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Function Generator Internal Resistance Theory

Discussion in 'Electronics Homework Help' started by PumpkinBreath, Feb 3, 2015.

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  1. PumpkinBreath

    PumpkinBreath

    2
    0
    Feb 1, 2015
    Hello all

    I am enrolled on a foundation program for electrical and electronic degree students. We have been set a simple test circuit to introduce us to the topic to test the internal resistance of a Function Generator (FG). I generated a DC Voltage of 0.0063V, coupled with an AC output Voltage of 1.003V at a frequency of 1.0048KHz.

    Using this output we tested the Internal Resistance of the Function Generator (Ri), through Simulated Variable Resistor (R) in parallel with a Digital Multimeter, at varying resistance values (20-200 Ohms, collectively; R). A table was produced to show the different Resistance values (R) against the Voltage across the Simulated Variable Resistor (Vr).

    The schematic and the graph are attached.

    So, then we were told to draw a line on the graph at Vr = 0.5V and use a Line of Best Fit through our graph to find a value for Ri where the X-Y axis crossed. From this line we were asked to derive an equation for Vr based on the:

    Supply Voltage (Vs)
    Internal Resistance of FG (Ri)
    Varied Resistance (R
    )

    I calculated that since;

    Vs = I(R+Ri) then,
    Vs = IRi + Vr thus
    Vr = Vs - IRi

    This makes sense seeing that:

    Vs = 1V
    Vr = 0.5V
    Ri = 65 Ohms
    I = 0.0077A therefore;

    1 - (7.7^10-3 x 65) = 0.5V

    I'm happy so far. So then they ask what is Vr when R = Ri?

    My query is that I don't understand this question.

    Surely when the value of R = Ri, then Vr will still = Vs - IRi because to calculate the Voltage across the Varied Resistor we still have work out the Supply Voltage (Vs) minus the sum of the Two Resistances multiplied by the Current (I)?

    Am I misreading the question perhaps?

    Any advice/guidance on this would be greatly appreciated because I am stumped as to whether they are looking for another formula or if I'm correct in my idea that nothing should change.

    Thanks very much!!
     

    Attached Files:

  2. Harald Kapp

    Harald Kapp Moderator Moderator

    11,646
    2,691
    Nov 17, 2011
    First let me welcome you to electronicspoint.

    You're probably thinking too complex. Surely the equation you derived is valid for any resistance R, therefore also for R=Ri. When you look at the series connection of Ri and R from the "pins" of the internal ideal voltage source, what do you see? This connection (2 resistors with a center tap) is such a common circuit that there is a name for it. Hint: what does this circuit do in a mathematical sense to the internal voltage? Or in other words: how can you express VR=f(Vinternal, R, Ri)? It is a very simple equation that gives the circuit its name.
    From that simple equation, what is VR when R=Ri? You don't even need concrete vaules for R and Ri because for R=Ri some simple math will have their absolute values canceled.

    I hope this helps. Come back if you need more guidance.
     
  3. PumpkinBreath

    PumpkinBreath

    2
    0
    Feb 1, 2015
    Hi Harald

    Thanks for your welcome note and your reply.

    Can I just clarify a couple of points please?

    Firstly, when you say; what does this circuit do in a mathematical sense to the internal voltage? Are you referring to the supply voltage or the voltage across the internal resistor?

    Secondly, how can you express VR=f(Vinternal, R, Ri)? What it symbolised by f?

    Thanks for your help on this.

    Regards
     
  4. Harald Kapp

    Harald Kapp Moderator Moderator

    11,646
    2,691
    Nov 17, 2011
    There is only one voltage source in your diagram, that is the one I mean.

    A general symbol for an expression f(x)=some function of the variable x, e.g. y=f(x), f(x)=x² - not that this is the function required here,
    You need to express Vr= (some equation with variables Ri, R and Vinternal).
     
  5. Merlin3189

    Merlin3189

    250
    69
    Aug 4, 2011
    Can I firstly congratulate PB on writing a question which is much clearer than many asked here.
    but I think here they are asking, what is the numerical value of Vr
    Saying Vr=Vs - IRi is not an answer, because you do not know what I is.
    When they asked earlier for an equaton for Vr, it was not good enough to give Vr=Vs-IRi because you cannot work out Vr without knowing I, and you don't know I

    So what you need is what Harald is getting at,
    Vr = an equation just using things they said, Vs, R and Ri

    That is something you can work out from your graph.
    I guess that is why they told you to do a straight line of best fit - it tells you what the equation is. It may help to remind you that a straight line equation is y = mx + c where m is the slope and c is the intercept on the y axis. That is probably something you are expected to know.

    Or, as Harald says, you can work out a formula from your circuit knowledge - just get rid of I.
     
    Harald Kapp likes this.
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