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Questions tagged [math]

Math or Mathematics is the abstract study of topics such as quantity (numbers), structure, space, and change.

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Why does tan (θ) equals -j in impedance of reactive circuits?

I'm having trouble understanding the maths for impedance. Suppose we have a voltage of \$V(t)=V_{0}sin({\omega}t)\$ and we plug this into the capacitor equation \$I(t)=C\frac{dV(t)}{dt}\$. This would ...
Ayush's user avatar
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2 answers
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Beat frequency - Square signal

This question comes from this one, LTspice - Beat frequency: It appears that when I did a FFT of two sinusoidal signals, there was no what is called beat frequency. When I do the same exercice with ...
Jess's user avatar
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3 answers
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LTspice - Beat frequency

Here is the theory from wikipedia: Here are my summation of sin on LTspice: The frequencies are 100 kHz and 120 kHz on the FFT. There is no frequencies at (f1+f2)/2 and no frequencies at (f1-f2)/2. ...
Jess's user avatar
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2 votes
3 answers
187 views

Where am I wrong in my derivation of RC charging circuit equation?

I'm trying to derive the RC charging circuit equation for capacitor voltage \$V_C\$ and charging time \$t\$. Here's my solution, We'll start by assuming the battery, resistor and capacitor are ...
Ayush's user avatar
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2 votes
4 answers
124 views

How is CRC5 calculated in detail for a USB token?

How is CRC5 calculated in detail for a USB token? ...
hugo289's user avatar
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1 answer
93 views

How to find the power factor of a component when the combined power factor and one other power factor is known? [closed]

Problem: A 2000 volt-ampere with a power factor of 0.8 lagging is combined with 500 volt-amperes of synchronous motors. If the overall power factor is 0.9 lagging, find the power factor of the ...
tryingtobeastoic's user avatar
1 vote
1 answer
74 views

Polarization Derivation

Can how I can find the phi and theta unit vectors as described (Eq. 4a and 4b) in the following paper on antenna cross polarization? I thought the thetha and phi unit vectors were the same as those of ...
DTBolt's user avatar
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1 answer
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How do I relate input and output signals and find the output for other input signals in LTI system?

I am studying about signals and systems. I came across a few practice problems. For the below question, I was able to mimic the input and output waves shown in ...
Ayush's user avatar
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3 votes
2 answers
157 views

How do I represent a signal as the real part of complex exponential and find the value of complex amplitude & complex frequency?

Context: I was solving some practice problems and came across this problem. I know the complex exponential is: $$ s(t)=Ae^{i({\omega}t+{\phi})}{\Rightarrow}Ae^{i{\phi}}e^{i{\omega}t} $$ Where \$Ae^{i{\...
Ayush's user avatar
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9 votes
4 answers
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Why does this battery use 4.2 V when its nominal voltage is 3.7 V?

I changed my headphone power circuit and I noticed it was using 4.2 V to charge a 3.7 V battery. I am confused why it is using 4.2 V. I know to charge a battery you need more voltage than its rating, ...
Ray's user avatar
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4 answers
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How to analyze a current sink for an ideal power amplifier

In preparing a design for a MOSFET RF Power Amplifier, I analyzed this idealized circuit: My analysis is in some ways consistent with simulation but in some ways gets very different results. Is my ...
SRobertJames's user avatar
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1 answer
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What is the reactive power of a capacitive circuit?

I want to understand the reactive power in a purely capacitive load. Surprisingly, I couldn't find the formula for this anywhere, so I derived it myself, and would like to ask 1. Is this formula ...
SRobertJames's user avatar
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1 answer
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Clarke transform seems to result in more current

I am looking into the Clarke transform for a balanced three-phase system (BLDC motor) and from all that I read, it tries to preserve magnitude. So if I apply this to the case of transforming three ...
Cheiron's user avatar
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1 answer
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How can I do inverse Laplace of this transfer function to get the step response of the RLC circuit?

I have found this to be my transfer function for the circuit. I have tried doing partial fraction decomposition, but I end up with an s on top which I don't understand what to do with.
Even's user avatar
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How to derive a generalized equation with respect to time for voltage across the inductor & current in an RL circuit with a DC PWM source?

Circuit connection: I have this resistor (96 Ω)-inductor (990 µH) circuit connected to a PWM source of frequency 62.5 kHz; And ...
in.yssh's user avatar
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2 votes
3 answers
137 views

Why does phasor multiplication produce a different result with actual sine multiplication?

I thought phasors were shortcuts to the Euler's formula when dealing with sine functions. For example, $$\begin{align}\cos(t+a)+\cos(t+b)&=Re\{e^{j(t+a)}+e^{j(t+b)}\}\\ &=Re\{e^{jt}[(\cos a + \...
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Math Check - Calculating Output of 819MW Electrical Generator and Transmission at 500kV?

If a steam turbine generator puts out 819MW at 18,500V (like a unit at Bruce Power Plant), then gets stepped-up for transmission at 500kV, assuming no change in resistance, is the current as follows? ...
Teragreg's user avatar
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1 answer
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Understanding semiconductor thermal resistance

Most datasheets I read through have a thermal resistance rating attached to the particular package the semiconductor comes in (i.e. TO-220, D2PAK, TO-3P, etc), usually in the form of θJA (junction-to-...
lemon's user avatar
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1 answer
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Complex-conjugate poles from transfer function [closed]

This comes from Sedra's Microelectronic Circuits, example 17.1. If I have a transfer function with a pole \$p_1 = \omega_0(-0.1736 + j0.9848)\$. The example talks about "combining \$p_1\$ with ...
ludicrous's user avatar
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Rigorous Definition of Resistors in Parallel when Circuit is Defined as a Graph

Sometimes electric circuits -at least the ones consisting of voltage sources, resistors, inductors, and capacitors- are defined rigorously as a graph, such as done here. Given the definition of a ...
Sam's user avatar
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1 answer
64 views

Rigorous definition for two circuits being equivalent [closed]

Circuits may be rigorously defined in terms of graphs and differentiable functions, as done here. Yet I have not being able to find a rigorous definition for two circuits (containing only voltage ...
Sam's user avatar
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2 answers
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RC response for any given voltage [closed]

Lets imagine a simple RC circuit in which the response voltage is defined by the following equation: $$ V(t) = V_{inf} \cdot (1-\exp(-t/\tau) $$ This is only true when a constant voltage is applied (...
Gerard Carrera Cardona's user avatar
2 votes
4 answers
863 views

How can I mathematically show that multiplication of j will cause a phase shift?

I have a simple question that I cannot seem to wrap my head around. let's say I have a function Asin(wt), if I multiply a '-j' by this function to get: -jAsin(w*t), I have been told that this is ...
Josh Girgis's user avatar
4 votes
3 answers
2k views

Overdrive voltage of NMOS vs PMOS

I'm confused whether the overdrive voltage for an NMOS/PMOS transistor is supposed to be $$V_{ov} = V_{gs}-V_t,$$ $$V_{ov} = V_{sg} - V_t,$$ or $$V_{ov} = V_{gs}-|V_t|$$ and whether it matters ...
Mikayla Eckel Cifrese's user avatar
2 votes
1 answer
325 views

System of First Order ODEs for a Parallel RLC Circuit

I understand the behaviour of an RLC Circuit in Series can be modelled by the equation: $$ L \frac{d^2Q}{dt^2}+R\frac{dQ}{dt}+\frac{Q}{C}=0 $$ Which can be represented by the system of First Order ...
Sterling Saini's user avatar
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1 answer
66 views

Mathematical relation between \$I\$-\$V\$-curve nonlinearity and harmonic distortion spectral components

A nonlinear resistor has a bent/distorted \$I\$-\$V\$-curve. We can approximate its \$I\$-\$V\$-curve with a polynomial model such as: $$I(V)=I_0 + \frac{1}{R_1}V + \frac{1}{R_2}V^2 + \frac{1}{R_3}V^3 ...
tobalt's user avatar
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How to find the direction of phase difference of sine signals using multiplier phase detector?

I am using a multiplier phase detector like here 1to find the phase difference between two phase shifted sine signals, and I got the value of magnitude but how to find if the signal 2 is leading/...
Rima's user avatar
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How do I calculate Io and n from the Shockley equation given two operation points?

In this exercise I'm given the Vd and Id in two operation points and I need to calculate Io and n from the Shockley equation. I've tried isolating Io and replacing it in the other equation but then I ...
Gabriel Corrales's user avatar
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1 answer
57 views

How we change equations in passive bandpass filters?

I tried it myself, but I couldn't understand how the equation ended up in the given form. After bringing it to that form, the cutoff frequency values can be determined, but since I couldn't do that, I'...
XcellentEEE's user avatar
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1 answer
137 views

I'm getting 11.547 kVA, but the answer is supposed to be 10 kVA. What am I doing wrong?

A 3-phase transformer bank consists of three identical 2300/230 V, 15 kVA single-phase transformers connected in delta/delta. The bank supplies a 20 kVA, unity p.f. 3-phase load. If one of the single-...
Ramesh Jayalalitha's user avatar
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2 answers
244 views

How do we get the gain and cut off frequency values of the active low-pass filter?

I'm trying to find the gain and cut off frequency values myself. But I can't get the same result when fiddling with the formula. The last screenshot is from my own solution. Where am I doing wrong?
XcellentEEE's user avatar
0 votes
4 answers
201 views

Input impedance of a round straight copper antenna

I got some help from a discussion of yesterday about network impedance matching for transferring data between antennas (Basic RF signal amplifier). The discussion was about that the current and the ...
user avatar
0 votes
1 answer
304 views

How much time the load would take to drop 1 volt of source battery?

I am trying to figure out how much time a load takes to drop 1 V of the power source. I have a load (vehicle tracker) of 12 V 0.1 A (as per the datasheet) and a car ...
Awais Saeed's user avatar
0 votes
2 answers
37 views

Correct way of referring to property of a component in an equation

What is the correct way of referring to voltage drop of a diode in an equation? For example I want to show the output voltage of the following circuit in an equation Imagine that the diode is labeled ...
DEKKER's user avatar
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1 vote
2 answers
67 views

Analyzing the complexity of a number in the Arduino IDE

I'm working on a project where I'm linking a calculator (TI-84) to an Arduino (Nano) and I want some way of classifying or quantifying how complex a single number is (small whole numbers being very ...
Lil Mami Chula's user avatar
2 votes
1 answer
86 views

Mistake in calculation of RMS current flyback primary switch node

I'm trying to calculate the RMS current of a flyback converters primary switch node. The Waveform is shown below: I'm okay with assuming it is a triangle wave with a duty cycle of 50%. The peak value ...
Antonio99200's user avatar
1 vote
3 answers
210 views

EE applications for parametric equations

I am trying to learn electronics, specifically audio amplifiers. I paused my study after realizing that my math skills (or rather my lack of math skills) were holding me back. I undertook a study of ...
nuggethead's user avatar
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0 votes
1 answer
40 views

Get a motor to move my camera based on a point in an image [closed]

Let's say that I have this image: Obviously, the camera is pointing to the center of the image, but I need it to point to the center of the bbox. I need to calculate how to get my motor to move so ...
David's user avatar
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0 votes
1 answer
145 views

Power absorbed by placing 50 Hz appliance on 60 Hz source

We know that we can calculate AC power using $$ S=VI^{*}=|S| \angle \varphi . $$ Given that a grid works as constant voltage source, we can calculate the absorbed power in $$ S = |I|^{2}Z = \frac {|V|^...
Muhammad Yasirroni's user avatar
1 vote
0 answers
84 views

Finding an analytical expression for a current distribution for conductors in parallel

Recently, I tried to set up an experiment at home to study what path the current takes at different frequencies for the circuit below. I think this will be a fun project, but I'll need your help. I ...
Tanamas's user avatar
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1 answer
641 views

Calculating inverse fourier transform and graphing it

Recently I stumbled upon Fourier transforms which means I am very new to it. I've been given a question from my professor to find the inverse Fourier transform of a frequency spectrum which is given ...
tom_ger's user avatar
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1 vote
1 answer
206 views

Construction of a Lagrangian function for a circuit

I was reading the paper "Introduction to quantum electromagnetic circuits", by U. Vool and M. Devoret and I am stuck in the construction of a Lagrangian function for the example LC circuit ...
axis's user avatar
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0 votes
0 answers
109 views

Self-capacitance formula for planar inductors

I'm designing a Rectangular Planar Spiral inductor with a rectangular conductor cross-section (it's not made from cylindrical wire) for use in an RLC circuit (an NFC tag), and I can not optimise the ...
WindowCleaner's user avatar
1 vote
2 answers
386 views

How to calculate the resistor values for the zener diode and the BJT base?

I try to convert ~12V signal from a car button (the input voltage can be from 10V to 14V) to a logic level signal for MCU, but the signal should to be inverted (1 = 0, 0 = 1). Below is my schema, but ...
Osoian Marcel's user avatar
8 votes
3 answers
2k views

What do the poles and zeros of a system physically represent?

I've been working with transfer functions and control models for a while, but I never really have gotten an intuitive understanding of what the poles and zeros of a system really represent. I was ...
your_best_friend's user avatar
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1 answer
58 views

How did he calculate the error in this example?

He found an error of about 18%. What is the error formula used in this example? From section 1.5.1 of the book Design of PLLs by Behzad Razav.
Zineddine Haboussi's user avatar
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0 answers
79 views

Where to start theremin project

I am studying electronics and would like to design a theremin that uses discrete components. I have read that RF oscillators such as those needed for a theremin are not likely to work if built on a ...
nuggethead's user avatar
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0 votes
1 answer
31 views

Am I solving this capacitance equation correctly?

The following is a datasheet excerpt about satisfying the clock-signal requirements for a low pass filter When using the internal oscillator, the capacitance (COSC) from CLK to ground determines the ...
Tim Cerka's user avatar
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0 votes
1 answer
100 views

Do not understand how to multiply exponential values

Show how the current i_3=7e^(jπ/4) can be multiplied by Z_3 (in exponential form) to give the voltage through the branch. Calculate using exponential values, then convert to polar so show value and ...
Jason's user avatar
  • 1
0 votes
0 answers
62 views

Digital value calculation clarification

I've done some math and I'd like someone to clarify if my math is right. I have a audio test chamber which the speaker is connected to and can tell me the dBSPL value that the speaker outputs. So i ...
whoknowsmerida's user avatar

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