81
votes
Accepted
Why is the time constant 63.2% and not 50% or 70%?
Other answers haven't yet hit upon what makes e special: defining the time constant as the time required for something to drop by a factor of e means that at any moment of time, the rate of change ...
- 47.3k
50
votes
Why is the time constant 63.2% and not 50% or 70%?
It's built into the mathematics of exponential decay associated with first-order systems. If the response starts at unity at t=0, then after one "unit of time", the response is \$e^{-1} = 0.36788\$. ...
- 178k
38
votes
Accepted
Why does hardware division take much longer than multiplication?
A divider maps much less elegantly to typical hardware. Take Lattice ICE40 FPGAs as examples.
Let us compare two cases: this 8x8 bit to 16 bit multiplier:
...
- 100k
37
votes
Accepted
Why is impedance represented as a complex number rather than a vector?
Complex numbers are similar to vectors, but have some extra mathematical properties that make them useful. Most notably, using the complex exponential \$e^{j\omega t}\$ instead of sines and cosines ...
- 22.3k
33
votes
Accepted
How do computers calculate sin values?
Typically high resolution sin(x) functions would be implemented with a CORDIC (COrdiate Rotation DIgital Computer) algorithm, which can be accomplished with a small number of iterations using only ...
27
votes
Accepted
Order of operations and rounding for microcontrollers
This is not a compiler issue: doing the division first here is the legal behaviour, as division and multiplication have equal precedence and are evaluated left-to-right. (Also, when in doubt: use ...
- 9,310
22
votes
Why does this battery use 4.2 V when its nominal voltage is 3.7 V?
A lithium ion cell may start with 4.2V across it, when it's 100% charged, but it quickly falls to about 3.7V, at about 80% charge.
Then it will stay at around 3.7V until charge falls to 20% or so, ...
- 47.3k
19
votes
Do working electrical engineers in circuit design ever use textbook formulas for rise time, peak time, settling time, etc
These calculations are absolutely used by professional EEs, for some on a daily basis. However, for many this job has been given to simulation software, such as LTSpice, which is also used on a daily ...
- 21.6k
17
votes
Accepted
Solving an ideal opamp-circuit leads to a contradiction
The error is in the assumption the I2 = I1.
The OpAmp can (in general) sink and source current.
When it would be sourcing current, this current would have to go to ground, either through R2 or through ...
- 10.9k
16
votes
How do computers calculate sin values?
Most computer trig libraries are based on polynomial approximations, which gives the best balance between speed an accuracy. For example, a dozen or so multiplication and add/subtract operations is ...
- 178k
15
votes
Why is impedance represented as a complex number rather than a vector?
Why are complex numbers used and not Vectors?
simply because there is no vector division defined in vector algebra, so simply you cannot use Ohm's law in division form, thereby making calculations ...
- 571
14
votes
Order of operations and rounding for microcontrollers
This is a fundamental C issue: you need to be extremely clear whether you're doing integer or floating-point arithmetic.
uint16_t temperature = reading*0.076295;
...
- 47.1k
13
votes
Do working electrical engineers in circuit design ever use textbook formulas for rise time, peak time, settling time, etc
You refer to these basic formulae at first and then find the real world has a lot of non-linear characteristics like XOR phase detectors in a second PLL loop response when you exceed the phase limit ...
- 148k
12
votes
Why is impedance represented as a complex number rather than a vector?
Just to remark on that you can represent impedance as a matrix:
$$
R + \mathrm j X \leftrightarrow \begin{bmatrix}
R & X \\
-X & R
\end{bmatrix}
$$
This is in fact the matrix ...
- 229
11
votes
Why does hardware division take much longer than multiplication?
We can have multiple layers of logic per clock cycle but there is a limit, exactly how many layers of logic we can have an how complex those layers can be will depend on our clock speed and our ...
- 23.1k
11
votes
Why is the time constant 63.2% and not 50% or 70%?
The decay of an RC parallel circuit with capacitor charged to Vo
v(t) = \$Vo(1-e^{-t/\tau})\$ , where \$\tau\$ is the time constant R\$\cdot\$C.
So v(\$\tau\$)/Vo is approximately 0....
11
votes
Implementing an absolute value function in C
The standard C library is providing the optimized solutions for many problems with considerations based on the architecture, compiler in use and others. The abs() ...
- 10.1k
11
votes
Accepted
Using a PCB trace as a heater / Hilbert Curves
I have some experience with PCB heaters using copper traces on polyimide (flex circuit) substrate. My goal has always been to use uniform copper trace width with consistent trace-to-trace spacing so ...
- 29.5k
10
votes
Accepted
how to solve this op-amp circuit?
Your circuit doesn't have negative feedback: -
Therefore it acts as a comparator with hysteresis and hence, the output changes state when the input voltage passes the hysteresis threshold points ...
- 473k
9
votes
Why does hardware division take much longer than multiplication?
Slow division is inherently iterative so it tends to take longer. There are somewhat faster slow division algorithms than the simple ones, using lookup tables. The SRT algorithm produces two bits per ...
9
votes
Acceleration when device is on tilt
Your main mistake is in not treating acceleration as a single vector. When the car is at rest, that vector will always be 1 g upwards. Don't look at just the X component of the raw accelerometer ...
- 315k
9
votes
Accepted
Is a CPU declarative?
Aren't you both wrong? To me this sounds like arguing that if someone thinks in English then their neurons are wired in English, which is nonsensical.
If you actually want to force application of the ...
- 57.3k
9
votes
Conundrum: High pass filter passes DC?
The resolution to the conundrum is that there really is no conundrum.
Your input, a step function, has infinite dc component (its Laplace Transform, \$1/s\$, goes to infinity as \$s\rightarrow 0\$). ...
- 2,912
9
votes
Conundrum: High pass filter passes DC?
You're confusing the steady-state response with the total response. The transfer function for that circuit is:
$$H(s)=\frac{s}{s+\frac{1}{RC}}$$
and if you solve for the step response:
$$h(t)=\text{e}^...
- 21.8k
8
votes
Do working electrical engineers in circuit design ever use textbook formulas for rise time, peak time, settling time, etc
Engineers design things because there is a customer that wants or needs something. The time parameters you are asking about and others effect how satisfied the customer will. I would say engineers ...
- 2,130
8
votes
Find the phase angle between two functions
Additionally, it seems to me which function leads which is rather relative as I can shift any function 360 deg, any easy reconciliation?
Absolutely. What is leading or lagging is up for ...
- 100k
8
votes
How to choose correct resistor values when designing a circuit?
That's not even the simplest circuit and the voltage divider or the resistance values make no sense for a LED circuit.
There is also one incorrect assumption - for a 5V LED and 3.3V LED in parallel, ...
- 172k
7
votes
Accepted
How are irrational numbers best represented and processed by computers?
There’s nothing special about computers in this context. An infinite number of nonrepeating decimal places cannot be stored or manipulated on a computer, on paper, or in a human brain.
Irrational ...
- 22.3k
7
votes
Accepted
Overdrive voltage of NMOS vs PMOS
Here are an N-channel MOSFET, and a P-channel one in a simple setup to demonstrate the conditions required to switch their channels "on" and "off":
simulate this circuit – ...
- 47.3k
Only top scored, non community-wiki answers of a minimum length are eligible