Electric circuits 2 (XE31EO2)

Basic problems for written part of the exam

Problems covers lectured subjects in following themes :

  1. Periodic nonsinusoidal steady state.
  2. Transient  analysis  (in time domain). For transient analysis problems the selection of the method is arbitrary, so problems are identical for both time domain and operational analysis.
  3. (Operational) transient analysis.
  4. Transfer characteristics of the linear circuis.
  5. Distributed circuits - lossless transmission line.
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  1. Periodic nonsinusoidal steady state

    1. The circuits according to the table below are supplied by the voltage source . Find the waveform of the current i(t ) drained from the source in the steady state for the circuit parameters listed below the corresponding circuit diagram.

      problem 1



      solution       		problem 2



      solution
      problem 3



      solution       		problem 4



      solution
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    2. The circuits acording to the table below are supplied by the current source  . Find the waveform of the input voltage u(t ) in the steady state for the circuit parameters listed below the corresponding circuit diagram.

      problem 1



      solution       		problem 2



      solution
      problem 3



      solution       		problem 4



      solution
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    3. The circuits according to the table below are supplied by the voltage source  . Find the waveform of the output voltage u 2(t ) in the steady state for the circuit parameters listed below the corresponding circuit diagram.

      problem 1



      solution       		problem 2



      solution
      problem 3



      solution       		problem 4



      solution
      problem 5





      solution       		problem 6



      solution
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    4. The circuits according to the table below are supplied by the current source . Find the waveform of the current  ix(t) in the steady state for the circuit parameters listed below the corresponding circuit diagram.

      problem 1



      solution       		problem 2



      solution
      problem 3



      solution       		problem 4



      solution
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  2. Transient analysis (in time domain).

    1. The circuits according to the table below are connected to the DC voltage source u1(t) = U1 at time t = 0. Find the waveform of the voltage u2(t), if the initial energy of the capacitor / inductor was zero (was not charged for t < 0). Draw the founded waveform. The circuit parameters are listed below the according circuit.

      problem 1



      solution       		problem 2



      solution
      problem 3



      solution       		problem 4



      solution
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    2. The circuits according to the table below contains two DC voltage sources U01, U02. The switch P is switched from the position 1 to the position 2 at t = 0. Find the waveform of the voltage ux(t). The circuit was in the steady state before the switching of the switch. Draw the founded waveform. The circuit parameters are listed below the according circuit.

      problem 1



      solution       		problem 2



      solution
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    3. The circuits according to the table below contains two DC voltage sources U01, U02. The switch P is switched from the position 1 to the position 2 at t = 0. Find the waveform of the current ix(t). The circuit was in the steady state before the switching of the switch. Draw the founded waveform. The circuit parameters are listed below the according circuit.

      problem 1



      solution       		problem 2



      solution
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    4. The circuits according to the table below contains DC voltage source U0. The switch S is switched off at t = 0. Find the waveform of the voltage ux(t). The circuit was in the steady state before the switching of the switch. Draw the founded waveform. The circuit parameters are listed below the according circuit.

      problem 1



      solution       		problem 2



      solution
      problem 3



      solution       		problem 4



      solution
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    5. The circuits according to the table below contains DC voltage source U0. The switch S is switched off at t = 0. Find the waveform of the current ix(t). The circuit was in the steady state before the switching of the switch. Draw the founded waveform. The circuit parameters are listed below the according circuit.

      problem 1



      solution       		problem 2



      solution
      problem 3



      solution       		problem 4



      solution
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    6. The circuits according to the table below contains DC current source I0. The switch S is switched on at t = 0. Find the waveform of the current ix(t). The circuit was in the steady state before the switching of the switch. Draw the founded waveform. The circuit parameters are listed below the according circuit.

      problem 1



      solution       		problem 2



      solution
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    7. The circuits in the table below are supplied by the DC current source I0. The switch S is switched on at t = 0. Find the waveform of the voltage ux(t). The circuit was in the steady state before the switching of the switch. Draw the founded waveform. The circuit parameters are listed below the according circuit.

      problem 1



      solution       		problem 2



      solution
      problem 3



      solution       		problem 4



      solution
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  3. (Operational) transient analysis

    The problems are same as well as in the previous  theme, as used method of the solution is not imposed and depends only on your will.
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  4. Transfer characteristics of the linear circuits 

    1. For the circuits according to the table below compute:
      1. Transfer function P(p) = U2(p) / U1(p) and convert it into the form suitable for drawing of frequency characteristics. Draw the asymptotic magnitude and phase frequency responses in logarithmics coordinates and mark breaking frequencies and constant values (of the horizontal asymptots).
      2. Unit step response a(t) and sketch it.
      3. Unit impulse response w(t) and sketch it.
      The circuit parameters are listed below the according circuit.
      Note: In the written part of the exam will be required calculation of one from this options only, that is either transfer function, or the unit step response, or the unit impulse response.

      problem 1







      solution: P(p), a(t), w(t)       		problem 2




      solution: P(p), a(t), w(t)
      problem 3




      solution: P(p), a(t), w(t)       		problem 4




      solution: P(p), a(t), w(t)
      problem 5






      solution: P(p), a(t), w(t)       		problem 6




      solution: P(p), a(t), w(t)
      problem 7




      solution: P(p), a(t), w(t)       		problem 8




      solution: P(p), a(t), w(t)
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    2. For the circuits according to the table below compute:
      1. Transfer function P(p) = U2(p) / U1(p) and convert it into the form suitable for drawing of frequency characteristics. Draw the asymptotic magnitude and phase frequency responses in logarithmics coordinates and mark breaking frequencies and constant values (of the horizontal asymptots).
      2. Unit step response a(t) and sketch it.
      3. Unit impulse response w(t) and sketch it.
      The circuit parameters are listed below the according circuit.
      Note: In the written part of the exam will be required calculation of one from this options only, that is either transfer function, or the unit step response, or the unit impulse response. .

      problem 1







      solution: P(p), a(t), w(t)       		problem 2




      solution: P(p), a(t), w(t)
      problem 3




      solution: P(p), a(t), w(t)       		problem 4




      solution: P(p), a(t), w(t)
      problem 5






      solution: P(p), a(t), w(t)       		problem 6




      solution: P(p), a(t), w(t)
      problem 7




      solution: P(p), a(t), w(t)       		problem 8




      solution: P(p), a(t), w(t)
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  5. Distributed circuits - losselss transmission line

    1. To the input of the lossless transmission line with parameters L, C at t = 0 is connected the DC voltage source U0 with internal resistance Ri = R0. Find the length l of the line and determine how the line is terminated, if the waveform of the voltage measured at the beginning of the line is only one short impulse of the amplitude Ua = U0/2 and the width of the pulse is t0. 


      solution


    2. Determine, how is necessary to terminate the transmission line to avoid reflection of the pulses transmitted from the beginning of the transmission line. Find the value of the load, if the parameters of the transmission line are L, C . 


      solution


    3. To the input of the lossless transmission line with parameters L, C of the length l is connected voltage source ui(t) with internal resistance Ri = R0. The voltage source sended into the transmission line one very short voltage pulse of the amplitude Ui and length t0. Draw the waveforms of the voltages u1(t) and u2(t) at the beginning and end of the transmission line, if the line is open terminated.


      solution


    4. To the input of the transmission line with parameters L, C of the length l is connected voltage source ui(t) with internal resistance Ri = R0. The voltage source sended into the transmission line one very short voltage pulse of the amplitude Ui and length t0. Draw the waveforms of the voltages u1(t) and u2(t) at the beginning and end of the transmission line, if the line is short terminated.


      solution


    5. To the input of the transmission line with parameters L, C of the length l is connected voltage source ui(t) with internal resistance Ri = R0. The voltage source sended into the transmission line one very short voltage pulse of the amplitude Ui and length t0. Draw the waveforms of the voltages u1(t) and u2(t) at the beginning and end of the transmission line, if the line is terminated by resistor Rs = R0.


      solution


    6. To the input of the transmission line with parameters L, C of the length l is connected voltage source ui(t) with internal resistance Ri = R0. The voltage source sended into the transmission line one very short voltage pulse of the amplitude Ui and length t0. Draw the waveforms of the voltages u1(t) and u2(t) at the beginning and end of the transmission line, if the line is terminated by resistor Rs.


      solution


    7. To the input of the transmission line with parameters L, C of the length l is connected voltage source ui(t) with internal resistance Ri = R0. The voltage source sended into the transmission line one very short voltage pulse of the amplitude Ui and length t0. Draw the waveforms of the voltages u1(t) and u2(t) at the beginning and end of the transmission line, if the line is terminated by resistor Rs. 


      solution


    8. To the input of the transmission line with parameters L, C of the length l is connected DC voltage source Ui0 with internal resistance Ri = R0.  Draw the waveforms of the voltages u1(t) and u2(t) at the beginning and end of the transmission line, if the the end of the line line is opened.


      solution


    9. To the input of the transmission line with parameters L, C of the length l is connected DC voltage source Ui0 with internal resistance Ri = R0.  Draw the waveforms of the voltages u1(t) and u2(t) at the beginning and end of the transmission line, if the the end of the line line is shorted


      solution


    10. To the input of the transmission line with parameters L, C of the length l is connected DC voltage source Ui0 with internal resistance Ri = R0.  Draw the waveforms of the voltages u1(t) and u2(t) at the beginning and end of the transmission line, if the the line is terminated by resistor  Rs = R0.


      solution


    11. To the input of the transmission line with parameters L, C of the length l is connected DC voltage source Ui0 with internal resistance Ri = R0.  Draw the waveforms of the voltages u1(t) and u2(t) at the beginning and end of the transmission line, if the the line is terminated by resistor Rs.


      solution


    12. To the input of the transmission line with parameters L, C of the length l is connected DC voltage source Ui0 with internal resistance Ri = R0.  Draw the waveforms of the voltages u1(t) and u2(t) at the beginning and end of the transmission line, if the the line is terminated by resistor Rs.


      solution


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