ColdCold
Newbie level 2
Re: 3 dB Bandwidth
maxwellequ and Kevin, the thing is you're BOTH mostly right! You're just speaking different languages. maxwellequ seems to be sticking to the continuous analog terminology, while Kevin, it seems to me, mixes the analog theory with digital terminology commonly used in the discrete, digital realm, that is, the use of discrete trigonometric calculus and the unit circle (ultimately the z-domain). Some folks are more comfortable staying in the continous, analog world and describing the exact same phenomena with sinusoids and continuous trigonometric calculus. But it doesn't matter. I've done all of this stuff both with paper and pencil and with MATLAB and the answers are always the same - but not only that...
they translate into precise, measurable results you can see in the lab. maxwellequ's statement that "sin45 has nothing to do with dBs" is incorrect. The frequency response can always be exactly described with zeros and poles on and within the unit circle in the z-domain. Kevin is somewhat correct in his arguments, albeit not very clear in his explanations, while maxwellequ's statements are more detailed, but entirely correct. And in response to checkmate's disdain for equations (lacking detail??!)... "We can't just use any equation that is unit consistent and assume it has to work" - WRONG! That's the whole point! We CAN assume their correctness, always. The equations NEVER lie and most of Kevin's assertions, like setting R=1 on both input and output, are totally valid. That's the beauty of math: you can set some things to known values and calculate exact reponses for the unknowns. The math (done correctly) is never wrong, my friend. Granted in the real world there are usually several other factors that we may or may not have taken into account in our initial equations, but if you know what they are and/or if you can measure them, then they too can be expressed in your equations if desired. It just depends on the level of accuracy you wish to obtain with your mathematical models.
Now, as for the equivalence of 6dB/octave and 20dB/decade in the stop-band (rolling off)... well, we're in the frequency domain for Bode plots, therefore, if "cf" is your current frequency,
magnitude at (cf*2) in dB = 20*log(cf*2) dB
20*log(cf*2) = 6.02059991 where the 2 represents the octave
20*log(cf*10) = 20.00000000 where the 10 represents the decade
and likewise...
20*log(cf*0.5) = -6.02059991 where the 0.5 represents the octave
20*log(cf*0.1) = -20.00000000 where the 0.1 represents the decade
does that make sense??
maxwellequ and Kevin, the thing is you're BOTH mostly right! You're just speaking different languages. maxwellequ seems to be sticking to the continuous analog terminology, while Kevin, it seems to me, mixes the analog theory with digital terminology commonly used in the discrete, digital realm, that is, the use of discrete trigonometric calculus and the unit circle (ultimately the z-domain). Some folks are more comfortable staying in the continous, analog world and describing the exact same phenomena with sinusoids and continuous trigonometric calculus. But it doesn't matter. I've done all of this stuff both with paper and pencil and with MATLAB and the answers are always the same - but not only that...
they translate into precise, measurable results you can see in the lab. maxwellequ's statement that "sin45 has nothing to do with dBs" is incorrect. The frequency response can always be exactly described with zeros and poles on and within the unit circle in the z-domain. Kevin is somewhat correct in his arguments, albeit not very clear in his explanations, while maxwellequ's statements are more detailed, but entirely correct. And in response to checkmate's disdain for equations (lacking detail??!)... "We can't just use any equation that is unit consistent and assume it has to work" - WRONG! That's the whole point! We CAN assume their correctness, always. The equations NEVER lie and most of Kevin's assertions, like setting R=1 on both input and output, are totally valid. That's the beauty of math: you can set some things to known values and calculate exact reponses for the unknowns. The math (done correctly) is never wrong, my friend. Granted in the real world there are usually several other factors that we may or may not have taken into account in our initial equations, but if you know what they are and/or if you can measure them, then they too can be expressed in your equations if desired. It just depends on the level of accuracy you wish to obtain with your mathematical models.
Now, as for the equivalence of 6dB/octave and 20dB/decade in the stop-band (rolling off)... well, we're in the frequency domain for Bode plots, therefore, if "cf" is your current frequency,
magnitude at (cf*2) in dB = 20*log(cf*2) dB
20*log(cf*2) = 6.02059991 where the 2 represents the octave
20*log(cf*10) = 20.00000000 where the 10 represents the decade
and likewise...
20*log(cf*0.5) = -6.02059991 where the 0.5 represents the octave
20*log(cf*0.1) = -20.00000000 where the 0.1 represents the decade
does that make sense??
