what is the reason if bandwidth increases then stability increases and if bandwidth decreases then stability decreases?
how transient response is dependent on the bandwidth?
Dear Josef,
when publish a pdf, remember to embedd all fonts otherwise, not everyone will able to read it.
Attached the fonts used in your pdf file, as can you seen only three are embedded (emb):
Dear Josef,
I do not want to disappoint you, nor to waste your time but in the doc I see the same fonts.
Many people share their MicrosoftWord files as they were like Swiss boxcutter, but they are not. If the reader don't have installed the same fonts on his computer, he cannot red the files.
The best thing for exchanging documents is to embedd and subset all fonts in the pdf file (it is the only way to submit papers to the most of the conferences). But I do not ask you to do this, for what I am concerned, I understand your document anyway.
Furhermore I do not know how to achieve this goal with Word since, usually, I keep a thousand miles away from it.
regards
S.
The rise time is (0,35 - 0,5)/3dB frequency. See chapter 12 in
https://www.researchgate.net/publication/281480600_Theory_of_electronic_circuits
Book Theory of electronic circuits
Stabilitty [inability to oscillate] has nothing to do with the bandwidth, but it does depend on the rate at which the gain falls off. First order low pass has a fall off rate of 6dB/octave and can give a max phase lag of 90 deg. With negative feedback it cannot oscillate, fortunately. Unfortunately "stability" may be used to describe several other phenomena. [One would be variation of a reference with temperature and time]
A second order low pass has a max phase shift of 180 deg, and is likely to oscillate with negative feedback possibly due to additional lag due to stray.
A third order low pass can provide a max phase lag of 270 deg and when its phase lag is 180 deg this adds to the negative feedback (phase inversion of 180 deg) and makes the feedback appear as positive. If there is adequate gain at this frequency, i.e > 1, then system will oscillate. That is why one uses a third order low pass filter in a phase shift oscillator. If the RC's are equal and without isolation by buffer, they give 180 deg phase lag at 6/(2.pi RC) and has a gain of 1/29 at this frequency. If feedback with inverting gain exceeding 29, the system will oscillate. You can have the oscillation at 1hz or 10Hz or any other frequency such as 100khz. so bandwidth of amplifier has no specific say in the possibility of creating oscillations, which is called instability.
One can bring in stability in a system using two known methods, add lag or add lead. Adding lag does not make things better, but the reduction in gain associated with this method helps stabilize the loop. adding lead certainly helps reducing the overall lag to les than say 150 deg, if one is aiming at 30 deg phase margin. Learn thoroughly about phase to understand this behavior of negative feedback systems. An oscillator does not oscillate if it has positive feedback at dc. It latches up like a Schmitt trigger. Oscillators should have finite gain at dc. They should have positive feedback at the oscillating frequency! In case you want to have further discussions contact me! [email protected]
transient response depends on the order of the system. A butterworth second order LPF has an overshoot of 4% for step response, be it for a 1hz filter or a 100khz filter. In actual time the response of the 100khz filter will be much faster. However transient response is of interest only if system does not oscillate! A system with low phase margin can give an oscillatory output for a disturbance. So it is good practice to keep the phase margin as at least 45 deg and gain margin as 6dB. A phase shift oscillator with inverting gain of 14.5 (instead of min 29 for oscillations) has a 6dB gain margin.
Beside the very good and long answer above few more comments: Without feedback an amplifier would not oscillate, so no BW vs stability trade-off. But also internally inside the transistors FB exists, so even an emitter follower could osc, e.g. under cap loads. Overshoot and phase margin are closely related, but for high-order systems or systems with allpass most formulas do not fit fit. Always double check in tran analysis! The trade-off betw stability and bandwith is hard to break, best try to make your over-all multi-stage amp as close as possible to a 1st order system, only if you can allow some overshoot, some tricks can help, but not much. A clever method is a high-BW amp with low FB in parallel for a more accurate LF-amp, but still here some problems remain, like no 100% pz cancellations.
Bandwidth of amplifier can be approximated by dc gain multiplied by -3dB dominant pole. Assume amplifier has only single pole. Then, one can say this amplifier has no stability problem. But for typical two stage amplifier. There are at least two pole which can be derived as symbolic formulas and can be plotted with matlab function called Bode plot which can plot magnitude and phase response. Stability of amplifier can be related with specification such as phase margin which can be measure how far of phase response from the point of unity gain frequency. Usually,good stability is more than 60 degree of phase margin.
There is a weak relation between OpAmp gain bandwidth product (GBW) and slew rate - but only a weak one:
In general, higher GBW comes with higher slew rates (as in V/s), but slew rates still vary greatly for the same GBW numbers: my best guess is that slew rate also depends on the intended area of application of the OpAmp: OpAmps intended to be used as a buffer (one indicator: stable at gain = 1) exhibit higher slew rates than OpAmps intended to be used at high gain numbers.
GBW versus Slew rate - it's a tricky question.
HF circuits have usually less DC gain, therefore operate with less resistances and higher currents.
This results under otherwise identical capacity ratios to higher slew rate and smaller time constants. Importantly is distribution of poles - how we can correct. etc. Within the technology used (parasitic capacitance) we always have only limited possibilities.
Vasile:
Mathematics is the same in all languages :-))
Josef
Yes, if we use a trick of type "current on demand" is many things possible.