In some of the reference text books, Modulation index of AM signal is defined as the ratio of Maximum value of message signal to that of Maximum value of carrier signal.
i.e., Modulation Index of AM wave = (Am/Ac)
and Modulation index of AM is also equal to the Absolute value of the product of ampltude sensitivity parameter ( Ka) and message signal m(t).
Modulation Index of AM wave = Absolute Value [Ka m(t)]=| Ka m(t) |
where, |m(t)|= Maximum value of mssage signal=Am
If both definitions are correct, then,
modulation Index of AM signal =(Am/Ac)= | Ka m(t) |=Ka|m(t)|=KaAm
Above equation results in : Ka= ( 1/ Ac)
Therefore can we consider amplitude sensitivity parameter ( Ka) is always equal to the reciprocal of carrier signal amplitude??
The whole problem you brought here can be solved directly by precise definition of the terms you brought.
According to the definitions you brought here , then your findings is okay.
Since the modulation index is = Am/AC, and the at the same time it is equal to Ka. Am, then one gets Ka= 1/Ac.
This is straight forward Algebra!
Mu question However why does one introduce Ka instead of 1/Ac.
What is the benefit of such term Ka ??
Best wishes
Let's see. We are assuming double sideband AM, DSB AM, in which the signal modulates the carrier symmetrically, above and below the carrier wave's zero axis.
The modulation index is the ratio we will permit, Am / Ac.
If we allow 100% modulation, that means that the message signal m(t) will cause the signal + carrier's amplitude to vary, from a max of Am + Ac to a min of 0. You will create bad distortion, if you allow more than this 100% modulation.
So, the total amplitude, signal and carrier:
Amax = Ac + Am
Amin = Ac - Am
If Am = Ac, then Amin = 0.
This "amplitude sensitivity" term, Ka, is nothing more than a factor,
The whole problem you brought here can be solved directly by precise definition of the terms you brought.
According to the definitions you brought here , then your findings is okay.
Since the modulation index is = Am/AC, and the at the same time it is equal to Ka. Am, then one gets Ka= 1/Ac.
This is straight forward Algebra!
Mu question However why does one introduce Ka instead of 1/Ac.
What is the benefit of such term Ka ??
Best wishes
Yes. This is what the confusion created in many standard communication text books. The benefit of Ka is not justified.
If you consider the carrier amplitude in a case where it is large, the ability to create a change in that amplitude is indeed small. Quite the opposite for small carrier amplitudes and hence the modulation sensitivity is greater. So there is an intuitive sense to this result.
Hi at all
the m=Vm/Vc when use a AM typical modulator like MC 1496 and mesure the m ( there many methods) the m is not equal with the the ratio Vm/Vc i thik the AM modulator (circuit) have a gain and this can be change the Vm/Vc
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