Questions tagged [formula-derivation]

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1answer
24 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
40 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
21 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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0answers
15 views

derive Equation between time and current in motor protection device

I am trying to imperilment The IT - characteristic feature for motor protection device.There are 2C,5C,10C curve feature . can someone suggest me how it can be implemented in C code. Is there any ...
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2answers
135 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
49 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
60 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
154 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
269 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
48 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
45 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
99 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
190 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
67 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
98 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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45 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
81 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
60 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
122 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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2answers
2k 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
1k 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
242 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
2k 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
267 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
34k 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
819 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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0answers
69 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
456 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
1k 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
3k 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
187 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
3k 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
223 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
52 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 ...
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1answer
227 views

Current gain in MOSFET CS Source degeneration

There is always some formulas for calculating "Au" or "Gu". But there are never given any equations that reffer to current gain in MOSFETs. I know current gain is almost infinite in normal CS ...
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29 views

Practical verification of equations

This question is reffering to MOSFET. If you calculate drain current with a specific formula you can also verify that same value with measurement. But if you calculate partial or overall gain, you ...
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1answer
5k views

I/O Resistance of common source MOSFET with source degeneration

Common Source MOSFET with source degenerations looks like this I am a bit confused about different input and output resistance statements (provided by different sources). Some of them say that ...
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1answer
739 views

Overall and partial MOSFET voltage gain

I am researching studies for common source MOSFET amplifier and I found two different terms for voltage gain - overall and partial. What is the difference between overall and partial gain when ...
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0answers
541 views

JFET transconductance vs. MOSFET transconductance

JFET's n-channel highest transconductance (from datasheets) is marked as In theory, the same value is defined as that applies for n-channel JFET. I haven't found equation which defines MOSFET's ...
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1answer
2k views

Real output resistance of MOSFET

This question is related to MOSFET. NMOSFET's resistance was till now defined in many different ways, for example as: or which value varies from 1-50k Ohm. And there is also drain-source on-state ...
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2answers
1k views

MOSFET finite output resistance in saturation mode

Since MOSFET has finite output resistance in saturation/active mode, the slope of unsignificanlty rising drain current is defined by Ua and slope parameter as lambda: This parameter (as I know) is ...
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1answer
90 views

Unknown Ψ variable in JFET's drain current equation

This question considers unipolar transistor, that is JFET. I really didn't find any other formula than this one which applies only for linear/ohmic/triode region of JFET U/I characteristic. What is ...
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1answer
179 views

Unipolar transistor's transconductance/admittance

Unipolar transistor basic variable transconductance is commonly marked by: It is commonly used in calculations where we need drain current, Ugs, rds(on), and similar. I have also seen many equations ...
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1answer
112 views

Inductance of Shielded Helical Resonators

I found an equation in a thesis which calculates the inductance for a helical coil inside of a cylindrical shield: $$L = (\pi N d_{coil})^{2}\frac{1}{l_{coil} +0.45 d_{coil}}\left(1 -\frac{d_{coil}^{...
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3answers
58 views

Where does the formula for Voltage in AC with inductance come from?

This is what the textbook says: I don't understand why does ωLIm equal Vm so if someone knows please explain it to me Thanks
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5answers
835 views

What is the origin of the capacitance formula?

Everyone knows capacitance is defined as C = Q/V, but why? Sure I understand the utility of it and its use, but can someone provide a motivation or historical context for this definition? I'm unable ...
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2answers
5k views

How to Derive Capacitive- and Inductive Reactance Formula

I've been searching around the internet to find out how to derive the reactance formula for capacitors and inductors. But I couldn't really find anything, so I thought why not make a post about it. ...
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2answers
95 views

Calculating for current in a single transistor amplifier(almost common collector?)

I was given this circuit for a practice test during one of my classes, but we were never shown how to actually solve it. It's just been bugging me so I wanted to know how others solved for all the ...
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2answers
17k views

Deriving the formula from 'scratch' for charging a capacitor

So the formula for charging a capacitor is: $$v_c(t) = V_s(1 - exp^{(-t/\tau)})$$ Where \$V_s\$ is the charge voltage and \$v_c(t)\$ the voltage over the capacitor. If I want to derive this formula ...
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1answer
457 views

SMPS Input Circuit - Formulas resolving diodes, capacitors, voltage, etc

For fun, I made a project from an old PSU and the parts inside it, and ended up with my new HVDC power supply. Consider this diagram: Whenever I plug this in to 120 VAC, I measure 350 VDC on the ...