Questions tagged [formula-derivation]

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19 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 ...
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0answers
45 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 ...
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1answer
46 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 ...
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0answers
31 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 ...
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1answer
46 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 (...
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2answers
112 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. ...
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1answer
59 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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3answers
148 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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1answer
56 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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2answers
62 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(...
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1answer
111 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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1answer
46 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 ...
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1answer
28 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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1answer
28 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 ...
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3answers
282 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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2answers
57 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 ...
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1answer
35 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_{...
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1answer
151 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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1answer
44 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 ...
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0answers
71 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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2answers
787 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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1answer
99 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 ...
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1answer
163 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 = ...
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0answers
175 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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3answers
749 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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1answer
49 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 ...
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1answer
57 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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1answer
136 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 ...
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2answers
635 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 ...
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1answer
70 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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2answers
180 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 ...
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0answers
61 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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1answer
173 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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1answer
68 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 ?
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1answer
150 views

Derivation of LC impedance transformation formula

Apologies in advance for this esoteric question (and source). I've been studying wideband LC oscillators recently and my search for an amplitude stabilized configuration led me to the Vackar ...
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3answers
5k views

independent control of frequency and duty cycle in 555 timer (formulas)

I want to control frequency and duty cycle of output pulse of 555 timer. I searched and find this schematic in a post in SOV but I don't know how calculate frequency and duty cycle in the circuit. ...
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1answer
3k views

Current draw calculations for a brush-less motor are way off

I've been attempting to calculate how much current a BLDC will draw given a known propeller size, thrust, internal resistance, Kv rating, Supply Voltage(Vin) and idle current. My propeller parameters ...
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2answers
397 views

MOSFET Biasing Problems

I am interested in finding Vgs for E-MOSFET for desired Id or/and Vds. Referring to those equations of drain current in saturation region, value of conduction parameter "K" would be nice to have but ...
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3answers
3k views

Basic formula for calculating required cable area

Trying to do a spreadsheet to figure out how much cable of different dimensions I will need for a low voltage DC electrical system, but got stuck on the formula for converting current draw, distance ...
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1answer
290 views

Calculating Antenna Gain

As far as I understand, and antenna like a simple dipole has a circular radiation pattern at the 2 edges, so the physical aperture in this case is circular. $${A = \pi * r^2}$$ Where r is the ...
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3answers
57k views

Relationship of Induction Motor Frequencies

I would like to know how the mechanical rotor frequency [Hz] can be obtained from the electrical stator frequency [Hz]? This is no homework! I have consulted several books as well as the web but could ...
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3answers
1k views

How to differ output & input resistance of small-signal model BJT?

I understand how input and output resistance of small-signal model for bipolar transistor is defined and how draw one. What I don't understand quite yet is how actually input and output resistance of ...
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79 views

Mason's Gain Formula with a not connected loops

We have the following path. I tried to create the gain with Mason's formula, which lead me to the following: ...
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0answers
558 views

Common Source JFET amplifier input voltage

I want to compare to different formulas which stand for same parameter/value. Here is common source JFET amplifier circuit schematic: Here is the first formula which should apply in general to all ...
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2answers
2k views

Common drain JFET output resistance “problem”

The output resistance of small signal model for common drain JFET amplifier equals $$ \frac{1}{g_\text{m}} || R_{\text{ds(on)}} \parallel R_\text{S} $$ and since $$ R_{\text{ds(on)}} =\frac{1}{g_\text{...
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3answers
4k views

Common Source JFET small signal equivalent circuit

This circuit is equivalent to small-signal common source JFET amplifier: If you look at the input and output impedance you can see that Zin = R1 || R2 and Zout = rd || Rd || Rl. It can be seen from ...
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1answer
330 views

I/O Voltage of JFET Common Source with source degeneration

For common source JFET (n-channel): Uin = Ugs (approximation for simplicity), but really Uin is a little bit lower because of input resistance, like so and Uout equals something like this: But how ...
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1answer
4k views

Bypass source capacitor JFET

I know there were some changes applied to voltage amplification formula of BJT when "Ce" (emitter bypass capacitor) was connected to the circuit. How is it with JFET (MOSFET too) and its bypass ...
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1answer
305 views

How to implement derivative, and create a delay of dozens of clock cycles?

I have uart entity which have the following signals (I write only the relevant - for tx) ...
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1answer
53 views

Calculate field strength for shielded isotropic transmitter

How to calculate the field strength of a shielded theoretical isotropic transmitter, if there is a hole in the shield for example. I am looking for a complex formula that also takes into account the ...