Overview: Embedded systems increasingly employ a combination of low speed serial, analog voltages and RF communications which are tightly synchronized in time. This session will discuss the background of performing time and frequency domain analysis on these systems with example measurements on a digitally controlled RF transmitter. What will you learn? The challenges of debugging embedded systems Frequency domain analysis and FFT basics Time gating, Dynamic range and Triggering considerations PLL locking measurement example

1. Synchronous Time and Frequency
Domain Analysis of Embedded
Systems

2. Agenda
l Complex Embedded Systems
l The Challenge of Debugging Embedded Systems
l Frequency domain analysis
l Time gating
l Dynamic range
l triggering
l Measurement Example: PLL locking
l SPI triggering
l Measuring settling time and transient spectrum
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3. Complex Embedded Systems
Digital signals
D/A
IQ modulator
D/A
RF signals
DSP
Micro controller Analog signals
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4. The Challenge of Debugging Embedded Systems
l Baseband digital, RF and analog signals are interdependent
l Feedback control of RF by microcontroller
l Low speed serial busses
l Critical timing relationships
l Interference between RF and digital signals
l Analyzing and debugging in the frequency domain
l Frequency domain analysis synchronized with time and digital domains
l Frequency analysis speed
l Sufficient sensitivity in both time and frequency domains
l Triggering ( time, digital and frequency)
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5. Fourier Transform Concept
Any real waveform can be
produced by adding sine waves
Spectrum changes
Over time
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6. Measurement Tools: Spectrum Analyzer
l Spectrum is measured by sweeping the local oscillator across the
band of interest
l Band pass filter after IF amplifier determines the frequency resolution (RBW)
l Very low noise due to IF gain and filtering
l Sweep can be fast over narrow span
l Real time operation possible over a limited frequency range using FFT after IF
filter
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7. Spectrum Measurement is a Function of Time
Glitches
time
f1 f2 f3 f4 f5 f6 f7
Measurement frequency
Center frequency of the RBW filter is swept across the Frequency range to build the
signal spectrum
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8. Discrete Fourier Transform
l Transform signal into N “bins”
l Each “bin” is the inner product
(sum of signal samples
multiplied by a base signal)
N 1 k
 i 2 n
X k   xn  e
l Base signals are from a set of
orthogonal functions N
l Resolution bandwidth filter is
determined by the number of n 0
samples at a given sample rate
f  1  fs
tint N
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9. Fourier Transform: Instantaneous Spectrum
f1 f2 f3 f4 f5 f6 f7
f1 f2 f3 f4 f5 f6
f7
f1 f2 f3 f4 f5 f6
f1 f2 f3 f4 f5 f6 f7
f1 f2 f3 f4 f5 f6 f7
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10. Frequency Domain Analysis
FFT Basics
FFT
ts f FFT
Integration time tint Total bandwidth fs
NFFT samples input for FFT NFFT filter output of FFT
l NFFT Number of consecutive samples (acquired in
time domain), power of 2 (e.g. 1024)
l ∆ fFFT Frequency resolution
l tint integration time
l fs sample rate
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11. FFT Implementation
Resolution Bandwidth
l Two important FFT rules
l RBW dependent on f s  tint  N FFT
l Integration time, e.g. 1 sec => 1 Hz,
100 ms => 10 Hz
l Highest measureable
f s NFFT
frequency dependent on
f max  
l Sample rate (e.g. fs = 2 GHz => fmax
= 1 GHz)
2 2tint
l Nyquist theorem: fs > 2 fmax
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12. FFT Implementation
Digital Down Conversion
l Conventional oscilloscopes
l Calculate FFT over entire acquisition
l Improved method:
l Calculate only FFT over span
of interest
l fC = center frequency of FFT
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13. FFT Implementation
Digital Downconversion
Traditional Oscilloscope FFT calculation
Time Domain Frequency
Domain
Zoom
t Windowing FFT
(f1…f2)
Record length f
f1 f2
Data aquisition Display
FFT calculation with digital downconverter
Time Domain DDC Frequency
Domain
Digital down- SW
conversion fc Windowing FFT Zoom
t
Record length (f3…f4)
Span f1…f2 f
f3 f4
(HW Zoom)
Data aquisition Display
=> FFT much faster & more flexible
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14. FFT Implementation
Overlapping FFT
l Conventional oscilloscopes
FFT over complete acquisition
first aquisition second aquisition third aquisition
FFT 1 FFT 2 FFT 3
l Improved approach
FFT can be split in several FFTs and also overlapped
first aquisition
 Faster processing,
FFT 1 FFT 2 FFT 3 FFT 4
faster display update rate
FFT 1  Ideal for finding
FFT 2 sporadic / intermittent
FFT 3
50% overlapping FFT 4
signal details
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15. Tradeoff for Windowing: Missed Signal Events
l All oscilloscope FFT processing uses windowing
l Spectral leakage eliminated
l However, signal events near window edges are attenuated or lost
Original Signal
Signal after Windowing
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16. FFT Overlap Processing
l Overlap Processing ensures no signal details are missed
Original Signal
…
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17. Time Gating
FFT
•Signal characteristics change over the acquisition interval
•Gating allows selection of specific time intervals for analysis
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18. Time Gating
Tg
FFT 1
f 
Tg
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19. Time Gating
l Frequency spectrum is
often a function of time
l Locking of a PLL
l EMI caused by time
domain switching
l Time gating allows the
user to select a specific
portion of the waveform
for frequency domain
analysis
l Window limits frequency
resolution
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20. Frequency domain measurement dynamic
range
l Analog to digital conversion (ADC) performance sets the
dynamic range
l Signal to noise ratio (ENOB)
l Frequency domain spurious
l Front-end amplifier gain
l Noise figure and sensitivity
20

21. Ideal ADC
l How can we measure with sufficient range in the
frequeny domain?
l The A/D converter sets the dynamic range
l K bit ADC (2K quantization levels)
l Effective Number Of Bits (ENOB) = K
Ideal ADC
s(t) sq (ti )
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22. Analog-to-Digital Converter - ENOB
l Effective Number of Bits (ENOB): A measure of signal fidelity
Effective Quantization Least Significant
Bits (N) Levels Bit ∆V
± ½ LDB Error
4 16 62.5 mV
5 32 31.3 mV
Quantatized
Digital Analog Waveforms
6 64 15.6 mV
Level typical
Sample 7 128 7.8 mV
Ideal ADC vertical 8bits = Points
256 Quantatizing levels Ideal 8 256 3.9 mV
8 Effective
+ + + < Number of Bits !
Offset Error Gain Error Nonlinearity Error Aperture Uncertainty
And Random Noise
l Higher ENOB => lower quantization error and higher SNR
=> better accuracy
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23. A Scope is more than an ADC….
Model of oscilloscope front-end
Variable Gain Analog Filter Non-Ideal ADC
Amplifier
p(t) q(t) s(t) sq (ti )
l Variable gain amplifier sets the V/div range and level into
the (non-ideal) ADC
l Analog filter prevents aliasing
l ADC generates quantized and sampled signal
l Amplifier and other components in the input chain add
noise to the ADC
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24. Signal to Noise and ENOB
l What noise level would be observed in the spectrum measured with
100 KHz resolution bandwidth?
l Assume 2 GHz instrument bandwidth with 8 ENOB (ideal ADC)
l SNRdB = 49.76 dB
l SNR = 92.8 dB
SNRdB  1.76
B
6.02
Displayed noise level is
 2E9 
reduced by the ratio of SNRdB  SNR  10  log 10 
full bandwidth to RBW  1E 5 
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25. Signal to Noise (6.8 ENOB)
84 dB
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26. Signal to Noise (5.1 ENOB)
70 dB
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27. Effect of interleaving in the frequency domain
Interleaved A/D Non-interleaved A/D
harmonics
Interleaving spurious
27

28. High Gain Amplifier Reduces Noise at 1 mV/div
Noise power
in 50 KHz
BW = -102
dBm ~ -148
dBm/Hz
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29. Triggering
l Triggers can be required different “domains”
l Time domain (edge, runt, width, etc.)
l Digital domain (pattern, serial bus)
l Frequency domain (amplitude/frequency mask)
l Sensitivity of time domain triggers
l Matching bandwidth with acquisition for all trigger types
l Noise reduction (filtering, hysteresis)
l Frequency domain triggers
l Processing speed of FFT
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30. Conventional Oscilloscope Triggering System
display
memory stored samples
ADC samples
sample time
time
meas signal time
base
stop acquisition
trigger
position of waveform on display
system
TDC locates trigger position
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31. Trigger Sets the Horizontal Position of the
Waveform trigger position
trigger level
samples
31

32. Trigger Positioning Error
trigger position
trigger position error
trigger level
32

33. Positioning Error Over Time (trigger jitter)
TT
T
A
A
A
33

34. Digital Trigger System
display
time sample time memory stored samples
base
meas signal ADC samples
stop acquisition
samples
trigger
position of waveform on display
system
34

35. Low Trigger Jitter in Digital System
35

36. Trigger Hysteresis
Hysteresis allows triggering on noisy edges
36

37. Narrow Pulse Width Trigger
37

38. Frequency Domain Triggering
l Mask test on spectrum
l Set for “stop on failure”
Gated FFT
Frequency
mask
38

39. Evaluation Board Schematic
Test point for
Loop Filter Voltage RF
Output
Test points for
CLK, DATA & LE
39

40. RF OUT + CLK & DATA (analog + SPI decoding)
RF carrier (time domain view)
SPI decoding
CLK
DATA
MOSI trigger pattern = 0003XXXXh
40

41. FFT Gating Off
RF carrier (time domain view)
Note Frequency overshoot. Also note the VCO Tuning Voltage
RF carrier, Gating OFF
(freq domain view)
Serial decoding of SPI data
VCO Tuning Voltage
VCO is programmed to toggle between 825 MHz and 845 MHz
41

42. FFT Gating On
RF carrier (time domain view) FFT Gate step size = 400 us
RF carrier, Gating ON
(freq domain view)
RF carrier, Gating OFF
(freq domain view)
Serial decoding of SPI data
VCO Tuning Voltage
VCO is programmed to move from 825 MHz to 845 MHz (single shot)
42

43. Multiple Gated FFTs
RF carrier (time domain view)
RF carrier position RF carrier position RF carrier position
after 400 us after 800 us after 1200 us
Serial decoding of SPI data
VCO Tuning Voltage
VCO is programmed to move from 825 MHz to 845 MHz (single shot)
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44. Summary
l FFT based spectrum analysis can be enhanced to enable
time-correlated spectrum analysis
l Improved throughput using digital down conversion
l High dynamic range A/D conversion
l High gain amplifier for small signal measurement
l Real time oscilloscope platform is ideal for digital, time and
frequency analysis
l Synchronized time and frequency domain analysis
l Serial protocol trigger and decode
l Parallel data channels
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45. Summary
l Watch the recorded webinar on this presentation here!
l http://bit.ly/SYqjzC
l Or scan the QR code on your mobile device:
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