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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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1answer
49 views

Impedance load matching

So I've done this so far, and know one of the components is a 50ohm resistor. However I dont know where to go from here. How do i decide if its an inductor or a capacitor? This is a past paper exam ...
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2answers
70 views

Current in charged RC circuit

I've the following circuit: simulate this circuit – Schematic created using CircuitLab The capacitor is charged up to 10 V according to the following formula (when the switch is closed): $$\...
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1answer
47 views

Maximum safe working voltage of capacitors

The answer is 30kV. My method led to an answer of 41KV, where did I go wrong? I believe I cant just add the Vmax(s) at the end, but what would I do instead and why?
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0answers
50 views

Help with determining the open circuit voltage

Can someone go through why Vxy= -84mV? Given the values off VB=180mv R1=22ohms R2=68ohms R3=150 ohms. Many thanks
2
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3answers
83 views

Mathematical help with Wheatstone bridge

This is a homework, so I won't ask for a complete solution, but can anyone tell me how should I approach this? I've been sitting now for hours without any progress, all that I know is the answer ...
2
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2answers
65 views

Where did this useful matrix decomposition come from for Nodal Analysis?

Background The equations formed when finding the nodal voltages of a circuit can be expressed using nodal analysis as a square system matrix \$\mathbf{S}\$ (lets say \$m\times m\$ where \$m\$ is the ...
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1answer
63 views

boolean algebra question regarding how to simplify a 5 input circuit

Background: I'm teaching myself computer architecture because I do not have a technical degree and want to learn this even though my finances won't ever allow me to have a formal education. I am doing ...
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2answers
62 views

I need an equation to calculate the time for a power percentage of a half cycle sine wave into a resistive load

I need to calculate the time a thyristor/triac needs to be on for a desired percentage of full power of each half cycle of the AC line input. On for the full half cycle will give me 100%. On for 1/2 ...
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0answers
46 views

Differential amplifier solving equations for iDS

In large signal analysis of differential amplifier there are some equations to determine iDS. If we simplify it looks like that : \$ \large 2x^2+2kx+k^2-2\frac{l}{m}=o\$ Is there an easy way to ...
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0answers
23 views

Price as a function of load on an electric grid(City modeling)

Thanks for your time. First some context and the actual question is marked further down. Context: I am modeling a city as a complex adaptive system and am building a model of an electric grid to run ...
0
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1answer
67 views

There is no math for adding the functions of two parallel filters. Or is it?

I want to add two "parallel" functions. Each of them describes the frequency response of that individual filter. Put in other words, I want to see what the frequency response looks like when the two ...
0
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1answer
63 views

Clarity on dB SPL calculation

Based on this post, let me assume that I have a input source of 94 dB SPL / 1 Pa that a microphone is picking sounds from. The microphone has a sensitivity of -46dBV/Pa , this gives 0.005012 V RMS/ ...
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1answer
37 views

Discrepancy in my dB SPL calculations

Having read through this post I tried an experiment. I connected a Extech sound level calibrator to a Type 4189 microphone. The output sensitivity of the microphone is 50 mV/Pa,-26 dB ± 1.5 dB re ...
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2answers
59 views

Deriving Capacitor Current Equation

I understand that the current through a capacitor is given by the capacitance multiplied by the rate of change of voltage. I also understand that this leads to infinite impedance for DC and virtually ...
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2answers
85 views

Fourier series coefficient for sin(wt+theta)

Am trying to find the Fourier series coefficient ck for the following function \begin{equation} x\left(t\right)=\sin\left(wt+\theta \right) \end{equation} Here is my work \begin{equation} c_k=\frac{1}{...
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2answers
115 views

Finding the average power dissipated in a resistor

Well, I've a series RL circuit that is powered by a voltage source. The input voltage is given by: $$\text{V}_{\text{in}}\left(t\right)=50+\frac{400}{\pi}\cdot\sum_{\text{n}=1}^\infty\frac{\sin\left(...
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1answer
46 views

Transforming a supply power [closed]

For a recent project i need to power a certain element with .7 amps and 5 volts. my input power is 5 volts, but i need to calculate a circuit for decreasing current. I looked for answers on google and ...
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4answers
103 views

Sinusoids represented using Euler's formula notation, confusion

EM plane waves are represented using the equation (ignoring amplitude) $$E(x,t) = e^{j (wt - kx)}$$ They are also represented in this form: $$E(x,t) = \cos(wt - kx)$$ I want to get the electric ...
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0answers
52 views

How to calculate the current produced by a solar panel?

The equation for calculating current when given voltage and temperature is known as the 5-Parameter model ie. \$I = I_{ph} - I_o[\exp(\frac{V + R_sI}{nV_t})-1] - (\frac{V+R_sI}{R_{sh}})\$ Since this ...
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2answers
61 views

Graphical nature of signal energy

In signals, we learn that the energy of a signal is the integral of its square. E.g. \$E=\int_{-\infty}^\infty x^2(t) dt\$ We know that integrals are the areas under the function in a graph. But ...
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1answer
43 views

Explanation of 5 Parameter Model for Solar Cells

I am having a hard time understanding this equation, the 5 Parameter model for photovoltaic cells. \$I = I_{ph} - I_o[\exp(\frac{V + R_sI}{nV_t})-1] - (\frac{V+R_sI}{R_{sh}})\$ My goal is to apply a ...
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1answer
60 views

How to calculate the transmission distance from satellite to earth (How to understand the formula) [closed]

I have this question in one of my tutorials and I cannot seem to find clarity in the question - I am trying to make an algorithm to do this all automatically but I need to understand the formula I ...
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0answers
47 views

RLC circuit with intial conditions

The circuit I have is given by the following schematic: simulate this circuit – Schematic created using CircuitLab I know a few things: The current in the circuit at \$t=0\$ equals \$\text{I}...
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2answers
109 views

Connecting the following structure of multipliers and adders in an elegant way in verilog

I am attempting to write a synthesizable verilog (or Systemverilog) module. I also want to make the modul parameterizable, which has presented a problem when trying to connect the following structure ...
1
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1answer
72 views

Compensate centrifugal force in accelerometer measurements

I'm working on a project that includes counting the revolutions of a cylinder connected to an engine. This engine runs at a minimum of 5 revolution per second and a maximum of 9 revolution per second. ...
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0answers
43 views

How do you calculate average absolute value of a sum of sin functions with different amplitudes and frequencies?

I cant seem to find the answer anywhere. I remember there was a simple formula for doing this but I dont have the book with it anymore. Finding where the function is positive and where is negative and ...
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2answers
131 views

Conversion from dBm to dB\$\mu\$V?

I am trying to derive the conversion from dBm to dB\$\mu\$V. So, please correct me If I am wrong. \begin{align} \textrm{dBm} &= 10 \log_{10} \left( \frac{P}{1\textrm{mW}} \right) = 10 \log(P) + ...
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1answer
111 views

Convert ADC value to real voltage

I want to measure the input voltage to my circuit. The input voltage is supposed to be anything between 7 to 35 Volts. I have a micro-controller with 12bit ADC. I am using a simple voltage divider to ...
-1
votes
2answers
2k views

Calculate battery state of charge percentage

What is the correct formula to calculate battery state of charge percentage based on the battery type (12v, 24v, 48v and so on) and the current battery voltage. For example if I have a 12v battery ...
4
votes
3answers
161 views

Order of precedence for parallel operator

In electrical engineering the parallel operator || gives half the harmonic mean of two values. E.g.: \$R_1 \parallel R_2 \equiv \frac{1}{1/R_1+1/R_2} \$ But how should you compute \$kR_1 \...
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1answer
86 views

Control Theory Integrator Phase Shift

Guess I should know the answer, but I can't come up with a good explanation. I always have to remember which sign cos and sin have after integration/differentiation. I usually do this by thinking of ...
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1answer
51 views

Finding current over controllable voltage source using nodal analysis

I have the following circuit: Let me explain the diagram a bit first: I0 is current in that direction, V0 is voltage and 2 V0 is also voltage times two. V1, V2, and V3 are my nodes. The 'S' by the ...
29
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5answers
14k views

Why is the time constant 63.2% and not 50% or 70%?

I am studying about RC and RL circuits. Why is the time constant equal to 63.2% of the output voltage? Why is it defined as 63% and not any other value? Does a circuit start working at 63% of output ...
1
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1answer
80 views

Finding the fourier series coefficients of the signal $$1+\sin (\omega_0 t) + \cos (\omega_0 t) + \cos (2\omega_0 t + \pi / 4) $$

I have come across this question that asks to find Fourier series coefficients of the following signal. $$1+\sin (\omega_0 t) + \cos (\omega_0 t) + \cos (2\omega_0 t + \pi / 4) $$ In my intuition, ...
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1answer
61 views

Control Theorie: Drawing Transition Matrix Trajectories

Given a transition matrix like e.g. $$ \phi(t)=\begin{bmatrix} e^{-3t} & 0 \\ 0 & e^{-3t} \end{bmatrix} $$ What is the analytical way of drawing x(t) for two given starting points? I only ...
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1answer
52 views

Multi phase vs single phase power factors

Are there any differences between calculating single phase and multi phase power factors? I'm open to general answers, but more specifically: If PF1=P/S, does PF3=(Pa+Pb+Pc)/(Sa+Sb+Sc)? Does ...
0
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1answer
40 views

2D Positioning Localization

I have a robot. My robot has three main sensors one is a gyro from which i can get my yaw, pitch, and roll. I also have an encoder in the x and y axis. How can I use these sensors together to reliably ...
2
votes
2answers
81 views

In a Wilson mirror, does Q3 need to have the same beta to cancel the base current error?

I'm learning about Wilson mirrors in the Art of Electronics Third Edition (pg. 102). It shows the following circuit: simulate this circuit – Schematic created using CircuitLab It then ...
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0answers
29 views

Find vertical shock from IMU during inclination

The PCB can be mounted in any orientation and from this the firmware must calculate the vertical shock that it experiences. As it would be calculation intensive to calculate he vertical shock for ...
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0answers
85 views

Calculation of Euler angles. But gets a change (delta) in change and not a constant value

What I've done will now: I'm using an IMU (MPU6000) to calculate the Euler angles of an object and for this, I'm using Madgwick AHRS algorithm. The MPU gives acceleration due to gravity (a) about the ...
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1answer
42 views

What's oscillatory instability in the delay differential equations?

Does DDE’s stability depend on forcing term and ODE’s stability does not depend?If yes, then is frequency analysis of stability applicable only to DDE and not ODE? In control systems, we study ...
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2answers
167 views

Poles and Zeros of Two Pole Compensation

I am known with the basics of what poles and zeros of transfer function are and how to determine them, but I certainly don't know how to apply such poles and zeros to the gain curve, which describes ...
4
votes
5answers
167 views

Average of a periodic voltage

I know that this question is math related, but I still don't get why we can say the following formula holds: I've a voltage \$V:\left[0,\infty\right]\to\mathbb{R}\$ and \$V\$ is periodic with \$T\$....
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1answer
119 views

Digital Multiplication, Subtraction, Division Integrated Circuits?

Having a hell of a time finding ICs that offer multiplication, subtraction and division? Are these functions just a product of adders and not worth the fab?
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0answers
62 views

Roll-off of a third-order active filter [duplicate]

I've a third order active filter, without zeros. I know that when \$f=0\$ the gain response is \$1\$. So the cutoff-frequency is located at: $$\left|\text{H}\left(\omega_0\right)\right|=\frac{1}{\...
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2answers
383 views

Roll-off of a filter

I know that the roll-off of a transfer function gain is given by: $$20\log_{10}\left(\left|\text{H}\left(\omega_2\right)\right|\right)-20\log_{10}\left(\left|\text{H}\left(\omega_1\right)\right|\...
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1answer
41 views

Why do the brightness, luminous efficacy and power of this lightbulb not agree?

A particular LED lightbulb has luminous flux (brightness) \$\Phi_{\rm v}=820\ \rm lm\$, consumes electrical energy at a rate of \$P=9\ \rm W\$, and has a luminous efficacy of \$\eta=83\ \rm lm/W\$. ...
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2answers
506 views

Role of complex number in electronics [duplicate]

Complex numbers contain imaginary numbers as we all know but often it is used for solving real life practical problems such as taking the impedance of a capacitor, inductor etc. Even in Signals and ...
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2answers
183 views

Does the resistor values used for opamp circuits come from the equations?

I've the following circuit: I used the LM741 as the opamp. The input resistance is \$2\cdot10^6\space\Omega\$, the output resistance is \$75\space\Omega\$ and the voltage gain is \$2\cdot10^5\$. ...
0
votes
1answer
276 views

RC step response equation derivation

So this isn't really a big question, but I really need to get something clarified from the derivation of the RC step response equation, which goes like this: $$V(t)=V_S+(V_0-V_S)e^{-\frac{t}{RC}}$$ ...