Mixed-Signal VLSI Design Course Code: EE719 Department: Electrical Engineering Lecture 4: January 19, 2020 Instructor Name: M. Shojaei Baghini E-Mail ID: mshojaei@ee.iitb.ac.in 1
2 2 Module 3 Coherent Sampling and FFT Simulation IIT-Bombay Lecture 4 M. Shojaei Baghini
3 3 References • Coherent Sampling vs. Window Sampling, Tutorial 1040, Maxim, March 29, 2002 • Exact Signal Measurements using FFT Analysis, Stefan Scholl, Course Material, 2016 IIT-Bombay Lecture 4 M. Shojaei Baghini
4 4 Coherent Sampling Example: Sampling window = 3 cycles with nonoverlapping samples ! " = !"$% &'( × * In general: + l N and K are integers with N > 2K (N: number of samples and K: number of cycles). l N and K don't have any common factor (co-prime numbers). IIT-Bombay Lecture 4 M. Shojaei Baghini
5 5 FFT Simulation l Practical sampling produces distortion. l Number of samples: N N-point FFT will provide the power of the discrete time signal at discrete normalized frequencies of 0, 2 p /N, 4 p /N, 6 p /N, ...., 2(N-1) p /N (normalization factor = f sampling ). l FFT bin = 2 p /N (bin number L corresponds to w =2 p L /N). • Window functions l How do we ensure simulation results are accurate? - Simulation accuracy options - Coherent sampling with N non-overlapping samples - Benchmarking simulations IIT-Bombay Lecture 4 M. Shojaei Baghini
6 6 Coherent Sampling - FFT Simulation Example f sampling =82MHz f signal =25.05444433MHz No. of signal cycles=2503 No. of samples (N points for FFT)=8192 25.05444433/82=2503.00009697/8192 SNR=59.3dB THD=-70.3dBc f sampling -3f signal f sampling -2f signal Example from TUTORIAL 1040, Maxim Coherent Sampling vs. Window Sampling March 29, 2002 IIT-Bombay Lecture 4 M. Shojaei Baghini 4
7 7 Noncoherent Sampling - FFT Simulation Example Spectral f sampling =82MHz f signal =25.2245MHz Leakage No. of signal cycles=2520 No. of samples (N points for FFT)=8192 25.2245/82=2519.98907/8192 SNR=51.6dB THD=-69.1dBc Example from TUTORIAL 1040, Maxim Coherent Sampling vs. Window Sampling March 29, 2002 IIT-Bombay Lecture 4 M. Shojaei Baghini
8 8 FFT Processing Gain (PG) !" = 10log(*/2) Exact Signal Measurements using FFT Analysis, Stefan Scholl, Course Material, 2016 IIT-Bombay Lecture 4 M. Shojaei Baghini
9 9 First Practice: FFT, Matlab Simulation Consider the condition of coherent sampling with the non- repeated samples for this exercise as you choose f s . • Choose a signal with 1 frequency (single tone) and then 2 frequency components (2-tone signal). • Start from f s > Nyquist rate but close to it and then increase f s (3 different values of f s ). Specify values of N and M. • For each value of f s , plot dB magnitude of FFT of the sampled signal (normalized to f s ) and label magnitude of main frequency components. Make sure highest frequency component is always at 0 dB for the reference. • Obtain SNR of the sampler in each case. • You may try one of the windowing methods and repeat the simulations to compare the results with rectangular windowing. IIT-Bombay Lecture 4 M. Shojaei Baghini
10 10 Module 4 Introduction to Sampling Switches Reference Section: Sampling Switches Chapter: Introduction to Switched-Capacitor Circuits Book: Design of Analog CMOS Integrated Circuits Behzad Razavi, 2017 • This part of the lecture is based on class notes only. IIT-Bombay Lecture 4 M. Shojaei Baghini
11 11 End of Lecture 4 IIT-Bombay Lecture 4 M. Shojaei Baghini
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