Chapter 1

Introduction to EEPro
Thank you for your purchase of EEPro, a member of the PocketProfessional Pro software series designed by da Vinci Technologies to meet the computational needs of students and professionals in the engineering and scientific fields. Many long hours and late nights have been spent by the designers of this software to compile and organize the subject material in this software. We hope you enjoy EEPro and that it serves as a valuable companion in your electrical engineering career. Topics in this chapter include:
Key Features of EEPro Download/Purchase Information Manual Ordering Memory Requirements
Differences between the TI 89 and TI 92 plus. Beginning EEPro Manual Organization Summary
1.1 Key Features of EEPro
The manual is organized into three sections representing the main menu headings of EEPro. Analysis AC Circuits Polyphase Circuits Ladder Network Filter Design Gain and Frequency Fourier Transforms Two-Port Networks Transformer Calculations Transmission Lines Computer Engineering Error Functions Capital Budgeting Equations Resistive Circuits Capacitors and Electric Fields Inductors and Magnetism Electron Motion Meters and Bridges RL and RC Circuits RLC Circuits AC Circuits Polyphase Circuits Electrical Resonance Operational Amplifier Circuits Solid State Devices Linear Amplifiers Class A, B, & C Amplifiers Transformers Motors and Generators Reference Resistor Color Chart Standard Component Values Semiconductor Data Boolean Expressions Boolean Algebra Transforms Constants SI Prefixes
These main topic headings are further divided into sub-topics. A brief description of the main sections of the software is listed below:
EE Pro for TI - 89, 92 Plus Introduction to EEPro
Analysis-(Chapters 2-14) Analysis is organized into 12 topics and 33 sub-topics. The tools in this section incorporate a wide variety of analysis methods used by electrical engineers. Examples include evaluation of AC circuit performance characteristics, designing signal filters, building and computing ladder network properties, plotting transfer functions, estimating transformer and transmission line characteristics, performing binary arithmetic operations, and estimating pay-back returns for different projects in capital budgeting. Many sections in analysis can perform calculations for numeric as well as symbolic entries. Equation Library (Chapters 15-31) This section contains over 700 equations organized under 16 topics and 105 subtopics. In any sub-topic, the user is able to select a set of equations, enter known values and compute results for unknown variables. The math engine is able to compute multiple or partial solution sets. A built-in unit management feature allows for the entry and expression of values in SI or other established measurement systems. Descriptions of each variable, unit selection, and appropriate diagrams are included in this section of the software. Reference (Chapters 32-41) The Reference section of EEPro contains tables of information commonly found in electrical engineering handbooks. Topics include physical and chemical properties of common semiconductor materials, a list of fundamental constants commonly used by electrical engineers, tables of Fourier, Laplace, and ztransforms, and a list of Boolean algebraic expressions. Added features are the ability to perform simple computations, such as estimating standard (or preferred) manufacturer component values for inductors, resistors, and capacitors, in addition to a resistor color chart guide which can compute resistance and tolerance from a resistors color band sequence.

I rb (hie) ICIS

Two-Port Network Can be added only in cascade connection. Choose z, y, h, g, a, or b for Input Parameters, and enter values for.11,.12,.21, and.22.
Zin_: I2/V1_: I2/I1_: Pout/Pin: V2/V1_: V2/I1_: (Input Impedance in ohms) Returns a real or complex number, variable name or algebraic expression. (Forward Transfer Admittance Returns a real or complex number, variable name or algebraic in Siemens) expression. (Current Transfer Ratio) Returns a real or complex number, variable name or algebraic expression. (Real Power Gain) Returns a real or complex number, variable name or algebraic expression. (Forward Voltage Transfer Ratio) Returns a real or complex number, variable name or algebraic expression. (Forward Transfer Impedance Returns a real or complex number, variable name or algebraic in ohms) expression.
5.2 Using the Ladder Network
General instructions for entering the elements and computing the parameters of a ladder network. 1. The initial screen prompts the user for entry of values for Frequency and Load. 2. Build the ladder by adding elements to it. Press to insert the first element. Choose an element type and press. Enter the appropriate values. Press to update the ladder with the new element just added. A second press of the key computes the electrical performance of the circuit. 3. New elements can be added or inserted by moving the highlight bar to the location desired and pressing. The new element will appear after the a highlighted element. 4. A circuit element can be deleted from the ladder by moving the highlight bar to the element and pressing. 5. Press to compute the overall ladder network parameters. 6. Previously calculated results are not automatically updated for new element entries; the user must press to re-solve for the circuit parameters for a new circuit configuration.

Example 5.1

What is the input impedance of the circuit shown below in Fig. 5.1 at 1 MHz and 10 MHz?

10E-6 H 50 pF

Load 50

Element 4

Element 3

Element 2

Element 1
Fig. 5.1 Ladder Network Example
Entering Load and Frequency
Partial list of Element Choices
Typical Edit Screen for an Element
List of all the Ladder Components

Output Screen at 1 MHz.

Output Screen at 10 MHz

1. 2. 3.

Enter 1E6 for Frequency. Enter 50 for Load. Press to add the first element and move the highlight bar in the pull down menu to Capacitor and press to display the input screen for the Capacitor. Select Parallel for Configuration of the capacitor and enter the value 50E-12 for C. Press to accept the element data and press to return a listing of the Ladder Network. Move the highlight bar to 1: Capacitor and press to enter the second element in this circuit. Move the highlight bar to Inductor to display the input screen for the new element. Choose Series for Config and enter the value 10E-6 for L. Press to accept the value and press to update the ladder. Enter the remaining two elements: a 100 pF (100E-12) capacitor in parallel and a 50 ohm resistor in series. Press to calculate the results displayed in the output screen as shown above. To delete an element from the network, highlight it and press , the delete key.

Poles:

Numer list:

Denom list:

H(s)_:

Press to select Roots or Coefficients. Determines whether the third and fourth fields are Zeros and Poles or Numer and Denom. (Constant Multiplier) Enter a real number. Default is 1. (Numerator Roots - if Roots is chosen for input type) Enter an array or list of real numbers. The number of zeros must be less than the number of poles. (Denominator Roots - if Roots is chosen for input type) Enter an array or list of real numbers. The number of poles must be greater than the number of zeros. (Numerator Coefficients - if Coefficients is chosen for input type) Enter an array or list of real numbers. The number of numerator coefficients must be less than the number of denominator coefficients. (Denominator Coefficients - if Coefficients is chosen for input type) Enter an array or list of real numbers. The number of denominator coefficients must be greater than the number of numerator coefficients. (Transfer Function) Returns a symbolic expression in the following form:
EE Pro for TI-89, 92 Plus Analysis - Gain and Frequency
s_ s_ 1. z1 z2 s_ s_ 1 1. p1 p2
IJ FG IJ KH K IJ FG IJ KH K

Eq. 7.1.1

(Partial Fraction Expansion) Returns a symbolic expression of the form:

Example 7.1

K1 K2 K3 + + +. s_ s_ s_ 1 p1 p2 p3

IJ FG K H

Eq. 7.1.2
Find the transfer function and its partial fraction expansion for a circuit with a zero located at -10 r/s and three poles located at -100 r/s, -1000 r/s and -5000 r/s. Assume that the multiplier constant is 100000.

1. 2. 3. 4.

Output screen
Partial view of Partial Fraction Expansion form for H(s)
Choose Roots for Inputs. Enter 100000 for Constant, {-10} for Zeros, and {-100 -1000 -5000} for Poles. Press to calculate H(s)_ and PFE_. To view H(s)_ in Pretty Print format, press and. Alternatively, the Bkey can be pressed to achieve the same result.
Now you are ready to go on to the next example. Press N to return to the Gain and Frequency screen and select Bode Diagrams.

7.2 Bode Diagrams

The behavior of the transfer function, as the frequency of a sinusoidal source varies, is of great interest to engineers. A very effective way to grasp the relationship between transfer function and frequency is to plot the magnitude and the argument of the transfer function on two separate graphs. These plots are often called Bode gain and phase plots. A gain plot shows the magnitude of the transfer function expressed in decibels (dB) as 20*LOG(Magnitude of Transfer Function) as a function of the logarithm of the radian frequency on the horizontal scale. The phase plot shows the argument of the transfer function expressed as the phase angle (i.e., ARG (Transfer Function) ) plotted as a function of the logarithm of the radian frequency on the horizontal scale.

Enter the values 0.001, 85.8, and.0015E-6 for L, R, and G, respectively. Enter the values 62E-9, 75, and 3 for C, ZL_, and d, respectively. Enter 2000 for f. Press to calculate the results. The input and output screen displays are shown above.

11.2 Line Parameters

This topic computes fundamental parameters of a transmission line from measured data. The algorithm used in this section solves for in the equation 11.2.1, where = + j. In general , Zsc_, and Zoc_ have complex values. In solving for , there is a principal value and a set of equivalent values because of the cyclical nature of the equation. Recognizing the fact that physical parameters such as R, L, G, C, and vp are all real and positive numbers, extreme caution should be exercised when entering input data. In particular, d should be less than one wavelength.

tan( d ) =

Zsc _ Zoc _

Eq. 11.2.1

Zoc_: (Open Circuit Impedance in ) Zsc_: (Short Circuit Impedance in ) Enter a real or complex number, variable or algebraic expression of defined terms. Enter a real or complex number, variable or algebraic expression of defined terms.
(Distance to Load Location/ unit length) (Frequency in Hertz)
Enter a real number or algebraic expression of defined terms or variable. Enter a real number or variable or algebraic expression of defined terms.
R: L: G: C: ZZ0: YY0: (Series Resistance in /unit length) (Series Inductance in H/unit length) (Shunt Conductance in Siemens/unit length) (Shunt Capacitance in F/unit length) (Characteristic Impedance in ) (Characteristic Admittance in ) (Neper Constant in 1/unit length) (Phase Constant in degrees or radians/unit length) (Phase Velocity in unit length/s) Returns a real number or algebraic expression. Returns a real number or algebraic expression. Returns a real number or algebraic expression. Returns a real number or algebraic expression. Returns a real number or algebraic expression. Returns a real number or algebraic expression. Returns a real or complex number or algebraic expression. Returns a real or complex number or an algebraic expression. Returns a real number or algebraic expression.

Example 11.2

A transmission line is measured to have an open circuit impedance of 103.6255 - 2.525*i, and an impedance under short circuit conditions of 34.6977 + 1.7896*i, at a distance 1 unit length from the load location. All measurements are conducted at 10 MHz. Compute all the line parameters.

Plot of Project 1

Overlay of Project 2

Chapter 15

Introduction to Equations
The Equations section of EEPro contains over 700 equations organized into 16 topic and 105 sub-topic menus. The user can select several equation sets from a particular sub-topic, display all the variables used in the set of equations, enter the values for the known variables and solve for the unknown variables. The equations in each sub-topic can be solved individually, collectively or as a sub-set. A unit management feature allows easy entry and display of results. Variables in selected equation sets can be graphed to examine the relationship between each other. Multiple and partial solutions are possible using techniques developed for EEPro. More information on a particular input can be displayed by highlighting the variable, press and /Type: to show a brief description of a variable and its entry parameters.
15.1 Solving a Set of Equations
Equations are accessed from the main level of the EEPro by pressing function key labeled "Equations." This displays a pull-down menu listing all the topics as shown in the screen display below. An arrow to the left of the bottom topic indicates more items are listed. Pressing 2 D jumps to the bottom of the menu. Scroll the highlight bar to an item using the arrow key D and press , or type the subject number appearing next to subject heading (Resistive Circuits is selected for this example). A second menu will appear listing more subjects (sub-topics) under the topic heading. Selecting a sub-topic displays a list of equations under the subject heading (Ohms Law and Power is selected below). Use the arrow key D to move the highlighter and press to select an equation or series of equations which are applicable to a specific problem (pressing selects all of the equations). Press to display all of the variables in the selected equations. As the cursor bar is moved, a brief description of each variable will appear in the status line at the bottom of the screen. Enter values for the known parameters, selecting appropriate units for each value using the toolbar menu which appear at the top of the screen. Press to compute values for the unknown parameters. Entered and calculated values are distinguished in the display; for entered values and for computed results.
EE Pro for TI - 89, 92 Plus Equations - Introduction to Equations
1. Pressing displays the Equations menu.
2. Press to display the menu in Resistive Circuits
3. Press to display the equations for Ohms Law.
4. Select equations by highlighting and pressing.
5. Press to display the variables in the selected equations. Enter the known variable values. Use the unit toolbar to select units.
6. Press to compute the unknown variables. Note: Computed results are distinguished from entered values.
Note: Only values designated as known will be used in a computation. A result displayed from an earlier calculation will not be used unless the user specifically designates the value by selecting the variable and pressing. Press to compute a new result for any input that is changed.

15.9 solve, nsolve, and csolve and user-defined functions (UDF)
When a set of equations is solved in EEPro, three different functions in the TI operating system (solve, numeric solve, and complex solve) are used to find the most appropriate solution. In a majority of cases, the entered values are adequate to find numeric solutions using either the solve or csolve functions. However, there are a few instances when functions external to the equation set (user-defined functions) are incorporated into the solving process and nsolve must be used. User defined functions which appear in some of the equation sets of EEPro are erfc(x) erf(x), eeGALV(RR2,.) and ni(TT). In most cases, when all the inputs to a UDF are known, solve or csolve can just pass a computed result to the equation. On the other hand if one is solving for a variable that is an input to the UDF, solve or csolve are unable to isolate the variable in an explicit form, and the operating system resorts to using nsolve. nsolve initiates a series of trial and error iterations for the unknown variable until the solution converges. It should be noted that the solution generated by nsolve is not guaranteed to be unique (i.e. this solving process cannot determine if multiple solutions exist.).
Table 15-1 User Defined Functions
User-defined Function erf(ts, p) erfc (x,D,t) eegalv (Rx, RR2, RR3, RR4, Rg, Rs, Vs) ni(TT) Topic Solid State Solid State Meters and Bridges Solid State Sub-topic PN Junction Current Semiconductor Basics Wheatstone Bridge Semiconductor Basics, PN Junctions, PN Junction Current, MOS Transistor I
15.10 Entering a guessed value for the unknown using nsolve
To accelerate the nsolve converging process and, if multiple solutions exist, enhance the possibility that nsolve resolves the correct solution, the user can enter a guessed value for the unknown which nsolve will use as an initial value in the first iteration of its solving process. Enter guessed a value for the variable in the input dialogue. Press /Opts, m/Want. Press / to compute a solution for the variable.
erfc(x,D,t) is a user defined function that appears in the Semiconductor Basics section of Solid State.
Only one input to a user defined function can be specified as an unknown.
EEPro displays a notice if the nsolve routine is used.
The user can enter a value for for the unknown and designate it as a guessed value to accelerate the nsolve convergence process.
15.11 Why can't I compute a solution?
If a solution is unable to be computed for an entered problem, you might check the following: 1. 2. 3. Are there at least as many equations selected as there are unknown parameters? Are the entered values or units for the known parameters reasonable for a specific case? Are the selected equations consistent in describing a particular case (for example, the choice of certain equations used in the calculation of diode properties depends on whether the donor density of the doping substance Nd, exceeds the acceptor density, Na in the Semiconductors section of Solid State)

EE Pro for TI - 89, 92 Plus Equations - Resistive Circuits

16.1 Resistance Formulas

Four equations in this topic represent the basic relationship between resistance and conductance. The first equation links the resistance R of a bar with a length len and a uniform crosssectional area A with a resistivity. The second equation defines the conductance G of the same bar in terms of conductivity , len and A. The third and fourth equations show the reciprocity of conductance G resistance R, resistivity and conductivity.

len A

Eq. 16.1.1

A len 1 G= R 1 =

.45_cm2. Compute the its resistance and conductance.
Eq. 16.1.2 Eq. 16.1.3 Eq. 16.1.4
Example 16.1 - A copper wire 1500_m long has a resistivity of 6.5_ohm*cm and a cross sectional area of
Solution - Upon examining the problem, two choices are noted. Equations 16.1.1, 16.1.2 and 16.1.4 or
16.1.1 and 16.1.3 can be used to solve the problem. The second choice was made here. Press to display the input screen, enter all the known variables and press to solve the selected equation set. The computed results are shown in the screen display shown here.

Entered Values

Computed results
-PQYP8CTKCDNGUNGPAOAQJOEO#AEO %QORWVGF4GUWNVU4'AQJO)'AUKGOGPU

16.2 Ohms Law and Power

The fundamental relationships between voltage, current and power are presented in this section. The first equation is the classic Ohm's Law, computes the voltage V in terms of the current I, and the resistance R. The next four equations describe the relationship between power dissipation P, voltage V, current I, resistance R and conductance G in a variety of alternate forms. The final equation represents the reciprocity between resistance R and conductance G.
V = I R P =V I P = I2 R P= V2 R
Eq. 16.2.1 Eq. 16.2.2 Eq. 16.2.3 Eq. 16.2.4

P = V 2 G R= 1 G

Eq. 16.2.5 Eq. 16.2.6
Example 16.2 - A 4.7_kohm load carries a current of 275_ma. Calculate the voltage across the load, power dissipated and load conductance.
Solution - Upon examining the problem, several choices are noted. Either Equations 16.2.1, 16.2.2 and 16.2.6, or 16.2.2, 16.2.3 and 16.2.5 or 16.2.2, 16.2.3 and 16.2.6 or 16.2.1, 16.2.2 and 16.2.5 or all the equations. Choose the last option, press to open the input screen, enter all the known variables and press to solve.
-PQYP8CTKCDNGU+AOC4AM %QORWVGF4GUWNVU8A82A9)AUKGOGPU

l 2 0 r r

Eq. 17.2.1
Example 17.2 - An aluminum wire suspended in air carries a charge density of 2.75E-15_coulombs/m. Find the electric field 50_cm away. Assume the relative permittivity of air to be 1.04.
Solution - Press to display the input screen, enter all the known variables, and press to solve the
selected equation set. The screen display above shows the computed results. -PQYP8CTKCDNGU %QORWVGF4GUWNVU N'AEQWNQODUOTAEOT 'TA8O

17.3 Charged Disk

These two equations describe the electric field and potential along the vertical axis through the center of a uniformly charged disk. The first equation defines the electric field along the z-axis of the disk with a radius ra and charge density of s, a distance z from the plane of the disk. The second equation computes the electrostatic potential Vz at an arbitrary point along the z-axis.

z s 2 0 r ra + z 2

IJ K j

Eq. 17.3.1

s 2 0 r

ra 2 + z 2 z

Eq. 17.3.2
Example 17.3 - A charged disc 5.5_cm in radius produces an electric field of.2_V/cm 50_cm away from the surface of the disc. Assuming that relative permittivity of air is 1.04, what is the charge density on the surface of the disc?

Computed Results

Solution - Select the first equation by pressing key, press to display the input screen for this equation, enter all the known variables, and press. The computed results are shown in the screen display above.
-PQYP8CTKCDNGUTCAEOT'\A8EO\AEO %QORWVGF4GUWNVUU'AEQWNQODO@

17.4 Parallel Plates

The five equations listed in this topic describe the electrical and mechanical forces in a parallel plate capacitor. Two plates are separated by a distance d which is small compared to the lateral dimensions so fringing field effects can be ignored. The first equation computes the electric field E at the plate for a potential difference V between the plates separated by a small distance d. The second equation calculates capacitance C with a dielectric given the relative permittivity r and area A. The third equation shows the charge Q on each parallel plate. The last two equations compute the mechanical properties associated with this parallel plate capacitor such as the Force F on the plates and energy W stored in the capacitor.

Example 27.2.2 - A linearly graded junction has an area of 100 2, a built-in voltage of 0.8578 V, and an applied
voltage of -5.V. The relative permittivity of silicon is 11.8. Under room temperature conditions, what is the junction capacitance, depletion layer width, and the linear-graded junction parameter?
Solution - Use equations 27.2.5-7 to compute the solution for this problem. Select these by highlighting each
equation and pressing the key. Press to display the input screen, enter all the known variables and press to solve the equations. The computed results are shown in the screen displays above. -PQYP8CTKCDNGU8CA88DKA8#LA@U66A- %QORWVGF4GUWNVUC.),'AO@%L'A(ZFA
27.3 PN Junction Currents
These equations characterize the relationships for computing currents in PN junctions. They can be classified into four categories. The first three equations define the junction currents. First, the junction current I is expressed in terms of the junction area Aj, diffusion coefficients Dn and Dp, diffusion lengths LLn and Lp, equilibrium densities of minority carriers npo and pno, applied bias Va, and temperature TT. The second equation is a simplified form the first equation where the current I0 is defined as the multiplier of the exponential term. In this form, it is often called Shockley equation. The third equation calculates this saturation current I0 in terms of the junction area Aj, diffusion coefficients Dn and Dp, diffusion lengths LLn and Lp, equilibrium densities of minority carriers npo and pno. It is used to simplify the first equation.
FG Dn npo + Dp pnoIJ FG e Lp H LLn KH F 1IJ I = I 0Ge H K F Dn npo + Dp pnoIJ I 0 = q Aj G Lp H LLn K

I = q Aj

q Va k TT

Eq. 27.3.1

Eq. 27.3.2

Eq. 27.3.3

The so-called Generation-Recombination current IRG0 at 0 bias is calculated by the fourth equation in terms of Aj, average recombination time o, intrinsic density ni, depletion width xd. The fifth equation shows that applying an external voltage Va, the generation recombination current IRG increases exponentially.

IRG 0 =

q Aj ni TT xd 2 o

Eq. 27.3.4

q Va q Aj ni TT xd 2k TT e 1 IRG = 2 o

Eq. 27.3.5

The small signal conducatnce of the junction is defined as Go, and is computed in terms of temperature TT and currents I and I0. The last two equations compute the charge storage time ts when the diode current is switched externally from IIf to Ir. It is seen from these two equations that ts depends strongly upon the minority carrier lifetime p.
q I + I0 k TT IIf ts = p ln 1 + Ir Go =

Eq. 27.3.6 Eq. 27.3.7

Ir 1+ IIf Example 27.3.1 - A PN Junction is characterized as having a junction area of 100 m2, an applied voltage of 0.5
V, and diffusion coefficients for electrons and holes of 35 cm2/s and 10 cm2/s, respectively. The diffusion lengths for electrons and holes are 25 m and 15 m. The minority carrier densities are 5 x 106 cm-3 (electrons) and 25 cm-3 (holes). Find the junction current and the saturation current for room temperature conditions.

Solution - Use all of the equations to compute the solution for this problem. Select these by highlighting each
equation and pressing the key. Press to display the input screen, enter all the known variables and press to solve the equations. The computed results are shown in the screen displays above. -PQYP8CTKCDNGUTDATTEAMTGA4NAM %QORWVGF4GUWNVU#K#X4KPA4QA
28.10 Differential Amplifier
The gain Ad in the differential mode of operation is given by the first equation. The common mode gain, Ac is defined in terms of the external collector and emitter resistances RCA and REA and the emitter resistance re. The last two equations show input resistance for differential and common mode inputs Rid & Ric.
1 Ad = gm RCA RCA Ac = 2 REA + re Rid = 2 rb + 0 re

Eq. 28.10.1 Eq. 28.10.2

Eq. 28.10.3 Eq. 28.10.4

Ric = 0 REA

Example 28.10 - A differential amplifier pair has a transconductance of 0.005 siemens, 0=0.98, 0=49. The external collector and external emitter resistances are 18 k and 10 k respectively. If the emitter resistance is 25 and the base resistance is 2 k, find the common mode, differential resistance and gains.
equation and pressing the key. Press to display the input screen, enter all the known variables and press to solve the equations. The computed results are shown in the screen displays above. -PQYP8CTKCDNGUIOAUKGOGPUTDAMTGAM4%#AM 4'#AM %QORWVGF4GUWNVU#E#F4KEA4KFA
28.11 Source-Coupled JFET Pair
The first two equations describe the differential Ad and common mode Ac gains for a source-coupled JFET pair in terms of the external drain, drain and source resistances RDA, rd and Rs. The third equation shows the amplification factor , in terms of the transconductance gm and the drain resistance. The final equation calculates the common mode rejection ratio CMRR.
1 gm rd RDA Ad = 2 rd + RDA RDA Ac = + Rs + rd + RDA

CMRR = gm Rs

Example 28.11 - Find the gain parameters of a source-coupled JFET pair amplifier if the external drain resistance is 25 k, and the source resistance is 100. The drain resistance is 12 k and the transconductance is 6.8 x 10-3 siemens.
equation and pressing the key. Press to display the input screen, enter all the known variables and press to solve the equations. The computed results are shown in the screen displays above. -PQYP8CTKCDNGUIOAUKGOGPUTFAM4&#AM4UA %QORWVGF4GUWNVU#E#F%/44

Chapter 29

Class A, B and C Amplifiers
This chapter covers the section called Class A, B and C Amplifiers. These amplifier circuits forms the basis of a class of power amplifiers used in a variety of applications in the industry.

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31.2 DC Generator

The first equation describes the relation between electrical radian frequency me, the mechanical radian frequency m, and the number of poles in the generator p. The next equation expresses the emf generated per turn Eta with the relative motion of the coil with respect to the magnetic field.

p m 2 p Eta = m

Eq. 31.2.1 Eq. 31.2.2
The next two equations illustrate two ways to express the induced armature emf Ea as a function of number of armature coils N, the number of parallel paths ap, number of poles p, the mechanical radian frequency m, a machine constant K, and flux. The machine constant K, is seen to be dependent purely on the characteristics of the machine.
N p m ap Ea = K m Np K= ap Ea =
Eq. 31.2.3 Eq. 31.2.4 Eq. 31.2.5
The sixth equation shows the conversion of mechanical energy available as torque T and mechanical angular velocity m to its electrical counterpart namely, the emf and current in the armature Ea, and Ia and the voltage and current in the field windings Ef and If. The next equation for torque connects T with K, , and the current Ia.
T m = Ea Ia + Ef IIf T = K Ia

Eq. 31.2.6 Eq. 31.2.7

The armature resistance is given by the equation for Ra in terms of N, ap, coil length L, area A and its resistivity.

N L ap 2 A

Eq. 31.2.8
Vf represents the voltage across the field winding carrying a current IIf and a resistance Rf. The terminal voltage Vt represents the induced voltage minus the IR drop in the armature.
Vf = Rf IIf Vt = K m Ra Ia

Eq. 31.2.9 Eq. 31.2.10

The final equation represents the shaft torque Ts needed to generate the induced emf, assuming a given value for equivalent loss of torque Tloss

Ts = K Ia + Tloss

Eq. 31.2.11
Example 31.2 - A six-pole DC generator rotates at a mechanical speed of 31 rad/s. The armature sweeps across a flux of 0.65 Wb. There are eight parallel paths and 64 coils in the armature. The armature current is 12 A. The field is supplied by a 25 V source delivering a current of 0.69 A. Find the torque and the voltages generated in the armature.

Display: Upper Half

Display: Lower Half
Solution - Choose the first six equations. Select these by highlighting each equation and pressing
. Press to display the input screen, enter all the known variables and press to solve the selected equation set. The computed results are shown in the screen displays above. -PQYP8CTKCDNGU %QORWVGF4GUWNVU CR'HA8+CA#++HAO#0A9DR OATU 'CA8'VCA8-6A0O OGATU
31.3 Separately-Excited DC Generator
The equations in this section describe the properties of a separately excited DC generator. The first equation computes the field current IIf in terms of field voltage Vfs, external shunt resistance re, and field coil resistance Rf. The next equation evaluates armature induced voltage Ea as a function of machine constant K, mechanical radian frequency m, and flux.

Example 39.1- Look up the value of.
1. 2. 3. Pi is the first value to appear in the constant sections. Make sure it is selected by the highlight bar using the arrow keys. Access the View function by pressing key. Press any key to return to the constants screen.
The number of significant digits displayed in Pretty Print can be changed in the 3 setting.

Chapter 40

40.1 Using SI Prefixes

SI Prefixes

The SI Prefixes section displays the prefixes used by the Systeme International [dUnit[eacute]s] (SI).
The prefixes are listed in the order shown in Table 40-1. The D key is used to move the highlight bar to select a SI prefix multiplier. The name of the prefix is displayed in the status line. The prefix and multiplier can be viewed by pressing the key.
Table 40-1 SI Prefix Table
Prefix Y: (Yotta) Z: (Zetta) E: (Exa) P: (Peta) T: (Tera) G: (Giga) M: (Mega) k: (Kilo) h: (Hecto) da: (Deka) Multiplier 1E24 1E21 1E18 1E15 1E12 1E9 1E6 1E3 1E2 1E1 Prefix d: (deci) c: (Centi) m: (Milli) : (Micro) n: (Nano) p: (Pico) f: (Femto) a: (Atto) z: (Zepto) y: (Yocto) Multiplier 1E-1 1E-2 1E-3 1E-6 1E-9 1E-12 1E-15 1E-18 1E-21 1E-24
EE Pro for TI -89, 92 Plus Reference - SI Prefixes

Chapter 41

Greek Alphabet
This section displays the Greek Alphabet and their names. There are several Greek letters supported by the TI - 89. To enter the Greek letters, the sequential keystrokes are listed in the TI-89 manual. They are repeated here for convenience of the user. Alternatively, 2 (or ) followed by will access an internal menu listing several Greek characters.

Key stroke Sequence

Table 40-1 Greek Key stroke Sequence Letter

Greek Letter

cj cjc cjb cje cj cjm cjy cjz cj cj cj cj cj cj cj cj
EE Pro for TI -89, 92 Plus Reference - Greek Alphabet

Appendix A Frequently Asked Questions
A complete list of commonly asked questions about the EEPro are listed here. Review this list for your questions prior to calling for Technical support. You might save yourself a phone call! The material is covered under four general headings.
A.1 Questions and Answers
General Questions Analysis Questions Equations Questions Reference Questions

A.2 General Questions

Cursor Movement
EE Pro for TI - 89, 92 Plus 13 Appendix D: TI-89 &TI 92 Plus: Display and Keystrokes Differences

Appendix E

General Error Messages Analysis Error Messages

Error Messages

Equations Error Messages Reference Error Messages
E.1 General Error Messages
1. NOTE: Make sure the settings in the 3 screen do not have the following configuration. Angle: DEGREE Complex Format: POLAR EEPro works best in the default mode settings of your calculator (ie. Complex Format: REAL, or Angle: RADIAN). If one of a set of error messages appears which includes An error has occurred while converting., Data Error, Domain Error, and/or Internal Error, check to see if the above settings in the 3 screen exists. If it does, change the or reset your calculator to the default mode settings (2 ). 2. Syntax Error -- occurs if the entered information does not meet the syntax requirements of the expected entry. Check to make sure extra parenthesis are removed and the entered value meets the legal rules for number entry. "Insufficient Table Space" or "Insufficient Memory" can occur when the system is low on available memory resources. Consult your TI-89 manual on methods of viewing memory status and procedures for deleting variables and folders to make more memory available. The message "Unable to save EEPro data" will be displayed if EEPro is unable to save information of its last location in the program before exiting due to low memory availability. Consult your TI-89 manual under the index heading: Memory-manage. "The variable prodata1 was not created by EEPro." EEPro uses a variable called prodata1 to recall its last location in the program when it is re-accessed. If this variable list is changed to a format which is non-recognizable to EEPro, it displays this message before overwriting.
6. "Data length exceeds buffer size. The variable name will be displayed instead. The variable's value may be viewed with VAR-LINK using or recalled to the author line of the HOME screen." 7. "An error has occurred while converting this variable's data for display. (The name of the variable is in the title of this dialog box.) There may be something stored in the variable that EEPro can't make sense of. You may be able to correct the problem by deleting the variable."
EE Pro for TI-89, 92 Plus Appendix E - Error Messages
storage error. This message is set to occur if the user attempts to enter a value into a variable which is locked or archived, or a memory error has occured. Check the current status of the variable by pressing and scrolling to the variable name, or check the memory parameters by pressing. Invalid variable reference. Conflict with system variable or reserved name. This can occur if a variable name is entered which is reserved by the TI operating system. A list of reserved variable names is included in Appendix F.