton for good voltage couplng), and the termnated C flter wll look exactly lke an untermnated flter The flter gan s one, the shft n cutoff frequency dsappears, and nput and output resstance become the same as before. Termnated L lowpass flters The parameters of the termnated L flters can be found smlarly: oltage Transfer Functon: H(j) = o = Input Impedance: Z = jl L, j/ c, c = ( L )/L. L Output Impedance: Z o = (jl), Here, the mpact of load s to shft the cutoff frequency to a lower value. Flter gan s not affected. Agan for L Z o or L (our condton for good voltage couplng), the shft n cutoff frequency dsappears and the flter wll look exactly lke an untermnated flter. ECE60L Lecture Notes, Sprng 004

7 Hghpass C flters C A seres C crcut as shown acts as a hghpass flter. For no load resstance (output open crcut), we have: o H(j) = o = /(jc) = j(/c) The gan of ths flter, H(j), s maxmum when denomnator s smallest,.e., leadng to H(j) max =. Then, the cutoff frequency can be found from H(j c ) = H(j) max = whch leads to c = C H(j) = j c / Input and output mpdenaces of ths flter can be found smlar to the procedure used for lowpass flters: Input Impedance: Z jc Output Impedance: Z o jc and and Hghpass L flters A seres L crcut as shown also acts as a hghpass flter. For no load resstance (output open crcut), we have: L o c L H(j) = j c / Input Impedance: Z jl and Output Impedance: Z o jl and ECE60L Lecture Notes, Sprng 004 3

8 Frstorder Hghpass Flters In general, the voltage transfer functon of a frstorder hghpass flter s n the form: H(j) = K j c / The maxmum value of H(j) = K s called the flter gan. For L and C hghpass flters, K =. H(j) = K H(j) = tan ( c /) ( ) c For hghpass L flters: c L For hghpass C flters: c = C Bode Plots of frstorder hghpass flters (K = ) are shown below. The asymptotc behavor of ths class of flters s: At low frequences, / c, H(j) (a 0dB/decade lne) and H(j) = 90 At hgh frequences, / c, H(j) (a lne wth a slope of 0) and H(j) = 0 H(j) H(j) ECE60L Lecture Notes, Sprng 004 4

9 Termnated C hghpass flters The parameters of the termnated C flters can be found smlarly: oltage Transfer Functon: From the crcut, C o L H(j) = o = L L /(jc) = j(/ C) wth L Ths s smlar to the transfer functon for untermnated C flter but wth resstance beng replaced by. Therefore, c = C = ( L )C and H(j) = j c / Here, the mpact of the load s to shft the cutoff frequency to a hgher frequency (as L < ). Input Impedance: Z = jc L Output Impedance: Z o jc L As long as L Z o or L (our condton for good voltage couplng), and the termnated C flter wll look lke a untermnated flter The shft n cutoff frequency dsappears and nput and output resstance become the same as before. Termnated L hghpass flters The parameters of the termnated L flters can be found smlarly: oltage Transfer Functon: H(j) / j c / Input Impedance: Z (jl) L c L L Output Impedance: Z o = (jl) We see that the load lowers the gan, K / < and shfts the cutoff frequency to a lower value. As long as L Z o or L (our condton for good voltage couplng), and the termnated L flter wll look lke a untermnated flter. ECE60L Lecture Notes, Sprng 004 5

10 Bandpass flters A band pass flter allows sgnals wth a range of frequences (pass band) to pass through and attenuates sgnals wth frequences outsde ths range. l : u : 0 l u : B u l : Q 0 B : Lower cutoff frequency; Upper cutoff frequency; Center frequency; Band wdth; Qualty factor. H(j ) l Pass Band u As wth practcal low and hghpass flters, upper and lower cutoff frequences of practcal band pass flter are defned as the frequences at whch the magntude of the voltage transfer functon s reduced by / (or 3 db) from ts maxmum value. Secondorder bandpass flters: Secondorder band pass flters nclude two storage elements (two capactors, two nductors, or one of each). The transfer functon for a secondorder bandpass flter can be wrtten as H(j) = H(j) = K ( jq 0 K ) 0 Q ( 0 0 ( ) H(j) = tan [Q 0 )] 0 The maxmum value of H(j) = K s called the flter gan. The lower and upper cutoff frequences can be calculated by notng that H(j) max = K, settng H(j c ) = K/ and solvng for c. Ths procedure wll gve two roots: l and u. H(j c ) = H(j) max = K = ( Q c ) ( 0 c = Q 0 0 c 0 c c 0 ± c 0 Q = 0 K Q ( c 0 0 c ) = ± ) ECE60L Lecture Notes, Sprng 004 6

11 The above equaton s really two quadratc equatons (one wth sgn n front of fracton and one wth a sgn). Solvng these equaton we wll get 4 roots (two roots per equaton). Two of these four roots wll be negatve whch are not physcal as c > 0. The other two roots are the lower and upper cutoff frequences ( l and u, respectvely): l = 0 4Q 0 Q u = 0 4Q 0 Q Bode plots of a secondorder flter s shown below. Note that as Q ncreases, the bandwdth of the flter become smaller and the H(j) becomes more pcked around 0. H(j) db H(j) Asymptotc behavor: At low frequences, / 0, H(j) (a 0dB/decade lne), and H(j) 90 At hgh frequences, / 0, H(j) / (a 0dB/decade lne), and H(j) 90 At = 0, H(j) = K (purely real) H(j) = K (maxmum flter gan), and H(j) = 0. There are two ways to solve secondorder flter crcuts. ) One can try to wrte H(j) n the general form of a secondorder flters and fnd Q and 0. Then, use the formulas above to fnd the lower and upper cutoff frequences. ) Alternatvely, one can drectly fnd the upper and lower cutoff frequences and use 0 l u to fnd the center frequency and B u l to fnd the bandwdth, and Q = 0 /B to fnd the qualty factor. The two examples below show the two methods. Note that one can always fnd 0 and k rapdaly as H(j 0 ) s purely real and H(j 0 ) = k ECE60L Lecture Notes, Sprng 004 7

12 Seres LC Bandpass flters Usng voltage dvder formula, we have H(j) = o = H(j) = jl /(jc) ( j L ) C L C o There are two approaches to fnd flter parameters, K, 0, u, and l. Method : We transform the transfer functon n a form smlar to general form of the transfer functon for second order bandpass flters: H(j) = K ( jq 0 ) 0 Note that the denomnator of the general form s n the form j... Therefore, we dvde top and bottom of transfer functon of seres LC bandpass flters by : H(j) = ( L j ) C Comparng the above wth the general form of the transfer functon, we fnd K =. To fnd Q and 0, we note that the magnary part of the denomnator has two terms, one postve and one negatve (or one that scales as and the other that scales as /) smlar to the general form of transfer functon of ndorder bandpass flters (whch ncludes Q/ 0 and Q 0 /). Equatng these smlar terms we get: Q 0 = L Q 0 = C Q 0 = L Q 0 = C We can solve these two equatons to fnd: 0 = Q = 0 L LC /L C ECE60L Lecture Notes, Sprng 004 8

13 The lower and upper cutoff frequences can now be found from the formulas on page 4. Method : In ths method, we drectly calculate the flter parameters smlar to the procedure followed for general form of transfer functon n page 3. Some smplfcatons can be made by notng: ) At = 0, H(j) s purely real and ) K = H(j = j 0 ). Startng wth the transfer functon for the seres LC flter: H(j) = ( j L ) C We note that the transfer functon s real f coeffcent of j n the denomnator s exactly zero (note that ths happens for = 0 ),.e., Also 0 L 0 C = 0 0 = LC K = H(j = j 0 ) = The cutoff frequences can then be found by settng: H(j c ) = K = ( c L ) = c C whch can be solved to fnd u and l smlar to page 3. Input and Output Impedance of bandpass LC flters Z = jl ( jc = j L ) C occurs at = 0 ( Z o = jl ) Z o jc max ECE60L Lecture Notes, Sprng 004 9

14 WdeBand BandPass Flters Bandpass flters can be constructed by puttng a hghpass and a lowpass flter back to back as shown below. The hghpass flter sets the lower cutoff frequency and the lowpass flter sets the upper cutoff frequency of such a bandpass flter. H (j ) H (j ) H (j ) X H (j ) l = u= c c c c An example of such a bandpass flter s two C lowpass and hghpass flters put back to back. These flters are wdely used (when approprate, see below) nstead of an LC flter as nductors are usually bulky and take too much space on a crcut board. C C o Low Pass Hgh Pass In order to have good voltage couplng n the above crcut, the nput mpedance of the hghpass flter (actually ) should be much larger than the output mpedance of the lowpass flter (actually ), or we should have. In that case we can use untermnated transfer functons: H(j) = H (j) H (j) = c = /( C ) c = /( C ) j/ c j c / H(j) = ( j/ c )( j c /) = ( c / c ) j(/ c c /) Agan, we can fnd the flter parameters by ether of two methods above. Transformng the transfer functon to a form smlar to the general form (left for students) gves: K = c / c Q = c / c c / c 0 = c c ECE60L Lecture Notes, Sprng

15 One should note that the Bode plots of prevous page are asymptotc plots. The real H(j) dffers from these asymptotc plots, for example, H(j) s 3 db lower at the cutoff frequency. A comparson of asymptotc Bode plots and real ones for frstorder hghpass flters are gven n page. It can be seen that H (j) acheves ts maxmum value ( n ths case) only when / c < /3. Smlarly for the low pass flter, H (j) acheves ts maxmum value ( n ths case) only when / c > 3. In the bandpass flter above, f c c (.e., c 0 c ), the center frequency of the flter wll be at least a factor of three away from both cutoff frequences and H(j) = H H acheves ts maxmum value of. If c s not c (.e., c < 0 c ), H and H wll not reach ther maxmum of and the flter H(j) max = H H wll be less than one. Ths can be seen by examnng the equaton of K above whch s always less than and approaches when c c. More mportantly, we can never make a narrow band flter by puttng two frstorder hghpass and lowpass flters back to back. When c s not c, H(j) max becomes smaller than. Snce the cutoff frequences are located 3 db below the maxmum values, the cutoff frequences wll not be c and c (those frequences are 3 db lower than H(j) max = ). The lower cutoff frequency moves to a value lower than c and the upper cutoff frequency moves to a value hgher than c. Ths can be seen by examnng the qualty factor of ths flter at the lmt of c = c Q = c / c c / c = = 0.5 whle our asymptotc descrpton of prevous page ndcated that when c = c, bandwdth becomes vanshngly small and Q should become very large. Because these flters work only when c c, they are called wdeband flters. For these wdeband flters ( c c ), we fnd from above: K = Q = H(j) = c / c j(/ c c /) 0 = c c We then substtute for Q and 0 n the expressons for cutoff frequences (page 4) to get: u = 0 4Q 0 Q = 0 Q ( ) 4Q l = 0 4Q 0 Q = ( ) 0 4Q Q ECE60L Lecture Notes, Sprng 004 3

16 Ignorng 4Q term compared to (because Q s small),we get: u = 0 Q = c c c / c = c For l, f we gnore 4Q term compared to, we wll fnd l = 0. We should, therefore, expand the square root by Taylor seres expanson to get the frst order term: u ( 0 ) Q 4Q = 0 Q Q = 0 Q = c What are WdeBand and NarrowBand Flters? Typcally, a wdeband flter s defned as a flter wth c c (or c 0 c ). In ths case, Q 0.35 (prove ths!). A narrowband flter s usually defned as a flter wth B 0 (or B 0. 0 ). In ths case, Q 0. ECE60L Lecture Notes, Sprng 004 3

17 Example: Desgn a bandpass flter to pass sgnals between 60 Hz and 8 khz. The load for ths crcut s MΩ. As ths s wdeband, bandpass flter ( u / l = f u /f l = 50 ), we use two low and hghpass C flter stages smlar to crcut above. The prototype of the crcut s shown below: C The hghpass flter sets the lower cutoff frequency, and the MΩ load sets the output mpedance of ths stage. Thus: C o MΩ 00 kω c (Hghpass) = l = C = π 60 Low Pass C = 0 3 kω Hgh Pass One should choose as close as possble to 00 kω (to make the C small) and C = 0 3 usng commercal values of resstors and capactors. A good set here are = 00 kω and C = 0 nf. The lowpass flter sets the upper cutoff frequency. The load for ths component s the nput resstance of the hghpass flter, = 00 kω. Thus: 00kΩ 0 kω c (Lowpass) = u = C = π C = 0 5 As before, one should choose as close as possble to 0 kω and C = 0 5 usng commercal values of resstors and capactors. A good set here are = 0 kω and C = nf. In prncple, we can swtch the poston of lowpass and hghpass flter stages n a wdeband, bandpass flter. However, the lowpass flter s usually placed before the hghpass flter because the value of capactors n such an arrangement wll be smaller. (Try redesgnng the above crcut wth lowpass and hghpass flter stages swtched to see that one capactor become much smaller and one much larger.) ECE60L Lecture Notes, Sprng

1E6 Electrical Engineering AC Circuit Analysis and Power Lecture 12: Parallel Resonant Circuits

1E6 Electrical Engineering AC Circuit Analysis and Power Lecture 12: Parallel Resonant Circuits E6 Electrcal Engneerng A rcut Analyss and Power ecture : Parallel esonant rcuts. Introducton There are equvalent crcuts to the seres combnatons examned whch exst n parallel confguratons. The ssues surroundng

More information

The circuit shown on Figure 1 is called the common emitter amplifier circuit. The important subsystems of this circuit are:

The circuit shown on Figure 1 is called the common emitter amplifier circuit. The important subsystems of this circuit are: polar Juncton Transstor rcuts Voltage and Power Amplfer rcuts ommon mtter Amplfer The crcut shown on Fgure 1 s called the common emtter amplfer crcut. The mportant subsystems of ths crcut are: 1. The basng

More information

Linear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits

Linear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.

More information

Frequency selective circuits

Frequency selective circuits Frequency selectve crcuts w pass Flters are used t pass lw-frequency sne waves and attenuate hgh frequency sne waves. The cutff frequency c s used t dstngush the passband ( c ).

More information

Section B9: Zener Diodes

Section B9: Zener Diodes Secton B9: Zener Dodes When we frst talked about practcal dodes, t was mentoned that a parameter assocated wth the dode n the reverse bas regon was the breakdown voltage, BR, also known as the peak-nverse

More information

Lesson 2 Chapter Two Three Phase Uncontrolled Rectifier

Lesson 2 Chapter Two Three Phase Uncontrolled Rectifier Lesson 2 Chapter Two Three Phase Uncontrolled Rectfer. Operatng prncple of three phase half wave uncontrolled rectfer The half wave uncontrolled converter s the smplest of all three phase rectfer topologes.

More information

8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by

8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by 6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng

More information

Multiple stage amplifiers

Multiple stage amplifiers Multple stage amplfers Ams: Examne a few common 2-transstor amplfers: -- Dfferental amplfers -- Cascode amplfers -- Darlngton pars -- current mrrors Introduce formal methods for exactly analysng multple

More information

Recurrence. 1 Definitions and main statements

Recurrence. 1 Definitions and main statements Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.

More information

9.1 The Cumulative Sum Control Chart

9.1 The Cumulative Sum Control Chart Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s

More information

Electric circuit components. Direct Current (DC) circuits

Electric circuit components. Direct Current (DC) circuits Electrc crcut components Capactor stores charge and potental energy, measured n Farads (F) Battery generates a constant electrcal potental dfference ( ) across t. Measured n olts (). Resstor ressts flow

More information

+ + + - - This circuit than can be reduced to a planar circuit

+ + + - - This circuit than can be reduced to a planar circuit MeshCurrent Method The meshcurrent s analog of the nodeoltage method. We sole for a new set of arables, mesh currents, that automatcally satsfy KCLs. As such, meshcurrent method reduces crcut soluton to

More information

Quantization Effects in Digital Filters

Quantization Effects in Digital Filters Quantzaton Effects n Dgtal Flters Dstrbuton of Truncaton Errors In two's complement representaton an exact number would have nfntely many bts (n general). When we lmt the number of bts to some fnte value

More information

An Alternative Way to Measure Private Equity Performance

An Alternative Way to Measure Private Equity Performance An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate

More information

Chapter 31B - Transient Currents and Inductance

Chapter 31B - Transient Currents and Inductance Chapter 31B - Transent Currents and Inductance A PowerPont Presentaton by Paul E. Tppens, Professor of Physcs Southern Polytechnc State Unversty 007 Objectves: After completng ths module, you should be

More information

SPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:

SPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background: SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and

More information

Chapter 12 Inductors and AC Circuits

Chapter 12 Inductors and AC Circuits hapter Inductors and A rcuts awrence B. ees 6. You may make a sngle copy of ths document for personal use wthout wrtten permsson. Hstory oncepts from prevous physcs and math courses that you wll need for

More information

Faraday's Law of Induction

Faraday's Law of Induction Introducton Faraday's Law o Inducton In ths lab, you wll study Faraday's Law o nducton usng a wand wth col whch swngs through a magnetc eld. You wll also examne converson o mechanc energy nto electrc energy

More information

Analysis of Small-signal Transistor Amplifiers

Analysis of Small-signal Transistor Amplifiers Analyss of Small-sgnal Transstor Amplfers On completon of ths chapter you should be able to predct the behaour of gen transstor amplfer crcuts by usng equatons and/or equalent crcuts that represent the

More information

Formula of Total Probability, Bayes Rule, and Applications

Formula of Total Probability, Bayes Rule, and Applications 1 Formula of Total Probablty, Bayes Rule, and Applcatons Recall that for any event A, the par of events A and A has an ntersecton that s empty, whereas the unon A A represents the total populaton of nterest.

More information

( ) Homework Solutions Physics 8B Spring 09 Chpt. 32 5,18,25,27,36,42,51,57,61,76

( ) Homework Solutions Physics 8B Spring 09 Chpt. 32 5,18,25,27,36,42,51,57,61,76 Homework Solutons Physcs 8B Sprng 09 Chpt. 32 5,8,25,27,3,42,5,57,,7 32.5. Model: Assume deal connectng wres and an deal battery for whch V bat = E. Please refer to Fgure EX32.5. We wll choose a clockwse

More information

Introduction: Analysis of Electronic Circuits

Introduction: Analysis of Electronic Circuits /30/008 ntroducton / ntroducton: Analyss of Electronc Crcuts Readng Assgnment: KVL and KCL text from EECS Just lke EECS, the majorty of problems (hw and exam) n EECS 3 wll be crcut analyss problems. Thus,

More information

Homework Solutions Physics 8B Spring 2012 Chpt. 32 5,18,25,27,36,42,51,57,61,76

Homework Solutions Physics 8B Spring 2012 Chpt. 32 5,18,25,27,36,42,51,57,61,76 Homework Solutons Physcs 8B Sprng 202 Chpt. 32 5,8,25,27,3,42,5,57,,7 32.5. Model: Assume deal connectng wres and an deal battery for whch V bat =. Please refer to Fgure EX32.5. We wll choose a clockwse

More information

Graph Theory and Cayley s Formula

Graph Theory and Cayley s Formula Graph Theory and Cayley s Formula Chad Casarotto August 10, 2006 Contents 1 Introducton 1 2 Bascs and Defntons 1 Cayley s Formula 4 4 Prüfer Encodng A Forest of Trees 7 1 Introducton In ths paper, I wll

More information

FORCED CONVECTION HEAT TRANSFER IN A DOUBLE PIPE HEAT EXCHANGER

FORCED CONVECTION HEAT TRANSFER IN A DOUBLE PIPE HEAT EXCHANGER FORCED CONVECION HEA RANSFER IN A DOUBLE PIPE HEA EXCHANGER Dr. J. Mchael Doster Department of Nuclear Engneerng Box 7909 North Carolna State Unversty Ralegh, NC 27695-7909 Introducton he convectve heat

More information

Lossless Data Compression

Lossless Data Compression Lossless Data Compresson Lecture : Unquely Decodable and Instantaneous Codes Sam Rowes September 5, 005 Let s focus on the lossless data compresson problem for now, and not worry about nosy channel codng

More information

The Full-Wave Rectifier

The Full-Wave Rectifier 9/3/2005 The Full Wae ectfer.doc /0 The Full-Wae ectfer Consder the followng juncton dode crcut: s (t) Power Lne s (t) 2 Note that we are usng a transformer n ths crcut. The job of ths transformer s to

More information

Semiconductor sensors of temperature

Semiconductor sensors of temperature Semconductor sensors of temperature he measurement objectve 1. Identfy the unknown bead type thermstor. Desgn the crcutry for lnearzaton of ts transfer curve.. Fnd the dependence of forward voltage drop

More information

Interleaved Power Factor Correction (IPFC)

Interleaved Power Factor Correction (IPFC) Interleaved Power Factor Correcton (IPFC) 2009 Mcrochp Technology Incorporated. All Rghts Reserved. Interleaved Power Factor Correcton Slde 1 Welcome to the Interleaved Power Factor Correcton Reference

More information

IDENTIFICATION AND CONTROL OF A FLEXIBLE TRANSMISSION SYSTEM

IDENTIFICATION AND CONTROL OF A FLEXIBLE TRANSMISSION SYSTEM Abstract IDENTIFICATION AND CONTROL OF A FLEXIBLE TRANSMISSION SYSTEM Alca Esparza Pedro Dept. Sstemas y Automátca, Unversdad Poltécnca de Valenca, Span alespe@sa.upv.es The dentfcaton and control of a

More information

3.4 Operation in the Reverse Breakdown Region Zener Diodes

3.4 Operation in the Reverse Breakdown Region Zener Diodes 3/3/2008 secton_3_4_zener_odes 1/4 3.4 Operaton n the everse Breakdown egon Zener odes eadng Assgnment: pp. 167171 A Zener ode The 3 techncal dfferences between a juncton dode and a Zener dode: 1. 2. 3.

More information

The OC Curve of Attribute Acceptance Plans

The OC Curve of Attribute Acceptance Plans The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4

More information

CIRCUITS AND ELECTRONICS. Filters

CIRCUITS AND ELECTRONICS. Filters 6.00 IUITS AND EETONIS Flters te as: Anant Agarwal and Jeffrey ang, course materals for 6.00 rcuts and Electroncs, Sprng 007. MIT 6.00 Fall 000 ecture 8 evew v I v c c c j j j eadng: Secton 4.5, 4.6, 5.3

More information

s-domain Circuit Analysis

s-domain Circuit Analysis S-Doman naly -Doman rcut naly Tme doman t doman near rcut aplace Tranform omplex frequency doman doman Tranformed rcut Dfferental equaton lacal technque epone waveform aplace Tranform nvere Tranform -

More information

CIRCUIT ELEMENTS AND CIRCUIT ANALYSIS

CIRCUIT ELEMENTS AND CIRCUIT ANALYSIS EECS 4 SPING 00 Lecture 9 Copyrght egents of Unversty of Calforna CICUIT ELEMENTS AND CICUIT ANALYSIS Lecture 5 revew: Termnology: Nodes and branches Introduce the mplct reference (common) node defnes

More information

3. Bipolar Junction Transistor (BJT)

3. Bipolar Junction Transistor (BJT) 3. polar Juncton Transstor (JT) Lecture notes: Sec. 3 Sedra & Smth (6 th Ed): Sec. 6.1-6.4* Sedra & Smth (5 th Ed): Sec. 5.1-5.4* * Includes detals of JT dece operaton whch s not coered n ths course EE

More information

4. Bipolar Junction Transistors. 4. Bipolar Junction Transistors TLT-8016 Basic Analog Circuits 2005/2007 1

4. Bipolar Junction Transistors. 4. Bipolar Junction Transistors TLT-8016 Basic Analog Circuits 2005/2007 1 4. polar Juncton Transstors 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 4. asc Operaton of the npn polar Juncton Transstor npn JT conssts of thn p-type layer between two n-type layers;

More information

1. Measuring association using correlation and regression

1. Measuring association using correlation and regression How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a

More information

Peak Inverse Voltage

Peak Inverse Voltage 9/13/2005 Peak Inerse Voltage.doc 1/6 Peak Inerse Voltage Q: I m so confused! The brdge rectfer and the fullwae rectfer both prode full-wae rectfcaton. Yet, the brdge rectfer use 4 juncton dodes, whereas

More information

THE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES

THE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES The goal: to measure (determne) an unknown quantty x (the value of a RV X) Realsaton: n results: y 1, y 2,..., y j,..., y n, (the measured values of Y 1, Y 2,..., Y j,..., Y n ) every result s encumbered

More information

Question 2: What is the variance and standard deviation of a dataset?

Question 2: What is the variance and standard deviation of a dataset? Queston 2: What s the varance and standard devaton of a dataset? The varance of the data uses all of the data to compute a measure of the spread n the data. The varance may be computed for a sample of

More information

EE201 Circuit Theory I 2015 Spring. Dr. Yılmaz KALKAN

EE201 Circuit Theory I 2015 Spring. Dr. Yılmaz KALKAN EE201 Crcut Theory I 2015 Sprng Dr. Yılmaz KALKAN 1. Basc Concepts (Chapter 1 of Nlsson - 3 Hrs.) Introducton, Current and Voltage, Power and Energy 2. Basc Laws (Chapter 2&3 of Nlsson - 6 Hrs.) Voltage

More information

1 Example 1: Axis-aligned rectangles

1 Example 1: Axis-aligned rectangles COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture # 6 Scrbe: Aaron Schld February 21, 2013 Last class, we dscussed an analogue for Occam s Razor for nfnte hypothess spaces that, n conjuncton

More information

Answer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy

Answer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy 4.02 Quz Solutons Fall 2004 Multple-Choce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multple-choce questons. For each queston, only one of the answers s correct.

More information

VRT012 User s guide V0.1. Address: Žirmūnų g. 27, Vilnius LT-09105, Phone: (370-5) 2127472, Fax: (370-5) 276 1380, Email: info@teltonika.

VRT012 User s guide V0.1. Address: Žirmūnų g. 27, Vilnius LT-09105, Phone: (370-5) 2127472, Fax: (370-5) 276 1380, Email: info@teltonika. VRT012 User s gude V0.1 Thank you for purchasng our product. We hope ths user-frendly devce wll be helpful n realsng your deas and brngng comfort to your lfe. Please take few mnutes to read ths manual

More information

ASSIGNMENT-4 HINTS &SOLUTIONS

ASSIGNMENT-4 HINTS &SOLUTIONS DEPARTMENT OF ELECTRNICS & COMMUNICATION ENGINEERING, KITSW COURSE: U14EI 205 - BASIC ELECTRONICS ENGINEERING ECE-I, Seester-II, 2015-16 ASSIGNMENT-4 HINTS &SOLUTIONS 1. Show that the percentage regulaton

More information

Causal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting

Causal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting Causal, Explanatory Forecastng Assumes cause-and-effect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of

More information

greatest common divisor

greatest common divisor 4. GCD 1 The greatest common dvsor of two ntegers a and b (not both zero) s the largest nteger whch s a common factor of both a and b. We denote ths number by gcd(a, b), or smply (a, b) when there s no

More information

Gibbs Free Energy and Chemical Equilibrium (or how to predict chemical reactions without doing experiments)

Gibbs Free Energy and Chemical Equilibrium (or how to predict chemical reactions without doing experiments) Gbbs Free Energy and Chemcal Equlbrum (or how to predct chemcal reactons wthout dong experments) OCN 623 Chemcal Oceanography Readng: Frst half of Chapter 3, Snoeynk and Jenkns (1980) Introducton We want

More information

The complex inverse trigonometric and hyperbolic functions

The complex inverse trigonometric and hyperbolic functions Physcs 116A Wnter 010 The complex nerse trgonometrc and hyperbolc functons In these notes, we examne the nerse trgonometrc and hyperbolc functons, where the arguments of these functons can be complex numbers

More information

Optical Signal-to-Noise Ratio and the Q-Factor in Fiber-Optic Communication Systems

Optical Signal-to-Noise Ratio and the Q-Factor in Fiber-Optic Communication Systems Applcaton ote: FA-9.0. Re.; 04/08 Optcal Sgnal-to-ose Rato and the Q-Factor n Fber-Optc Communcaton Systems Functonal Dagrams Pn Confguratons appear at end of data sheet. Functonal Dagrams contnued at

More information

Bipolar Junction Transistor (BJT)

Bipolar Junction Transistor (BJT) polar Juncton Transstor (JT) Lecture notes: Sec. 3 Sedra & Smth (6 th Ed): Sec. 6.1-6.4* Sedra & Smth (5 th Ed): Sec. 5.1-5.4* * Includes detals of JT dece operaton whch s not coered n ths course F. Najmabad,

More information

Chapter 4 Financial Markets

Chapter 4 Financial Markets Chapter 4 Fnancal Markets ECON2123 (Sprng 2012) 14 & 15.3.2012 (Tutoral 5) The demand for money Assumptons: There are only two assets n the fnancal market: money and bonds Prce s fxed and s gven, that

More information

We are now ready to answer the question: What are the possible cardinalities for finite fields?

We are now ready to answer the question: What are the possible cardinalities for finite fields? Chapter 3 Fnte felds We have seen, n the prevous chapters, some examples of fnte felds. For example, the resdue class rng Z/pZ (when p s a prme) forms a feld wth p elements whch may be dentfed wth the

More information

Generator Warm-Up Characteristics

Generator Warm-Up Characteristics NO. REV. NO. : ; ~ Generator Warm-Up Characterstcs PAGE OF Ths document descrbes the warm-up process of the SNAP-27 Generator Assembly after the sotope capsule s nserted. Several nqures have recently been

More information

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ). REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or

More information

Series Solutions of ODEs 2 the Frobenius method. The basic idea of the Frobenius method is to look for solutions of the form 3

Series Solutions of ODEs 2 the Frobenius method. The basic idea of the Frobenius method is to look for solutions of the form 3 Royal Holloway Unversty of London Department of Physs Seres Solutons of ODEs the Frobenus method Introduton to the Methodology The smple seres expanson method works for dfferental equatons whose solutons

More information

Implementation of Deutsch's Algorithm Using Mathcad

Implementation of Deutsch's Algorithm Using Mathcad Implementaton of Deutsch's Algorthm Usng Mathcad Frank Roux The followng s a Mathcad mplementaton of Davd Deutsch's quantum computer prototype as presented on pages - n "Machnes, Logc and Quantum Physcs"

More information

2.4 Bivariate distributions

2.4 Bivariate distributions page 28 2.4 Bvarate dstrbutons 2.4.1 Defntons Let X and Y be dscrete r.v.s defned on the same probablty space (S, F, P). Instead of treatng them separately, t s often necessary to thnk of them actng together

More information

CHAPTER 6 Frequency Response, Bode Plots, and Resonance

CHAPTER 6 Frequency Response, Bode Plots, and Resonance ELECTRICAL CHAPTER 6 Frequency Response, Bode Plots, and Resonance 1. State the fundamental concepts of Fourier analysis. 2. Determine the output of a filter for a given input consisting of sinusoidal

More information

Ring structure of splines on triangulations

Ring structure of splines on triangulations www.oeaw.ac.at Rng structure of splnes on trangulatons N. Vllamzar RICAM-Report 2014-48 www.rcam.oeaw.ac.at RING STRUCTURE OF SPLINES ON TRIANGULATIONS NELLY VILLAMIZAR Introducton For a trangulated regon

More information

Aryabhata s Root Extraction Methods. Abhishek Parakh Louisiana State University Aug 31 st 2006

Aryabhata s Root Extraction Methods. Abhishek Parakh Louisiana State University Aug 31 st 2006 Aryabhata s Root Extracton Methods Abhshek Parakh Lousana State Unversty Aug 1 st 1 Introducton Ths artcle presents an analyss of the root extracton algorthms of Aryabhata gven n hs book Āryabhatīya [1,

More information

Luby s Alg. for Maximal Independent Sets using Pairwise Independence

Luby s Alg. for Maximal Independent Sets using Pairwise Independence Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent

More information

Complex Number Representation in RCBNS Form for Arithmetic Operations and Conversion of the Result into Standard Binary Form

Complex Number Representation in RCBNS Form for Arithmetic Operations and Conversion of the Result into Standard Binary Form Complex Number epresentaton n CBNS Form for Arthmetc Operatons and Converson of the esult nto Standard Bnary Form Hatm Zan and. G. Deshmukh Florda Insttute of Technology rgd@ee.ft.edu ABSTACT Ths paper

More information

Communication Networks II Contents

Communication Networks II Contents 8 / 1 -- Communcaton Networs II (Görg) -- www.comnets.un-bremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP

More information

Brigid Mullany, Ph.D University of North Carolina, Charlotte

Brigid Mullany, Ph.D University of North Carolina, Charlotte Evaluaton And Comparson Of The Dfferent Standards Used To Defne The Postonal Accuracy And Repeatablty Of Numercally Controlled Machnng Center Axes Brgd Mullany, Ph.D Unversty of North Carolna, Charlotte

More information

Systematic Circuit Analysis (T&R Chap 3)

Systematic Circuit Analysis (T&R Chap 3) Systematc Crcut Analyss TR Chap ) Nodeoltage analyss Usng the oltages of the each node relate to a ground node, wrte down a set of consstent lnear equatons for these oltages Sole ths set of equatons usng,

More information

Lecture 2: Absorbing states in Markov chains. Mean time to absorption. Wright-Fisher Model. Moran Model.

Lecture 2: Absorbing states in Markov chains. Mean time to absorption. Wright-Fisher Model. Moran Model. Lecture 2: Absorbng states n Markov chans. Mean tme to absorpton. Wrght-Fsher Model. Moran Model. Antonna Mtrofanova, NYU, department of Computer Scence December 8, 2007 Hgher Order Transton Probabltes

More information

Multivariate EWMA Control Chart

Multivariate EWMA Control Chart Multvarate EWMA Control Chart Summary The Multvarate EWMA Control Chart procedure creates control charts for two or more numerc varables. Examnng the varables n a multvarate sense s extremely mportant

More information

Describing Communities. Species Diversity Concepts. Species Richness. Species Richness. Species-Area Curve. Species-Area Curve

Describing Communities. Species Diversity Concepts. Species Richness. Species Richness. Species-Area Curve. Species-Area Curve peces versty Concepts peces Rchness peces-area Curves versty Indces - mpson's Index - hannon-wener Index - rlloun Index peces Abundance Models escrbng Communtes There are two mportant descrptors of a communty:

More information

Texas Instruments 30X IIS Calculator

Texas Instruments 30X IIS Calculator Texas Instruments 30X IIS Calculator Keystrokes for the TI-30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the

More information

Solutions to First Midterm

Solutions to First Midterm rofessor Chrstano Economcs 3, Wnter 2004 Solutons to Frst Mdterm. Multple Choce. 2. (a) v. (b). (c) v. (d) v. (e). (f). (g) v. (a) The goods market s n equlbrum when total demand equals total producton,.e.

More information

The covariance is the two variable analog to the variance. The formula for the covariance between two variables is

The covariance is the two variable analog to the variance. The formula for the covariance between two variables is Regresson Lectures So far we have talked only about statstcs that descrbe one varable. What we are gong to be dscussng for much of the remander of the course s relatonshps between two or more varables.

More information

State function: eigenfunctions of hermitian operators-> normalization, orthogonality completeness

State function: eigenfunctions of hermitian operators-> normalization, orthogonality completeness Schroednger equaton Basc postulates of quantum mechancs. Operators: Hermtan operators, commutators State functon: egenfunctons of hermtan operators-> normalzaton, orthogonalty completeness egenvalues and

More information

Experiment 8 Two Types of Pendulum

Experiment 8 Two Types of Pendulum Experment 8 Two Types of Pendulum Preparaton For ths week's quz revew past experments and read about pendulums and harmonc moton Prncples Any object that swngs back and forth can be consdered a pendulum

More information

Extending Probabilistic Dynamic Epistemic Logic

Extending Probabilistic Dynamic Epistemic Logic Extendng Probablstc Dynamc Epstemc Logc Joshua Sack May 29, 2008 Probablty Space Defnton A probablty space s a tuple (S, A, µ), where 1 S s a set called the sample space. 2 A P(S) s a σ-algebra: a set

More information

CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES

CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable

More information

A High Q Band Pass Filter Using Two Operational Amplifiers

A High Q Band Pass Filter Using Two Operational Amplifiers Jurnal f Physcal Scences, l., 007, 33-38 A Hgh Q Band Pass Flter Usng Tw Operatnal Amplfers Seema ana*, Kapl Dev Sharma** and Krat Pal*** *DA Centenary Publc Schl, Hardwar INDIA **Department f Physcs,

More information

Harvard University Division of Engineering and Applied Sciences. Fall Lecture 3: The Systems Approach - Electrical Systems

Harvard University Division of Engineering and Applied Sciences. Fall Lecture 3: The Systems Approach - Electrical Systems Harvard Unversty Dvson of Engneerng and Appled Scences ES 45/25 - INTRODUCTION TO SYSTEMS ANALYSIS WITH PHYSIOLOGICAL APPLICATIONS Fall 2000 Lecture 3: The Systems Approach - Electrcal Systems In the last

More information

Applied Research Laboratory. Decision Theory and Receiver Design

Applied Research Laboratory. Decision Theory and Receiver Design Decson Theor and Recever Desgn Sgnal Detecton and Performance Estmaton Sgnal Processor Decde Sgnal s resent or Sgnal s not resent Nose Nose Sgnal? Problem: How should receved sgnals be rocessed n order

More information

Mean Molecular Weight

Mean Molecular Weight Mean Molecular Weght The thermodynamc relatons between P, ρ, and T, as well as the calculaton of stellar opacty requres knowledge of the system s mean molecular weght defned as the mass per unt mole of

More information

Introduction to Chemical Engineering: Chemical Reaction Engineering

Introduction to Chemical Engineering: Chemical Reaction Engineering ========================================================== Introducton to Chemcal Engneerng: Chemcal Reacton Engneerng Prof. Dr. Marco Mazzott ETH Swss Federal Insttute of Technology Zurch Separaton Processes

More information

1 Approximation Algorithms

1 Approximation Algorithms CME 305: Dscrete Mathematcs and Algorthms 1 Approxmaton Algorthms In lght of the apparent ntractablty of the problems we beleve not to le n P, t makes sense to pursue deas other than complete solutons

More information

Frequency Selective IQ Phase and IQ Amplitude Imbalance Adjustments for OFDM Direct Conversion Transmitters

Frequency Selective IQ Phase and IQ Amplitude Imbalance Adjustments for OFDM Direct Conversion Transmitters Frequency Selectve IQ Phase and IQ Ampltude Imbalance Adjustments for OFDM Drect Converson ransmtters Edmund Coersmeer, Ernst Zelnsk Noka, Meesmannstrasse 103, 44807 Bochum, Germany edmund.coersmeer@noka.com,

More information

RESEARCH ON DUAL-SHAKER SINE VIBRATION CONTROL. Yaoqi FENG 1, Hanping QIU 1. China Academy of Space Technology (CAST) yaoqi.feng@yahoo.

RESEARCH ON DUAL-SHAKER SINE VIBRATION CONTROL. Yaoqi FENG 1, Hanping QIU 1. China Academy of Space Technology (CAST) yaoqi.feng@yahoo. ICSV4 Carns Australa 9- July, 007 RESEARCH ON DUAL-SHAKER SINE VIBRATION CONTROL Yaoq FENG, Hanpng QIU Dynamc Test Laboratory, BISEE Chna Academy of Space Technology (CAST) yaoq.feng@yahoo.com Abstract

More information

EE101: Op Amp circuits (Part 4)

EE101: Op Amp circuits (Part 4) EE11: Op Amp crcuts (Part 4) M. B. Patl mbpatl@ee.tb.ac.n www.ee.tb.ac.n/~sequel Department of Electrcal Engneerng Indan Insttute of Technology Bombay M. B. Patl, IIT Bombay Half-wave rectfer Consder a

More information

Microwave Multi-Level Band-Pass Filter Using Discrete-Time Yule-Walker Method

Microwave Multi-Level Band-Pass Filter Using Discrete-Time Yule-Walker Method Mcrowave Mult-Level Band-Pass Flter Usng Dscrete-Tme Yule-Walker Method Chng-Wen Hsue, Jer-We Hsu, Yen-Jen Chen Department of Electronc Engneerng, Natonal Tawan Unversty of Scence and Technology 43 Keelung

More information

n + d + q = 24 and.05n +.1d +.25q = 2 { n + d + q = 24 (3) n + 2d + 5q = 40 (2)

n + d + q = 24 and.05n +.1d +.25q = 2 { n + d + q = 24 (3) n + 2d + 5q = 40 (2) MATH 16T Exam 1 : Part I (In-Class) Solutons 1. (0 pts) A pggy bank contans 4 cons, all of whch are nckels (5 ), dmes (10 ) or quarters (5 ). The pggy bank also contans a con of each denomnaton. The total

More information

where the coordinates are related to those in the old frame as follows.

where the coordinates are related to those in the old frame as follows. Chapter 2 - Cartesan Vectors and Tensors: Ther Algebra Defnton of a vector Examples of vectors Scalar multplcaton Addton of vectors coplanar vectors Unt vectors A bass of non-coplanar vectors Scalar product

More information

x f(x) 1 0.25 1 0.75 x 1 0 1 1 0.04 0.01 0.20 1 0.12 0.03 0.60

x f(x) 1 0.25 1 0.75 x 1 0 1 1 0.04 0.01 0.20 1 0.12 0.03 0.60 BIVARIATE DISTRIBUTIONS Let be a varable that assumes the values { 1,,..., n }. Then, a functon that epresses the relatve frequenc of these values s called a unvarate frequenc functon. It must be true

More information

The Magnetic Field. Concepts and Principles. Moving Charges. Permanent Magnets

The Magnetic Field. Concepts and Principles. Moving Charges. Permanent Magnets . The Magnetc Feld Concepts and Prncples Movng Charges All charged partcles create electrc felds, and these felds can be detected by other charged partcles resultng n electrc force. However, a completely

More information

NOTE: The Flatpak version has the same pinouts (Connection Diagram) as the Dual In-Line Package. *MR for LS160A and LS161A *SR for LS162A and LS163A

NOTE: The Flatpak version has the same pinouts (Connection Diagram) as the Dual In-Line Package. *MR for LS160A and LS161A *SR for LS162A and LS163A BCD DECADE COUNTERS/ 4-BIT BINARY COUNTERS The LS160A/ 161A/ 162A/ 163A are hgh-speed 4-bt synchronous counters. They are edge-trggered, synchronously presettable, and cascadable MSI buldng blocks for

More information

DEFINING %COMPLETE IN MICROSOFT PROJECT

DEFINING %COMPLETE IN MICROSOFT PROJECT CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMI-SP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,

More information

Comparison of Control Strategies for Shunt Active Power Filter under Different Load Conditions

Comparison of Control Strategies for Shunt Active Power Filter under Different Load Conditions Comparson of Control Strateges for Shunt Actve Power Flter under Dfferent Load Condtons Sanjay C. Patel 1, Tushar A. Patel 2 Lecturer, Electrcal Department, Government Polytechnc, alsad, Gujarat, Inda

More information

"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *

Research Note APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES * Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789-794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC

More information

SIMPLE LINEAR CORRELATION

SIMPLE LINEAR CORRELATION SIMPLE LINEAR CORRELATION Smple lnear correlaton s a measure of the degree to whch two varables vary together, or a measure of the ntensty of the assocaton between two varables. Correlaton often s abused.

More information

HÜCKEL MOLECULAR ORBITAL THEORY

HÜCKEL MOLECULAR ORBITAL THEORY 1 HÜCKEL MOLECULAR ORBITAL THEORY In general, the vast maorty polyatomc molecules can be thought of as consstng of a collecton of two electron bonds between pars of atoms. So the qualtatve pcture of σ

More information

2. Introduction and Chapter Objectives

2. Introduction and Chapter Objectives eal Analog Crcuts Chapter : Crcut educton. Introducton and Chapter Objectes In Chapter, we presented Krchoff s laws (whch goern the nteractons between crcut elements) and Ohm s law (whch goerns the oltagecurrent

More information

z(t) = z 1 (t) + t(z 2 z 1 ) z(t) = 1 + i + t( 2 3i (1 + i)) z(t) = 1 + i + t( 3 4i); 0 t 1

z(t) = z 1 (t) + t(z 2 z 1 ) z(t) = 1 + i + t( 2 3i (1 + i)) z(t) = 1 + i + t( 3 4i); 0 t 1 (4.): ontours. Fnd an admssble parametrzaton. (a). the lne segment from z + to z 3. z(t) z (t) + t(z z ) z(t) + + t( 3 ( + )) z(t) + + t( 3 4); t (b). the crcle jz j 4 traversed once clockwse startng at

More information

6. EIGENVALUES AND EIGENVECTORS 3 = 3 2

6. EIGENVALUES AND EIGENVECTORS 3 = 3 2 EIGENVALUES AND EIGENVECTORS The Characterstc Polynomal If A s a square matrx and v s a non-zero vector such that Av v we say that v s an egenvector of A and s the correspondng egenvalue Av v Example :

More information