From: Mike Saunders (email@example.com)
Date: Fri May 26 2000 - 11:10:50 PDT
Dr. Johnson doesn't go into any real specifics regarding the limitations on
Fknee. As far as EMI is concerned, the text states "Fknee is no substitute
for full-blown Fourier analysis. It can't predict electromagnetic
emissions, whose properties depend on the detailed spectral behavior at
frequencies well above Fknee." My take on this statement is that according
to Fourier series expansion, a square wave consists of an infinite set of
discrete frequency components, the fundamental plus odd harmonics of
decreasing amplitude. For faster and faster Tr, a true square wave is
approached and the amplitudes of the odd harmonics increase. These can and
will radiate depending upon board geometries, impedance mismatches
(reflections) etc. The main jist of the use for Fknee seems to be in
determining whether a digital circuit (driver, transmission line, load, IC,
driver...) will pass a digital signal (practically) undistorted or not.
His statement does seem to contradict other EMI papers I've seen which call
out a similar definition to Fknee. The "logic bandwidth" as defined is
1/(pi*Tr) = 0.318/Tr, and is defined at the point where the slope changes from
-20dB/decade to -40dB/decade. This is the bandwidth necessary to pass the
signal without degrading the edge rate, and is a little lower than
Johnson's 0.5/Tr. Maybe he's just trying to be extra careful.
Of course, EMI depends not only on the edge rate, but also on the clock
rate. Any conductor over 1/20 of its wavelength is considered to be an
antenna for EMI purposes. Using f = c/wavelength (c = 3*10^8 M/S), EMI @
300MHz can radiate from an antenna (trace) just 2" long. (For 1/20 *
wavelength = 2", 1 * wavelength ~ 1Meter.) Reducing the clock rate reduces
the beginning of the -20dB/decade slope, located at 1/(pi*T), and therefore
will also reduce emissions. 1/(pi*Tr) still occurs at the same place, but
the spectrum's amplitude will already be lower by that time when slower
clock rates are used.
Take this info as you will. I have the book so I wanted to answer the
question as to what the derivation of Fknee was.
At 09:16 AM 5/26/2000 PDT, Barry Ma wrote:
>Can you detail what you mentioned: "He also states that for EMI, frequencies
>well above Fknee ARE important and should not be ignored" at the end of your
>---------- Original Text ----------
>From: "Mike Saunders" <firstname.lastname@example.org>, on 5/26/00 7:29 AM:
>Howard Johnson's book uses a D flip flop clocked at several nominal rates
>as an example of a typical digital signal. The output merely toggles, with
>10%-90% rise/fall times which are about 1% of the overall period. Then, he
>shows a plot of the spectral power density of the output, based on
>frequency components relative to the sample clock. In this plot, the
>spectral power density rolls off at a rate of about -20dB/decade when
>plotting signal amplitude (y) vs. frequency (x, log scale). However, by
>the knee frequency, the spectrum is already at 6.8dB(V) below the straight
>-20dB/decade slope. After this knee frequency, the slope rolls off
>exponentially, indicating that since most of the energy is contained below
>the knee frequency, the behavior of a circuit at frequencies above this
>frequency will hardly affect digital performance. He also asserts that the
>behavior of a circuit AT the knee frequency determines how well it can
>handle a steep edge. Dr. Johnson does qualify Fknee, saying it can be used
>as a quick way to relate the time domain to the frequency domain.
>Therefore, it can be used as a quick rule of thumb to determine whether or
>not particular frequencies should be taken into account. He also states
>that for EMI, frequencies well above Fknee ARE important and should not be
>At 03:35 PM 5/25/2000 -0700, you wrote:
>> I've seen the derivation for the BW = 0.35/tr(10% - 90%).
>> I haven't seen the derivation for the BW = 0.5/tr
>>Barry Ma wrote:
>>> There is another way to figure out what is the highest frequency we
>might need to take care of:
>>> Howard Johnson call it Fknee = 0.5/Tr. Given Tr = 0.4 ns, We have Fknee
>= 1.25 GHz.
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