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|S11| > 1

 

I've been analyzing Touchstone files Rudy Severns, N6LF, has recorded with his NanoVNA-H4. The magnitude of S11 is greater than 1 for many files. For example, after calibration right at the VNA connector, |S11| was 1.0007 maximum for the open cal part itself. For the short the maximum was 1.0005. For both, |S11| > 1 for all 401 points from 0.1 to 50 MHz.

The images show calculated permittivity and conductivity for a ground probe with the rods in air. The image with most of the points missing used uncorrected data. The other image is for normalized data where |S11| = 1 maximum.

Although normalization solves the problem for my software, I'm curious why |S11| is ever > 1.

Brian

2.gif
1.gif

 

On 6/13/22 1:31 PM, Brian Beezley wrote:
I've been analyzing Touchstone files Rudy Severns, N6LF, has recorded with his NanoVNA-H4. The magnitude of S11 is greater than 1 for many files. For example, after calibration right at the VNA connector, |S11| was 1.0007 maximum for the open cal part itself. For the short the maximum was 1.0005. For both, |S11| > 1 for all 401 points from 0.1 to 50 MHz.

The images show calculated permittivity and conductivity for a ground probe with the rods in air. The image with most of the points missing used uncorrected data. The other image is for normalized data where |S11| = 1 maximum.

Although normalization solves the problem for my software, I'm curious why |S11| is ever > 1.

Brian

Measurement uncertainty? You're essentially measuring (V refl)/(V incident) with a noisy sensor.?? 1 part per 1000 (1.001) is 60dB.. the SNR of the measurement is in that ballpark.

Calibration peculiarities - you determine the cal coefficients with noisy measurements, so the combination of cal coefficient high, and measurement high,.

The ADC measuring the output of the mixer has an ideal SNR of ~90 dB.? It's a 16 bit adc, so there's some quantization uncertainty. Then there's the arithmetic aspect. The basic software multiplies the ADC numbers by sin and cos, then sums to get I/Q.?? That's done with 16 bit signed integers, 32 bit products, but then truncated before integrating.

There's also the single precision floating point calculation of the various calibration coefficients using single precision float (32 bit, with 24 bit mantissa/significand).
 

15070000 -1.000470519 -0.000045675
15194750 -1.000452399 -0.000081647
15319500 -1.000464559 -0.000072501
15444250 -1.000433683 -0.000034980
15569000 -1.000416160 -0.000060047
15693750 -1.000486493 -0.000025182
15818500 -1.000452280 -0.000066847

Jim, that's a data sample for the short. The real part is consistently beyond -1.0004. The open is similarly beyond +1. The largest |S11| I found in other .s1p files was 1.0037. I think it is some sort of systematic issue, not noise. Most users will never notice it since the effect is so tiny. My application is sensitive to errors at extreme S11 values, which yield nonphysical results (negative conductivity).

I forgot to mention that the VNA firmware for the open and short was DiSlord 1.2.

Brian
 

On 6/14/22 4:29 AM, Brian Beezley wrote:
15070000 -1.000470519 -0.000045675
15194750 -1.000452399 -0.000081647
15319500 -1.000464559 -0.000072501
15444250 -1.000433683 -0.000034980
15569000 -1.000416160 -0.000060047
15693750 -1.000486493 -0.000025182
15818500 -1.000452280 -0.000066847
Jim, that's a data sample for the short. The real part is consistently beyond -1.0004. The open is similarly beyond +1. The largest |S11| I found in other .s1p files was 1.0037. I think it is some sort of systematic issue, not noise. Most users will never notice it since the effect is so tiny. My application is sensitive to errors at extreme S11 values, which yield nonphysical results (negative conductivity).

I forgot to mention that the VNA firmware for the open and short was DiSlord 1.2.

Brian

Interesting - I wonder if it's a "round off" or truncation error of some sort.? The "detector" mixes with I/Q 5 kHz, summing, and there could be a 1/2 LSB bias or something like that.

here's the raw I/Q calculation code:

void dsp_process(int16_t *capture, size_t length)

{

uint32_t *p = (uint32_t*)capture;

uint32_t len = length / 2;

uint32_t i;

int32_t samp_s = 0;

int32_t samp_c = 0;

int32_t ref_s = 0;

int32_t ref_c = 0;

for (i = 0; i < len; i++) {

uint32_t sr = *p++;

int16_t ref = sr & 0xffff;

int16_t smp = (sr>>16) & 0xffff;

int32_t s = sincos_tbl[i][0];

int32_t c = sincos_tbl[i][1];

samp_s += smp * s / 16;

samp_c += smp * c / 16;

ref_s += ref * s / 16;

ref_c += ref * c / 16;

}

acc_samp_s = samp_s;

acc_samp_c = samp_c;

acc_ref_s = ref_s;

acc_ref_c = ref_c;

}

raw (uncalibrated) gamma is calculated here

void calculate_gamma(float gamma[2])

{

#if 1

// calculate reflection coeff. by samp divide by ref

float rs = acc_ref_s;

float rc = acc_ref_c;

float rr = rs * rs + rc * rc;

//rr = sqrtf(rr) * 1e8;

float ss = acc_samp_s;

float sc = acc_samp_c;

gamma[0] =(sc * rc + ss * rs) / rr;

gamma[1] =(ss * rc - sc * rs) / rr;

#elif 0

gamma[0] =acc_samp_s;

gamma[1] =acc_samp_c;

#else

gamma[0] =acc_ref_s;

gamma[1] =acc_ref_c;

#endif

}



this is the code that applies the calibration:

if (cal_status & CALSTAT_APPLY)

apply_error_term_at(i);

static void apply_error_term_at(int i)

{

// S11m' = S11m - Ed

// S11a = S11m' / (Er + Es S11m')

float s11mr = measured[0][i][0] - cal_data[ETERM_ED][i][0];

float s11mi = measured[0][i][1] - cal_data[ETERM_ED][i][1];

float err = cal_data[ETERM_ER][i][0] + s11mr * cal_data[ETERM_ES][i][0] - s11mi * cal_data[ETERM_ES][i][1];

float eri = cal_data[ETERM_ER][i][1] + s11mr * cal_data[ETERM_ES][i][1] + s11mi * cal_data[ETERM_ES][i][0];

float sq = err*err + eri*eri;

float s11ar = (s11mr * err + s11mi * eri) / sq;

float s11ai = (s11mi * err - s11mr * eri) / sq;

measured[0][i][0] = s11ar;

measured[0][i][1] = s11ai;

// CAUTION: Et is inversed for efficiency

// S21m' = S21m - Ex

// S21a = S21m' (1-EsS11a)Et

float s21mr = measured[1][i][0] - cal_data[ETERM_EX][i][0];

float s21mi = measured[1][i][1] - cal_data[ETERM_EX][i][1];

float esr = 1 - (cal_data[ETERM_ES][i][0] * s11ar - cal_data[ETERM_ES][i][1] * s11ai);

float esi = - (cal_data[ETERM_ES][i][1] * s11ar + cal_data[ETERM_ES][i][0] * s11ai);

float etr = esr * cal_data[ETERM_ET][i][0] - esi * cal_data[ETERM_ET][i][1];

float eti = esr * cal_data[ETERM_ET][i][1] + esi * cal_data[ETERM_ET][i][0];

float s21ar = s21mr * etr - s21mi * eti;

float s21ai = s21mi * etr + s21mr * eti;

measured[1][i][0] = s21ar;

measured[1][i][1] = s21ai;
 

I think need recalibrate.
Calibration must remove all errors.
 

I've asked Rudy to remeasure the short and open using MA (magnitude/angle) mode. That might shed some light on where the inaccuracy lies. Also, I think he was using averaging. It might be interesting to disable it.

Brian
 

On 6/14/22 7:26 AM, Brian Beezley wrote:
I've asked Rudy to remeasure the short and open using MA (magnitude/angle) mode. That might shed some light on where the inaccuracy lies. Also, I think he was using averaging. It might be interesting to disable it.

Brian

what would be interesting is to measure it without calibration, and with, and make sure there's not some mis calibration going on somehow.
 

Thanks for the reply, DiSlord. I'll check with Rudy, but I believe he calibrated at the VNA SMA immediately before the measurement since normally he never measures without a cable..

Brian
 

Thank you, Jim!!!

Again, we are not running a metrology lab nor do our measurements approach
those of HP, R&S, Tek, and others. Something my PhD friends tell me is
that error analysis and assignment of error bars is no longer taught - not
even at CU/Boulder. I had a required course dedicated to that musing to
obtain my Physics degree some 50+ years ago at Michigan State U.

The students today have no idea how the error bar is established or even
what it truly indicates. Several of us have tried introducing our STEM
students at LTO (Little Thompson Observatory <starkids.org>) to the concept
of measurement errors and how they affect final outcomes. We usually get
wrinkled foreheads and "why".

Yes, 5 parts in E-5 is -86 dB. Yes, the HP 8753C noise floor can measure
below that. But, not our inexpensive NANOVNAs. Mine typically shows a
noise floor of -60 dB, depending on frequency and measurement type.

Again, thank you to those who put these VNAs at a reachable price in the
hands of us amateurs and those who want to learn the "fine points" of RF
engineering.

Never measure the temperature with more than one thermometer.

Never determine the time of day with more than one Cesium clock.

Never determine _________with more than one _________.

Dave - W?LEV

On Tue, Jun 14, 2022 at 12:02 AM Jim Lux <jim@...> wrote:

On 6/13/22 1:31 PM, Brian Beezley wrote:
I've been analyzing Touchstone files Rudy Severns, N6LF, has recorded
with his NanoVNA-H4. The magnitude of S11 is greater than 1 for many files.
For example, after calibration right at the VNA connector, |S11| was 1.0007
maximum for the open cal part itself. For the short the maximum was 1.0005.
For both, |S11| > 1 for all 401 points from 0.1 to 50 MHz.

The images show calculated permittivity and conductivity for a ground
probe with the rods in air. The image with most of the points missing used
uncorrected data. The other image is for normalized data where |S11| = 1
maximum.

Although normalization solves the problem for my software, I'm curious
why |S11| is ever > 1.

Brian

Measurement uncertainty? You're essentially measuring (V refl)/(V
incident) with a noisy sensor. 1 part per 1000 (1.001) is 60dB.. the
SNR of the measurement is in that ballpark.

Calibration peculiarities - you determine the cal coefficients with
noisy measurements, so the combination of cal coefficient high, and
measurement high,.

The ADC measuring the output of the mixer has an ideal SNR of ~90 dB.
It's a 16 bit adc, so there's some quantization uncertainty. Then
there's the arithmetic aspect. The basic software multiplies the ADC
numbers by sin and cos, then sums to get I/Q. That's done with 16 bit
signed integers, 32 bit products, but then truncated before integrating.

There's also the single precision floating point calculation of the
various calibration coefficients using single precision float (32 bit,
with 24 bit mantissa/significand).








--
*Dave - W?LEV*
*Just Let Darwin Work*
--
Dave - W?LEV
 

On 6/14/22 9:24 AM, W0LEV wrote:
Thank you, Jim!!!

Again, we are not running a metrology lab nor do our measurements approach
those of HP, R&S, Tek, and others. Something my PhD friends tell me is
that error analysis and assignment of error bars is no longer taught - not
even at CU/Boulder. I had a required course dedicated to that musing to
obtain my Physics degree some 50+ years ago at Michigan State U.

The students today have no idea how the error bar is established or even
what it truly indicates. Several of us have tried introducing our STEM
students at LTO (Little Thompson Observatory <starkids.org>) to the concept
of measurement errors and how they affect final outcomes. We usually get
wrinkled foreheads and "why".

Yes, 5 parts in E-5 is -86 dB. Yes, the HP 8753C noise floor can measure
below that. But, not our inexpensive NANOVNAs. Mine typically shows a
noise floor of -60 dB, depending on frequency and measurement type.

Again, thank you to those who put these VNAs at a reachable price in the
hands of us amateurs and those who want to learn the "fine points" of RF
engineering.

Never measure the temperature with more than one thermometer.

Never determine the time of day with more than one Cesium clock.

Never determine _________with more than one _________.

Dave - W?LEV

"sig figs" is taught in high school and undergrad.

If you do any sort of hard science classes they cover measurement uncertainties as part of the class (e.g. in lab) - Most lab classes discuss this (Undergrad chem lab certainly does).

The more sophisticated stuff is covered in classes like numerical analysis - if you're doing signal processing, for instance, round off and error propagation are a big thing. Same with classes on numerical solutions of differential equations, in connection with things like Runge-Kutta.? I doubt there's many classes that specifically care about "calibration uncertainty" - you're on your own with mfr notes and the professional literature.

As a grad student, you'd be expected to get this knowledge in some way - there are a variety of short courses offered by various government labs as well as industry. For instance NIST has annual meeting in certain fields, and there's often some short courses associated with it.
 

On 4k IFBW as i can see H4 measure error (due to noise) on 100-200MHz near ~1e-4 (on linear trace)
On 100Hz IFBW, near 1e-5
 

Jim, I can assure you our STEM students know nothing about significant
figures! Terry (Dr. Terry Bullett) and I have tried, but no knowledge of
the concept. They are Juniors going into their senior year and have had
Chem. and Physics (not "advanced" phys which is seldom taught due to low
demand).

Dave - W?LEV

On Tue, Jun 14, 2022 at 5:49 PM Jim Lux <jim@...> wrote:

On 6/14/22 9:24 AM, W0LEV wrote:
Thank you, Jim!!!

Again, we are not running a metrology lab nor do our measurements
approach
those of HP, R&S, Tek, and others. Something my PhD friends tell me is
that error analysis and assignment of error bars is no longer taught -
not
even at CU/Boulder. I had a required course dedicated to that musing to
obtain my Physics degree some 50+ years ago at Michigan State U.

The students today have no idea how the error bar is established or even
what it truly indicates. Several of us have tried introducing our STEM
students at LTO (Little Thompson Observatory <starkids.org>) to the
concept
of measurement errors and how they affect final outcomes. We usually get
wrinkled foreheads and "why".

Yes, 5 parts in E-5 is -86 dB. Yes, the HP 8753C noise floor can measure
below that. But, not our inexpensive NANOVNAs. Mine typically shows a
noise floor of -60 dB, depending on frequency and measurement type.

Again, thank you to those who put these VNAs at a reachable price in the
hands of us amateurs and those who want to learn the "fine points" of RF
engineering.

Never measure the temperature with more than one thermometer.

Never determine the time of day with more than one Cesium clock.

Never determine _________with more than one _________.

Dave - W?LEV

"sig figs" is taught in high school and undergrad.

If you do any sort of hard science classes they cover measurement
uncertainties as part of the class (e.g. in lab) - Most lab classes
discuss this (Undergrad chem lab certainly does).

The more sophisticated stuff is covered in classes like numerical
analysis - if you're doing signal processing, for instance, round off
and error propagation are a big thing. Same with classes on numerical
solutions of differential equations, in connection with things like
Runge-Kutta. I doubt there's many classes that specifically care about
"calibration uncertainty" - you're on your own with mfr notes and the
professional literature.

As a grad student, you'd be expected to get this knowledge in some way -
there are a variety of short courses offered by various government labs
as well as industry. For instance NIST has annual meeting in certain
fields, and there's often some short courses associated with it.











--
*Dave - W?LEV*
*Just Let Darwin Work*
--
Dave - W?LEV
 

On 6/14/22 11:19 AM, DiSlord wrote:
On 4k IFBW as i can see H4 measure error (due to noise) on 100-200MHz near ~1e-4 (on linear trace)
On 100Hz IFBW, near 1e-5
That's "total power" or 1E-4 on I and 1E-4 on Q (so 1.4E-4 on absolute voltage)?
 

Measurement of a short at the VNA connector after clearing cal:

49002000 -0.869956992 0.080768176
49126750 -0.869913280 0.080994536
49251500 -0.869870784 0.081221216
49376250 -0.869828352 0.081447216
49501000 -0.869784000 0.081672776
49625750 -0.869736192 0.081898376
49750500 -0.869684800 0.082123680
49875250 -0.869630720 0.082347872
50000000 -0.869575232 0.082570920

After calibrating:

49002000 -1.000384927 -0.000153716
49126750 -1.000387430 -0.000148167
49251500 -1.000389814 -0.000142248
49376250 -1.000392199 -0.000138649
49501000 -1.000394344 -0.000137316
49625750 -1.000395775 -0.000135393
49750500 -1.000395656 -0.000129219
49875250 -1.000393629 -0.000117017
50000000 -1.000389934 -0.000100459

After switching to MA mode. File stayed in RI mode but data changed:

49002000 -0.999972800 0.000051251
49126750 -0.999974336 0.000058021
49251500 -0.999975360 0.000064329
49376250 -0.999976000 0.000067545
49501000 -0.999977344 0.000067800
49625750 -0.999980672 0.000067987
49750500 -0.999986496 0.000071876
49875250 -0.999994304 0.000081417
50000000 -1.000003099 0.000095119

These are excerpts of a 401-point file from 0.1 to 50 MHz. At lower frequencies the last data set is beyond -1 like the second one.

Observations:

1. |S11| > 1 after calibration.

2. MA mode leaves file in RI mode but affects the data.

Brian
 

Settings:

401 points, 0.1-50 MHz, bandwidth 100 Hz, arithmetic 4X smoothing, power = 4 mA

Brian
 

Brian,
As a reference point, when calibrated, the HP 8753D has a linear magnitude reflection uncertainty of 0.015 or so when the reflection magnitude is near 1.
I am not sure if that means the repeatability is limited to that or if that is due to imperfections of the standards used.
(Source: Quick Reference Guide, 08753-90259, page 7-5)

--John Gord

On Tue, Jun 14, 2022 at 02:45 PM, Brian Beezley wrote:


Measurement of a short at the VNA connector after clearing cal:

49002000 -0.869956992 0.080768176
49126750 -0.869913280 0.080994536
49251500 -0.869870784 0.081221216
49376250 -0.869828352 0.081447216
49501000 -0.869784000 0.081672776
49625750 -0.869736192 0.081898376
49750500 -0.869684800 0.082123680
49875250 -0.869630720 0.082347872
50000000 -0.869575232 0.082570920

After calibrating:

49002000 -1.000384927 -0.000153716
49126750 -1.000387430 -0.000148167
49251500 -1.000389814 -0.000142248
49376250 -1.000392199 -0.000138649
49501000 -1.000394344 -0.000137316
49625750 -1.000395775 -0.000135393
49750500 -1.000395656 -0.000129219
49875250 -1.000393629 -0.000117017
50000000 -1.000389934 -0.000100459

After switching to MA mode. File stayed in RI mode but data changed:

49002000 -0.999972800 0.000051251
49126750 -0.999974336 0.000058021
49251500 -0.999975360 0.000064329
49376250 -0.999976000 0.000067545
49501000 -0.999977344 0.000067800
49625750 -0.999980672 0.000067987
49750500 -0.999986496 0.000071876
49875250 -0.999994304 0.000081417
50000000 -1.000003099 0.000095119

These are excerpts of a 401-point file from 0.1 to 50 MHz. At lower
frequencies the last data set is beyond -1 like the second one.

Observations:

1. |S11| > 1 after calibration.

2. MA mode leaves file in RI mode but affects the data.

Brian
 

I do not have a VNA. I rely on Rudy Severns, N6LF, for data. He recalibrated his VNA at the SMA connector, measured a short there, and now MA mode does not affect the file data. In addition, |S11| is no longer greater than 1.

Sorry for the confusion. I would delete my original post if I could.

Brian
 

Thanks to DAve W0LEV and others for bring up the subject of error analysis and significant figures.
My own background is like Dave¡¯s; a physics degree in 1965. Our professor in senior labs was very big on
error analysis. It¡¯s a hard subject. I asked at our local hospital regarding uncertainty and error in lab tests.
I never got a good answer.
A friend of mine, an engineering professor, made a joke ¡­. ¡°If you want to be absolutely certain about a measurement, only measure once.¡± Do I need to explain?

Chuck KF8TI

On Jun 14, 2022, at 1:49 PM, Jim Lux <jim@...> wrote:

On 6/14/22 9:24 AM, W0LEV wrote:
Thank you, Jim!!!

Again, we are not running a metrology lab nor do our measurements approach
those of HP, R&S, Tek, and others. Something my PhD friends tell me is
that error analysis and assignment of error bars is no longer taught - not
even at CU/Boulder. I had a required course dedicated to that musing to
obtain my Physics degree some 50+ years ago at Michigan State U.

The students today have no idea how the error bar is established or even
what it truly indicates. Several of us have tried introducing our STEM
students at LTO (Little Thompson Observatory <starkids.org>) to the concept
of measurement errors and how they affect final outcomes. We usually get
wrinkled foreheads and "why".

Yes, 5 parts in E-5 is -86 dB. Yes, the HP 8753C noise floor can measure
below that. But, not our inexpensive NANOVNAs. Mine typically shows a
noise floor of -60 dB, depending on frequency and measurement type.

Again, thank you to those who put these VNAs at a reachable price in the
hands of us amateurs and those who want to learn the "fine points" of RF
engineering.

Never measure the temperature with more than one thermometer.

Never determine the time of day with more than one Cesium clock.

Never determine _________with more than one _________.

Dave - W?LEV

"sig figs" is taught in high school and undergrad.

If you do any sort of hard science classes they cover measurement uncertainties as part of the class (e.g. in lab) - Most lab classes discuss this (Undergrad chem lab certainly does).

The more sophisticated stuff is covered in classes like numerical analysis - if you're doing signal processing, for instance, round off and error propagation are a big thing. Same with classes on numerical solutions of differential equations, in connection with things like Runge-Kutta. I doubt there's many classes that specifically care about "calibration uncertainty" - you're on your own with mfr notes and the professional literature.

As a grad student, you'd be expected to get this knowledge in some way - there are a variety of short courses offered by various government labs as well as industry. For instance NIST has annual meeting in certain fields, and there's often some short courses associated with it.
 

Chuck,

Take a read of Bob Witte¡¯s measurement equipment books, written when he was at HP. Joe Carr¡¯s tests and measurements book is another one rendering a cogent treatment of measurement errors without going very deep into the statistical deep-end. This work is based upon formal true-score theory: the central issue of which is whether the observed score¡¯s errors are correlated with the true score and/or the observed score.

73,

Frank
K4FMH
 

Frank:
Thanks for the tip about Bob Witte¡¯s books.
Chuck KF8TI

On Jun 15, 2022, at 7:55 PM, Frank K4FMH <frankmhowell@...> wrote:

Chuck,

Take a read of Bob Witte¡¯s measurement equipment books, written when he was at HP. Joe Carr¡¯s tests and measurements book is another one rendering a cogent treatment of measurement errors without going very deep into the statistical deep-end. This work is based upon formal true-score theory: the central issue of which is whether the observed score¡¯s errors are correlated with the true score and/or the observed score.

73,

Frank
K4FMH

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