Problem 11.8 - CHALLENGE PROBLEM! Phasor Analysis at Two Frequencies
*
* NOTE: This is a three-part problem.
* 1. Use hand calculation (or PSpice steady-state analysis) to find
* the voltage across the parallel circuit FOR EACH OF THE CURRENT
* SOURCES SEPARATELY. Note especially that each of the sources is
* at a different frequency. Solve for the initial (t=0) voltage
* on the capacitor and the inductor current from the steady state
* sinusoidal time-function voltages at each separate frequency.
* 2. Use the SIN function and .TRAN analysis for each of the sources
* separately. Obtain PROBE graphs of the voltage response of the
* circuit for each of the separate sources. The PROBE graphs will
* not show a start-up transient in the waveforms if you have
* correctly calculated the initial conditions for each source.
* 3. Obtain the total solution by using the two SIN sources together.
* The initial conditions will be the simple addition of the t=0
* voltage and current magnitudes from the separate analyses above.
* Obtain a PROBE graph of the complete voltage response.
*
* The VERY important message contained in Part 3 is that the sum of
* sinusoidal waveforms at different frequencies is NOT A SINUSOIDAL
* WAVEFORM. You cannot add, subtract, multiply, or divide phasors
* resulting from analyses at different frequencies.
*
*Part 1: Write two separate steady-state analysis programs (or hand-
* calculate) to find the steady state response and the t=0 initial
* conditions. This exercise is left totally to the student. You may
* exit this program and write a separate program, or insert your
* program immediately below.
*
* (insert steady-state program here, or hand calculate values.)
*
* SOLUTION: For the source IA, the t=0 values are 76.8 amperes and 3.6
* volts. For the source IB, the t=0 values are -7.68 amperes
* and 1.44 volts.
*
*
Problem 11-8, Part 2: CHALLENGE PROBLEM! Circuit Analysis at One Frequency
*
* Choose one source to be the active source. Solve for the time-domain
* response. Obtain a PROBE graph of the response to this source.
*
.OPT NOPAGE NOBIAS
IA 0 1 SIN(0 90 ??????? 0 0 90)
R1 1 0 .11111
L1 1 0 .0625 IC=???? ; Enter initial conditions due to IA
C1 1 0 4 IC=????
.TRAN ??? 20 0 ??? UIC ; Use a 20-second analysis interval
; for each of the sources. Complete
; the .TRAN command statement.
.PROBE
.END
Problem 11.8, Part 3. CHALLENGE PROBLEM! Circuit Analysis at One Frequency
*
* Choose one source to be the active source. Solve for the time-domain
* response. Obtain a PROBE graph of the response to this source.
*
.OPT NOPAGE NOBIAS
IB 0 1 SIN(0 36 ?????? 0 0 90)
R1 1 0 .11111
L1 1 0 .0625 IC=???? ; Enter initial conditions due to IB.
C1 1 0 4 IC=????
.TRAN ??? 20 0 ??? UIC ; Complete the .TRAN command.
.PROBE
.END
Problem 11.8, Part 4. CHALLENGE PROBLEM! Complete Time-Domain Response
*
* Make both sources active together in the circuit. A frequency
* domain solution is meaningless in this case. The total response
* can only be expressed as the superposition (sum) of the two time
* domain responses from Parts 2 and 3. Use PROBE to obtain a graph
* of the total time domain response. Add the expression for the
* time domain (superposition) solution. The two curves must agree.
*
.OPT NOPAGE NOBIAS
IA 0 1 SIN(0 90 ??????? 0 0 90)
IB 0 1 SIN(0 36 ??????? 0 0 90)
R1 1 0 .11111
L1 1 0 .0625 IC=???? ; Enter the sum of the initial
C1 1 0 4 IC=???? ; conditions from the above.
.TRAN ??? 20 0 ??? UIC ; Complete the .TRAN command.
.PROBE
.END