frequency & amplitude { confused }

[junee]

Hi...,

well, I'll jump straight into the theory.

Wave equation is a ii order hyperbolic PDE

by solving it with the principles of
superposition( Fourier concepts )

we can take the solution of the wave equation as

y = A cos( 2 * pi * f + phi )

I think this is the back bone of the most of the
electronic stuff.

From a given crystal we can produce only
frequency, but not amplitude.

my doubts was,

(1) how amplitude was produced depending our requirements ?
what is logic behind that ?

cheers
nimo
________

It’s a good thing we have gravity, or else when birds
died they’d just stay right up there.Hunters would be all confused.


StevenWright, comedian.

 

[[email protected]]

Hi...,

well, I'll jump straight into the theory.

Wave equation is a ii order hyperbolic PDE

by solving it with the principles of
superposition( Fourier concepts )

we can take the solution of the wave equation as

y = A cos( 2 * pi * f  + phi )

I think this is the back bone of the most of the
electronic stuff.

From a given crystal we can produce only
frequency, but not amplitude.

 my doubts was,

(1) how amplitude was produced depending our requirements ?

Tolerably complete mathematical descriptions of real electronics
include non-linear terms.

Crystal oscillators mostly rely on (non-linear) output stage clipping
to limit the amplitude; the Q of the crystal is high enough that
harmonics that this produces are too low to be easily measured.

what is logic behind that ?

The logic reduces to the observation that we build it, see if it
works, and if it works we analyse it to make sure that we understand
the way it works, so that we can be reasonably sure that it will keep
on working.

Sometimes we build a nathematical model and see if that works, but no
model is perfect, so we've still got to build the real thing at some
point or other, just to check whether we've made the right
simplifications.

 

[Nimo]

Tolerably complete mathematical descriptions of real electronics
include non-linear terms.

Crystal oscillators mostly rely on (non-linear) output stage clipping
to limit the amplitude; the Q of the crystal is high enough that
harmonics that this produces are too low to be easily measured.


The logic reduces to the observation that we build it, see if it
works, and if it works we analyse it to make sure that we understand
the way it works, so that we can be reasonably sure that it will keep
on working.

Sometimes we build a nathematical model and see if that works, but no
model is perfect, so we've still got to build the real thing at some
point or other, just to check whether we've made the right
simplifications.

thanks bill for the clarifications;

but my doubt was..,

How amplitude(of a wave) was produced from an Oscillator,
where as it is only capable of producing Frequency ( for provided
inputs )

take for example Quartz crystal, it can produce the wave which
we can have control over its frequency.., but how it's amplitude is
handled ?

got my doubt ?
________
so long
nimo

I was amazed that cats had holes cut into their fur
precisely in those places where they had eyes.’

Georg Christoph Lichtenberg
(1742–1799)

 

[whit3rd]

take for example Quartz crystal, it can produce the wave which
we can have control over its frequency.., but how it's amplitude is
handled ?

The linear-model equations that yield the frequency do NOT INCLUDE
the amplifier large-signal model. All amplifiers (tubes, transistors,
op amps, even sparkgaps near breakdown) have operating curves
that (at one point or the other) have a power gain. The majority
of oscillator circuits do not bias the amplifiers to remain in that
power-gain region, so the amplifier will clip/distort/turn off for
large
parts of the cycle.

The exception is a class of not-very-power-efficient oscillators
that give low-distortion sinewaves, including phase shift oscillators
and Wien bridge oscillators. Dynamic gain-control techniques are
employed to stabilize these amplifiers (notably, the resistance
temperature dependence of a lamp filament acted to limit the
gain in HP200 series audio oscillators). A 10 kHz oscillator
that employs a gain-of-3 amplifier will be 10% in error on its
amplitude
after one second if the gain is 3.000 02 ; this accuracy of gain is
too high to achieve with fixed components, there HAS to be
a robotic feedback to keep it going.

 

[Nimo]

If the output of the oscillator has an amplitude of zero, it has no
usable output signal.

Correct;


The equations you mentioned in your first post may not indicate any
output amplitude, but for any oscillator to be useful, it must produce
a signal of some amplitude.

voila; what my point is.,

How can we produce required "Amplitude" for our needs ?

where as different crystals can only produce frequencies., that means

we can have control over crystal's frequency, but not amplitude., that
means

=> how that mighty Amplitude "modulation" is done ?

I find it more amazing that the cat's eyes are located so that they
line up with the holes in the fur.

clever., keep it up