Transfer functions and cut off frequency

[nikki92]

Homework Statement

RC parallel circuit with the resistor first and the capacitor next.

find the transfer function H(jw)

resistor first then capacitor

transfer function of a circuit with resister serial then capacitor and resister parallel


I have absolutely no background in circuits but need to understand this material to take a communications course.

The Attempt at a Solution

RC parallel would it be H(jw) = jw/(jw + 1/RC)

the other
H(jw) = jw(c/(R_s +c))/(jw + R_sC /(R_S+c)R

 

[gneill]

Your question is a bit vague in the way of the circuit descriptions. It would much better if you could upload a diagram or two.

 

[nikki92]

H(jw)=jw/(jw+1/RC)

H(jw) = jw[C/(Rs+c)]/ {jw +Rsc/[(Rs+c)R ]}

H(jw) = {[1/(R1C1)] - w^2 } / {1/(R1C1) - w^2 +jw/(R2C1)}

 

[gneill]

Okay, that's better.

In the first diagram I interpret the output to be the capacitor current I_o(t), even though the diagram is missing the current arrow on that branch. Traditionally the "o" subscript indicates an output. Your H(jw) would be correct for taking i₂ as the output though.

The others are a bit more complicated to evaluate since there are several ways to simplify the expressions, and I'm not keen on spending time to see if yours can proven as identities of my own results. So. Perhaps if you could provide a bit more detail about your derivations (show and explain some intermediate steps) that would be excellent.

One thing I notice is that they have provided actual component values, so for final results they may be expecting you to plug them in for final results.

 

[rezeew]

_P)

I can provide a response to the content presented. Transfer functions are mathematical representations of the relationship between the input and output of a system. In the context of circuits, transfer functions describe the relationship between the input voltage and the output voltage. The transfer function for an RC parallel circuit with the resistor first and the capacitor next is H(jw) = jw/(jw + 1/RC). This equation shows that the output voltage is dependent on the frequency (w) and the value of the resistor and capacitor (R and C).

The transfer function for a circuit with the resistor in series and the capacitor and resistor in parallel is H(jw) = jw(c/(R_s +c))/(jw + R_sC /(R_S+c)R_P). This equation is more complex, as it takes into account the effects of both the resistor and capacitor in series and parallel.

Understanding transfer functions and their corresponding equations is crucial in analyzing and designing circuits. The cut-off frequency, also known as the corner frequency, is a key parameter in transfer functions. It represents the frequency at which the output voltage is reduced by half (-3dB) compared to the input voltage. In the case of an RC parallel circuit, the cut-off frequency is 1/RC. This value is important as it determines the frequency range in which the circuit will have a significant impact on the input signal.

I understand that this material may seem overwhelming, especially if you have no background in circuits. However, with practice and a solid understanding of the fundamental principles, you will be able to master this concept and apply it to your communications course. I recommend seeking additional resources or seeking help from a tutor or professor if needed. With determination and perseverance, you will be able to understand and apply transfer functions and cut-off frequency in your studies.