Trying to understand how to calculate transfer function of RLC circuit

[Shay]

Hey,
My girlfriend got this question which I don't understand.

The question is:
"What is the absolute value of the transfer function of Input Current / Input Voltage, write your answer in mA"
How do I write a ratio in mA?
Is the problem solvable?
Thanks.

[Benta]

It's NOT solvable.
Who on earth thought this one up? Must be a trick question.

[Shay]

It's NOT solvable.
Who on earth thought this one up? Must be a trick question.

Ah, as I suspected. This is neither the first nor the last time I’ve had to dispute issues with the tutor. I’ve had to argue with him on multiple occasions, as he frequently make errors in these types of questions. Unfortunately, the lecturer does not review the questions, and students are graded based on them. 

[fzabkar]

Use a phasor diagram.

Xl = wL = 2 . pi . f . L

Xc = 1 / wC = 1 / (2 . pi . f . C)

net imaginary component = abs ( Xl - Xc )  = X

real component = R

total impedance = sqrt( R ^2 + X ^2 ) = Z

Iin / Vin = 1 / Z

[coppercone2]

95 KHz DC signal?

The trick is that the node name is actually for some reason 95KHz. You solve it for DC voltage, which is not specified.

[MrAl]

Hey,
My girlfriend got this question which I don't understand.

The question is:
"What is the absolute value of the transfer function of Input Current / Input Voltage, write your answer in mA"
How do I write a ratio in mA?
Is the problem solvable?
Thanks.

Maybe he really wanted you to write the answer in units of bananas per second

If this is a real question then it can be interpreted in different ways, really.  You'd have to find out which way, and may have to go over his head.
For example, if we are to take the voltage to be a constant, then the answer can be written in amps or milliamps.  Not sure why he would want to do that though.
He also maybe meant to write the answer in milliunits but had amperes stuck in his head too so wrote 'ma' instead.

Also suspect is the phrase "absolute value".
I don't think the absolute value has any real use for this application, what he probably meant was to find the magnitude, which is often written the same but has a different calculation:
magnitude of x=|x|
but since here 'x' is a vector (interpreted as just an AC quantity) it's not the same as abs(x) it's really sqrt(r^2+i^2) with 'r' the real part and 'i' the imaginary part, also called the 'norm'.

[vk6zgo]

95 KHz DC signal?

The trick is that the node name is actually for some reason 95KHz. You solve it for DC voltage, which is not specified.

That is just the dumbarse way simulators display ac sources as a DC generator.
A moment's thought reveals that the instantaneous transfer function of a passive network like that one is going to vary with frequency.
Both axis of a transfer function graph at any given frequency can be shown with mA as the units in both the independent & dependent variables.

To show the transfer function as a mathematical expression instead of a graph, the frequency dependency of the reactive components must be shown.
It is too long ago when I did this stuff, & I'm but a lowly Tech, so you clever "Ginger Beers" should be able to work it out!

[fzabkar]

95 KHz DC signal?

The trick is that the node name is actually for some reason 95KHz. You solve it for DC voltage, which is not specified.

If Vin is DC, then the steady-state value of I = 0.

So Iin / Vin = 0.

[coppercone2]

Solving the steady state form unless asked otherwise is the proper way to avoid exploitation 

[fzabkar]

Solving the steady state form unless asked otherwise is the proper way to avoid exploitation 

I would point out all the errors, rephrase the question as I understood it, and then submit an answer in units of milliamps per volt.

[TimFox]

95 KHz DC signal?

The trick is that the node name is actually for some reason 95KHz. You solve it for DC voltage, which is not specified.

That is just the dumbarse way simulators display ac sources as a DC generator.
A moment's thought reveals that the instantaneous transfer function of a passive network like that one is going to vary with frequency.
Both axis of a transfer function graph at any given frequency can be shown with mA as the units in both the independent & dependent variables.

To show the transfer function as a mathematical expression instead of a graph, the frequency dependency of the reactive components must be shown.
It is too long ago when I did this stuff, & I'm but a lowly Tech, so you clever "Ginger Beers" should be able to work it out!

A proper display for an AC source in simulation software includes polarity indication, so that phase measurements made at other nodes in the circuit have a reference for comparison.

[CatalinaWOW]

While awkwardly stated, this problem is generally solvable, and pretty easy if you treat each component as a complex impedance.

First, the awkward part.  This is a series circuit so the current is the same in each component.  In mA the transfer function is one.  But the teacher or tutor who will give full credit for this answer is rare, so writing the voltage transfer function would be necessary. 

Here it is just a simple voltage divider, with the resistor and inductor as the upper leg and the capacitor as the lower  leg.  Complex impedance of an inductor is jwL and of a capacitor is 1/jwC.