Using MathCAD

SCC Spring-08Electronic Technology

Wang Ngx-2638

ngw@scc.losrios.edu

Overview

• About MathCAD• Using MathCAD as an interactive calculator• Using MathCAD with formulas• Equation solver• Convenient features• Advanced features• Example : AC calculations• Conclusion

General features• MathCAD

– WYSIWYG– K to 4-year College level.– Simple, easy to use.– Not intended for heavy-duty number crunching.

• MatLab– Programming style.– Up to M.S. level – Extensive training required.– Suitable for heavy-duty number crunching.

Calculator Mode

• The Calculator Tool Bar

• The “=“ key (It is the output command)

• Examples: 1+1=2 1/3=0.333 sin(1)=0.841 sin(1deg)=0.017 1mi=1931m 1mi=6336ft

Interactive: just edit the numbers sin(45deg)=0.707

Complex Calculations

• Use i or j for the imaginary part (5+3j)+(2-4j)= (5+3j)-(2-4j)= (5+3j)*(2-4j)= (5+3j)/(2-4j)= (5+3j)^2= =

• Polar/Rectangular conversion: |5+3j|= arg(5+3j)= (type deg) 2e^45j*deg=

• “j” can be placed in front by typing: 1j*45deg

j35

Formulas

• You need to provide data: use the “:” key as the input command (it will look like :=).

• Then you need to enter the formula.

• Use the “=“ key to obtain the result.

• Example: Enter the followings E:3V R:2 I:E/R I=

Equation solver

Find(x,y,...)Solves a system of equations.Minerr(x,y,...)Approximate solution to a system of equations.root(f(x),x,a,b)Solves one equation in one unknown.lsolve(M,v)Solves a system of linear equations.polyroots(v)Solves for the roots of the polynomial whose

coefficients are in v.

Example: Using the “root” commandThis QuickSheet can be used to find a solution to the equation f x( ) 0 for a function f(x) you specify, using the built-in root

function.

Enter a function f(x):

f x( ) x3

ex

Enter a guess value for the solution (modify as necessary):

x 3

soln root f x( ) x( )

Note: For a complex solution, input a complex guess value.

Solution:

soln 0.773

Convenient features

• Use the worksheet as handouts.• Specify the unit of the results.• Change the input data and the results will

be updated automatically.Note: Data must be placed above formulas.

• Many built-in functions (root, …)• Comments can be entered after the “ key.• You can save the worksheet.• Resource center: Tutorials, quick sheets, …

Advanced features• Symbolic process: The symbolic menu bar

– Examples: type x^2”space”-1”space” and then select “Factor” from the symbolic menu bar.

• Graphs: see attached Bode Plot example.

• Array and range variables: Use the “;” key. See attached example.

• Programming: The programming menu bar has the basic programming commands.

• Calculus, differential equations, matrices, optimization, statistics, …

Bode Plot Example

T 10

41

j

105

1j

103

1j

104

dB_T 20 log T

_T arg T 180

1 10 1001 1031 10

41 10

51 10

60

1020304050607080

dB_T ( )

1 10 1001 10

31 10

41 10

51 10

6180

135

90

45

0

_T ( )

1 10 1001 1031 10

4504540353025201510

50

20 log1

1j

100

1 10 100 1 10

31 10

490

67.5

45

22.5

0

arg1

1j

100

180

Range Variables

E 0V 3V 9V E0

3

6

9

V R 10 I E( )

E

R I E( )

0

0.3

0.6

0.9

A

f 1Hz 5Hz f1

2

3

4

5

Hz L 10H XL f( ) 2f L XL f( )

62.832

125.664

188.496

251.327

314.159

Examples: RLC circuit impedance

R1 R2

R3C1

C2

L

ZTotal 1.013 103 158.114i ZTotal Z4 R1

Z4 12.579 158.114i Z4 Z31

jXC1( )1

1

Z3 2 103 6.283i Z3 Z2 R2

Z2 0.013 6.283i Z2 Z11

jXL( )1

1

Z1 3 103 79.577i Z1 R3 j XC2

XL 6.283XC2 79.577XC1 159.155

XL 2 f LXC21

2 f C2 XC11

2 f C1

L 1mHC2 2FC1 1F

R3 3kR2 2kR1 1kf 1KHz

Conclusion

MathCAD is a versatile teaching tool:

• Calculation steps (formulas)

• Demonstrate specific effects

• Graphics

• Exam/Homework problems

• Partial credit

• Course note