Questions tagged [formula-derivation]

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3 votes
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61 views

Power system question: How do you derive the reactive power transfer equation?

I'm reading the EPRI Power System Dynamics Tutorial textbook. On page 3-12, it defines the reactive power as $$ Q_{S}=\frac{V_{S}^2}{Z}(V_{S}X_{L}-X_{L}V_{R}\cos\delta+RV_{R}\sin\delta-\frac{V_{S}}{X_{...
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3 votes
3 answers
147 views

Derivation help: gain of 2 NMOS in series

I am trying to find the gain (Vout/Vin) of the circuit below, this is not a real circuit that I have, I am just trying to learn more about circuit analysis. The circuit reminds me of a cascode circuit ...
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0 votes
2 answers
100 views

TLC555 Constant Frequency, Adjustable Duty Cycle [closed]

For my Senior Design Project, I am designing a battery charger based on a synchronous buck converter topology. The MCU (Teensy LC) I'm using cannot produce PWM with a high enough frequency (488.28Hz), ...
0 votes
1 answer
79 views

How can one calculate at surface the electric or magnetic field strength for 50Hz 240VAC wire at 1 meter depth?

How can one approximately calculate at surface the electric or magnetic field strength for 50Hz 240VAC wire buried at 1 meter soil depth for a given current? Say in sandy clay soil with no mineral ...
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2 votes
2 answers
153 views

How do you get from the low-pass filter formula to the code?

I am just wondering how the author deduced this code from this formula. This is the step response of a low-pass filter. $$v_{out}(t)=V_i\cdot(1-e^{-ω_0\cdot t}), \text{ where } ω_0 = \frac{1}{R\cdot C}...
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-1 votes
4 answers
116 views

Inconsistency of electrical loss function

We have a function to calculate electrical losses for resistances and it is that $$P = I^2 \cdot R $$ If we consider this formula, our teachers generally say that if you want to decrease the losses, ...
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1 vote
1 answer
133 views

Deriving power formulas for transmission lines

I'm trying to derive formulas for active power (\$P_s\$) and reactive power (\$Q_s\$) at the sending end of a transmission line shown below: Where: \$E_s\$ and \$E_r\$ are voltage magnitudes \$X\$ is ...
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1 vote
0 answers
187 views

Formula for calculating instantaneous power in pure inductive and pure capacitive circuit

According to the material provided by a faculty this is what the formulas were and how they were derived. According to the derivation we did in class, we were getting: P = -VrmsIrmssin 2ωt for pure ...
1 vote
0 answers
59 views

Can someone confirm my derivation of the generalized power law from Practical Electronics, 4th edition?

I dont know how to use LaTeX, so I used Mathcha and took a snip from there.
0 votes
0 answers
32 views

Looking for a formula to calculate the resitance needed to make a proximity sensor shorter! RCWL-0516

I want to decrease the range of this cheap sensor dramatically from 5m to 5cm! Im not sure which equation I use to calculate this. I'm assuming but not sure if there is a bigger resister value that I ...
  • 1
0 votes
1 answer
111 views

Overall Gain for Mixer Circuit

I am working on an audio mixer circuit for balanced studio gear. The circuit consists of two unity gain balanced line receivers (THAT1200), going into a pair of voltage dividers controlled by a shared ...
-1 votes
1 answer
78 views

Transfer function : Determination [closed]

I have the below circuit, here, I have Is and Va are measurable quantities. Rc1..Rc4 and Rbd are unknown variables for which I intend to derive transfer function. I have flexibility of adding ...
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2 votes
1 answer
196 views

How to derive the formula from this circuit?

This is the schematic to measure the \$R_{iso}\$. There is a switch, Q2 for the measurement. I need to find how to derive the \$Y_{iso}\$ from this circuit schematic. To find it out, I tried to use ...
1 vote
1 answer
168 views

Transfer function : Complex network

For the attached circuit attached in LTspice spice, I am trying to find the transfer function interms of Rc1,Rc2,Rc3 and Rc4. For that I have switches which I configure to turn on/off and measure the ...
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0 votes
1 answer
30 views

Dificulty deriving voltage reference ripple

I have this voltage reference circuit and I need to derive the equation that gives me the influence of \$\Delta\$Vio on the output Vref which is my Vo, I have derived the equation for Vo when \$\Delta\...
0 votes
1 answer
85 views

Can anyone explain the difference between these two forms of PID controllers?

Usually, when people talk about PID controller, I think of the "parallel form" of PID controllers, I know how it is derived (we just need to add all 3 three P I D controllers together). This ...
0 votes
1 answer
1k views

How to calculate fuse i2t rating when current is known?

How do I convert the fuse current rating to the i2t value? For example, in this circuit simulator, when adding a fuse, the only values that can be specified are the i2t value and resistance. The fuse ...
  • 2,524
0 votes
0 answers
92 views

Find i/o pole of the cascade (BJT)

I have to obtain the pole of this circuit and the conversion function, but I can not do it . How many poles does this circuit have? And what are their relationships according to the arrangement of ...
0 votes
1 answer
188 views

Help finding multiple feedback (MFB) high-pass filter design formulas?

I can't seem to find some easily code-able formulas for MFB high pass filter. I have found plenty for the low pass filter, but absolutely none for the high pass filter. For example, the formulas on ...
1 vote
0 answers
79 views

Is mmf the same as the magnetic force?

In the following system, I created the following equation in terms of what I assumed to be the force acting on the movable object with a mass M. The reluctance of the core is neglected, so the total ...
2 votes
1 answer
84 views

How to deal with controling force by positioning oscillating magnet?

I am trying to code up a closed loop control system on force generated by the paring of strong rare earth magnets. I do not have much experience with PID logic but i have a weak grasp of the basics (...
-2 votes
2 answers
130 views

Where does Ohm's Law, Kirchhoff circuit laws, etc, come from? [closed]

I know that these various laws that we use are often commonly accepted in practice but I am always curious how far down the rabbit hole you can do until you hit something that you just accept as true. ...
1 vote
1 answer
112 views

Derivation of energy in capacitor

While searching for something totally unrelated to this, I came a cross a website that derived it in this fashion: the instanteous power in a capacitor is given by $$p_c= v_c(t)\cdot i_c$$ since $$i_c(...
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0 votes
3 answers
269 views

Is this a proper way to find the derivate of a 12-bit ADC?

I'm seeking a solution to find the derivative of an 12-bit ADC. It's for STM32 but let's say it's for likely for an arbitrary micro controller. ...
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0 votes
1 answer
104 views

Deriving Wheatstone bridge equation

I have the following circuit: Here I have obtained the equation of Ud = U * ((deltaR / R)/(4+2(deltaR/R))). But I'm stuck on the part on how to derive that formula. Any help or guidance is ...
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0 votes
2 answers
132 views

Proof for Peak Time for an Underdamped Second-Order System

I've been attempting to prove the taught result that: $$T_p=\frac{\pi}{\omega_n\sqrt{1-\zeta^2}}\textrm{.}$$ From the time-domain form of an underdamped response, we have $$c(t)=K_1e^{-\sigma_dt}\cos(...
5 votes
1 answer
347 views

Equation to calculate voltage divider resistor value for an input of op-amp

I found this guide for a temperature sensing circuit design with NTC thermistor by Texas Instruments. According to my opinion, optimum R1 value is calculated so that the voltage divider can provide ...
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0 votes
1 answer
150 views

Formula to calculate power from a solar panel?

I am currently working on a project that works with solar panels on Mars and I am trying to calculate how much power I would get from a solar panel on the surface. I have values such as solar ...
0 votes
1 answer
36 views

RC Calculation With Charge Already On Capacitor

Is there a formula for charging/discharging a capacitor which is already charged to a certain voltage? For example, if I charge a capacitor to 3v, then switch to a 1v power source, how can V(t) be ...
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2 votes
1 answer
32 views

How to properly calculate current of a variable capacitor?

So the formula i(t)=CdV/dt works for a constant value of a capacitor, but in a variable capacitor, i found the next formula on another site i(t)=C(t)*dV(t)/dt + V(t)*dC(t)/dt Is this formula ...
0 votes
3 answers
654 views

Why do most textbooks use the inverse formula 1/rtotal for parallel resistance?

I was calculating the parallel resistance for a circuit, but just couldn't get the correct answer despite several attempts. I felt incredibly dumb when I watched a video on how to calculate parallel ...
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0 votes
2 answers
72 views

Derivation needed

I am using a chip that has the following circuit in it where V_in is inputted on the left and V_out is measured on the right. This circuit is sometimes called the "lumped-element delay lines." I was ...
0 votes
1 answer
52 views

Derivation of diode voltage in three phase full wave diode rectifier

Considering ideal diode in 3 phase full wave diode rectifier we can present the system in picture below. I found the final equation for \$v_{D6}\$, but can not figure it out how it was derived. \$v_{...
1 vote
1 answer
411 views

Differential equation of a RRC circuit as Voltage output/voltage input?

So in this presentation i have got, there is a RRC circuit, and they get this differential equation, but there is no procedure explained how they have got it. This is basicially a series RRC circuit ...
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2 votes
1 answer
89 views

Trying to find value of two capacitors using resonant frequencies in three conditions, but wrong formula is derived

I was trying to find capacitance of two capacitors in the following way. Connect each capacitor individually to a same inductor and find resonant frequency in each case. Connect the same capacitors ...
0 votes
0 answers
119 views

Derive DC motor formula with drum driving a conveyor belt

The setup is a DC motor directly connected via its shaft to a drum which drives a horizontal conveyor belt. There is a load of mass, M, on the conveyor belt. I am stuck on trying to figure out what '...
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0 votes
2 answers
2k views

Derive current through "charging" inductor formula

I don't know if it's just me but I can't find a single resource that derives a general equation for the current through an inductor. My text book just says "assume the equation if of the form ..." but ...
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0 votes
1 answer
199 views

Deriving the Integral Voltage-Current Relationship of a Capacitor

I am having trouble understanding the derivation of the capacitor voltage equation in my circuits textbook. Here is the process they followed from the textbook My confusion is: when the initial ...
0 votes
1 answer
249 views

Confusion with derivation of average power formula [closed]

I know that average power is equal to \$VmIm/2 * PF\$. I can show that this is equivalent to \$(1/2)Re(VI^*)\$ by writing VI* in magnitude phase form. However, I also know that complex power \$S = ...
2 votes
0 answers
190 views

Current derivative in RLC circuit

How to find the current derivative(di/dt) at t = 0+ in the first loop?
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-2 votes
3 answers
1k views

What is generic formula for min and max levels of rectified AC voltage?

For example, if i have 1 phase AC voltage with 1 volt peak level and rectify it., i would get some pulsating voltage V = abs(sin(t+0*pi)). Its minimum is 0 volts ...
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1 vote
1 answer
60 views

Derivatives in time and phasor domains do not match

Given that voltage can be represented in the time domain as the following: $$V(t) = \vec{\mathbf{|V|}}\cos{(\omega t + \phi_V)}$$ It can be shown that in the phasor domain, this is the equivalent ...
0 votes
1 answer
72 views

Reasons and assumptions behind the use of per unit length quantities in the telegraph equations

I am working out the derivations of the telegraph equations of a transmission line $$\begin{gathered} \frac{{\partial V}}{{\partial x}} = - L\frac{{\partial I}}{{\partial t}} - RI \hfill \\ \...
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1 vote
1 answer
164 views

Deducing the value of a variable resistor in configurable voltage divider

Two variable resistors (RS & RE) and one static resistor (RC) are connected to a high impedance input analog input pin of a micro-controller. The static resistor is connected to ground and the two ...
0 votes
2 answers
1k views

Maximum power transfer derivation

In my textbook, the author showed the calculus derivation of what value of load resistance is needed such that it will absorb maximum power from the source, while keeping the Thevenin voltage and ...
0 votes
1 answer
74 views

How was this formula of voltage on capacitor achieved?

We know that voltage across a capacitor is given by But there is this other formula How this second formula was deducted mathematically from the first one? or from another one?
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1 vote
2 answers
251 views

Voltage divider equation tunnel diode - Art of Electronics

Early on in the book "The Art of Electronics" (p.15, 2nd edition) a voltage divider circuit is described: an input voltage \$V_{in}\$ over a tunnel diode \$D\$ and a resistor \$R\$, and an output ...
0 votes
0 answers
67 views

Critical Maximum current for a DC-DC Buck Converter

I was wondering how one would go about the derivation for the output to input voltage ratio for a DC-DC Buck converter given the critical max current that is found to be $$ I_{crit} = \frac{V_{in}T}{...
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0 votes
1 answer
221 views

Deriving resonance frequency of RLCC circuit

I am trying to determine the resonance frequency of an RLC resonator with added capacitor, as shown below: simulate this circuit – Schematic created using CircuitLab Two cases are easy to ...
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-5 votes
1 answer
87 views

Rectangular signal

Can someone explain me how do I take the first derivative of the given function and how will this function look like ?