Transcript The story of Knee Frequency

The story
of
Knee Frequency
Ruxin Xie
11.05.2013
Why it’s called Knee frequency
Knee Frequency?
Knee Frequency?
Knee Frequency?
Definition of the Knee frequency
Note:
• Pulse shape hardly matters
• K = 0.35 is typically used
• K = 0.5 for conservative approximation
• Imprecise measurement
Advantage:
• Simply defined based on rise time
• Easy benchmark of frequency effect
Pulse Type
K
Exponential
1st order
0.35
Exponential
2nd order
0.34
Gaussian
0.32
90%
Amplitude (Linear scale)
Amplitude (Linear scale)
How to calculate the Knee frequency
10%
Frequency (Hz)
Time
E(t) =
50%
FFT
−𝑡2
A0exp(2𝜎2)
Set E(t) = 10%, t10% = 𝜎 2𝑙𝑛10
10
E(t) = 90%, t90% = 𝜎 2ln( 9 )
Tr10%-90% = | t90% -t10% | = 1.69𝜎
E(𝜔) =
−𝜔2𝜎2
A1exp(
)
2
Set E(𝜔) = 0.5, 𝜔 = 2𝑙𝑛2/𝜎
Since 𝜎 = Tr10%-90% /1.69, 𝜔 = 2𝜋f
f = 0.32/ Tr10%-90%
Simulation Results
Assume Square wave signal, Tr10%-90% = 1ns, T = 10ns, Duty Cycle = 50%
fknee = 0.32/ Tr10%-90% = 0.32/1ns = 0.32 GHz
Simulation Results
K = 0.27
K = 0.32
K = 0.5
Thank you!
Questions?