# Questions tagged [laplace-transform]

Questions regarding or involving Laplace Transforms with respect to Electrical Engineering.

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### Why does MATLAB show a pole in bode plot of an underdamped second order system at natural frequency?

I am using the sisotool in MATLAB to obtain the bode plot of the following transfer function: MATLAB marks a pole at wo which is approximately 11.18 What is the meaning of this? How would you even ...
57 views

### Integral Controller design

For this system, what method do I use to select a value of Ki? Gh and Gt are first-order blocks with time constants Th and Tt-
50 views

### Find the range of variables based on the steady-state response

I have a transfer function as below: $$G(s) = \dfrac{s(s+2)}{s^2+(b+2)s+ab}$$ Now with input as $$u(t) = \sin{t}$$ The maximum steady-state response of y(t) is less than 1, I would like to ...
1 vote
55 views

### Laplace transform of multiple sources in a circuit

I came across this circuit and couldn't solve it. From what I know the Laplace transform of a DC source would be the constant divided by the $s$ variable. However, does this only applies to sources ...
65 views

### Is the Laplace transform of an integral the same as the Laplace transform of a constant?

I was analyzing the circuit of an amplifier to know its response, the schematic is the following: What I did is the following: I considered $(v_{in}$ as the input signal; $v_{out}$ as the output ...
33 views

### Barkhausen stability criterion and poles location in s domain

For studying stability, I am actually working with 2 methods : Here is the Barkhausen stability criterion : The loop gain is equal to unity in absolute magnitude, that is, $$|\beta A|= 1$$ and the ...
1 vote
62 views

### Transfer function of capacitor and resistor connected in series and one resistor connected in parallel with the capacitor

I have been trying to derive the transfer function H(s) of the circuit diagram. I know how to derive CR circuit, but I'm stock on connecting another resistor with the capacitor. Can anyone help me ...
1 vote
134 views

### Find the transfer function H(s) assuming a signal input i,in(t) and signal output, i,out(t)

I am having trouble answering this question for my Signals and Systems class and would appreciate any assistance. Find the transfer function, $H(s)$, assuming a signal input $i_{in}(t)$ and signal ...
1 vote
57 views

### How to separate Transient and Steady-State Expression from Periodic Summation Response?

Background My question comes from here, it's a response of 1st order LPF RC circuit from an arbitrary periodic input. How to determine the transient response of a circuit to causal periodic inputs? ...
163 views

### Solving an RLC circuit with two voltage sources using Laplace transforms

What is the Laplace transform for an RLC circuit with two voltage sources? I tried to find I(s), but the calculation gets complicated.
60 views

### Laplace inverse transform of an exponential multiplying another function

I was trying to understand the inverse transform of $Y(s)=F(s)e^{-as}$, but on different sources I found three different answers (H being the step): $f(t-a)$, $H(t)f(t-a)$ and $H(t-a)f(t-a)$. ...
78 views

### Knowing the transfer function of a system and the output, how can I get the input?

I have a system composed by k-thermocouple + metal handpiece, the thermocouple is drowned into the handpiece. If I manage to estimate a transfer function of the system so-made, for example trough ...
1 vote
68 views

### Sources remaining in the open part of the circuit after the switch is closed

Below there is a circuit from the book Nilsson & Riedel Electrical Circuits 9th Edition. The switch in the circuit been in position x for a long time. At t = 0, the switch moves instantaneously ...
1 vote
41 views

### Laplace transform of some functions

What would be the Laplace transform of these functions? $f(t) = [5u(t)]^{2} - u(t)$ $f(t) = tu(2t)$ As for the first function, it is like multiplying two unit step functions which is not ...
184 views

1 vote
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### What is up with this series/parallel calculation? Inverse Laplace looks strange

I'm trying to find an analytic solution for this circuit. If the cap is inverted (series resistor to ground) the solution is straightforward. In this case I ended up with a strange cos term that makes ...
1k views

### Why is a capacitor to ground a low frequency pole, instead of a high frequency zero?

In building my intuition about how analog circuits relate to the s-plane, I am wondering why a pole emerges from a capacitor to ground, for example in a simple lowpass filter consisting of only a ...
249 views

### How do I find Vo in the circuit?

I1 + I2 = I3 I1 = Vi/Z1 ... Z1 = (1+sCR1)/sC I1= Vi(sC)/(1+sCR1) I2= Vi/R1 I3= -Vo/R1 I1 + I2 = I3 Vi[(sc)/(1+sCR1) + (1/R1)] =-Vo/R1 -Vi[(R1sC)/(1+sCR1) + 1] = Vo How do I change back to time domain?
1 vote
138 views

### Differential equation of a LC circuit in series with a parallel RLC circuit

I have the following RLC circuit. I am having trouble finding an expression for the natural response of this circuit. I found a similar question, but I was unable to simplify exactly like was done in ...
1 vote
140 views

### Why are they called delayed integrators

I'm quite confused as to why we call a system with transfer function $$\frac{1}{s+\alpha}$$ a delayed integrator. It does not seem to be an integrator in the first place since it convolves with an ...
The place that I am confused is that for $i_1(t)$ im trying to use the loop method to develop the first equation which is $$v(t)-L_1\frac{di}{dt}-(R_1+R_2)i_1(t)=0$$ and then use $i_2(t)$ for the ...
### Inverse of $e^{as}F(s)$; t-axis translation rule
t-axis translation rule is easy to prove using the definition of laplace transform; the rule is: $$\mathcal{L\{u(t-a)f(t-a)\} = e^{-as}F(s)}$$ I know this works only when we shift the function to the ...