Questions tagged [laplace-transform]
Questions regarding or involving Laplace Transforms with respect to Electrical Engineering.
330 questions
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How do I estimate the max current of a series RLC circuit during transients?
I have a series RLC circuit with an applied voltage of
$$
v(t) =
\begin{cases}
V_{DC}+V_{AC}sin(\omega_s t), & t\ge0 \\
0, & t<0
\end{cases}
$$
I want to know what the worst case current ...
- 125
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(Co)sine wave generator questions
If we have a circuit with open-loop Α gain equal to 1 and feedback β a 2nd-order differentiator we will get in the output a (co)sine wave. Proof:
$$H(s)=\frac{A(s)}{A(s)\beta(s)+1}=\frac{1}{1+s^{2}}$$ ...
2
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Interpretation of Laplace Variable
Through my study of circuits and signal processing, it is my understanding that the complete response of an LTI system is the sum of a transient response and a steady-state response. When analyzing ...
- 334
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How can I continue to reduce this block diagram to a single-circuit diagram?
What I’ve done so far
Combined W₁ and Wₓ into an equivalent block W₁ₓ (second image).
Moved the summing junction, then combined W₁ₓ in series with W₂ to form W₁ₓ·₂, combined (1/W₁ₓ) in series with W₄...
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Laplace transform; \$G(s)=\frac{1}{s+3}\$ and \$y(0-)=7\$
Consider a first-order system with the transfer function \$G(s) = \frac{Y(s)}{U(s)} = \frac{1}{s+3}\$ and initial condition \$y(0-) = 7\$. Applying a unit impulse at the origin for \$t > 0\$, ...
- 121
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How would you know if this system is stable or not?
I'm having trouble deciding whether a system whose characteristic equation is
\$1200y''(t) + b·y'(t) + (1.02·10^6) y(t) = f(t)\$
(where \$f(t)\$ is a negative unit step that occurs between \$t=10\$ ...
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Laplace transform for linear circuits - Initial value problem with generalized impedances?
I'm currently attempting to generalize a trivial circuit composed of from simple \$R\$, \$C\$ to more complex parasitic \$R\$, \$L\$, \$C\$ modeling of real components. This would be in the context of ...
- 169
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How does Verilog-A realize analog laplace domain transfer functions? [closed]
I am not able to understand how the functions like laplace_nd are implemented in verilog-A? (Laplace_nd takes the coefficients of the numerator and denominator of a s-domain transfer function and ...
- 279
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How to find the Inverse Laplace Transform of \$\frac{1}{(s^2+1)^2}\$ or \$\frac{s^2}{(s^2+1)^2}\$ by PFE?
From the Laplace transform table formula 11 and 12, we have \$\mathcal{L^{-1}}\{\frac{s^2}{(s^2+1)^2}\} =\frac{1}{2}(sin t + tcos t)\$ and \$\mathcal{L^{-1}}\{\frac{1}{(s^2+1)^2}\} =\frac{1}{2}(sin t -...
- 131
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Nodal analysis with inverse Laplace transform of a simple RC circuit with an AC voltage source gone wrong?
simulate this circuit – Schematic created using CircuitLab
This is a simple RC circuit with an AC voltage source, \$E = V_0 \cos(\omega t)\$. In the sinusoidal state, \$Y_{\text{resistor}} = G\$ ...
- 13
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Conditions for network stability [closed]
Apart from poles lying in the left half of the \$s\$-plane, there is one more condition for stability:
If the transfer function is \$H(s) = N(s)/D(s)\$ then degree of \$N(s)\$ should be less than that ...
- 43
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Trying to understand the exact math behind use of decoupling capacitors
From what I have read so far decoupling caps help in reducing the supply droop due to trace inductors in case the load draws large current transients. The capacitor works to supply the current ...
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Find v(s) in the circuit below(voltage through the capacitor)
Capacitor initial conditions = 10v, inductor = 2A. Input is the current font.Find voltage through the capacitor
I think i got it but i have no clue whether its right or not, would like to know what i ...
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Solving complex opamp circuits
I'm having some troubles understanding how to solve complex circuits with opamps like the following:
During my lab course (I'm a physics major) the professor showed us the solution of very simple ...
- 87
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Transfer function of differential controller
I found an op amp circuit that is designed to be a derivative controller (D-controller)
simulate this circuit – Schematic created using CircuitLab
and the transfer function $$ \frac{V_o}{V_i} = -...
- 61