Analog Channel Testing

1
Analog Channel Testing

• Overview
• Gain and level tests
• Phase tests
• Distortion tests
• Signal rejection tests
• Noise tests
• Summary

2
Types of Analog Channels

• Analog channels Any non-sampled circuit with
  analog input and analog outputs
• Continuous time filters, amplifiers, analog
  buffers, PGAs, single-ended to differential
  converters and vice versa, and cascaded
  combinations of any of the above.

Filter input (test mode)
Single-ended to Differential power amp
TESTIN
Analog Bus DfT for a DAC Mixed-Signal Channel
PGA
Low-pass Filter
OUTP
Digital samples
DAC
OUTN
Volume control
DAC Reference voltage
TESTOUT
PGA output (test mode)
Normal mode
Force input
Monitor output
3
Types of AC Parametric Tests

• Analog and sampled channels share many AC
  parametric test specifications mainly in the
  following categories
• Gain, phase, distortion, signal rejection, and
  noise.
• A major trick to making accurate AC measurements
  is proper use of software calibrations
• In discussions hereon, assume
• Signal source voltage.
• Voltage-to-current or current-to-voltage circuits
  will be needed in cases where the DUT produces AC
  current outputs or require AC current inputs.
• General-purpose digitizers and AWGs are perfect.
• All expressed in dB

4
Gain and Level Tests Absolute Voltage Levels

• Absolute voltage level The RMS value of the
  signal under test, evaluated at the test tones
  frequency.
• Measure the total signal RMS, including noise,
  distortion, ...
• Offer a good way to detect grossly defective
  circuits very quickly.
• Loading conditions during test are very
  important.
• Test engineers job is to determine the worst case
  loading conditions for a given AC test.
• Device data sheets usually list specific loading
  conditions.
• Units of measure are
• RMS volts, peak Volts, peak-to-peak Volts, dBV
  and dBm.

Defective Low-pass filter
Input signal
Clipped output signal
5
Absolute Voltage Levels (cont.)

• Decibels can be abused as well
• The decibel unit represents a ratio of values,
  and as such it is inappropriate to refer to an
  absolute voltage level using dB without a
  reference level.
• Decibels is commonly referenced as dBV or dBm
• A specified load impedance must be linked to the
  dBm specification

Output signal 1.0V Peak, single ended 2.0V
Peak-to-peak, single-ended 0.707V RMS,
single-ended 2.0V Peak, differential 4.0V
Peak-to-peak, differential 1.414V RMS,
differential
1.0V
OUTP
OUTN
1.0V
Gain 2
Input signal 1.0V Peak 2.0V Peak-to-peak 0.707V
RMS
Equivalent voltage measurement for
single-ended and differential signals
6
Absolute Gain and Gain Error

• Absolute gain The ratio of output AC signal
  level divided by the input signal level at a
  specified frequency.
• Often specified as a max and min absolute gain
  level.
• Sometimes a channels gain is specified in terms
  of its error relative to the ideal absolute gain
  Gain error.
• Gain errors are frequently the result of
  component mismatch in the DUT.
• In order to distinguish between distortion and
  gain errors, gain tests are often performed a few
  dBs below full scale.
• Typically 1 to 3 decibels below full scale.

7
Example of Absolute Gain and Gain Error (1/3)

• Sampling system configuration during LPF input
  measurement
• A digitizer sampling at 8kHz captures 256 samples
  of the sine wave (generated by AWG) at the input
  to the filter.
• The FFT of the captured waveform shows a signal
  amplitude of 1.25V RMS at 37th FFT spectral bin.
• What is the frequency of the test signal?

8kHz sampling rate, 256 samples
DUT Low-pass filter
OUTP
1.25V RMS
FFT
AWG
Digitizer
OUTN
8
Example of Absolute Gain and Gain Error (2/3)

• Sampling system configuration during LPF output
  measurement
• The digitizer is then connected to the output of
  the filter.
• It captures 1024 samples of the output of the
  filter (differentially) using a 16-kHz sampling
  rate.
• The output FFT shows a signal amplitude of 1.025V
  RMS in one of the spectral bins.
• Assume the digitizer is perfectly accurate in
  both configurations.

16kHz sampling rate, 1024 samples
DUT Low-pass filter
OUTP
1.025V RMS
FFT
AWG
Digitizer
OUTN
9
Example of Absolute Gain and Gain Error (3/3)

• Which spectral bin in FFT of the output signal
  most likely showed the 1.025V RMS signal level?
• What is the gain (in dBs) of the low-pass filter
  at this frequency?
• Suppose the ideal filter gain at this frequency
  is -1.50 dB. What is the gain error of the filter
  at this frequency?
• Is the filter output too high or too low?
• The output is lower than it should be.

10
Gain Tracking Error

• Gain tracking error The variation in the gain G
  of a channel w.r.t. a reference gain GREF as the
  signal level Vin changes.
• Ideally, a channel should have a constant gain,
  regardless of the signal level.
• Sources
• Small circuit defects can cause non-linearity in
  gain at different signal levels.
• Quantization errors in a DAC or ADC channel
  usually most severe in low amplitude signals.
• Gain tracking is calculated by measuring the gain
  at a reference level, usually the 0-dB level of
  the channel, and then measuring the gain at other
  signal levels.
• Gain tracking error is calculated at each signal
  level by subtracting the reference gain GREF from
  the measured gain G at that level.

11
PGA Gain Tests (1/3)

• A programmable gain amplifier (PGA) can be set to
  multiple gain settings using a digital control
  signal.
• A 32-step PGA that has an ideal step size of
  1.5dB.
• If its lowest gain setting is 0dB ? 32 gain step
  0dB, 1.5dB, 3.0dB, 4.5dB, ..., 46.5dB.
• Gain range ? highest gain lowest gain 46.5dB

250
PGA
200
1.5dB per step
150
Gain (V/V)
Gain setting
100
PGA gain curve
50
0
Gain setting (0-31)
-50
0
5
10
15
20
25
30
35
12
PGA Gain Tests (2/3)

• Absolute gain at each step is often less
  important than the difference in gain between
  adjacent steps.
• PGA specifications are usually tested at a
  particular frequency, such as 1 kHz.
• Possible measurement techniques
• The absolute gain of each step can be measured by
  leaving the input signal unchanged and observing
  the output voltage.
• Adjust the input level at each step to produce a
  fairly constant output level at least 3 dB lower
  than the full scale output.
• This avoids clipping while producing a strong
  output signal level which is less susceptible to
  noise, yielding better repeatability in the
  measurement.
• If the PGA is designed correctly, a binary
  weighted PGA allows six measurements to be made
  for a 32 step PGA. (superposition)

13
PGA Gain Tests (3/3)

• Fact The actually measured gains and calculated
  gain (by superposition) are usually
  non-identical.
• Question Whether or not we can change to a
  super-position calculation instead of a full
  measurement process.
• The answers depend on
• How tight or loose are the test limits?
• If the limits are loose ? we can probably
  tolerate the errors in the superposition
  calculations.
• If the average device performance is very close
  to the test limits ? superposition may not be
  acceptable.
• Conclusions about superposition should be made
  from a fairly large set (for instance, over at
  least thousands of devices) of results not from a
  single chip.

14
Frequency Response (1/2)

• Frequency response
• Similar to gain tracking error since it is a
  measurement of gain under varying signal
  conditions, relative to a reference gain.
• Unlike gain tracking tests, it measures the
  variation in gain of the circuit as the signal
  frequency is varied.
• One frequency is chosen as the reference gain,
  all other gains are measured relative to the
  reference.
• All non-reference gains are called relative
  gains.
• Frequency response is usually measured using
  coherent equal-level multitone signals to save
  test time.
• Sometimes the test must be broken down into an
  in-band and out-of-band test due to the large
  difference in signal amplitudes.

15
Frequency Response (2/2)

• Multitone signal, should be equal-level
• For example, to produce a four-tone multitone
  signal with 100-mV RMS signal level, each must be
  set to 50 mV RMS.
• The frequencies of the tones should be chosen so
  that they do not produce harmonic or
  inter-modulation distortion overlaps.
• The phase of each tone is randomly selected to
  produce a signal with an acceptable peak-to-RMS
  ratio.
• Settling time of an AC measurement is determined
  by the characteristics of the DUT and tester.
• In general, the lower the frequency being tested,
  the longer the settling time.

16
Example of Frequency Response Measurement

• A band-pass filter formed by cascading a 60Hz
  high-pass filter with a 3.4 kHz low-pass filter.
• Frequency response spec.
• Reference frequency 1 kHz.
• -3.01 dB gain points 170 190 Hz 3460 3650
  Hz.

Freq.
Lower Limit
Upper Limit
lt10 Hz
None
-30 dB
50 Hz
None
-25 dB
60 Hz
None
-23 dB
Gain (dB)
200 Hz
-1.28 dB
0.0 dB
300 Hz
-0.5 dB
0.5 dB
3000 Hz
-0.5 dB
0.5 dB
3400 Hz
-1.35 dB
0.0 dB
4000 Hz
None
-14.0 dB
gt4600 Hz
None
-32.0 dB
Specifications at intermediate points are
determined by linear interpolation between
specified points.
Frequency (Hz)
Ideal Filter frequency response and gain mask
17
Example of Frequency Response Measurement

• Problem 1 Which subset of frequencies should be
  measured in production?
• Sweep the frequency from 0 to 8 kHz in 1-Hz steps
  is not practical ? A limited number of tones must
  be chosen.

• Solution
• Determine the frequencies that are most likely to
  cause the filter to fail through a detailed Monte
  Carlo or sensitivity analysis.
• In this example, peaks and valleys of the in-band
  ripple are 850, 1600, 2310, 2860, and 3150 Hz.
• Next, select frequencies at the center of the
  out-of-band side lobes, _at_ 100, 4430 and 4860 Hz.

18
Example of Frequency Response Measurement

• Problem 2 The -3 dB cutoff frequencies are
  specified. However, we do not have time to search
  for the exact frequency that results in a
  relative gain of -3.01 dB.
• Solution
• Method 1 Place two frequencies at the upper and
  lower limits of the -3dB points (170, 190, 3460,
  and 3650 Hz) and perform Interpolation to find
  the approximate location.
• Method 2 (Pass/fail test) Gain _at_ 190Hz (or
  3460Hz) must be greater than -3.01dB and gain _at_
  170Hz (or 3650Hz) must less than -3.01dB.
• We eliminate 10- and 50- Hz tests from spec.
  table since they require long test time and the
  ideal characteristics are so far from the
  specified mask.

19
Example of Frequency Response Measurement

• As a result, test frequencies selected
• 60, 100, 170, 190, 200, 300, 850, 1000 (ref.
  freq.), 1600, 2310, 2860, 3000, 3150, 3400, 3460,
  3650, 4000, 4430, 4600, 4860 Hz.
• Usually, these frequencies must be slightly
  adjusted to accommodate coherent DSP-based
  testing.
• The lowest out-of-band gain specification is -32
  dB here
• ? O.K. for one set measurement.
• If lt-80 dB, may needs two set of measurement.
• Since it is difficult to measure such a small
  signal in the presence of the much larger in-band
  signals.
• 20 tones ? each tone sets to 223.6
  mV RMS.

20
Example of Frequency Response Measurement

• Input test signal 20 tones digitized at 16 kHz
  and 2048 samples.
• Spectrum of input test signal.
• Spectrum of output signal.

21
Example of Frequency Response Measurement

• Table of test results (Notice fail regions!)

Frequency
Absolute Gain
Relative Gain (Freq. Resp.)
Lower Limit
Upper Limit
1000 Hz (ref.)
0.168 dB
0.00 dB
-0.50 dB
0.50 dB
60 Hz
-57.44 dB
-57.27 dB
NA
-23 dB
100 Hz
-33.62 dB
-33.79 dB
NA
-13.24 dB
(Interpolated)
170 Hz
-4.87 dB
-5.04 dB
NA
-3.01 dB
190 Hz
-1.89 dB
-2.06 dB
-3.01 dB
NA
-1.296 dB Fail
0.0 dB
200 Hz
-1.128 dB
-.1.280 dB
300 Hz
0.013 dB
-0.155 dB
-0.5 dB
0.5 dB
850 Hz
0.181 dB
0.013 dB
-0.5 dB
0.5 dB
1600 Hz
0.017 dB
-0.151 dB
-0.5 dB
0.5 dB
2310 Hz
0.266 dB
0.098 dB
-0.5 dB
0.5 dB
2860 Hz
0.018 dB
-0.150 dB
-0.5 dB
0.5 dB
3000 Hz
0.071 dB
-0.097 dB
-0.5 dB
0.5 dB
3150 Hz
0.170 dB
0.002 dB
-0.853 dB
0.292 dB
3400 Hz
-1.264 dB
-1.432 dB Fail
-1.35 dB
0.0 dB
3460 Hz
-2.29 dB
-2.46 dB
-3.01 dB
NA
3560 Hz
-4.55 dB
-4.72 dB
NA
-3.01 dB
3460 Hz
-16.82 dB
-16.99 dB
NA
-14.0 dB
3560 Hz
-32.21 dB
-32.38 dB
NA
-32.0 dB
-75.40 dB
-32.0 dB
3460 Hz
-75.23 dB
NA
3560 Hz
-32.52 dB
-32.69 dB
NA
-32.0 dB
22
Remark on Frequency Response Measurement

• Frequency response can also be measured by
  applying a narrow impulse to the circuit under
  test and observing the filters impulse response.
• The Fourier transform of the impulse response is
  the filter frequency response.
• The advantage is that this gives the full
  frequency response at all frequencies in the FFT
  spectrum.
• The problem with impulse response is that you can
  not measure the response at a particular
  frequency with any great accuracy.
• Energy in a narrow impulse is very small ? makes
  the measurement susceptible to noise
• Also, frequency overlap and distortion may
  corrupt the gain at any single frequency.

23
Phase Tests (1/2)

• If phase response is specified in the data sheet,
  it can be calculated using the FFT results
  collected during the frequency response test.
• The amplitude of the kth tone is calculated
  according to
• The phase shift of the kth tone can be calculated
  using

24
Phase Tests (2/2)

• A negative phase shift indicates a positive time
  delay (i.e. the output lags the input), while a
  positive phase shift indicates the opposite.
• Ex Analog delay line producing a 90? phase
  shift (phase lag)
• Polar notation (magnitude and phase) is limited
  to a phase shift of at most ?180?.
• A phase shift of 190? translates into a shift of
  170?.
• Test engineer has to correct this wrapping
  effect.

Delay line T 1/4 P
Input signal
Delayed output signal
25
Example of Phase Test (1/4)

• Example
• Measure the phase response of a 100?s analog
  delay line from 900Hz to 9.9KHz in 10 tones.
• Use a 1024-point samples with fundamental
  frequency 100Hz.
• Use odd harmonics (i.e., use spectral bins 9,
  19, 29, 39, etc.) to get x-symmetrical signal.
• Also, use random phase shift to produce a
  peak-to-RMS ratio ? 3.351
• Solution
• Multitone input signal
• Tones 900, 1.9k, 2.9k, 2.9k, 4.9k, 5.9k, 6.9k,
  7.9k, 8.9k, 9.9k (Hz)
• Phase of each tone is chosen to produce a peak to
  RMS ratio of 3.351

26
Example of Phase Test (2/4)

• Input signal
• Calculate signal phases for digitized input

Frequency
Real Part
Imaginary Part
Phase (degree)
900 Hz
-0.199009
0.245755
231.0
1.9 kHz
-0.223607
0.223608
225.0
2.9 kHz
0.238660
0.207465
-41.0
3.9 kHz
0.286600
-0.133643
-25.0
-0.071136
4.9 kHz
-0.308123
167.0
5.9 kHz
-0.190311
0.252550
233.0
6.9 kHz
0.313150
0.044010
-8.0
7.9 kHz
-0.215668
-0.231275
133.0
8.9 kHz
-0.071136
-0.308123
103.0
9.9 kHz
-0.308123
-0.071136
167.0
27
Example of Phase Test (3/4)

• Output signal
• Calculate signal phases for digitized output

Frequency
Real Part
Imaginary Part
Phase (degree)
900 Hz
-0.298347
0.104827
-199.4
1.9 kHz
-0.293618
-0.117421
158.2
2.9 kHz
-0.252395
0.190517
217.0
3.9 kHz
-0.119020
0.292974
247.0
0.033096
4.9 kHz
-0.314893
-6.0
5.9 kHz
0.285237
-0.133008
25.0
6.9 kHz
-0.105152
-0.298233
109.4
7.9 kHz
-0.258195
0.182579
215.3
8.9 kHz
-0.274162
-0.157590
150.1
9.9 kHz
-0.316175
-0.005777
179.0
28
Example of Phase Test (4/4)

• Phase shift output phase input phase

Frequency
Phase Shift (Out In)
?360 Phase Adj.
Actual Phase
900 Hz
199.4 231.0 -31.6
0
-31.6
1.9 kHz
158.2 255.0 -66.8
0
-66.8
2.9 kHz
217.0 (-41.0) 258.0
-360
-102.0
3.9 kHz
247.9 25.0 222.9
-360
-137.1
4.9 kHz
-6.0 167.0 -173.0
0
-173.0
5.9 kHz
25.0 233.0 -208.0
0
-208.0
6.9 kHz
109.4 (-8.0) 117.4
-360
-242.6
7.9 kHz
215.3 133.0 82.3
-360
-277.7
8.9 kHz
150.1 103.0 47.1
-360
-312.9
9.9 kHz
179.0 167.0 12.0
-360
-348.0
29
Group Delay

• Phase shift expressions
• 1. Degrees or radians
• 2. Fraction of cycle
• 3. Seconds
• Group delay ?(f) (in sec)
• A measurement of time shift versus frequency
• Defined as the change in phase shift divided by
  the change in frequency
• Typically measured with tone pairs centered
  around the frequency of interest

30
Group Delay Distortion

• A constant group delay indicates a circuit that
  shifts each signal component by a constant amount
  of time
• ? The relative time shifts of the various signal
  components unchanged
• ? Input/output signals that are identical in
  shape but shifted in time
• If on the other hand, group delay varies over
  frequency
• ? A circuit shifts various signal components
  relative to one another
• ? This results in a change in shape as well as a
  shift in time.
• ? This is called Group Delay Distortion.
• Definition
• May cause signal clipping and data corruption
  (since in data communications, phase usually
  carries information)

31
Example of Group Delay (Distortion)

• Example
• Calculate the group delay and group delay
  distortion of the 100-?s delay line from the data
  gathered in the previous example.
• Solution
• 900Hz ? 1.9 kHz ?f 1 kHz,

Test Tone Pairs
Phase Change (deg)
Group Delay
Group Delay Distortion
900 Hz and 1.9 kHz
-66.8 (-31.6) -35.2
-97.78 ?s
135 ns
1.9 kHz and 2.9 kHz
-102.0 (-66.8) -35.2
-97.78 ?s
135 ns
-97.50 ?s
2.9 kHz and 3.9 kHz
-137.1 (-102.0) -35.1
415 ns
3.9 kHz and 4.9 kHz
-173.0 (-137.1) -35.9
-99.72 ?s (max)
-1.8 ?s
4.9 kHz and 5.9 kHz
-208.0 (-173.0) -35.0
-97.22 ?s
694 ns
5.9 kHz and 6.9 kHz
-242.6 (-208.0) -34.6
-96.11 ?s (min)
1.8 ?s
6.9 kHz and 7.9 kHz
-277.7 (242.6) -35.1
-97.50 ?s
415 ns
7.9 kHz and 8.9 kHz
-312.9 (-277.7) -35.2
-97.78 ?s
135 ns
8.9 kHz and 9.9 kHz
-348.0 (-312.9) -35.1
-97.50 ?s
415 ns
32
Distortion Tests

• Harmonic distortion
• Arises when a signal passes through a non-linear
  circuit
• When passing a single tone through a CUT, the
  harmonic distortion components appears at integer
  multiples of the test tone frequency, Ft.
• Ft called fundamental tone. (not to be confused
  with the fundamental frequency of the sampling
  system, Ff)
• X-symmetrical distortion gives only odd harmonics
  (3Ft, 5Ft, etc.)
• Asymmetrical distortion gives both odd and even
  harmonics.
• Signal to total harmonic distortion
• Defined as the ratio of the RMS signal level of
  the test tone divided by the total RMS of the odd
  and even harmonic distortion components.

33
Various Signal to Noise and Distortion Formulae
Distortion Metric
Expression
(V/V)
(dB)
Signal to 2nd Harmonic Distortion (S/2nd)
Signal to 3rd Harmonic Distortion (S/33d)
Signal to Total Harmonic Distortion (S/THD)
Signal-to-noise (S/N)
Signal to Total Harmonic Distortion
Noise (S/THDN) or (SINAD)
or
or
34
Test Low-level Distortion Components

• Low-level distortion components can be extremely
  difficult and time-consuming to measure.
• Especially if the value is close to the noise
  floor of the DUT and/or ATE measurement hardware.
• Lead to unrepeatable measurement.
• Solved by averaging the results of several
  measurement or collect more samples.
• Number of samples ?4x ? The non-repeatability ?2x
• Causing long test times.
• Data collection time DSP processing time.

35
Example of Harmonic Distortion Test
Ff 10 kHz/512 19.531 Hz For coherent testing,
test signal is actually at 51th bins
996.094 Hz
CUT
Digitizer Fs 10 kHz 512 samples
Test signal 1 kHz Sine wave
Voltage Follower
FFT Spectral Bin
Frequency
RMS Value
51
1 kHz (fundamental tone)
1.025 V
Test results
102
2 kHz (second harmonic)
1.23 mV
153
3 kHz (third harmonic)
2.54 mV
204
4 kHz (fourth harmonic)
0.78 mV
255
5 kHz (fifth harmonic)
0.32 mV

• Solution

S/2nd
S/3rd
S/THD
36
Inter-modulation Distortion

• Inter-modulation distortion
• Very similar to signal to harmonic distortion
  testing, except that two test tones are applied
  to the DUT at once.
• Distortion components may appear at any sum or
  difference of any multiple of the test tones
• Inter-modulation frequency F p ? F1 q ? F2
• F1 and F2 are two test tones.
• p and q may be any positive integer.
• p q k ? kth-order inter-modulation
  components.

F1
F2
v
F1F2
F1F2
F12F2
2F1F2
F12F2
2F1F2
freq
37
Example of Inter-modulation Distortion

• Example
• A multitone test signal consists of a sum of two
  1.0-V RMS sine waves, one at 1 kHz and the other
  at 1.1 kHz. Calculate the frequencies of the 2nd,
  3rd and 4th inter-modulation components.
• The signal RMS at 100 Hz is 193 ?V and the signal
  RMS at 2.1 kHz is 232 ?V. Calculate the signal to
  2nd IMD ratio, in dB.
• Solution
• 2nd components _at_ 1.0 kHz ? 1.1 kHz 100 Hz and
  2.1 kHz
• 3rd components _at_ 2 ?1.0 kHz ? 1.1 kHz 900 Hz
  and 3.1 kHz
• and 1.0 kHz ? 2 ? 1.1
  kHz 1.2 kHz and 3.2 kHz
• 4th components _at_ 2 ?1.0 kHz ? 2 ? 1.1 kHz 200
  Hz and 4.2 kHz
• and 3 ? 1.0 kHz ? 1.1
  kHz 1.9 kHz and 4.1 kHz
• and 1.0 kHz ? 3 ? 1.1
  kHz 2.3 kHz and 4.3 kHz
• Signal to 2nd IMD ratio is given by

38
Signal Rejection Tests

• A measure of a channels ability to prevent an
  undesired signal from propagating to the
  channels output.
• The undesired signal may originate in
• Power supply (PSRR)
• Another supposedly separate circuit
  (Channel-to-channel Crosstalk)
• Channel itself (CMRR)
• Common-mode rejection ratio (CMRR)
• A measurement of how well a channel with a
  differential input can reject a common mode
  signal.
• Ideally, Vout GVdiff G(INP - INN) 0 if INP
  INN.
• Due to mismatched components in the input
  circuit, a small amount of common mode signal
  usually feeds through to the output

39
AC Common-Mode Rejection Ratio (AC CMRR)

• Defined as the AC gain of the channel with a
  common mode input divided by the gain of the
  channel with a normal, differential input.
• Multitone testing can be used to measure CMRR at
  several frequencies at once, saving test time.
• It is often expressed in decibel units.

INN
VOUT
INP
VM
Vcm
Vout
VMID