User manual TEXAS INSTRUMENTS EE PRO

[. . . ] PocketProfessionalTM Series EEPro #UQHVYCTG#RRNKECVKQP 1P6+CPF6+2NWU User's Guide June 1999 da Vinci Technologies Group, Inc. Western Blvd Suite 250 Corvallis, OR 97333 www. dvtg. com Notice This manual and the examples contained herein are provided "as is" as a supplement to EEPro application software available from Texas Instruments for TI-89, and 92 Plus platforms. ("da Vinci") makes no warranty of any kind with regard to this manual or the accompanying software, including, but not limited to, the implied warranties of merchantability and fitness for a particular purpose. Da Vinci shall not be liable for any errors or for incidental or consequential damages in connection with the furnishing, performance, or use of this manual, or the examples herein. [. . . ] Press , , to display the input screen , enter all of the known variables and press , , to solve for the unknowns. -PQYP8CTKCDNGU. AOJGPT[4AQJO%AHCTCFHA*\ %QORWVGF4GUWNVUATCFU:. A::%A :A<OAATCF EE Pro for TI-89, 92 Plus Equations RLC Circuits 47 22. 2 Parallel Admittance The admittance of a parallel RLC circuit consists of a magnitude, Ym, and phase angle . Both can be calculated in terms of the conductance G and susceptance B. The conductance G is expressed in terms of resistance R, while the susceptance B is expressed in terms of the inductive and capacitive components BL and BC. c Ym h G= 2 = G2 + B2 Eq. 22. 2. 7 = tan -1 FG G IJ H BK 1 R B = BL + BC -1 BL = L BC = C = 2 f circuit admittance parameters at a frequency of 10 MHz. Example 22. 2 - A parallel RLC Circuit consists of a 10, 000 ohm resistor, 67 henry and . 01 farads. Find the Input and calculated results (upper half) Input and calculated results (lower half) Solution - All of the equations need to be used to solve this problem. Press , , to display the input screen and enter the values of all known variables. -PQYP8CTKCDNGUHA/*\4AQJO. AJGPT[%AHCTCF %QORWVGF4GUWNVU;OAUKGOGPU)AUKGOGPU$. AUKGOGPU $%AUKGOGPUATCFATCFU 22. 3 RLC Natural Response These equations compute the complex frequencies of an RLC circuit. In general, every RLC circuit has two complex frequencies s1 and s2 with real and imaginary parts s1r, s1i, s2r, and s2i. These frequencies are complex conjugates of each other which are computed from the resonant frequency 0, and Neper's frequency , defined by the final two equations. EE Pro for TI-89, 92 Plus Equations RLC Circuits 48 s1r = real - + 2 - 02 e s1i = image - + s2r = reale - - s2i = image - - 1 LC 1 = 2 RC j -0 j -0 j -0 j 2 2 2 2 2 2 Eq. 22. 3. 6 0 = Example 22. 3 A series RLC circuit of Example 22. 1 is used to compute the circuit parameters. Input and calculated results (upper half) Input and calculated results (lower half) Solution - All of the equations are needed to solve the parameters from these given set of variables. Press , , to access the input screen and enter all known variables, press , , to solve for the unknowns. -PQYP8CTKCDNGU. AOJGPT[4AQJO%AHCTCF %QORWVGF4GUWNVUUTATCFUUKATCFU ATCFUUTATCFUUKATCFU 22. 4 Underdamped Case The equations in this section represent the transient response of an underdamped RLC circuit. The classical radian frequency 0 is calculated from the inductance, L and the capacitance, C in Equation 22. 4. 1. The damped resonant frequency d is expressed in equation 22. 4. 3 in terms of 0 and . The voltage across the capacitor v, is defined in terms of two constants B1 and B2. B1 is equivalent to the initial capacitor voltage V0, and B2 is related to the initial inductor current I0, C, d and resistance R. The voltage v has an oscillation frequency of d. 1 LC 1 = 2 RC 0 = Eq. 22. 4. 2 EE Pro for TI-89, 92 Plus Equations RLC Circuits 49 d = 02 - 2 v = B1 e - t cos d t + B2 e - t sin d t B1 = V 0 B2 = - Eq. The initial current in the inductor is 10 mA and the initial charge in the capacitor is 2. 5 V. Calculate the resonant frequency and the voltage across the capacitor 1 s after the input stimulus has been applied. Example 22. 4 - A parallel RLC circuit is designed with a 1000 resistor, a 40 mH inductor and a 2 Calculated Results (Upper display) Calculated Results (Lower display) Solution - All of the equations need to be selected to solve this problem. Press , , and enter the known variables followed by a second press of , , to solve for the unknowns. -PQYP8CTKCDNGU%A(+AO#. AO*4AVAU %QORWVGF4GUWNVUATU$A8$A8XA8 FATUATU 22. 5 Critical-Damping The equations in this section represent the RLC transient response of a critically-damped circuit. [. . . ] These messages include: "One or more equations has no unknowns. . . . . " This message occurs if one or more of the selected equations in a solution set has all of its variables defined by the user. This can be remedied by pressing N, deselecting the equation(s) where all of the variables are defined and resolving the solution set by pressing , , twice. To determine which equation has all of its variables defined, press N to view the equations, select an equation in question by highlighting the equation and pressing , and pressing , , to view the list of variables. A `` next to a variable indicates a value has been specified for that variable by the user. [. . . ]