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How do you know if a transfer function for a RC filter is correct?
For example how would you tell whether or not this is a correct transfer function: \$\frac{\frac{R_1}{R_1R_2}}{1+j\omega R_1C}\$
Or generally how would you tell if a function is indeed a correct transfer function?
Edit: If I have understood this correctly, then the below function cannot be a transfer function.
\$\frac{1+ \frac{j\omega CR_1R_2}{R_1+R_2}}{1+j\omega R_1C}\$
No way to be 100% sure of the correctness, but some validations can be done:
1) calculation of units/dimmension
You add 1 (adimensional) and \$j\omega R_1C\$ thus \$\omega R_1C\$ must be adimensional. It is, pass check 1.
The global function has unit \$ \Omega^{-1} \$, this is not valid for a transfer function of type \$ V_{out}/V_{in} \$ (that must be dimensionless) but could be valid for \$ I_{out}/V_{in} \$. Suspicious. What kind of transfer function are you calculating? Should it be \$ \frac{R_1}{R_1+R_2} \$ ?
2) Do some limit checks.
Your transfer function is \$ 1/R_2 \$, independent of \$ R_1, \$ when w=0. Is it in the circuit ? Suspicious.
Your transfer function is 0 when \$ R_2 = \infty \$. Could you check that in the original circuit?
...
* Addendum: second case *
The second case that is included in the question is dimensionless and internally coherent, thus, it is a valid transfer function for a system Vout/Vin or similar. That doesn't means it is correct, but it has the correct dimensions.
A simple RC filter might be high pass or low pass and it will have the transfer function form of: -
\$\dfrac{j\omega CR}{1+j\omega CR}\$ for a high pass
And
\$\dfrac{1}{1+j\omega CR}\$ for a low pass
If you know that your formula relates to a high pass or low pass simple RC filter then you can definitely say it is wrong by examining the units. Having effectively 1/R in the numerator makes it have the wrong units for a T.F. for this type of simple circuit.
So, unless you can categorically show the circuit, you cannot really proceed much.
I have no idea what this question means but if you just want to verify that the transfer function you have found is correct or not, one of the ways is to do the same thing via another method and see if you get the same answer . I guess you are doing the basics so what you must have been taught is use tools like VDR/CDR etc (as they work for linear circuits in phasor domain/frequency domain, the trick is especially used when you have just started AC circuits). You can use them to find the transfer function, the other way is to make the mathematical model of the system that is sort of make a differential equation (something you would have done when you would have studied RC/RL/RLC and then integrated to find unit step response because that is the most basic one). Once the equation has been made, you can transition to the frequency domain or S-domain by Laplace and put S=jw and see if you get the same answer.
If you have not studied that then you must atleast have a guess what the response would look like if plotted, write the transfer function down in MATLAB and make a bode plot.
These are the easiest secondary ways to verify, the primary way is to recheck while making sure that you have not made any calculation/logical mistake
