Questions tagged [math]

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

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How to show that all power in an RC circuit is delivered to the resistor

I am new to electronics and I've been working my way through the Art of Electronics. I've have been able to complete all the exercises up to this point but I have been struggling on this one. Right ...
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How do I mathematically model a magnetic levitation system?

I am working on a magnetic levitation system project using PID control, and I am getting confused as to how I am supposed to mathematically model this system for my paper. Where am I supposed to start?...
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Understanding the Formula for Amperage with Copper

From the beginning of Practical Electronics for Inventors: This makes sense to me up until the term $$1A = \left( \frac{1C}{1s} \right) \left( \frac{\text{electron}}{-1.602 \times 10^{-19} C} \right)$...
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Small signal analysis of MOSFET circuit

The other day I got the following exercise on one of my exams: For those who don't speak German, for transistor 1 lambda is 0, but not for the others. The backgate-effekt should be neglected ...
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Vout/Vin equation in time domain vs frequency domain

While studying op-amp circuits, I notice a pattern between the Vout/Vin equation in time domain and the frequency domain. For example: (images from Microelectronics by Bahzad Razavi, 2/e) The ...
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Magnitute and phase, operational amplifier

I was solving exercises related to operational amplifiers and I got to a part where I am not sure how I am getting the arg part of the result. Can someone please explain this to me. Thank you very ...
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Why is the line-neutral fault current 1.5x higher than the line-line fault current?

My commercial wiring textbook and several documents discussing fault current calculations stated "The L-N fault current is higher than the L-L fault current at the secondary terminals of a single-...
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Why is this signal considered odd when v(t) is not equal to -v(-t)?

In the solution of a problem, that asked to find the Fourier Series of the waveform, shown below. The coefficient of cosine part an is taken taken 0, because it is ...
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Finding the mathematical function that describes voltage across diode and resistor circuit

I have the following circuit: simulate this circuit – Schematic created using CircuitLab Where \$\text{V}_\text{i}\left(t\right)=\hat{\text{u}}\sin\left(\omega t+\varphi\right)\$ and the ...
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Linearization of a set of equations of a system is linearized about multiple points, or should it be a single point?

Linearization of a set of equations of a system is linearized about multiple points, or should it be a single point? I have 10 wind turbine generators in a system. Every generator has three ...
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What is the difference between state variable and algebraic variable?

A set of differential-algebraic equations (DAE) can be represented as $$\frac{dx}{dt}=f(x,z,u)$$ $$0=g(x,z,u)$$ where \$x\$ = state variable, \$z\$ = algebraic variable, and \$u\$ = input variables. ...
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First order low pass filter - Calculate capacitance change

I'm trying to calculate the relative change in permittivity of a capacitor. I have created a circuit that feeds a 80MHz square wave signal into a first order low pass filter. I don't know the ...
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Transmission Line Differential Equation

I was reading the transmission line chapter of Engineering Electromagnetics by Buck and William H. Hayt. I don't understand why the following is true: $$\frac{\partial{^{2}V}}{\partial{z}^2}=LC\frac{\...
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Combining sinusoidal waveforms

Please can someone assist me with how to work this out? I know the answers as this is a practice question, but not sure how to get there. Two AC waveforms are described by the expressions: V1 = 190 ...
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How should fuse selection be made in discrete-time alternating current?

In my circuit,I have a resistive load(Lamp).(Rlamp=1 ohm).At the ends of the lamp is voltage V(t) in the picture.In the picture, there is the first 12 seconds of the signal.But you may think that ...
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Divide a number by x without using /, %, and * [closed]

I want to design and implement hardware in HDL (verilog) to perform division by 3, 5, and 7 specifically. The aim is to achieve this operation in a single cycle. Are there any general methods to ...
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How do I calculate an incomplete sinusoidal signal's average value and RMS value?

I couldn't be sure because there are parts with size 0 in the signal.
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Using a PCB trace as a heater / Hilbert Curves

I'm considering making a PCB to use as a heater for a 3d printer bed. This has been common practice for ~10 years (https://www.thingiverse.com/thing:3919). I was playing around with KiCad and python, ...
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math conjugate problem

why is the equation on the left equals the right? know would I derive it?
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Frequency Modulation - Why don't we modulate the carrier by multiplying message signal m(t) directly with f_car?

I am master student of computer science and I have got a problem/question from the domain of communication engineering. So: I'm listening to a lecture that's about Layer 1 stuff, and recently we ...
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2 votes
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Impulse Response of LTI Systems to Dirac Delta

I am reading a book on Linear Time-Invariant systems and came across the following: $$y(t) = T\{x(t)\}$$ where input $$x(t) = \int_{-\infty}^\infty x(\tau)\delta(t-\tau)\text{d}\tau$$ \$\delta\$ is ...
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Why is BMC/k-induction used in RTL formal verification?

One popular approach for proving safety properties in formal verification of RTL designs is a combination of BMC and \$k\$-induction, which appears to stem from "Checking safety properties using ...
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Derivation of zero state response for LTI system with convolution

Consider this derivation of the zero-state response \$y_{zs} \$ for an LTI system caused by an input \$x(t) \$: - $$\begin{smallmatrix}\begin{array}{r|cc} \text{Input} & \text{Output} & \text{...
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Calculating voltage and current of constant wattage loads along a very long cable

I am struggling with a calculation where I'm either missing something really simple or the maths is advanced beyond my current capability. I have tried rearranging wattage / ohms law calculations but ...
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Linearity and how it affects the response of a system

I've been reading Schaum's outlines for Signals and Systems, and stumbled across the beginning of impulse responses. However, I saw this: Which I understood as the impulse response being "what ...
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Causality on an accumulator system

Can anybody explain why is this system not causal. $$T[x[n]] = \sum_{k=n_0}^{n} x[k]]$$ How does it depend from future inputs when $$n < n_0$$. From what i've searched if \$n_0\$ was \$-\infty\$ it ...
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BIBO stability on a accumulator system from oppenheimer book

Is this stability correct?. If im getting it right, x[k] has a bounded value(M), so the interval between the summatory times this value tells the max value of output. But shouldn't it be |n - no + 1|M?...
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Ramp(sin(t)) whats the graph of this function? [closed]

If T = 1 and ramp(t/T), when you substitute t for sin(t), the interval 0<t<=1 is now sin(0)< sin(t)<=sin(1) or is it 0< sin(t)<= 1?.Thank you.
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How can I plot the frequency response of the equation below using MATLAB?

$$\boxed{\dfrac{V_{\text{out}}(j\omega)}{V_{\text{in}}(j\omega)}=\dfrac{2\times10^9}{(1+10j\omega)(100\times10^3j\omega+20\times10^3j\omega+2\times10^9-20\times10^3j\omega}}$$ and $$\dfrac{V_{\text{...
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Finding out the magnetic field inside the cross section of the torus which is wrapped by conductive wire and the current flows it

As shown in the diagram , the torus of radius of \$~ R ~\$ exists . The wire is wrapped around the torus . $$ N:=\text{total number of the turns of the wire around the torus } $$ The current is ...
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\$\Vert\boldsymbol{E}_{}\Vert=\Vert\boldsymbol{v}_{}\Vert\cdot\Vert\boldsymbol{B}_{}\Vert\cdot\sin^{}\left(\theta\right)~\$is seemingly not applied

I want your help to find whether the misprint exists or not . $$ H :=\text{magnitude of the uniform magnetic field which comes from leftside} $$ $$ a:=\text{radius of the cylinder-formed ...
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Going from transfer function to state space model

This is section from Linear Systems Control by Hendricks, and it is about going from a transfer function to a state space: - In eq. 2.40 they have a transfer function \$\frac{Y(s)}{U(s)} \$, where \$...
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How do I find the magnitude of a complicated complex number? [closed]

How do I find the magnitude of something like $$1+(Z_c+R) \times Z_l$$? (\$Z_l\$ is the impedance of an inductor.)
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How to calculate resistors for an optocoupler?

I am a self-learner (for now) on electronics. I am trying to understand how to calculate resistor values when using an optocoupler and an ESP32 For my little project I want to sense several 220v wires ...
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Which circuit components are used in a pointer? [closed]

For a computer to do basic math, it can use logic gates like AND and OR. These logic gates can be made out of voltage sources and resistors, as seen on Wikipedia. For a computer to do multi-digit ...
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Is \$j\sin(\omega t)\$ just \$\sin(\omega t+90)\$?

If so, then the Euler formula is much less aesthetic in my view... And, in IQ modulation, is the Q signal \$j\sin(\omega t)\$, or \$\sin(\omega t)\$?
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How do I calculate the noise spectral density of a RF LNA with just noise figure spec?

The LNA of of interest is PGA-105+. It says it has a noise figure of 3dB (I'm using that number my for calculations.) That gives me a noise factor of 1.995, which is the ratio of the SNR on the input ...
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Solutions to wave equations

In the following steps for a solution to the Telegrapher's equations, I don't understand how equation 9.17 follows from 9.16. Substituting in \$\gamma\$ as given, it seems that the result should be \$...
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Mistake in finding KCL and KVL in op-amp circuit

I have the following op-amp circuit: simulate this circuit – Schematic created using CircuitLab I know that \$\text{V}_1=0\$ and \$\text{V}_3=0\$ in the case of an ideal op-amp circuit. I wrote ...
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Derivation of Dolph-Taylor Synthesis

Today, I was trying to deduce by myself the Dolph-Taylor Synthesis. After arriving at the expression: $$AF(\theta) = P_{N-1} \left( \cos \left( \frac{\psi}{2} \right) \right) = T_{N-1} \left(x_o \cos \...
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3 votes
2 answers
205 views

Does the frequency response \$H(j\omega) \$ exist for system with unstable poles?

This question arose from a discussion between me and TimWescott in the comments here. The question is: Does \$H(j\omega) \$ exist for systems with poles in the RHP (unstable poles)? My own answer to ...
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Conceptual question regarding the Laplace transformation

In preparation for an exam in linear signals and system my instructed handed us a couple of conceptual questions that should prepare us. I ran into the following: Which statements regarding the ...
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(Almost) Wheatstone bridge

I have this wheatstone bridge: Rmeasure is the impedance of my voltmeter between A and B. My goal is to have the equation of R1/R2. Because Umeasure changes if \$R_2\$ or \$R_1\$ changes. the values ...
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Equivalent resistance in BJT small-signal : Rpi in parallel with Beta*Ib

I'm currently reading Vorperian's book on Fast Analytical Circuits techniques. On page 129 he states : I'm not sure I understand correctly the statement I highlighted in yellow. Is it some kind of ...
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555 Timer duty cycle changing formula

I am making a PWM motor speed controller. I used the Astable mode thinking it would work; it did not. Using an oscilloscope I noticed that I am only changing the frequency not the duty cycle by ...
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2 votes
2 answers
152 views

Getting the wrong KCL equations in op-amp circuit

I have the following op-amp circuit: simulate this circuit – Schematic created using CircuitLab When I use and apply KCL, we can write the following set of equations: $$ \begin{cases} \text{K}...
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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 ...
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Help developing rpm calculation from encoder pulses

I have having a bit of difficulty calculating rpm of a motor using feedback from an encoder. The encoder datasheet is attached here: Encoder datasheet. The encoder has two channels at 1000 PPR, so ...
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Encoder line count vs PPR

I am slightly confused about the terminology of rotary incremental encoders. The encoder in question is a dual channel quadrature encoder. I have attached the datasheet here: Nidec RE30E-1000-213-1 ...
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2 votes
2 answers
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How are irrational numbers best represented and processed by computers?

My question is closely related to this one: How do computers understand decimal numbers? However, that question deals with rational numbers only. I was wondering if irrational numbers can be ...
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