[SI-LIST] Re: 3dB or Knee Frequency
- From: "Dagostino, Tom" <tom_dagostino@xxxxxxxxxxx>
- To: "'cclewell@xxxxxxxxxxxxxx'" <cclewell@xxxxxxxxxxxxxx>,"'Anand.Kuriakose@xxxxxxxxxx'" <Anand.Kuriakose@xxxxxxxxxx>,si-list@xxxxxxxxxxxxx
- Date: Thu, 13 Jun 2002 09:11:29 -0700
The derivation I saw (over 25 years ago) for the equation BW = 0.35/Tr assumed
a critically damped 2 pole response when measuring risetime between 10 and 90%.
Different factors other than 0.35 can be proven for different reference
percentage (20-80% which I think the 0.5 come from) and different responses
(damping and number of poles).
For filters the -3dB frequency indicates where the output power of a test
frequency applied to the input is less than 0.5 of the input. For example, the
simple RC network mentioned will output low frequency components with less than
3dB attenuation but any component above the knee frequency will be attenuated
by 3 dB or more. The knee frequency has nothing to do with the highest
frequency present in the signal but tells the designer where the roll off in
amplitude begins. For a single pole response the amplitude will roll off -20
dB per decade, 2 pole will roll off at -40 dB per decade above the knee
frequency.
For signals there is a similar concept for energy content. A step with 100
psec risetime will have more energy in higher frequency harmonics, (out to 3.5
GHz BW) than a step with 100 nsec risetimes (3.5 MHz BW). To pass a 1 MHz
square wave with 100 psec edges without degrading the rise time implies the
bandwidth of the transmission medium needs to be 3 to 5 times the bandwidth of
the step. SystemRisetime = SQRT(Steprisetime^^2 + Mediumrisetime^^2). From
inspection if both the medium and stimulus have the same risetime (100 psec)
the output risetime will be 140 psec.
If one considers bit error rate then the significance of the bandwidth of the
medium becomes clear. As the bandwidth of the medium decreases then the rise
and fall times of the signal at the output becomes slower and slower closing
the eye in the eye diagram.
Tom Dagostino
Modeling Manager
Mentor Graphics Corp.
SAS
tom_dagostino@xxxxxxxxxx
503-685-1613
-----Original Message-----
From: Clewell, Craig [mailto:cclewell@xxxxxxxxxxxxxx]
Sent: Thursday, June 13, 2002 6:00 AM
To: 'Anand.Kuriakose@xxxxxxxxxx'; si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: 3dB or Knee Frequency
Anand,
I believe the t = .35/BW comes from a unit step into an RC circuit.
If you have a series circuit consisting of a unit step source u(t) with a
resistor and capacitor than the equations fall out like this...
Vc = 1-e^(-t/RC) ~~~ Therefore, t = -RC * ln(1-Vc) and since BW = 1/(2pi
RC) you get... t = [-1/(2pi * BW)] * ln(1-Vc)
If you use a rise time of 10 - 90% and substitute... t = [-1/(2pi *BW)] *
(ln(0.1) - ln(0.9) ~~~ Therefore t = 0.35 / BW.
Regards,
Craig Clewell
-----Original Message-----
From: Anand.Kuriakose@xxxxxxxxxx [mailto:Anand.Kuriakose@xxxxxxxxxx]
Sent: Wednesday, June 12, 2002 11:47 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] 3dB or Knee Frequency
Hi All,
When we talk about high edge rate signals, we talk about two terms namely
1> 3 dB frequency, which is related to the edge rate as approximately
0.35/Tr
and
2> Knee frequency (mentioned in Howard Johnson's famous book and many
SI-list
mails) which is given as 0.5/Tr.
Questions:
1> What is Knee frequency? Does it relate to the highest harmonic present
in
the signal with significant energy? How relevant it is in High speed board
design as against 3dB frequency?
2> To determine the decoupling caps, we have to determine the highest
significant frequency involved in the switching signals. Now the question is
should we consider the 3dB frequency ( mentioned in High Speed Digital
Design by Stephen Hall) or the knee frequency ( in Howards Johnson's Black
MAgic) as the best approximation? Let us consider Tr=1ns. Then we have
3dB
frequency = 350Mhz and Knee frequency = 500 Mhz.
Regards,
Anand.
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