Onoufrios Theofylaktos, Joseph D. Warner, and Charles J. Sheehe

Glenn Research Center, Cleveland, Ohio

High-Data-Rate Quadrax Cable Microwave

Characterization at the NASA Glenn

Structural Dynamics Laboratory

NASA/TM—2012-217609

October 2012
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Onoufrios Theofylaktos, Joseph D. Warner, and Charles J. Sheehe

Glenn Research Center, Cleveland, Ohio

High-Data-Rate Quadrax Cable Microwave

Characterization at the NASA Glenn

Structural Dynamics Laboratory

NASA/TM—2012-217609

October 2012

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

The authors would like to acknowledge the vibration laboratory personnel Jim Szelagowski and Joseph Ursic for all of their effort 

and time spent on this project. Special thanks goes to Elizabeth McQuaid for making the calibration kits and boxes.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2012-217609 1

High-Data-Rate Quadrax Cable Microwave Characterization at the 

NASA Glenn Structural Dynamics Laboratory 

Onoufrios Theofylaktos, Joseph D. Warner, and Charles J. Sheehe

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Summary

An experiment was performed to determine the degradation in the bit-error-rate (BER) in the highdata-rate cables chosen for the Orion Service Module due to extreme launch conditions of vibrations with 

a magnitude of 60g. 

The cable type chosen for the Orion Service Module was #8 quadrax cable.

The increase in electrical noise induced on these #8 quadrax cables was measured at the NASA Glenn 

vibration facility in the Structural Dynamics Laboratory. The intensity of the vibrations was set at 32g,

which was the maximum available level at the facility. The cable lengths used during measurements were 

1, 4, and 8 m.

The noise measurements were done in an analog fashion using a performance network analyzer 

(PNA) by recording the standard deviation of the transmission scattering parameter S21 over the frequency 

range of 100 to 900 MHz. The standard deviation of S21 was measured before, during, and after the 

vibration of the cables at the vibration facility. We observed an increase in noise by a factor of 2 to 6.

From these measurements we estimated the increase expected in the BER for a cable length of 25 m and 

concluded that these findings are large enough that the noise increase due to vibration must be taken in to 

account for the design of the communication system for a BER of 10–8

.

Introduction

Quadrax cables have been selected to be used on the Orion Service Module (SM). The maximum path 

length the service module may need to span is approximately 25 m. The Orion Team has proposed to use 

802.3 Clause 39 as a recommended standard for the quadrax cable properties (Ref. 1). The cables are to 

carry low-voltage differential signals (LDVS). Because of the length of the cable and the voltage drop 

across them, there is concern that noise due to vibration of the cable introduced during the launch of the 

Orion SM might increase the bit error rate (BER) at the detector to be greater than 10–8

. 

To determine the expected increase in the BER the standard deviation 21 of the transmission 

scattering parameter (transmission coefficient) S21 was measured before, during, and after vibration at 32g 

using a performance network analyzer (PNA). The increase in 21 during vibration can be related to the 

expected increase in the BER of the communication system. The method of relating 21 to BER is shown 

later in this report.

The measurement of 21 was performed over the frequency range of 100 to 900 MHz. This frequency 

range covers the fundamental frequency of 625 Mbps when using the proposed 5-bit word length.

The communication system is designed to send 625 Mbps down each wire pair in the #8 quadrax cable.

The level of the signal traveling down one of the quadrax pairs must exceed the minimum voltage detection 

by at least 5.61 standard deviations of the noise voltage as determined by the measurements of S21.
NASA/TM—2012-217609 2

Cable and Balun Description

Several quadrax cables of different length are planned to be used in the Orion SM and elsewhere.

These cables are manufactured by W.L. Gore. An Agilent PNA was used to analyze 1-, 4-, and 8-m 

quadrax cables to obtain the full set of S-parameters. 

The model of the Gore quadrax cables that were measured was ACN1037, and the part numbers for 

the 8-m cables are DDA0187-SPSA-0800_1 and DDA0187-SPSA-0800_2, for the 4-m cable is

DDA0187-SPSA-0400_1, and for the 1-m cable is DDA0187-SPSA-010_1. Inside these quadrax cables 

there are two pair of 150- , 24 American Wire Gauge (AWG) wires. These two pairs are arranged so that 

the two planes that each pair forms are orthogonal to each other. The cross section of the wire geometry 

does not vary down the length of the cable (Ref. 2).

To be able to measure the transmission loss and the noise on each of the cable with the PNA, we used 

a 150- to 50- balance-to-unbalance transformer (balun). This arrangement necessitated the use of 

“pigtails” (Ref. 2) from Gore to mate the quadrax cables to the baluns. The pigtails were constructed as 

follows: one end of each of the pigtail cables was four wires without the sheath and on the other end was 

either a male or female quadrax connector. These 0.61-m cables part numbers are DDA0187-SPSA0061_J1 with the male #8 quadrax connector and a pigtail 3214735-02_PIGTAIL, and DDA0187-SPSA0061_J2 with a female #8 quadrax connector and a pigtail 3214735-02_PIGTAIL.

The baluns used were procured from Pulse Engineering under part number HFB050150. The turns 

ratio of these transformers was 3. The specification of the baluns gave a maximum operating frequency of 

1200 MHz, although in this experiment the maximum frequency was limited to only 900 MHz because of 

anomalies in the baluns’ performance above 900 MHz. Each transformer had a 50- SMA connector at 

the one port (primary) and three 838-μm (inner diameter) DB-type sockets at the 150- port (secondary).

The middle socket on the 150- side (secondary) was internally connected to the primary ground.

The S-parameter measurements on the cables were done with the PNA connected to the 50- port of 

the baluns and the pigtails connected to the 150- port of the baluns. The cables that were measured were 

connected between the quadrax connectors of the pigtail cables.

Experimental Approach

To make the noise measurements of the cables, first the baluns had to be characterized and then 

calibrated out of the measurement on the cable. After that was done, the cable S-parameters were 

measured before the vibration run of the cable, during the time the cable was being vibrated at the 

maximum acceleration, and then after the vibration run. 

The radiofrequency (RF) measurements (S-parameters) were done using a PNA (M/N: N5230A, S/N:

MY46400910). The PNA’s most recent calibration was performed in December of 2010 (Agilent Cal

1-2869640062-1). The cable lengths measured were 1, 4, 8, and 16 m long. Two 8-m daisy-chained 

cables were used for the 16-m measurement with a bulkhead connector (Fig. 1), and without a bulkhead 

connector (Fig. 2). Comparing the measured noise and losses in the 16-m cable with and without the 

bulkhead fitting characterizes the bulkhead fitting for launch applications.

The cable S-parameters were measured between 100 to 900 MHz using 6401 points. Each cable set 

was measured before, during, and after vibration, 36 times in each case. The individual sets of scans taken 

before, during, and after vibration of the cables were averaged to calculate the standard deviation of the

S-parameters at each frequency point. There was no weighting factor used in determining the average 

value or the standard deviation of the S-parameters. The S21 parameters between sets were compared to 

determine the increase in the noise due to vibration of the cables.
NASA/TM—2012-217609 3
NASA/TM—2012-217609 4

Between 100 and 900 MHz the extinction and reflection coefficients were measured versus frequency 

for the different lengths of cable. The extinction and reflection coefficients were extrapolated to

1250 MHz after which the insertion loss at 1250 MHz and cable length of 25 m was calculated. Note

1250 MHz is twice the fundamental highest digital rate of 625 Mbps, and 25 m was the estimated longest 

cable run on Orion.

Characterization of Balun Ensemble at 50 W Using the PNA

To calibrate the baluns and the cable measurements, in-house calibration kits were fabricated as there 

were no 150- certified quadrax calibration kits available. The calibration kits were made—one for each 

gender with open quadrax connectors, shorted quadrax connectors, and load quadrax connectors. The 

shorted connectors connected the two wires in each pair of the quadrax connectors together making sure 

the two pair of wires did not touch one another. The open connectors left the wires open inside of the 

quadrax connector. The load connectors were made by placing a 150- , 0.1 percent accurate noninductive resistor across each pair of wires. The through measurements connected the two ends of the 

quadrax cables together. Figure 3 shows the schematic of the calibration of the 150- baluns. 

Calibration procedure for the baluns:

(1) Specify Frequency range from 100 to 2000 MHz.

(2) Calibrate out PNA cables with 50 Ω connector terminations.

(3) Place balun circuits between PNA cables (Fig. 3).

(4) Measure 2-Port S-parameters of balun ensemble using the PNA.

(5) Disassemble/assemble and verify repeatability of measurement.

(6) Document results.

(7) Calibrate out PNA cables with balun ensemble (Fig. 4). Each balun box should be terminated 

using the 150-Ω test kit as shown in Figure 5 prior to testing of any cables.

The calibration results of the baluns are given in Reference 2.
NASA/TM—2012-217609 5
NASA/TM—2012-217609 6

Characterization of Quadrax Cable

The characterization procedure of the quadrax cable under static and dynamic conditions for the

measurements before, during, and after vibration is listed below:

(1) Set frequency range between 100 and 900 MHz.

(2) Place cable of the device under test (DUT) between the two balun boxes.

(3) Measure 2-port S-parameters of each DUT using the PNA.

(4) Repeat (3) and save a total of 36 files.

(5) Repeat (2) for different lengths of cable (24 AWG only).

(6) Document results.

Data Analysis

The PNA gives the S-parameters in decibels. Prior to averaging the S-parameters, they were all 

converted from decibels to a simple ratio of powers from the magnitude of the S-parameters. After this 

conversion was done the average and the standard deviations were computed for all the S-parameter from 

the 36 sweeps of the frequency range.

Only the S21-parameters were used for subsequent analyses to determine the effect of vibration on the 

noise in the system because only the properties of S21 affect the bit error rate of the system (Ref. 3). From 

the measurement of S21 one can relate the magnitude and the noise to the energy in one bit (Eb) to the 

average energy of the noise (N0) within one bit time period (Tb). The relationship of Eb/N0 to the 

magnitude of S21 and its standard deviation σ21 is given by Equation (1) (Ref. 3):

21

21

0 = SN

Eb (1)

where

b Tb R

V E

2

= (2)

V is the voltage of the bit pulse, and R is the impedance of the circuit or the resistance over which the 

signal is measured.

Equation (1) assumes that the noise is additive white gaussian noise across the bandwidth of the 

system to be able to calculate N0.

The Eb/N0 can be turned into a ratio of the reference voltage divided by the standard deviation simply 

by taking its square root. This is true for uncorrelated bits. So for uncorrelated bits the relationship is

N0

V Eb

v

= (3)

where V/ v is the number of standard deviations of the voltage noise that the system can handle before a 

bit is incorrectly detected; note V v = 2Eb N0 for bi-polar shift keying (BPSK) (Ref. 3). For 

correlated signals one must multiply Eb by the number of bits that are correlated together. For correlated 

BPSK modulation this factor is 2.

Since calculations of BER curves use the Q function, it is easy to relate measured analog noise in the 

system to the system BER.
NASA/TM—2012-217609 7

The Q function is defined as

÷

÷

2

1 erf

2

1 ( ) x Q x (4)

where x is the number of standard deviations and erf is the error function; therefore V v x = .

Cable Losses

The losses in the cables are plotted below. Figure 6 gives the cable loss in the 8-m cable-1 (8M1).

Figure 7 gives the cable loss in the 8-m cable-2 (8M2). Figure 8 gives the cable loss in the 16-m cable 

without a bulkhead connection (16MNB). Figure 9 gives the cable loss in the Gore 16-m cable with a 

bulkhead connection (16MBH). The cable loss is given in Equation (5). It is 1 minus the reflection 

coefficient minus the transmission coefficient:

Cable loss = 1 – S11 – S21 (5)

In each of the figures the losses before, during, and after the vibration are plotted. As one can see, the 

losses are gradually increasing with frequency. The high frequency peaks in the plots come from the 

standing waves in the cable. Furthermore, the cable loss due to vibration is higher than the cable loss 

before and after vibration.

In all four cable measurements the losses increase monotonically with frequency except in the region 

of 600 to 700 MHz. From the size of the standing wave in that region, the impedance is not as well 

matched as at other frequencies, but always the losses measured during vibration is greater than before or 

after vibrating. As one can see between cable 8M1 and 8M2, which are of the same length, 8 m, there is 

virtually no difference in the cable losses as seen in Figures 6 and 7.

The standard deviation in the cable losses from Figures 6 to 9 is plotted in Figures 10 to 13 and is 

determined from the propagation of errors using the uncertainties of S11 and S21 by utilizing the following 

equation:

σcable loss = 2

21

2

11 + (6)
NASA/TM—2012-217609 8
NASA/TM—2012-217609 9
NASA/TM—2012-217609 10

It can be seen from Figures 10 to 13 that there is an increase in the uncertainty in cable loss σcable loss

during vibration compared to before or after vibrating the cables. Also a small consistent difference is 

observed in the σcable loss between before and after vibrating the cables with the σcable loss being slightly 

smaller after vibration than before. We do not have a definite reason for this effect, but will suggest there 

may be some type of relaxation of strain in the cable due to the vibration.

The σcable loss for both the 8- and 16-m lengths before and after vibrations are very similar; however,

the uncertainty in the cable losses for the 8- and 16-m length measurements during vibration are 

dramatically different.
NASA/TM—2012-217609 11

The σcable loss for the measurements of the 16-m cable is significantly higher than for the measurements 

of the 8-m cable. This is consistent with induced noise due to vibrations along the length of the cable. For 

the two 8-m cables there is not a significant difference in σcable loss between similar measurements: those 

before, during, and after vibration of 8M1 and 8M2. Any changes in the magnitude of the noise of

σcable loss seen between Figures 10 and 11 are due to physical differences during the wrapping and securing 

of the cable onto the vibration platform. 

The differences seen between measurements on cables 16MNB and 16MBH can be explained by the 

difference in how the two 8-m cables are connected to each other and held together.

What is significant in all of the measurements on the cable lengths of 8 and 16 m is the increase in 

σcable loss when the cables are vibrated.

The σcable loss is the RF-noise in the cables that must be known and used to determine the BER of the 

data sent down the cables. For the 8-m cable 8M1 in Figure 10 the σcable loss increases by a factor of 3.5 to 

6.5 when vibrated over either static magnitude, and in Figure 11 the factor for 8M2 is 2.5 to 7.5. For the 

16-m length cables Figure 12 shows an increase in σcable loss of a factor of 11 to15 during vibration as 

opposed to not vibrating for 16MNB; in Figure 13 the factor for 16MBH is 26 to 42. The difference 

between the two factors may be due to the bulkhead fitting being elevated above the vibration table with 

the cable connectors held in place by the fitting as opposed to the two 8-m cables being taped down to the 

vibration table.

For the same cables, the change Δ in the cable losses CL depicted in Figures 14 to 17 is defined as

( ) [ (after vibration) (before vibration)] 2

1 = CL during vibration CL + CL (7)

From Figures 14 and 15 one sees that the in the cable loss is similar in magnitude and trend. Although 

this is a small sample, it seems that the construction of the cables is consistent enough that the cables 

could be interchanged in the final construction of the communication system.
NASA/TM—2012-217609 12
NASA/TM—2012-217609 13

The observed in the cable losses due to vibration is small compared to the total loss observed for 

the cables. This means that the signal strength at the end of the cable does not vary much because of 

vibration. For example, the difference in the signal strength at the end of the cable for the 8M1 cable at 

900 MHz will be 0.0065 (Fig. 14), whereas the total loss is 0.58 (Fig. 6).

From Figures 16 and 17 one sees that there is a consistent increase in Δ between cable 16MNB and 

16MBH. That Δ in 16MBH is 0.004 greater that the Δ for 16MNB. Still the Δ is very small compared to 

the total losses in the cable whether it is being vibrated or not. For example, the difference in the signal 

strength at the end of the cable for the 16MNB cable at 900 MHz will be 0.011 (Fig. 16).

As one can see, the ratio of the difference in the cable losses divided by the average of the cable 

losses is the same for the two different lengths of cable (8 and 16 m).

Relating Cable Losses and Their Uncertainties to the BER

The previous report (Ref. 3) described how the BER from these measurements is dependent upon the 

increase in the noise in the signal due to vibration. This noise can be described by the standard deviation 

( 21) of S21, which is defined as the ratio of the measured transmitted power at the end of the cable 

divided by the transmitted power at the beginning of the cable, or the transmission coefficient of the 

power. Also S21 is related to the voltage along the cable as given in Equation (8) where V is the voltage 

along the cable and V0 is the voltage at the beginning of the cable,

2

0

2

21

( ) ( )

V

V x S x = (8)

where x is the distance along the cable (l is the overall length of the cable).

From the standard propagation of error method, the standard deviation of the voltage at the end of the 

cable V(l) is estimated from 21. That relationship is given in Equations (9) and (10):

2 ( )

( ) ( )

21

0 21

S l

V l l V = (9)
NASA/TM—2012-217609 14

Then substituting Equation (8) for V0 into Equation (9),

( )

2 ( )

( ) ( )

21

21

S l

V l l l V = (10)

Once V and V are determined at the end of the cable, the BER of the data is estimated using the Q

function. For uncorrelated bits (i.e., no coding) x is simply V V .

For Orion the given acceptable BER for this communication line was 10–8

.

From the inverse Q function the number of standard deviations away from the average signal voltage 

level V at the end of the cable needed for a probability of 10–8 is 5.61. The detection voltage for a signal 

bit must be greater than V + VM, where VM is given below:

V (l) (l) M V 5.61 (11)

The method to scale 21 with the length of the cable is by recognizing that the noise in the voltage due 

to the ohmic losses of any passive device like the quadrax cable is proportional to the square root of the 

resistance R of the component. Since 21 is the uncertainty in the S21, which is a ratio of powers, then 21

is proportional to R. Therefore,

÷ = ÷

2

1

21 1 21 2 ( ) ( ) l

l l l (12)

where l1 is the length of the cable for the estimated 21 and l2 is the length of the cable for the measured 

21. Equations (8), (9), and (11) imply

÷ = ÷ ÷

÷ ÷

÷ ( ) ( )

( ) 2.81

( ) ( )

( )

2

5.61

( )

( ) 0

21

0 21

21

21

V l

V

S l

l

V l

V

S l

l

V l

VM l (13)

To be able to attain a BER of 10–8 or better, the ratio of the voltage at the end of the cable to the input 

voltage must be greater than the value given in Equation (12). Equation (12) will give the limitation on 

the length of the cable possible for a BER of 10–8 or better for a particular voltage detection level. Of 

course the factor 5.61 in Equation (11) obtained from the inverse Q function will differ for a different 

BER needed.

To be able to extrapolate Equation (13) to different lengths of cable than what was measured, one 

needs to know the extinction coefficient for the cable loss. The voltage extinction coefficient beta β is 

given in Equation (14):

l V (l) =V 10 0 (14)

Note that if the length of the cable is doubled,

( ) ( ) 2

0 0

2

÷ = ÷ V

V l

V

V l (15)

Combining terms from Equations (12), (14), and (15) into Equation (13) and taking the ratios of VM/V

at the actual measured length lA (8 or 16 m) and the extrapolated length lE needed for Orion (lE = 25 m) 

one obtains
NASA/TM—2012-217609 15

( )

21

21 10

( )

( ) 2.81

( )

( ) E A l l

A

E

A

A

E

M E

l

l

S l

l

V l

V l

÷

÷ ÷÷ (16)

where lA is the length of the measured cables, either 8 or 16 m, and lE is the length of cable needed for the 

Orion SM, 25 m.

The can be calculated from S21 by remembering that S21 is proportional to the square of the voltage.

This gives a function of S21 versus the length of the cable:

l l S (l) = S (0)×10 = S (0)×10 212

21 21 (17)

( ) 21 11 S 0 =1 S (18)

where S11 is the reflection coefficient for the power measurement and is the extinction coefficient for 

the cable loss.

Therefore,

÷ = ÷ ( )

1 log 1

21

11

10 S l

S

l (19)

Data from the 16-m cable were used to predict the noise level and the BER at a vibration level of 32g 

for a 25-m cable with the highest fundamental frequency of 625 MHz and its first harmonic at 1250 MHz.

For this case lA = 16 m and lE = 25 m. Substituting Equation (19) into Equation (16) results in

÷

÷

÷

÷ ÷÷ ÷÷

1

2

1

21

11

21

21

( )

1

( )

2.81 ( )

( )

( ) A

E

l

l

A A

E

A

A

E

M E

S l

S

l

l

S l

l

V l

V l (20)

Substituting 16 for lA and 25 for lE in Equation (20) at a given frequency gives

32

9

(16)

1

16

25

(16)

2.81 (16)

(25)

(25)

21

11

21

21

÷ ÷ ÷ ÷

÷ S

S

V S

VM (21)

The ratio of the voltage of the signal at the end of the cable to the voltage at the beginning of the 

cable that is needed to obtain a BER of 10–8 for the cables measured in this study is shown in Figures 18

to 21 as a function of frequency. Also in these figures there has been a simple polynomial fit versus

frequency for the measurements during vibration.

In Figure 22 the graphs of VM/V before vibration are plotted together for comparison. The noise VM/V

for all four cables is extremely small, and it appears that the noise does not depend on the cable length.

When the cables are not vibrated, achieving a BER of 10–8 is very easy because for low-voltage 

differential signals (LVDS) V is typically 1.35 V. With the signal level at 1.35 V the standard deviation of 

the voltage at the end of the 16-m cable corresponds to approximately 1.1 mV or greater at 900 MHz 

using the VM/V from Figure 22. So the difference between the mean of the signal level and the detection 

threshold of the instrument only needs to be 1.1 mV or greater for a BER better than 10–8

.
NASA/TM—2012-217609 16
NASA/TM—2012-217609 17
NASA/TM—2012-217609 18

In Figure 23, VM/V for the four cables from Figures 18 to 21 during vibration is compared. As it can 

be seen between Figures 22 and 23, VM/V is much greater during vibration than when the cables are not 

being vibrated.

For LVDS, the difference between the mean of the signal level and the detection threshold of the 

instrument needs to be 36 mV or greater at 900 MHz for a BER better than 10–8 for a 16-m cable with the 

bulkhead fitting and only approximately 13 mV for the 16-m cable without the bulkhead fitting.

Estimating VM/V for the Orion Cables

Having established a methodology to determine the ratio of the standard deviation needed for a 

particular BER to the mean signal level voltage in a cable and how to extrapolate this ratio to different 

frequencies and different cable lengths, the standard deviation of the mean voltage for the Orion cable is 

now estimated at the needed length and at 1250 MHz. To do this estimate the cable length is extrapolated 

from 16 to 25 m, and VM/V versus frequency is extrapolated to 1250 MHz.
NASA/TM—2012-217609 19

In Figures 18 to 21, the data during vibration was fitted to a polynomial as given in those figures.

Then for cables 16MNB and 16MBH a linear line was made tangent to the polynomial-fitted curve at the 

upper frequency region. The data, the fitted curves to the data, and the tangential line to these fitted 

curves are depicted in Figure 24.

To obtain the needed VM/V for the 25-m Orion cable at 1250 MHz Equation (21) is rewritten:

32

9

(16 m,1250 MHz)

1 (1250 MHz)

16

25 (25 m,1250 MHz) (16 m,1250 MHz)

21

11

÷ ÷ ÷ ÷ ÷ S

S

V

V

V

VM M (22)

The equation of the fitted line for the 16MBH cable in Figure 24 is

( ) 1.17 10 0.0162 11 f = × f +

V

VM (23)

where f is the frequency in Hz. Evaluating Equation (23) for f at 625 and 1250 MHz results in VM/V(f) 

equaling 0.024 and 0.031, respectively.

The equation of the line for the 16MNB cable is

( ) 2.68 10 0.0065 12 f = × f +

V

VM (24)

Evaluating this expression for f at 625 and 1250 MHz results in VM/V equaling 0.0082 and 0.0099, 

respectively.

Because the value of VM/V is based on the tangential line to the fitted curve at 625 MHz, its value is 

almost identical to the value of VM/V (f) for the value calculated from the polynomial in Figure 26; 

therefore, the straight line Equations (23) and (24) for VM/V (625 MHz) can be used instead of the 

polynomial equation for both 16MBH and 16MNB cables.
NASA/TM—2012-217609 20

Extinction Coefficient Alpha a and S11

The extinction coefficient for S21 that is given in Equation (19) is plotted in Figure 25 for cable 

8M1, and a straight line is fitted to the data. This line was used to extrapolate to 1250 MHz. It is this 

value of extrapolated that was used in the subsequent calculations.

The fitted line to the data in Figure 25 is

( ) 4.75 10 0.0092 11 f = × f + (25)

This results in a value of 0.039 at 625 MHz and 0.069 at 1250 MHz.

In Figure 26 the reflection coefficient S11 is plotted along with the fitted line to the curve. The peak in 

the S11 between 650 and 700 MHz is due to the property of the baluns used in the measurement. One can see 

the S11 is less than about 0.5 percent over the entire frequency range when the peak to the baluns is ignored.
NASA/TM—2012-217609 21

A straight line is fitted to the S11 data for cable 8M1 in Figure 26. This fitted line to the data in

Figure 26 is given in Equation (26):

( ) 4.00 10 0.0001 12 S11 f = × f + (26)

This results in a value of 0.0026 at 625 MHz and 0.0051 at 1250 MHz.

Extrapolating the measured value to cable lengths of 25 m and 1250 MHz requires knowledge of S11

and at 1250 MHz. The transmission coefficient S21 for 25 m at both 625 and 1250 MHz from

Equations (17), (18), (25), and (26) is now calculated:

(25m, 625 MHz) (1 0.0026)10 0.11 0.039(25) S21 = = , which is –9.76 dB (27a)

(25m,1250 MHz) (1 0.0051)10 0.019 0.069(25) S21 = = , which is –17.27 dB (27b)

The equations versus frequency for all the cables measured are given in Table I including those in

Figures 25 and 26. Table I also includes the estimate of S21 for a length of 25 m and at frequencies of

625 and 1250 MHz. In Table I, f is given in megahertz.

It is seen in Table I the extinction coefficient and the reflection coefficient for each cable before, during, 

and after vibration are approximately the same except for cable 16MBH, which is the cable with the 

bulkhead fitting. It is not unreasonable to suggest that the bulkhead fitting increase loss down the cable 

when it is being vibrated since the bulkhead fitting introduces a moment arm of approximately 4 cm. 

To determine the BER for quadrax cables with a length of 25 m and at 625 and 1250 MHz while 

being vibrated at 32g the S21 must be converted into a voltage ratio. This voltage ratio is the minimal 

voltage difference between the signal voltage at the end of the cable, and the detection voltage that 

determines if a bit is a “one” or a “zero.”

For cables 16MBH and 16MNB Equations (21) and (23) along with results from Table I are used to 

calculate VM/V at the desired frequency and length. The results are summarized in Table II. An example of

the calculation method for the 16MBH cable at a frequency of 625 MHz is presented:

( ) ( )

( ) 0.073

0.094

1 0.0026 0.0375

16 m, 625 MHz

1 625 MHz

16

25 25 m, 625 MHz 0.024

0.28125

21

11 32

9

= ÷ = ÷ = S

S

V

VM (28)

Thus the voltage above the detection voltage divided by the input voltage must be at least 7.3 percent.

TABLE I.—CABLE PROPERTIES AND TRANSMISSION CHARACTERISTICS

Vibration Cable Extinction coefficient,

α(f)

Reflection coefficient,

S11(f)

Transmission coefficient 

at f = 625 MHz,a

S21,

dB

Transmission coefficient

at f = 1250 MHz,

a

S21,

dB

Before

8M1 4.75  ̇ 10–11f + 0.0092 4.00  ̇ 10–12f + 0.0001 –9.76 –17.27

8M2 4.80  ̇ 10–11f + 0.0094 4.00  ̇ 10–12f + 0.0001 –9.76 –17.16

16MNB 4.80  ̇ 10–11f + 0.0094 5.00  ̇ 10–12f + 0.0001 –9.76 –17.14

16MBH 4.80  ̇ 10–11f + 0.0094 4.00  ̇ 10–12f + 0.0001 –10.01 –17.52

During

8M1 4.70  ̇ 10–11f + 0.0094 4.00  ̇ 10–12f + 0.0001 –9.76 –17.02

8M2 4.80  ̇ 10–11f + 0.0094 4.00  ̇ 10–12f + 0.0001 –9.76 –17.16

16MNB 4.80  ̇ 10–11f + 0.0094 5.00  ̇ 10–12f + 0.0001 –9.76 –17.16

16MBH 5.00  ̇ 10–11f + 0.01 4.00  ̇ 10–12f + 0.0001 –10.26 –18.27

After

8M1 4.60  ̇ 10–11f + 0.0094 4.00  ̇ 10–12f + 0.0001 –9.51 –16.77

8M2 4.70  ̇ 10–11f + 0.0094 4.00  ̇ 10–12f + 0.0001 –9.76 –17.02

16MNB 4.80  ̇ 10–11f + 0.0095 5.00  ̇ 10–12f + 0.0001 –9.76 –17.14

16MBH 4.80  ̇ 10–11f + 0.0094 5.00  ̇ 10–12f + 0.0001 –9.76 –17.14 a

For cable length of 25 m.
NASA/TM—2012-217609 22

TABLE II.—VALUE OF VM/V AT 25 m CABLE LENGTH

Cable 625 MHz 1250 MHz

16MBH 0.073 0.158

16MNB 0.024 0.047

The 32g-induced voltage noise VM/V (625 MHz) is between 2.4 and 7.3 percent; the corresponding 

values at 1250 MHz are between 4.7 and 15.8 percent. Therefore, for a BER of 10–8

, the signal level must 

be 0.073V from the detection voltage that separates a one from a zero at 625 MHz while it must 0.158V at 

1250 MHz.

Results

The evaluation of α, S11, and S21 at 625 MHz is given in Table III and at 1250 MHz is given in

Table IV.

As can be seen in Tables III and IV the extinction coefficient and the reflection coefficient S11

double as the frequency is doubled. The transmission coefficient S21 though increases by 7 to 8 dB as the 

frequency is doubled. This is consistent with both α and S11 doubling. 

TABLE III.—ESTIMATIONS OF , S11, AND S21 FOR 25 m OF 8M1, 8M2, 16MNB, AND 16MBH CABLES AT

625 MHz AND RANDOM VIBRATION LEVELS OF 32g BEFORE, DURING, AND AFTER VIBRATION

Cable Extinction coefficient,

,

m–1

Reflection coefficient,

S11

Transmission coefficient,

S21,

dB

Before During After Before During After Before During After

8M1 0.039 0.039 0.038 0.0026 0.0026 0.0026 –9.76 –9.76 –9.51

8M2 0.039 0.039 0.039 0.0026 0.0026 0.0026 –9.76 –9.76 –9.76

16MNB 0.040 0.039 0.039 0.0032 0.0032 0.0032 –9.76 –9.76 –9.76

16MBH 0.040 0.041 0.040 0.0026 0.0026 0.0026 –10.01 –10.26 –10.01

TABLE IV.—ESTIMATIONS OF , S11, AND S21 FOR 25 m of 8M1, 8M2, 16MNB, AND 16MBH CABLES AT

1250 MHz AND RANDOM VIBRATION LEVELS OF 32g BEFORE, DURING, AND AFTER VIBRATION

Cable Extinction coefficient,

,

m–1

Reflection coefficient,

S11

Transmission coefficient,

S21,

dB

Before During After Before During After Before During After

8M1 0.069 0.068 0.067 0.0051 0.0051 0.0051 –17.27 –17.02 –16.77

8M2 0.069 0.069 0.068 0.0051 0.0051 0.0051 –17.16 –17.16 –17.02

16MNB 0.069 0.069 0.069 0.0064 0.0064 0.0064 –17.14 –17.14 –17.14

16MBH 0.070 0.073 0.071 0.0051 0.0051 0.0051 –17.52 –18.27 –17.77

Conclusions

The proposed Orion cables, in 25-m lengths, when going through a single bulkhead connection while 

being randomly vibrated to 32g, are expected to have a loss of 10.3 dB at 625 MHz (fundamental 

frequency) and 18.3 dB at 1250 MHz (first harmonic). We have determined the extinction coefficient and 

the reflection coefficient of the quadrax cables versus frequency along with estimating the transmission 

coefficient at 625 and 1250 MHz for a 25-m cable.

The 10.3 dB estimated cable loss at 25 m and 625 MHz exceeds the IEEE Standard 802.3 Clause 39 

recommended 8.8 dB1. It is incumbent upon the designers to take these variations into account.

Most importantly we have determined the voltage ratio of noise to input signal voltage that must be 

met to achieve a bit error rate (BER) of 10–8

. For a typical input voltage of 1.35 V the signal voltage about 

the detection threshold must be at least 216 mV for a BER of 10–8 during launch.
NASA/TM—2012-217609 23

Future Work

Our research only involved a very small sample of these wires. A larger sample size would result in

better fidelity and the ability to characterize the quadrax connectors for scenarios where link budgets are 

tight. In addition to the analog method used here, a digital method should be utilized with a digital 

sequence generator and a bit error rate tester.

References

1. IEEE Std 802.3-2005 (Revision of IEEE Std 802.3-2002 including all approved amendments). IEEE 

Standard for Information Technology, IEEE, New York, NY, clause 39, 2005, p. 138.

2. Theofylaktos, Onoufrios; and Warner, Joseph D.: Calibration Procedure for Measuring S-Parameters 

in Balun Applications on 150-Ohm High-Speed Cables. NASA/TM—2012-217296, 2012.

3. Warner, Joseph D.; and Theofylaktos, Onoufrios: Correlation Between Analog Noise Measurements 

and the Expected BER of a Digital Signal Propagating Through Passive Components. NASA/TM—

2012-217238, 2012.
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High-Data-Rate Quadrax Cable Microwave Characterization at the NASA Glenn Structural 

Dynamics Laboratory 

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Theofylaktos, Onoufrios; Warner, Joseph, D.; Sheehe, Charles, J. 

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WBS 644423.06.32.03.03.03 

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John H. Glenn Research Center at Lewis Field 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

An experiment was performed to determine the degradation in the bit-error-rate (BER) in the high-data-rate cables chosen for the Orion 

Service Module due to extreme launch conditions of vibrations with a magnitude of 60g. The cable type chosen for the Orion Service 

Module was #8 quadrax cable. The increase in electrical noise induced on these #8 quadrax cables was measured at the NASA Glenn

vibration facility in the Structural Dynamics Laboratory. The intensity of the vibrations was set at 32g, which was the maximum available 

level at the facility. The cable lengths used during measurements were 1, 4, and 8 m. The noise measurements were done in an analog 

fashion using a performance network analyzer (PNA) by recording the standard deviation of the transmission scattering parameter S21 over 

the frequency range of 100 to 900 MHz. The standard deviation of S21 was measured before, during, and after the vibration of the cables at 

the vibration facility. We observed an increase in noise by a factor of 2 to 6. From these measurements we estimated the increase expected 

in the BER for a cable length of 25 m and concluded that these findings are large enough that the noise increase due to vibration must be 

taken in to account for the design of the communication system for a BER of 10-8.

15. SUBJECT TERMS

Microwave characterization; RF cables; Vibration degradation 

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