# Tag Info

### 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 ...
• 44.5k

### 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 $e^{-1} = 0.36788$. ...
• 165k
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: ...
• 78.2k
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 ...
• 20.6k
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 ...
• 331k
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 ...
• 4,291

### 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 ...
• 20.3k

### Acceleration when device is on tilt

Only a sketch of a solution. Take all 3 axes into consideration. Acceleration due to gravity, regardless of tilt, will always be 1G, as a vector sum of X,Y,Z, no matter what the tilt. You can ...
• 66k
Accepted

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 ...
• 10.4k

### 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 ...
• 165k

### 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; ...
• 45k

### Performing FFT at low frequencies but high resolution?

I assume for "high speed" you mean a small delay from data collection to the resultant FFT. With a low sample rate, your computational ability isn't the limiting factor, given modern computers. The ...
• 2,798

### 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 ...

### 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 ...
Accepted

• 17.7k