Pulse Response Lab help

Discussion in 'Homework Help' started by testing12, Mar 17, 2011.

  1. testing12

    Thread Starter Member

    Jan 30, 2011
    80
    2
    Hello eveyone,

    I would like to know if i can use i(t) = v/Rth for the following curcuit and data. We tried to get a screen shot for i(t) but it didnt work out (very stressful lab). I managed to piece together the voltage from the file.

    Here is what i have:
    [​IMG]

    My theoretical value for the time constant (Tau) is 10.7 microseconds (from the circuit above). Can someone please confirm?

    Also, can someone help me to obtain i(t) so i could compare the emperical value of tau to the theoretical value?

    I should also mention we have been studying pulse response with DC SOURCES, this is probably where the trouble comes in for the function generator for me. and we have been using the following formula:

    v(t) = V(infinity) + [v(0) - V(infinity)]e^(-t/tau)

    tau= Rth*c
    my Rth = 1070 ohms.

    Thank you for your help!
     
    Last edited: Mar 17, 2011
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    Your theoretical time constant is correct.

    With regard to the experimental value of the time constant you would estimate from your graph the time after t=0 at which the capacitor voltage has reached 63.2% of its steady-state value. That time would correspond to the time constant.
     
  3. testing12

    Thread Starter Member

    Jan 30, 2011
    80
    2
    Thank you I will post back with my current graph later tonight and try to obtain tau from that also.

    It would be great to obtain i(t) from the voltage data on channel 1 because i lost the data from channel 2 and only have a rough sketch of voltage at channel 2.

    My final task is to complete the following table:

    [​IMG]

    I understand how Rtotal and tau are obtained theoretically and empirically, but not ic(max) (theoretically yes) but not empirically. The reason is that ic is max at t=0, (for the above voltage graph) and it looks like a line approaching infinity, how do i put a value on ic, max in that case?
     
    Last edited: Mar 18, 2011
  4. testing12

    Thread Starter Member

    Jan 30, 2011
    80
    2
    bump please
     
  5. Adjuster

    Well-Known Member

    Dec 26, 2010
    2,147
    300
    Your graph looks as if the generator was producing alternating negative and positive pulses, but only positive pulses were captured. Unless you have data for the missing parts of the waveform, it will be difficult to estimate the peak current. One way forward might be to assume that the waveform was symmetrical about 0V, but this may not be correct.

    Since you do not seem to have the very first part of the rising edge recorded, you might try to estimate the initial rate of rise by measuring the slope of the start of the falling edge. You may object that the slopes may not be the same: maybe so, but do you have better information? Clearly you would need to expand the X axis around the area of interest to get an estimate of the initial slope.

    Once you had that, you could estimate the initial current from I = C*dV/dt. Unfortunately, the estimated slope will be affected by the presence of the 20 ohm resistor, so this method would not be all that accurate.

    Another way to estimate the peak current would be to assume that the total peak to peak voltage appears instantaneously across the total 1070 ohms. This assumes that the generator rise and fall times are negligible compared to R*C. Probably so, but not necessarily.

    Here it would be vital to know whether the generator was producing negative as well as positive voltages, as in the latter case the peak to peak voltage could be double the measured peak value. Your measured amplitude is about 4.8V, so the current could be approximately 4.8V/1070Ω = 4.5mA, or more likely something like twice as much, 9.0mA. Again, if the generator output is alternating but not symmetrical, this answer will not be correct.
     
  6. testing12

    Thread Starter Member

    Jan 30, 2011
    80
    2
    Excellent post thank you. I think you mentioned exactly what I was having trouble with as well as answered my question about ic. We are studying pulse response of a rc circuit with a dc source, the function generator does produce negative and positive voltages. The lab manual asks for a 3 volt peak voltage and square wave at 1 kHz. Then we were asked to move the vertical position on the scope to the bottom of the screen and graph by hand. I think this was done to simulate what we would see if it were a true dc source being applied rather then an alternating source. In addition the time base was set to 100 microseconds as to see only half the pulse. I think it would be safe to use vs/rth for ic max, any thoughts?
    Thank you so much for your replies.
     
    Last edited: Mar 18, 2011
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