Electronics > Projects, Designs, and Technical Stuff
Shaping of signal only with analog components
ricko_uk:
Hi,
I have to feed the current (not the voltage) through a solenoid so that it follows a bell-curve shape as shown in the attached picture or as close as possible given the requirements below. That pulse is only once off (not repetitive).
The main requirements are:
- there is no micro or any other means to use DAC to create that waveform. It needs to be created just by analog means/components.
- the PSU can only be turned on and off so possibly the rising edge can be created when turning on and the falling edge when the power is turned off
- the solenoid is has an inductance of 40mH and a DCR of 26R
- the voltage applied is only 12V
- ideally the "curvature" of the three "knees" bottom left curve, bottom right curve and curve at the top/apex to be adjustable (i.e. their radius for lack of better word) by changing the values of the components (not the solenoid)
Could anybody with analog experience suggest any solution?
Many thanks :)
m98:
What do you want to achieve with that, and what timescale should the pulse be on? Do you want to limit EMI? Then just use a parallel capacitor on the solenoid.
nfmax:
You want to generate what looks like a Gaussian pulse? It's a little-known fact, but if you cascade a series of identical low-pass filters, of whatever response, the impulse response becomes closer and closer to a Gaussian as the number of stages increases. The LTSpice model attached shows 16 cascaded RC filters (with 'perfect' voltage buffers between stages) converting a rectangular pulse into a pretty good Gaussian. Four quad OPAMPs would do the job. Then you feed the voltage output into a standard voltage-to-current converter stage driving your solenoid. NO micros involved!
It may not be what you want, but it may help
T3sl4co1l:
Nice thing about the bell curve, it's an eigenfunction of the Fourier transform, down to proportional constants.
Okay, bigwords, let me explain.
"Eigenfunction" here just means it looks the same after FT. A Gaussian pulse has a Gaussian spectrum and vice versa.
So what? You can construct a filter with a Gaussian frequency response, and a short impulse through it will have a Gaussian waveform. (The pulse must be much shorter than the time constant of the filter, otherwise it smears out a bit -- somewhere between an impulse, and a square wave with sigmoidal rising and falling edges.)
Downside: the Gaussian function is not a rational function, i.e., it's composed of elementary functions, not a ratio of polynomials. The best you can do is a truncated polynomial best-fit. (There are plenty of polynomial functions with similar hilly shapes, 1/(1+x^2) for example, but none of them have the exponential cutoff of the Gaussian -- which has consequences in terms of statistics, analysis, etc. In particular, the hilly shape is only in the frequency domain. Rational polynomials are not eigenfunctions of the Fourier transform, so you won't get the same waveform as spectrum, only arbitrarily close.)
And a best-fit means you're probably going to need a lot of poles, i.e., a lot of L and C (or R, C and opamps). Which means, while it could still be adjustable... you might want to look at why you want this, rather than to just go and do it. :)
Another way to understand this limitation, is to consider causality: a Gaussian wave has infinite extents, no beginning or end, only exponential cutoffs in either direction. An arbitrarily long filter, can have arbitrarily long delay, but it still must have zero output for t < 0, and some approximation of an exponential tail for 0 < t << t_peak. (The exponential decay after t_peak is quite normal, at least.)
So a better question is, why do you need such a particular waveform?
Also, you provide some units (L, R, V), but not enough to even determine whether your request is fundamentally possible -- that is, the pulse width and height. Presumably the width is greater than 2ms and the height is less than 500mA...
Given your last requirement, it seems you don't want a Gaussian as such, but perhaps a piecewise linear velocity or acceleration function? Which does not have exponential cutoffs (beyond the settling time inherent in the system), and has, say, quadratic sections transitioning between regions. These can be constructed by multiply integrating square pulses, the heights of which determine the curvature and the durations of which determine the breakpoints (if the output amplitude is constant, these might be timed by comparator, so that the integrator gain doesn't need to be trimmed).
Tim
Marco:
--- Quote from: ricko_uk on July 23, 2020, 02:15:19 pm ---- ideally the "curvature" of the three "knees" bottom left curve, bottom right curve and curve at the top/apex to be adjustable (i.e. their radius for lack of better word) by changing the values of the components (not the solenoid)
--- End quote ---
Pretty much impossible in analogue ... if you just wanted the first two knees and kept it symmetric you could create a gaussian and distort the top somehow, but this implies sequencing.
You can do it with analogue components, but it's a partly digital function.
Navigation
[0] Message Index
[#] Next page
Go to full version