Title: Computation of Noise Spectral Density in Switched Capacitor Circuits using the MixedFrequencyTime Te
1Computation of Noise Spectral Density in Switched
Capacitor Circuits using the Mixed-Frequency-Time
Technique
- Vinita Vasudevan and Ramakrishna Mokkapati
- Indian Institute of Technology Madras
2Outline
- Existing methods
- Algorithm for computation of noise spectral
density - Methods of solution
- Results
- Advantages and limitations
3Previous Work
Use the Adjoint Network Technique Okumura et
al,1993,Telichevsky et al, 1996,Yuan and Opal,
2000
4Previous work Contd
Find the impulse response h(t,t)
Rice, 1970 Toth, Yusim,Suyama - 1999
Assuming white noise input
5Noise Algorithm - Definitions
Expected power spectral density, PSD,
6DefinitionsContd.
x(t) is a stationary process
x(t) is a non-stationary process
7Circuit Equations
x(t) state vector, v(t) large signal
excitation
If noise xn(t), is regarded as a perturbation
A(t) Jacobian at steady state
B(t) Spectral intensity of noise sources
W(t) Wiener process
8Noise Equations
Define
9Application toSwitched Capacitor Circuits
- Linear periodically switched ( for noise
analysis) - Output noise is cyclo-stationary with a
periodequal to clock period
wc clock frequency
wm measurement frequency
(Steady state)
10Computation of PSD
- K(t) contains a tone at ? and spectral
componentsat ? ? n?c - To compute the PSD, we need the component d0
of KN(t) - Shooting Newton technique or the
mixed-frequency-time technique
11Shooting Newton Method
- Assumes K(t) is periodic This occurs for
example,if ? All components of K(t) are
periodic with period - Start with an initial guess K(0)
- Integrate equations for the cross-spectral
density for one output period - Correct K(0) Use Newton method
- Integrate for one more cycle usingcorrected K(0)
12Cross-spectral Density from Shooting Newton Method
13Mixed Frequency-Time Method
- Sample K(t) at t0 and tTc
- Solve using Newton method
- Only two integrations over a clock cycle are
required to compute the power spectral densityat
a particular frequency - Very efficient especially when ?ltlt ?cor ? ? ?c
14Equivalent circuits
15Results Low Pass Filter
Average CPU Time per frequency MFT 17.86
seconds SN 80.38 seconds
16Results Second order bandpass filter
Average CPU Time per frequency MFT 19.07
seconds SN 846.87 seconds
17Advantages and Limitations
- Algorithm can be used for all circuits in which
noise is regarded as a perturbation - Noise can be stationary/cyclo-stationary
- Can be easily integrated into a circuit simulator
- All noise sources considered simultaneously
- Aliasing sidebands not considered seperately
- For an N node network, N(N1)/2 equations for the
covariance matrix - Additional filtering networks for 1/f noise
18C2
V
AV
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