# S domain analysis problem, just need a little help

• Derill03
In summary, the conversation discusses finding expressions for v1 and v2 using nodal analysis. The equations for v1 and v2 involve a current source and 2 ohm resistor in series, which may be ignored for nodal analysis. The capacitor impedance is also mentioned, with the correct value being 5/s. The final expression for v2 is ((v1-v2)/(5/s)) - v2/2s - 5/s.
Derill03
Okay i need to find expressions for v1 and v2 and I am using nodal analysis:

these are not the final the equations just initial equations by first look

I am good finding expression for v1,
(2/s)-(v1/1)-((v1-v2)/(2/s)) = 0

Where i am stuck is with the current source and 2 ohm res. in series

For v2,
((v1-v2)/(2/s))-(v2/2s)-(v2/2)-(5/s) = 0 this is my derivation that I am unsure of

the reason i think this is wrong for v2 is in my head i see instead of v2/2 - 5/s i see something like ((v2-v)/2)-(5/s)? where v is voltage between current source and res

Can anyone help me understand where I am right or wrong thanks

**BTW see attachment for circuit**

#### Attachments

• circuit.jpg
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For nodal analysis you're only concerned with summing the currents. The 2Ω resistor in series with the 5u(t) current source is not going to alter that current that it pulls from the V2 node. So ignore the resistor!

FYI, your entries for the capacitor impedance look a bit off. 1/(s*200 mF) should yield something like 5/s.

so would v2 be:

((v1-v2)/(5/s)) - v2/2s - 5/s?

my mistake on the cap transformation it is 5/s which is equal to 1/0.2s my bad

Derill03 said:
so would v2 be:

((v1-v2)/(5/s)) - v2/2s - 5/s?

my mistake on the cap transformation it is 5/s which is equal to 1/0.2s my bad

That looks fine

Based on the nodal analysis equations provided, it seems like you are trying to solve for the voltages v1 and v2 in a circuit with a current source and a 2 ohm resistor in series. It is important to note that nodal analysis is a method used to solve for unknown voltages in a circuit, not currents. Therefore, your equations for v1 and v2 should only include voltage terms, not current terms.

In your equation for v1, it looks like you are using the current division rule to solve for the current through the 2 ohm resistor. However, this is not necessary since you are already using nodal analysis to solve for the voltage across the 2 ohm resistor.

For v2, it is correct to use the current source and 2 ohm resistor in series, as shown in your equation. However, the voltage term v2/2 should be multiplied by the conductance (1/2) instead of the impedance (2) since it is in series with a current source. Additionally, the voltage term (v2-v)/2 should be multiplied by the impedance (2) since it is in parallel with the current source.

I would recommend redrawing the circuit and double-checking your equations to ensure that all voltage terms are correctly represented. Remember to also consider the direction of the current through each element when writing your nodal equations. I hope this helps and good luck with your analysis!

## What is S domain analysis?

S domain analysis is a mathematical technique used to analyze and understand the behavior of linear systems in the frequency domain. It involves converting the time-domain representation of a system into the frequency-domain, using the Laplace transform.

## Why is S domain analysis important?

S domain analysis is important because it allows us to easily analyze and understand the behavior of complex systems using mathematical tools. It also helps in designing control systems for various engineering applications.

## What are the steps involved in S domain analysis?

The steps involved in S domain analysis include modeling the system, applying the Laplace transform to obtain the transfer function, analyzing the transfer function using various techniques, and then converting the results back to the time-domain if necessary.

## What are the advantages of S domain analysis?

One of the main advantages of S domain analysis is that it allows us to easily solve complex mathematical equations involving differential equations. It also provides a clear understanding of the behavior of a system in the frequency domain, which is crucial in designing control systems.

## What are the limitations of S domain analysis?

S domain analysis is limited to linear systems, meaning that it cannot be applied to nonlinear systems. It also assumes that the system is time-invariant, which may not always be the case in real-world applications. Additionally, it requires strong mathematical skills and knowledge to perform the analysis accurately.

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